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1. Quantum logarithmic multifractality

Author

Weitao Chen, Olivier Giraud, Jiangbin Gong, and Gabriel Lemarié

Subjects
Physics, QC1-999
Abstract

Through a combination of rigorous analytical derivations and extensive numerical simulations, this work reports an exotic multifractal behavior, dubbed “logarithmic multifractality,” in effectively infinite-dimensional systems undergoing the Anderson transition. In contrast to conventional multifractality observed in finite dimensions, logarithmic multifractality at infinite dimension introduces an algebraic behavior with respect to the logarithm of system size or time. We demonstrate this phenomenon across eigenstate statistics, spatial correlations, and wave packet dynamics. Our findings offer crucial insights into strong finite-size effects and slow dynamics in complex systems undergoing the Anderson transition, such as the many-body localization transition.

Published
2024
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2. Topological order in random interacting Ising-Majorana chains stabilized by many-body localization

Author

Nicolas Laflorencie, Gabriel Lemarié, and Nicolas Macé

Subjects
Physics, QC1-999
Abstract

We numerically explore Z_{2}-symmetric random interacting Ising-Majorana chains at high energy. A very rich phase diagram emerges with two topologically distinct many-body localization (MBL) regimes separated by a much broader thermal phase than previously found. This is a striking consequence of the avalanche theory. We further find MBL spin-glass order always associated to a many-body spectral pairing, presumably signaling a strong zero mode operator which opens fascinating perspectives for MBL-protected topological qubits.

Published
2022
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3. Coherent forward scattering peak and multifractality

Author

Maxime Martinez, Gabriel Lemarié, Bertrand Georgeot, Christian Miniatura, and Olivier Giraud

Subjects
Physics, QC1-999
Abstract

It has recently been shown that interference effects in disordered systems give rise to two nontrivial structures: the coherent backscattering (CBS) peak, a well-known signature of interference effects in the presence of disorder, and the coherent forward scattering (CFS) peak, which emerges when Anderson localization sets in. We study here the CFS effect in the presence of quantum multifractality, a fundamental property of several systems, such as the Anderson model at the metal-insulator transition. We focus on Floquet systems, and find that the CFS peak shape and its peak height dynamics are generically controlled by the multifractal dimensions D_{1} and D_{2}, and by the spectral form factor. We check our results using a one-dimensional Floquet system whose states have multifractal properties controlled by a single parameter. Our predictions are fully confirmed by numerical simulations and analytic perturbation expansions on this model. Our results, which we believe to be generic, provide an original and direct way to detect and characterize multifractality in experimental systems.

Published
2021
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4. Controlling symmetry and localization with an artificial gauge field in a disordered quantum system

Author

Clément Hainaut, Isam Manai, Jean-François Clément, Jean Claude Garreau, Pascal Szriftgiser, Gabriel Lemarié, Nicolas Cherroret, Dominique Delande, and Radu Chicireanu

Subjects
Science
Abstract

Periodically kicked rotors are useful in exploring localization phenomenon. Here the authors use ultracold Cs atoms kicked by short laser pulses and show that the periodic modulation results into interference signals as a signature of weak and strong localizations.

Published
2018
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5. Chain breaking and Kosterlitz-Thouless scaling at the many-body localization transition in the random-field Heisenberg spin chain

Author

Nicolas Laflorencie, Gabriel Lemarié, and Nicolas Macé

Subjects
Physics, QC1-999
Abstract

Despite tremendous theoretical efforts to understand subtleties of the many-body localization (MBL) transition, many questions remain open, in particular concerning its critical properties. Here we make the key observation that MBL in one dimension is accompanied by a spin freezing mechanism which causes chain breaks in the thermodynamic limit. Using analytical and numerical approaches, we show that such chain breaks directly probe the typical localization length and that their scaling properties at the MBL transition agree with the Kosterlitz-Thouless scenario predicted by phenomenological renormalization group approaches.

Published
2020
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6. Phase diagram of the anisotropic Anderson transition with the atomic kicked rotor: theory and experiment

Author

Matthias Lopez, Jean-François Clément, Gabriel Lemarié, Dominique Delande, Pascal Szriftgiser, and Jean Claude Garreau

Subjects
Science, Physics, QC1-999
Abstract

We realize experimentally a cold-atom system, the quasiperiodic kicked rotor, equivalent to the three-dimensional Anderson model of disordered solids where the anisotropy between the x direction and the y – z plane can be controlled by adjusting an experimentally accessible parameter. This allows us to study experimentally the disorder versus anisotropy phase diagram of the Anderson metal–insulator transition. Numerical and experimental data compare very well with each other and a theoretical analysis based on the self-consistent theory of localization correctly describes the observed behavior, illustrating the flexibility of cold-atom experiments for the study of transport phenomena in complex quantum systems.

Published
2013
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7. Coherent forward scattering as a robust probe of multifractality in critical disordered media

Author

Maxime Martinez, Gabriel Lemarié, Bertrand Georgeot, Christian Miniatura, Olivier Giraud, Information et Chaos Quantiques (LPT), Laboratoire de Physique Théorique (LPT), Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche « Matière et interactions » (FeRMI), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), MajuLab, National University of Singapore (NUS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Centre for Quantum Technologies [Singapore] (CQT), National University of Singapore (NUS), Institut de Physique de Nice (INPHYNI), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Nanyang Technological University [Singapour], Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), and Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)

Subjects
[PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Quantum Gases (cond-mat.quant-gas), General Physics and Astronomy, FOS: Physical sciences, [NLIN]Nonlinear Sciences [physics], Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Chaotic Dynamics (nlin.CD), Condensed Matter - Quantum Gases, Nonlinear Sciences - Chaotic Dynamics
Abstract

We study coherent forward scattering (CFS) in critical disordered systems, whose eigenstates are multifractals. We give general and simple arguments that make it possible to fully characterize the dynamics of the shape and height of the CFS peak. We show that the dynamics is governed by multifractal dimensions $D_1$ and $D_2$, which suggests that CFS could be used as an experimental probe for quantum multifractality. Our predictions are universal and numerically verified in three paradigmatic models of quantum multifractality: Power-law Random Banded Matrices (PRBM), the Ruijsenaars-Schneider ensembles (RS), and the three-dimensional kicked-rotor (3DKR). In the strong multifractal regime, we show analytically that these universal predictions exactly coincide with results from standard perturbation theory applied to the PRBM and RS models., Comment: 24 pages, 10 figures

Published
2022
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8. Coherent Forward Scattering Peak and Multifractality

Author

Olivier Giraud, Bertrand Georgeot, Christian Miniatura, Gabriel Lemarié, Maxime Martinez, Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), MajuLab (UMI 3654), National University of Singapore (NUS)-Sorbonne Université (SU), Centre for Quantum Technologies [Singapore] (CQT), National University of Singapore (NUS), Institut de Physique de Nice (INPHYNI), Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA), Department of Physics, National University of Singapore, Singapore, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), School of Physical and Mathematical Sciences, MajuLab, CNRS-UCA-SU-NUS-NTU International Joint Research Unit, Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche « Matière et interactions » (FeRMI), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), MajuLab, National University of Singapore (NUS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Nanyang Technological University [Singapour], ANR-17-EURE-0009,NanoX,Science et Ingénierie à l'Echelle Nano(2017), ANR-17-CE30-0024,COCOA,Contrôle de systèmes complexes d'atomes froids(2017), ANR-19-CE30-0013,GLADYS,De la nature vitreuse des systèmes quantiques désordonnés(2019), and ANR-18-CE30-0017,MANYLOK,Localisation à N corps avec le Kicked Rotor(2018)

