Search

We compute the fluctuations of the number of bosons with a given momentum for the Tonks-Girardeau gas at zero and finite temperature in a harmonic trap. We show that correlations between opposite momentum states $p$, which is an important fingerprint of long range order in weakly interacting Bose systems are suppressed. Non trivial correlations, including negative correlations are observed for momenta smaller or of the order of the inverse radius of the gas. The full distribution of the number of bosons with momentum $p$ exhibits an interesting crossover from a non trivial distribution at zero momentum to an exponential distribution. The distribution of the quasi-condensate occupation is also studied. Experimental relevance of our findings for recent cold atoms experiments are discussed., Comment: 12 pages, 9 figures

The single-particle spectral function of a strongly correlated system is an essential ingredient to describe its dynamics and transport properties. We develop a general method to calculate the exact spectral function of a strongly interacting one-dimensional Bose gas in the Tonks-Girardeau regime, valid for any type of confining potential, and apply it to bosons on a lattice to obtain the full spectral function, at all energy and momentum scales. We find that it displays three main singularity lines. The first two can be identified as the analogs of Lieb-I and Lieb-II modes of a uniform fluid; the third one, instead, is specifically due to the presence of the lattice. We show that the spectral function displays a power-law behaviour close to the Lieb-I and Lieb-II singularities, as predicted by the non-linear Luttinger liquid description, and obtain the exact exponents. In particular, the Lieb-II mode shows a divergence in the spectral function, differently from what happens in the dynamical structure factor, thus providing a route to probe it in experiments with ultracold atoms., 10 pages, 3 figures

We derive an exact description of the non-equilibrium dynamics at finite temperature for the anyonic Tonks-Girardeau gas extending the results of Atas et al. [Phys. Rev. A 95, 043622 (2017)] to the case of arbitrary statistics. The one-particle reduced density matrix is expressed as the Fredholm minor of an integral operator with the kernel being the one-particle Green's function of free fermions at finite temperature and the statistics parameter determining the constant in front of the integral operator. We show that the numerical evaluation of this representation using Nystr\"{o}m's method significantly outperforms the other approaches present in the literature when there are no analytical expressions for the overlaps of the wave-functions. We illustrate the distinctive features and novel phenomena present in the dynamics of anyonic systems in two experimentally relevant scenarios: the quantum Newton's cradle setting and the breathing oscillations initiated by a sudden change of the trap frequency., Comment: 22 pages, 9 figures, RevTeX 4.1

Bosonic atoms confined in optical lattices are described by the Bose-Hubbard model and can exist in two different phases, Mott insulator or superfluid, depending on the strength of the system parameters, such as the on-site interaction between particles and the hopping parameter. Differently from classical phase transitions, the Mott-insulatorsuperfluid transition can happen even at zero temperature, driven by quantum fluctuations, thus characterizing a quantum phase transition. For the homogeneous system, we can approximate the particle excitations as a mean-field over time, thus providing a local Hamiltonian, which makes possible the evaluation of physical properties from a single lattice site. From the Landau theory of second-order phase transitions, it is possible to expand the thermodynamic potential in a power series in terms of the order parameter, giving rise to the Mott-insulator-superfluid phase diagram. As the condensate density goes from a finite value to a vanishing one when the system transits from superfluid to a Mott insulator, it can be considered as the order parameter of the system. In the vicinity of the phase boundary, it is possible to consider the hopping term as a perturbation, since it contains the order parameter. Thence, one can apply perturbation theory in order to calculate important physical quantities, such as the condensate density. However, due to degeneracies that happen to exist between every two adjacent Mott lobes, nondegenerate perturbation theory fails to give meaningful results for the condensate density: it predicts a phase transition due to the