Subjects
Floquet theory, Anderson localization, Anderson Localization, Forward scatter, FOS: Physical sciences, Coherent backscattering, Interference (wave propagation), Condensed Matter::Disordered Systems and Neural Networks, 01 natural sciences, 010305 fluids & plasmas, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Physics [Science], 0103 physical sciences, Coherent Backscattering, Statistical physics, [NLIN]Nonlinear Sciences [physics], 010306 general physics, Quantum, Anderson impurity model, Physics, Multifractal system, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Nonlinear Sciences - Chaotic Dynamics, Quantum Gases (cond-mat.quant-gas), Chaotic Dynamics (nlin.CD), Condensed Matter - Quantum Gases
Abstract

It has recently been shown that interference effects in disordered systems give rise to two non-trivial structures: the coherent backscattering (CBS) peak, a well-known signature of interference effects in the presence of disorder, and the coherent forward scattering (CFS) peak, which emerges when Anderson localization sets in. We study here the CFS effect in the presence of quantum multifractality, a fundamental property of several systems, such as the Anderson model at the metal-insulator transition. We focus on Floquet systems, and find that the CFS peak shape and its peak height dynamics are generically controlled by the multifractal dimensions $D_1$ and $D_2$, and by the spectral form factor. We check our results using a 1D Floquet system whose states have multifractal properties controlled by a single parameter. Our predictions are fully confirmed by numerical simulations and analytic perturbation expansions on this model. Our results, which we believe to be generic, provide an original and direct way to detect and characterize multifractality in experimental systems., 7 pages, 3 figures

Published
2021

9. Chaos-assisted long-range tunneling for quantum simulation

Author

Gabriel Lemarié, Bertrand Georgeot, David Guéry-Odelin, Maxime Martinez, Juliette Billy, Olivier Giraud, Denis Ullmo, Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Laboratoire Collisions Agrégats Réactivité (LCAR), MajuLab (UMI 3654), National University of Singapore (NUS)-Sorbonne Université (SU), Centre for Quantum Technologies [Singapore] (CQT), National University of Singapore (NUS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche « Matière et interactions » (FeRMI), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), MajuLab, National University of Singapore (NUS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), ANR-17-EURE-0009,NanoX,Science et Ingénierie à l'Echelle Nano(2017), and ANR-17-CE30-0024,COCOA,Contrôle de systèmes complexes d'atomes froids(2017)

Subjects
Physics, Quantum Physics, Range (particle radiation), [PHYS.PHYS.PHYS-SOC-PH]Physics [physics]/Physics [physics]/Physics and Society [physics.soc-ph], Lattice (group), FOS: Physical sciences, General Physics and Astronomy, Quantum simulator, Nonlinear Sciences - Chaotic Dynamics, 01 natural sciences, Term (time), [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Quantum Gases (cond-mat.quant-gas), Robustness (computer science), Quantum mechanics, 0103 physical sciences, Modulation (music), [NLIN]Nonlinear Sciences [physics], Chaotic Dynamics (nlin.CD), Condensed Matter - Quantum Gases, Quantum Physics (quant-ph), 010306 general physics, Quantum, ComputingMilieux_MISCELLANEOUS, Quantum tunnelling
Abstract

We present an extension of the chaos-assisted tunneling mechanism to spatially periodic lattice systems. We demonstrate that driving such lattice systems in an intermediate regime of modulation maps them onto tight-binding Hamiltonians with chaos-induced long-range hoppings $t_n \propto 1/n$ between sites at a distance $n$. We provide a numerical demonstration of the robustness of the results and derive an analytical prediction for the hopping term law. Such systems can thus be used to enlarge the scope of quantum simulations to experimentally realize long-range models of condensed matter., Comment: 13 pages, 10 figures

Published
2021

10. Symmetry Violation of Quantum Multifractality: Gaussian fluctuations versus Algebraic Localization

Author

Bertrand Georgeot, Olivier Giraud, Gabriel Lemarié, A. M. Bilen, Ignacio García-Mata, Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires] (CONICET)-Facultad de Ciencias Exactas y Naturales [Mar del Plata], Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP)-Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), MajuLab (UMI 3654), National University of Singapore (NUS)-Sorbonne Université (SU), Centre for Quantum Technologies [Singapore] (CQT), National University of Singapore (NUS), Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche « Matière et interactions » (FeRMI), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), MajuLab, National University of Singapore (NUS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), ANR-17-EURE-0009,NanoX,Science et Ingénierie à l'Echelle Nano(2017), ANR-17-CE30-0024,COCOA,Contrôle de systèmes complexes d'atomes froids(2017), ANR-19-CE30-0013,GLADYS,De la nature vitreuse des systèmes quantiques désordonnés(2019), and ANR-18-CE30-0017,MANYLOK,Localisation à N corps avec le Kicked Rotor(2018)

Subjects
Physics, Anderson localization, Quantum Physics, Gaussian, FOS: Physical sciences, Disordered Systems and Neural Networks (cond-mat.dis-nn), Multifractal system, Eigenfunction, Condensed Matter - Disordered Systems and Neural Networks, 16. Peace & justice, 01 natural sciences, Symmetry (physics), 010305 fluids & plasmas, symbols.namesake, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Quantum state, 0103 physical sciences, symbols, Quantum Physics (quant-ph), 010306 general physics, Random matrix, Quantum, Mathematical physics
Abstract

Quantum multifractality is a fundamental property of systems such as non-interacting disordered systems at an Anderson transition and many-body systems in Hilbert space. Here we discuss the origin of the presence or absence of a fundamental symmetry related to this property. The anomalous multifractal dimension $\Delta_q$ is used to characterize the structure of quantum states in such systems. Although the multifractal symmetry relation \mbox{$\Delta_q=\Delta_{1-q}$} is universally fulfilled in many known systems, recently some important examples have emerged where it does not hold. We show that this is the result of two different mechanisms. The first one was already known and is related to Gaussian fluctuations well described by random matrix theory. The second one, not previously explored, is related to the presence of an algebraically localized envelope. While the effect of Gaussian fluctuations can be removed by coarse graining, the second mechanism is robust to such a procedure. We illustrate the violation of the symmetry due to algebraic localization on two systems of very different nature, a 1D Floquet critical system and a model corresponding to Anderson localization on random graphs., Comment: Closest to published version

Published
2021

11. Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking

Author

Maxime Dupont, Nicolas Laflorencie, Gabriel Lemarié, Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées, Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)

Subjects
Quantum phase transition, Density matrix, Fluids & Plasmas, Quantum Monte Carlo, FOS: Physical sciences, 02 engineering and technology, 01 natural sciences, law.invention, Condensed Matter - Strongly Correlated Electrons, Engineering, law, Quantum mechanics, 0103 physical sciences, cond-mat.dis-nn, 010306 general physics, Quantum, Randomness, ComputingMilieux_MISCELLANEOUS, Boson, Physics, Condensed Matter::Quantum Gases, Strongly Correlated Electrons (cond-mat.str-el), Ergodicity, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, 021001 nanoscience & nanotechnology, Physical Sciences, Chemical Sciences, cond-mat.str-el, [PHYS.COND.CM-SCE]Physics [physics]/Condensed Matter [cond-mat]/Strongly Correlated Electrons [cond-mat.str-el], 0210 nano-technology, Bose–Einstein condensate
Abstract

Building on large-scale quantum Monte Carlo simulations, we investigate the zero-temperature phase diagram of hard-core bosons in a random potential on site-centered Cayley trees with branching number $K=2$. In order to follow how the Bose-Einstein condensate (BEC) is affected by the disorder, we focus on both the zero-momentum density, probing the quantum coherence, and the one-body density matrix (1BDM) whose largest eigenvalue monitors the off-diagonal long-range order. We further study its associated eigenstate which brings useful information about the real-space properties of this leading eigenmode. Upon increasing randomness, we find that the system undergoes a quantum phase transition at finite disorder strength between a long-range ordered BEC state, fully ergodic at large scale, and a new disordered Bose glass regime showing conventional localization for the coherence fraction while the 1BDM displays a non-trivial algebraic vanishing BEC density together with a non-ergodic occupation in real-space. These peculiar properties can be analytically captured by a simple phenomenological description on the Cayley tree which provides a physical picture of the Bose glass regime., 21 pages, 16 figures

Published
2020

12. Chaos-assisted tunneling resonances in a synthetic Floquet superlattice

Author

M. Arnal, Olivier Giraud, G. Chatelain, David Guéry-Odelin, Denis Ullmo, Bertrand Georgeot, Juliette Billy, Gabriel Lemarié, Maxime Martinez, N. Dupont, Atomes Froids (LCAR), Laboratoire Collisions Agrégats Réactivité (LCAR), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Information et Chaos Quantiques (LPT), Laboratoire de Physique Théorique (LPT), Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse)

Subjects
[PHYS.COND.GAS]Physics [physics]/Condensed Matter [cond-mat]/Quantum Gases [cond-mat.quant-gas], Superlattice, FOS: Physical sciences, Quantum simulator, 01 natural sciences, 010305 fluids & plasmas, Physics::Fluid Dynamics, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Quantum mechanics, 0103 physical sciences, Quantum system, 010306 general physics, Quantum, Quantum tunnelling, Research Articles, Quantum computer, Physics, Condensed Matter::Quantum Gases, Quantum Physics, Optical lattice, Multidisciplinary, SciAdv r-articles, Quantum chaos, 3. Good health, Nonlinear Sciences::Chaotic Dynamics, Condensed Matter::Soft Condensed Matter, Quantum Gases (cond-mat.quant-gas), [NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD], Condensed Matter - Quantum Gases, Quantum Physics (quant-ph), Research Article
Abstract

Resonances in quantum transport are observed through chaos-assisted tunneling with a quantum gas in a shaken optical lattice., The field of quantum simulation, which aims at using a tunable quantum system to simulate another, has been developing fast in the past years as an alternative to the all-purpose quantum computer. So far, most efforts in this domain have been directed to either fully regular or fully chaotic systems. Here, we focus on the intermediate regime, where regular orbits are surrounded by a large sea of chaotic trajectories. We observe a quantum chaos transport mechanism, called chaos-assisted tunneling, that translates in sharp resonances of the tunneling rate and provides previously unexplored possibilities for quantum simulation. More specifically, using Bose-Einstein condensates in a driven optical lattice, we experimentally demonstrate and characterize these resonances. Our work paves the way for quantum simulations with long-range transport and quantum control through complexity.

Published
2020

13. Two critical localization lengths in the Anderson transition on random graphs

Author

Rémy Dubertrand, John Martin, Olivier Giraud, Ignacio García-Mata, Gabriel Lemarié, Bertrand Georgeot, Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires] (CONICET)-Facultad de Ciencias Exactas y Naturales [Mar del Plata], Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP)-Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP), Institut de Physique Nucléaire, Atomique et de Spectroscopie, CESAM, Université de Liège, Bât. B15, B - 4000 Liège, Institut für Theoretische Physik [Regensburg], Universität Regensburg (UR), Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Information et Chaos Quantiques (LPT), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées, Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)

Subjects
FOS: Physical sciences, 01 natural sciences, 010305 fluids & plasmas, purl.org/becyt/ford/1 [https], [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], 0103 physical sciences, [PHYS.COND]Physics [physics]/Condensed Matter [cond-mat], 010306 general physics, Condensed Matter - Statistical Mechanics, Mathematical physics, Random graph, Physics, G100, Quantum Physics, Statistical Mechanics (cond-mat.stat-mech), LOCALIZATION, Observable, purl.org/becyt/ford/1.3 [https], Disordered Systems and Neural Networks (cond-mat.dis-nn), Renormalization group, Condensed Matter - Disordered Systems and Neural Networks, RANDOM, GRAPH, Quantum Physics (quant-ph), QUANTUM, Critical exponent
Abstract

We present a full description of the nonergodic properties of wavefunctions on random graphs without boundary in the localized and critical regimes of the Anderson transition. We find that they are characterized by two critical localization lengths: the largest one describes localization along rare branches and diverges with a critical exponent $\nu_\parallel=1$ at the transition. The second length, which describes localization along typical branches, reaches at the transition a finite universal value (which depends only on the connectivity of the graph), with a singularity controlled by a new critical exponent $\nu_\perp=1/2$. We show numerically that these two localization lengths control the finite-size scaling properties of key observables: wavefunction moments, correlation functions and spectral statistics. Our results are identical to the theoretical predictions for the typical localization length in the many-body localization transition, with the same critical exponent. This strongly suggests that the two transitions are in the same universality class and that our techniques could be directly applied in this context., Comment: 6 pages, 3 figures; Corresponds to the published version

Published
2019

14. Kane-Fisher weak link physics in the clean scratched XY model

Author

Gabriel Lemarié, Ilaria Maccari, Claudio Castellani, Information et Chaos Quantiques (LPT), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Università degli Studi di Roma 'La Sapienza' = Sapienza University [Rome], Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3)

Subjects
Length scale, Dimension (graph theory), FOS: Physical sciences, 02 engineering and technology, Superfluid-Insulator Transition, XY model, Condensed Matter Physics, 01 natural sciences, Superfluidity, Condensed Matter - Strongly Correlated Electrons, 0103 physical sciences, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, Scaling, Condensed Matter - Statistical Mechanics, ComputingMilieux_MISCELLANEOUS, Mathematical physics, Physics, Statistical Mechanics (cond-mat.stat-mech), Strongly Correlated Electrons (cond-mat.str-el), Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Renormalization group, 021001 nanoscience & nanotechnology, Classical XY model, 0210 nano-technology, Statistical mechanics, Intensity (heat transfer), Energy (signal processing)
Abstract

The nature of the superfluid-insulator transition in 1D has been much debated recently. In particular, to describe the strong disorder regime characterized by weak link proliferation, a scratched-XY model has been proposed [New J. Phys. \textbf{18}, 045018 (2016)], where the transport is dominated by a single anomalously weak link and is governed by Kane-Fisher weak link physics. In this article, we consider the simplest problem to which the scratched-XY model relates: a single weak link in an otherwise \textit{clean} system, with an intensity $J_W$ which decreases algebraically with the size of the system $J_W\sim L^{-\alpha}$. Using a renormalization group approach and a vortex energy argument, we describe the Kane-Fisher physics in this model and show that it leads to a transition from a transparent regime for $K>K_c$ to a perfect cut for $K, Comment: 11 pages, 4 figures

Published
2019

15. Glassy properties of Anderson localization: pinning, avalanches and chaos

Author

Gabriel Lemarié, Information et Chaos Quantiques (LPT), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées, Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)

Subjects
Anderson localization, Spin glass, FOS: Physical sciences, General Physics and Astronomy, Interference (wave propagation), 01 natural sciences, Condensed Matter::Disordered Systems and Neural Networks, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], 0103 physical sciences, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, Condensed Matter - Statistical Mechanics, Universal conductance fluctuations, Physics, Chaos (genus), Quantum Physics, Statistical Mechanics (cond-mat.stat-mech), Condensed matter physics, biology, Conductance, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, biology.organism_classification, Thermodynamic limit, Polymer physics, Quantum Physics (quant-ph)
Abstract

I present the results of extensive numerical simulations which reveal the glassy properties of Anderson localization in dimension two at zero temperature: pinning, avalanches and chaos. I first show that strong localization confines quantum transport along paths which are pinned by disorder but can change abruptly and suddenly (avalanches) when the energy is varied. I determine the roughness exponent $\zeta$ characterizing the transverse fluctuations of these paths and find that its value $\zeta=2/3$ is the same as for the directed polymer problem. Finally, I characterize the chaos property, namely the fragility of the conductance with respect to small perturbations in the disorder configuration. It is linked to interference effects and universal conductance fluctuations at weak disorder, and more spin-glass-like behavior at strong disorder., Comment: 6 + 5 (supplemental material) pages, 4 + 6 figures. Corresponds to the published version

Published
2019

16. Weak- versus strong-disorder superfluid—Bose glass transition in one dimension

Author

Elmer V. H. Doggen, Gabriel Lemarié, Sylvain Capponi, Nicolas Laflorencie, Information et Chaos Quantiques (LPT), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Fermions Fortement Corrélés (LPT) (FFC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées

Subjects
Quantum Monte Carlo, FOS: Physical sciences, Condensed Matter::Disordered Systems and Neural Networks, 01 natural sciences, 010305 fluids & plasmas, Superfluidity, Condensed Matter - Strongly Correlated Electrons, Critical line, Quantum mechanics, 0103 physical sciences, [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], 010306 general physics, Luttinger parameter, Matrix product state, ComputingMilieux_MISCELLANEOUS, Boson, Physics, Condensed Matter::Quantum Gases, Quantum Physics, Condensed matter physics, Strongly Correlated Electrons (cond-mat.str-el), Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Zero temperature, Glass transition, Quantum Physics (quant-ph)
Abstract

Using large-scale simulations based on matrix product state and quantum Monte Carlo techniques, we study the superfluid to Bose glass-transition for one-dimensional attractive hard-core bosons at zero temperature, across the full regime from weak to strong disorder. As a function of interaction and disorder strength, we identify a Berezinskii-Kosterlitz-Thouless critical line with two different regimes. At small attraction where critical disorder is weak compared to the bandwidth, the critical Luttinger parameter $K_c$ takes its universal Giamarchi-Schulz value $K_{c}=3/2$. Conversely, a non-universal $K_c>3/2$ emerges for stronger attraction where weak-link physics is relevant. In this strong disorder regime, the transition is characterized by self-similar power-law distributed weak links with a continuously varying characteristic exponent $\alpha$., Comment: 4+epsilon pages, 3 figures, 6-epsilon pages of supplementary material. Comments welcome

Published
2017

17. Chaos-assisted tunneling in the presence of Anderson localization

Author

Bertrand Georgeot, Elmer V. H. Doggen, Gabriel Lemarié, Information et Chaos Quantiques (LPT), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées, Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse)

Subjects
Anderson localization, Distribution (number theory), Chaotic, FOS: Physical sciences, 01 natural sciences, 010305 fluids & plasmas, tunneling, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Quantum mechanics, Mesoscale and Nanoscale Physics (cond-mat.mes-hall), 0103 physical sciences, Ergodic theory, [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], 010306 general physics, Scaling, Condensed Matter - Statistical Mechanics, Quantum tunnelling, Physics, Quantum Physics, Condensed Matter - Mesoscale and Nanoscale Physics, Statistical Mechanics (cond-mat.stat-mech), Condensed matter physics, Cauchy distribution, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Nonlinear Sciences - Chaotic Dynamics, Quantum chaos, Nonlinear Sciences::Chaotic Dynamics, [NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD], Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), quantum chaos
Abstract

Tunneling between two classically disconnected regular regions can be strongly affected by the presence of a chaotic sea in between. This phenomenon, known as chaos-assisted tunneling, gives rise to large fluctuations of the tunneling rate. Here we study chaos-assisted tunneling in the presence of Anderson localization effects in the chaotic sea. Our results show that the standard tunneling rate distribution is strongly modified by localization, going from the known Cauchy distribution in the ergodic regime to a log-normal distribution in the strongly localized case. We develop an analytical single-parameter scaling theory which accurately describes the numerical data, for both a deterministic and a disordered model. Several possible experimental implementations using cold atoms, photonic lattices or microwave billiards are discussed., Comment: 6 pages, 2 figures. Comments welcome

Published
2017

18. Return to the Origin as a Probe of Atomic Phase Coherence

Author

Clément Hainaut, Radu Chicireanu, Jean-François Clément, Pascal Szriftgiser, Dominique Delande, Jean Claude Garreau, Gabriel Lemarié, Nicolas Cherroret, Samir Zemmouri, Isam Manai, Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 (PhLAM), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Information et Chaos Quantiques (LPT), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Laboratoire Kastler Brossel (LKB (Jussieu)), Université Pierre et Marie Curie - Paris 6 (UPMC)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Quantum decoherence, Wave packet, Dephasing, FOS: Physical sciences, General Physics and Astronomy, 6470qj, Astrophysics::Cosmology and Extragalactic Astrophysics, Interference (wave propagation), 01 natural sciences, 010305 fluids & plasmas, law.invention, Standing wave, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], law, 0545Mt, Quantum mechanics, 0103 physical sciences, 0375-b, [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], Physics::Atomic Physics, 010306 general physics, Quantum, Astrophysics::Galaxy Astrophysics, Physics, Quantum Physics, Oscillation, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Laser, 7215Rn, Astrophysics::Earth and Planetary Astrophysics, Atomic physics, Quantum Physics (quant-ph)
Abstract

International audience; We report on the observation of the coherent enhancement of the return probability (" enhanced return to the origin " , ERO) in a periodically kicked cold-atom gas. By submitting an atomic wave packet to a pulsed, periodically shifted laser standing wave, we induce an oscillation of ERO in time and explain it in terms of a periodic, reversible dephasing in the weak-localization interference sequences responsible for ERO. Monitoring the temporal decay of ERO, we exploit its quantum coherent nature to quantify the decoherence rate of the atomic system.

Published
2017

19. Coherent backscattering and forward-scattering peaks in the quantum kicked rotor

Author

Gabriel Lemarié, Christian Miniatura, David Guéry-Odelin, Cord A. Müller, Information et Chaos Quantiques (LPT), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées, Fachbereich Physik [Konstanz], University of Konstanz, Atomes Froids (LCAR), Laboratoire Collisions Agrégats Réactivité (LCAR), Institut Non Linéaire de Nice Sophia-Antipolis (INLN), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Department of Physics Faculty of Science Singapore, National University of Singapore (NUS), Centre for Quantum Technologies [Singapore] (CQT), School of Physical and Mathematical Sciences, Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)

Subjects
Physics, Elastic scattering, Anderson localization, [PHYS.COND.GAS]Physics [physics]/Condensed Matter [cond-mat]/Quantum Gases [cond-mat.quant-gas], Rotor (electric), Forward scatter, Position and momentum space, Coherent backscattering, 01 natural sciences, 010305 fluids & plasmas, law.invention, law, Quantum mechanics, 0103 physical sciences, Forward scattering peaks, 010306 general physics, Rotation (mathematics), Quantum, ComputingMilieux_MISCELLANEOUS
Abstract

We propose and analyze an experimental scheme using the quantum kicked rotor to observe the newly predicted coherent forward-scattering peak together with its long-known twin brother, the coherent backscattering peak. Contrary to coherent backscattering, which arises already under weak-localization conditions, coherent forward scattering is only triggered by Anderson or strong localization. So far, coherent forward scattering has not been observed in conservative systems with elastic scattering by spatial disorder. We propose to turn to the quantum kicked rotor, which has a long and successful history as an accurate experimental platform to observe dynamical localization, i.e., Anderson localization in momentum space. We analyze the coherent forward-scattering effect for the quantum kicked rotor by extensive numerical simulations, both in the orthogonal and unitary class of disordered quantum systems, and show that an experimental realization involving phase-space rotation techniques is within reach of state-of-the-art cold-atom experiments. Published version

Published
2017

20. Scaling Theory of the Anderson Transition in Random Graphs: Ergodicity and Universality

Author

Ignacio García-Mata, Olivier Giraud, Rémy Dubertrand, John Martin, Bertrand Georgeot, Gabriel Lemarié, Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires] (CONICET)-Facultad de Ciencias Exactas y Naturales [Mar del Plata], Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP)-Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP), Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Information et Chaos Quantiques (LPT), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées, Institut de Physique Nucl'eaire, Atomique et de Spectroscopie, Université de Liège, Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)

Subjects
Anderson localization, F300, Ciencias Físicas, Physics::Optics, FOS: Physical sciences, General Physics and Astronomy, Condensed Matter::Disordered Systems and Neural Networks, 01 natural sciences, GRAPHS, 010305 fluids & plasmas, purl.org/becyt/ford/1 [https], Delocalized electron, 0103 physical sciences, FOS: Mathematics, Ergodic theory, [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], Statistical physics, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, Scaling, Condensed Matter - Statistical Mechanics, random graphs, Condensed Matter::Quantum Gases, Random graph, Physics, Quantum Physics, COMPLEX, Statistical Mechanics (cond-mat.stat-mech), Condensed matter physics, ddc:530, Probability (math.PR), Ergodicity, transition, LOCALIZATION, purl.org/becyt/ford/1.3 [https], Disordered Systems and Neural Networks (cond-mat.dis-nn), Multifractal system, Condensed Matter - Disordered Systems and Neural Networks, 530 Physik, Universality (dynamical systems), Astronomía, [NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD], ergodicity, Condensed Matter::Strongly Correlated Electrons, Quantum Physics (quant-ph), QUANTUM, Mathematics - Probability, CIENCIAS NATURALES Y EXACTAS
Abstract

We study the Anderson transition on a generic model of random graphs with a tunable branching parameter $1, Comment: 5+5 pages, 4+4 figures

Published
2017
Full Text
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21. Routes towards the experimental observation of the large fluctuations due to chaos assisted tunneling effects with cold atoms

Author

David Guéry-Odelin, Rémy Dubertrand, Bertrand Georgeot, Juliette Billy, Gabriel Lemarié, Université de Liège, Information et Chaos Quantiques (LPT), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées, Atomes Froids (LCAR), Laboratoire Collisions Agrégats Réactivité (LCAR), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse)

Subjects
Physics, Quantum Physics, F300, FOS: Physical sciences, Position and momentum space, Fixed point, 01 natural sciences, Symmetry (physics), 010305 fluids & plasmas, Momentum, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Quantum Gases (cond-mat.quant-gas), Quantum mechanics, 0103 physical sciences, Quantum system, Pendulum (mathematics), Condensed Matter - Quantum Gases, Quantum Physics (quant-ph), 010306 general physics, Wave function, Quantum tunnelling, ComputingMilieux_MISCELLANEOUS
Abstract

In the presence of a complex classical dynamics associated with a mixed phase space, a quantum wave function can tunnel between two stable islands through the chaotic sea, an effect that has no classical counterpart. This phenomenon, referred to as chaos assisted tunneling, is characterized by large fluctuations of the tunneling rate when a parameter is varied. To date the full extent of this effect as well as the associated statistical distribution have never been observed in a quantum system. Here we analyze the possibility of characterizing these effects accurately in a cold atom experiment. Using realistic values of the parameters of an experimental setup, we examine through analytical estimates and extensive numerical simulations a specific system that can be implemented with cold atoms, the atomic modulated pendulum. We assess the efficiency of three possible routes to observe in detail chaos assisted tunneling properties. Our main conclusion is that due to the fragility of the symmetry between positive and negative momenta as a function of quasimomentum, it is very challenging to use tunneling between classical islands centered on fixed points with opposite momentum. We show that it is more promising to use islands symmetric in position space, and characterize the regime where it could be done. The proposed experiment could be realized with current state-of-the-art technology., Comment: 20 pages, 26 figures

Published
2016

22. Multifractality of quantum wave functions in the presence of perturbations

Author

Ignacio García-Mata, Rémy Dubertrand, Olivier Giraud, Gabriel Lemarié, Bertrand Georgeot, John Martin, Information et Chaos Quantiques (LPT), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Université de Liège, Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires] (CONICET)-Facultad de Ciencias Exactas y Naturales [Mar del Plata], Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP)-Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP), Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse)

Subjects
Characteristic length, F300, Ciencias Físicas, FOS: Physical sciences, Otras Ciencias Físicas, purl.org/becyt/ford/1 [https], Fractal, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], [NLIN]Nonlinear Sciences [physics], Statistical physics, Localizacion, Wave function, Scaling, Anderson impurity model, Quantum, Mathematics, Quantum Physics, ddc:530, 05.45.Df, 05.45.Mt, 71.30.+h, 05.40.-a, 05.45.Df, 05.45.Mt, 71.30.+h, 05.40.−a, Disordered Systems and Neural Networks (cond-mat.dis-nn), purl.org/becyt/ford/1.3 [https], Condensed Matter - Disordered Systems and Neural Networks, 530 Physik, Nonlinear Sciences - Chaotic Dynamics, Quantum chaos, Cuantica, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), Random matrix, CIENCIAS NATURALES Y EXACTAS
Abstract

We present a comprehensive study of the destruction of quantum multifractality in the presence of perturbations. We study diverse representative models displaying multifractality, including a pseudointegrable system, the Anderson model and a random matrix model. We apply several types of natural perturbations which can be relevant for experimental implementations. We construct an analytical theory for certain cases, and perform extensive large-scale numerical simulations in other cases. The data are analyzed through refined methods including double scaling analysis. Our results confirm the recent conjecture that multifractality breaks down following two scenarios. In the first one, multifractality is preserved unchanged below a certain characteristic length which decreases with perturbation strength. In the second one, multifractality is affected at all scales and disappears uniformly for a strong enough perturbation. Our refined analysis shows that subtle variants of these scenarios can be present in certain cases. This study could guide experimental implementations in order to observe quantum multifractality in real systems., 20 pages, 27 figures

Published
2015

23. Scanning gate microscopy of quantum contacts under parallel magnetic field: Beating patterns between spin-split transmission peaks or channel openings

Author

Gabriel Lemarié, Geneviève Fleury, Jean-Louis Pichard, Andrii Kleshchonok, Service de physique de l'état condensé (SPEC - UMR3680), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Information et Chaos Quantiques (LPT), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Supported by the EU Marie Curie network 'NanoCTM' (project no.234970), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3)

Subjects
Physics, Spins, Field (physics), Condensed matter physics, Condensed Matter - Mesoscale and Nanoscale Physics, Quantum point contact, scanning gate microscopy, FOS: Physical sciences, quantum dot, Scanning gate microscopy, Fabry-Pérot interference fringes, Condensed Matter Physics, 3. Good health, Electronic, Optical and Magnetic Materials, Magnetic field, Mesoscale and Nanoscale Physics (cond-mat.mes-hall), Zeeman energy, Electron interferometer, quantum point contact, [PHYS.COND.CM-MSQHE]Physics [physics]/Condensed Matter [cond-mat]/Mesoscopic Systems and Quantum Hall Effect [cond-mat.mes-hall], Spin-½
Abstract

We study the conductance $g$ of an electron interferometer created in a two dimensional electron gas between a nanostructured contact and the depletion region induced by the charged tip of a scanning gate microscope. Using non-interacting models, we study the beating pattern of interference fringes exhibited by the images giving $g$ as a function of the tip position when a parallel magnetic field is applied. The analytical solution of a simplified model allows us to distinguish between two cases: (i) If the field is applied everywhere, the beating of Fabry-P\'erot oscillations of opposite spins gives rise to interference rings which can be observed at low temperatures when the contact is open between spin-split transmission resonances. (ii) If the field acts only upon the contact, the interference rings cannot be observed at low temperatures, but only at temperatures of the order of the Zeeman energy. For a contact made of two sites in series, a model often used for describing an inversion-symmetric double-dot setup, a pseudo-spin degeneracy is broken by the inter-dot coupling and a similar beating effect can be observed without magnetic field at temperatures of the order of the interdot coupling. Eventually, numerical studies of a quantum point contact with quantized conductance plateaus confirm that a parallel magnetic field applied everywhere or only upon the contact gives rises to similar beating effects between spin-split channel openings., Comment: 11 pages, 17 figures

Published
2015

24. Two scenarios for quantum multifractality breakdown

Author

Ignacio García-Mata, Bertrand Georgeot, Gabriel Lemarié, John Martin, Olivier Giraud, Rémy Dubertrand, Information et Chaos Quantiques (LPT), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées, Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires] (CONICET)-Facultad de Ciencias Exactas y Naturales [Mar del Plata], Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP)-Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP), Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Institut de Physique Nucléaire, Atomique et de Spectroscopie, Université de Liège, Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)

Subjects
METAL-AISLANTE, F300, Ciencias Físicas, General Physics and Astronomy, Perturbation (astronomy), FOS: Physical sciences, Otras Ciencias Físicas, purl.org/becyt/ford/1 [https], RUIDO, Fractal, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], TRANSICION, Ergodic theory, Statistical physics, Quantum, Anderson impurity model, Quantum fluctuation, Physics, Quantum Physics, purl.org/becyt/ford/1.3 [https], Multifractal system, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Nonlinear Sciences - Chaotic Dynamics, Quantum chaos, [PHYS.COND.CM-GEN]Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other], [NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD], CHAOS, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), CIENCIAS NATURALES Y EXACTAS
Abstract

We expose two scenarios for the breakdown of quantum multifractality under the effect of perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations. In the other one, the fluctuations of the wave functions are changed at every scale and each multifractal dimension smoothly goes to the ergodic value. We use as generic examples a one-dimensional dynamical system and the three-dimensional Anderson model at the metal-insulator transition. Based on our results, we conjecture that the sensitivity of quantum multifractality to perturbation is universal in the sense that it follows one of these two scenarios depending on the perturbation. We also discuss the experimental implications., Comment: 5 pages, 4 figures, minor modifications, published version

Published
2014

25. Critical Properties of the Superfluid - Bose Glass Transition in Two Dimensions

Author

Gabriel Lemarié, David J. Luitz, Nicolas Laflorencie, Juan Pablo Álvarez Zúñiga, Fermions Fortement Corrélés (LPT) (FFC), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Information et Chaos Quantiques (LPT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse)

Subjects
Quantum phase transition, Physics, [PHYS]Physics [physics], Condensed matter physics, Quantum Monte Carlo, General Physics and Astronomy, FOS: Physical sciences, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Scale invariance, 3. Good health, Superfluidity, Critical point (thermodynamics), Probability distribution, Critical exponent, Boson
Abstract

We investigate the superfluid (SF) to Bose glass (BG) quantum phase transition using extensive quantum Monte Carlo simulations of two-dimensional hard-core bosons in a random box potential. $T=0$ critical properties are studied by thorough finite-size scaling of condensate and SF densities, both vanishing at the same critical disorder $W_c=4.80(5)$. Our results give the following estimates for the critical exponents: $z=1.85(15)$, $\nu=1.20(12)$, $\eta=-0.40(15)$. Furthermore, the probability distribution of the SF response $P(\ln\rho_{\rm sf})$ displays striking differences across the transition: while it narrows with increasing system sizes $L$ in the SF phase, it broadens in the BG regime, indicating an absence of self-averaging, and at the critical point $P(\ln\rho_{\rm sf}+z \ln L)$ is scale invariant. Finally, high-precision measurements of the local density rule out a percolation picture for the SF-BG transition., Comment: 4 pages, 5 figures + supplementary material

Published
2014
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26. Spin wave theory for 2D disordered hard-core bosons

Author

Juan Pablo Álvarez Zúñiga, Gabriel Lemarié, Nicolas Laflorencie, Fermions Fortement Corrélés (LPT) (FFC), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Information et Chaos Quantiques (LPT), Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3)

Subjects
Physics, Strongly Correlated Electrons (cond-mat.str-el), Phase (waves), FOS: Physical sciences, Inverse, Observable, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, 01 natural sciences, 010305 fluids & plasmas, Condensed Matter - Strongly Correlated Electrons, Mean field theory, Spin wave, Quantum mechanics, [PHYS.COND.CM-GEN]Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other], 0103 physical sciences, 010306 general physics, Randomness, Excitation, Boson
Abstract

A spin-wave (SW) approach for hard-core bosons is presented to treat the problem of two dimensional boson localization in a random potential. After a short review of the method to compute 1/S-corrected observables, the case of random on-site energy is discussed. Whereas the mean-field solution does not display a Bose glass (BG) phase, 1/S corrections do capture BG physics. In particular, the localization of SW excitations is discussed through the inverse participation ratio., TIDS15 conference

Published
2013

27. Universal scaling of the order-parameter distribution in strongly disordered superconductors

Author

Anand Kamlapure, Claudio Castellani, Somesh Chandra Ganguli, Lara Benfatto, G. Seibold, Pratap Raychaudhuri, Gabriel Lemarié, D. Bucheli, José Lorenzana, Information et Chaos Quantiques (LPT), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3)

Subjects
Superconductivity, Physics, Condensed matter physics, Condensed Matter - Superconductivity, superconductivity, Parameter distribution, Order (ring theory), FOS: Physical sciences, 02 engineering and technology, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, 021001 nanoscience & nanotechnology, Condensed Matter Physics, 01 natural sciences, Electronic, Optical and Magnetic Materials, Superconductivity (cond-mat.supr-con), Distribution (mathematics), Condensed Matter::Superconductivity, 0103 physical sciences, disordered superconductors, 010306 general physics, 0210 nano-technology, Scaling, ComputingMilieux_MISCELLANEOUS
Abstract

We investigate theoretically and experimentally the statistical properties of the inhomogeneous order-parameter distribution (OPD) at the verge of the superconductor-insulator transition (SIT). We find within two prototype fermionic and bosonic models for disordered superconductors that one can identify a universal rescaling of the OPD. By performing scanning-tunneling microscopy experiments in three samples of NbN with increasing disorder we show that such a rescaling describes also with an excellent accuracy the experimental data. These results can provide a breakthrough in our understanding of the SIT., Comment: 11 pages, 8 figures, revised version submitted to PRB

Published
2013

28. Thermal enhancement of interference effects in quantum point contacts

Author

Adel Abbout, Jean-Louis Pichard, Gabriel Lemarié, Service de physique de l'état condensé (SPEC - UMR3680), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), and ANR-08-BLAN-0030,ITEM-Th,Interaction et Transport à l'Echelle Mésoscopique - Theorie(2008)

Subjects
Theory of Quantum Mesoscopic Systems, Quantum point contact, 85.35.Ds,07.79.-v,73.23.-b, 72.10.-d, General Physics and Astronomy, FOS: Physical sciences, 02 engineering and technology, Plateau (mathematics), Interference (wave propagation), 01 natural sciences, 0103 physical sciences, Mesoscale and Nanoscale Physics (cond-mat.mes-hall), 010306 general physics, Quantum, Electron interferometer, [PHYS.COND.CM-MSQHE]Physics [physics]/Condensed Matter [cond-mat]/Mesoscopic Systems and Quantum Hall Effect [cond-mat.mes-hall], Physics, Condensed Matter - Mesoscale and Nanoscale Physics, Condensed matter physics, Conductance, Quantum interferences, 021001 nanoscience & nanotechnology, Wavelength, Quantum Point Contact, Scanning Gate Microscopy, Electron Interferometer, 0210 nano-technology, Fermi gas
Abstract

We study an electron interferometer formed with a quantum point contact and a scanning probe tip in a two-dimensional electron gas. The images giving the conductance as a function of the tip position exhibit fringes spaced by half the Fermi wavelength. For a contact opened at the edges of a quantized conductance plateau, the fringes are enhanced as the temperature T increases and can persist beyond the thermal length l_T. This unusual effect is explained assuming a simplified model: The fringes are mainly given by a contribution which vanishes when T -> 0 and has a decay characterized by a T-independent scale.

Published
2010

29. Classical diffusive dynamics for the quasiperiodic kicked rotor

Author

Gabriel Lemarié, Jean Claude Garreau, Pascal Szriftgiser, Dominique Delande, Laboratoire Kastler Brossel (LKB (Jussieu)), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Service de physique de l'état condensé (SPEC - UMR3680), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 (PhLAM), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Centre d'Etudes et de Recherches Lasers et Applications (CERLA), Université de Lille, Sciences et Technologies, Université Pierre et Marie Curie - Paris 6 (UPMC)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Anisotropic diffusion, Chaotic, FOS: Physical sciences, Context (language use), 01 natural sciences, 010305 fluids & plasmas, law.invention, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], law, 0103 physical sciences, 010306 general physics, Quantum, Anderson impurity model, Physics, Quantum Physics, Rotor (electric), Nonlinear Sciences - Chaotic Dynamics, Atomic and Molecular Physics, and Optics, Nonlinear Sciences::Chaotic Dynamics, Condensed Matter - Other Condensed Matter, Classical mechanics, Quasiperiodic function, [NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD], Matter wave, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), Other Condensed Matter (cond-mat.other)
Abstract

We study the classical dynamics of a quasiperiodic kicked rotor, whose quantum counterpart is known to be an equivalent of the 3D Anderson model. Using this correspondence allowed for a recent experimental observation of the Anderson transition with atomic matter waves. In such a context, it is particularly important to assert the chaotic character of the classical dynamics of this system. We show here that it is a 3D anisotropic diffusion. Our simple analytical predictions for the associated diffusion tensor are found in good agreement with the results of numerical simulations., 8 pages, 7 figures, submitted to Jour. Mod. Opt.

Published
2010

30. Critical State of the Anderson Transition: Between a Metal and an Insulator

Author

Pascal Szriftgiser, Gabriel Lemarié, H. Lignier, Jean Claude Garreau, Dominique Delande, Laboratoire Kastler Brossel (LKB (Jussieu)), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Service de physique de l'état condensé (SPEC - UMR3680), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 (PhLAM), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Laboratoire Aimé Cotton (LAC), École normale supérieure - Cachan (ENS Cachan)-Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)-École normale supérieure - Cachan (ENS Cachan)

Subjects
Phase transition, Anderson localization, [PHYS.COND.GAS]Physics [physics]/Condensed Matter [cond-mat]/Quantum Gases [cond-mat.quant-gas], Wave packet, General Physics and Astronomy, 01 natural sciences, 010305 fluids & plasmas, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Critical point (thermodynamics), Quantum critical point, Quantum mechanics, 0103 physical sciences, 03.75.-b, 05.45.Mt, 72.15.Rn, Anderson transition, Cold atoms, 010306 general physics, Physics, [PHYS.PHYS.PHYS-ATOM-PH]Physics [physics]/Physics [physics]/Atomic Physics [physics.atom-ph], Condensed matter physics, Time evolution, Quantum chaos, kicked rotor, [NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD], Matter wave, quantum chaos
Abstract

4 pages, 3 figures, submitted to PRL; International audience; Using a three-frequency one-dimensional kicked rotor experimentally realized with a cold atomic gas, we study the transport properties at the critical point of the metal-insulator Anderson transition. We accurately measure the time-evolution of an initially localized wavepacket and show that it displays at the critical point a scaling invariance characteristic of this second-order phase transition. The shape of the momentum distribution at the critical point is found to be in excellent agreement with the analytical form deduced from self-consistent theory of localization.

Published
2010

31. Universality of the Anderson transition with the quasiperiodic kicked rotor

Author

Dominique Delande, Gabriel Lemarié, and Benoît Grémaud

Subjects
Physics, Quantum Physics, Critical phenomena, Numerical analysis, General Physics and Astronomy, FOS: Physical sciences, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter::Disordered Systems and Neural Networks, Universality (dynamical systems), Nonlinear Sciences::Chaotic Dynamics, Quantum Gases (cond-mat.quant-gas), Quasiperiodic function, Quantum mechanics, Condensed Matter::Strongly Correlated Electrons, Condensed Matter - Quantum Gases, Quantum Physics (quant-ph), Scaling, Critical exponent, Anderson impurity model
Abstract

We report a numerical analysis of the Anderson transition in a quantum-chaotic system, the quasiperiodic kicked rotor with three incommensurate frequencies. It is shown that this dynamical system exhibits the same critical phenomena as the truly random 3D-Anderson model. By taking proper account of systematic corrections to one-parameter scaling, the universality of the critical exponent is demonstrated. Our result $\nu = 1.59 \pm 0.01$ is in perfect agreement with the value found for the Anderson model., Comment: 4 figures, 3 tables (published version)

Published
2009
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32. Observation of the Anderson Metal-Insulator Transition with Atomic Matter Waves: Theory and Experiment

Author

Pascal Szriftgiser, Gabriel Lemarié, Julien Chabé, Jean Claude Garreau, Benoît Grémaud, Dominique Delande, Laboratoire Kastler Brossel (LKB (Jussieu)), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 (PhLAM), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Centre d'Etudes et de Recherches Lasers et Applications (CERLA), Université de Lille, Sciences et Technologies, Centre for Quantum Technologies [Singapore] (CQT), National University of Singapore (NUS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Quantum phase transition, dynamical localization, 03.75.-b, 72.15.Rn, 64.70.Tg, 05.45.Mt, FOS: Physical sciences, 01 natural sciences, 010305 fluids & plasmas, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Quantum mechanics, 0103 physical sciences, Anderson transition, [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], 010306 general physics, Wave function, Anderson impurity model, Physics, quantum phase transitions, [PHYS.PHYS.PHYS-OPTICS]Physics [physics]/Physics [physics]/Optics [physics.optics], Quantum Physics, Condensed matter physics, Disordered Systems and Neural Networks (cond-mat.dis-nn), cold atoms, Condensed Matter - Disordered Systems and Neural Networks, Nonlinear Sciences - Chaotic Dynamics, Atomic and Molecular Physics, and Optics, Quantum chaos, Universality (dynamical systems), kicked rotor, Quasiperiodic function, [NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD], Matter wave, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), Critical exponent, quantum chaos, Physics - Optics, Optics (physics.optics)
Abstract

Using a cold atomic gas exposed to laser pulses -- a realization of the chaotic quasiperiodic kicked rotor with three incommensurate frequencies -- we study experimentally and theoretically the Anderson metal-insulator transition in three dimensions. Sensitive measurements of the atomic wavefunction and the use of finite-size scaling techniques make it possible to unambiguously demonstrate the existence of a quantum phase transition and to measure its critical exponents. By taking proper account of systematic corrections to one-parameter scaling, we show the universality of the critical exponent $\nu=1.59\pm0.01,$ which is found to be equal to the one previously computed for the Anderson model., Comment: 19 pages, 15 figures, submitted to PRA

Published
2009
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33. Experimental Observation of the Anderson Metal-Insulator Transition with Atomic Matter Waves

Author

Julien Chabé, Gabriel Lemarié, Jean Claude Garreau, Pascal Szriftgiser, Benoît Grémaud, and Dominique Delande

Subjects
Quantum phase transition, Physics, Anderson localization, Condensed matter physics, General Physics and Astronomy, Condensed Matter::Disordered Systems and Neural Networks, 01 natural sciences, Quantum chaos, 010305 fluids & plasmas, Nonlinear Sciences::Chaotic Dynamics, Quasiperiodic function, Quantum mechanics, 0103 physical sciences, Condensed Matter::Strongly Correlated Electrons, Matter wave, Metal–insulator transition, 010306 general physics, Anderson impurity model, Critical exponent
Abstract

We realize experimentally an atom-optics quantum-chaotic system, the quasiperiodic kicked rotor, which is equivalent to a 3D disordered system that allows us to demonstrate the Anderson metal-insulator transition. Sensitive measurements of the atomic wave function and the use of finite-size scaling techniques make it possible to extract both the critical parameters and the critical exponent of the transition, the latter being in good agreement with the value obtained in numerical simulations of the 3D Anderson model.

Published
2008

34. Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree

Author

Ankita Chakrabarti, Cyril Martins, Nicolas Laflorencie, Bertrand Georgeot, Éric Brunet, Gabriel Lemarié

Subjects
Physics, QC1-999
Abstract

We study the random transverse field Ising model on a finite Cayley tree. This enables us to probe key questions arising in other important disordered quantum systems, in particular the Anderson transition and the problem of dirty bosons on the Cayley tree, or the emergence of non-ergodic properties in such systems. We numerically investigate this problem building on the cavity mean-field method complemented by state-of-the art finite-size scaling analysis. Our numerics agree very well with analytical results based on an analogy with the traveling wave problem of a branching random walk in the presence of an absorbing wall. Critical properties and finite-size corrections for the zero-temperature paramagnetic-ferromagnetic transition are studied both for constant (independent of the system volume) and algebraically vanishing (scaling as an inverse power law with the system volume) boundary conditions. In the later case, we reveal a regime which is reminiscent of the non-ergodic delocalized phase observed in other systems, thus shedding some light on critical issues in the context of disordered quantum systems, such as Anderson transitions, the many-body localization or disordered bosons in infinite dimensions.

Published
2023
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35. Coherent forward scattering as a robust probe of multifractality in critical disordered media

Author

Maxime Martinez, Gabriel Lemarié, Bertrand Georgeot, Christian Miniatura, Olivier Giraud

Subjects
Physics, QC1-999
Abstract

We study coherent forward scattering (CFS) in critical disordered systems, whose eigenstates are multifractals. We give general and simple arguments that make it possible to fully characterize the dynamics of the shape and height of the CFS peak. We show that the dynamics is governed by multifractal dimensions $D_1$ and $D_2$, which suggests that CFS could be used as an experimental probe for quantum multifractality. Our predictions are universal and numerically verified in three paradigmatic models of quantum multifractality: Power-law Random Banded Matrices (PRBM), the Ruijsenaars-Schneider ensembles (RS), and the three-dimensional kicked-rotor (3DKR). In the strong multifractal regime, we show analytically that these universal predictions exactly coincide with results from standard perturbation theory applied to the PRBM and RS models.

Published
2023
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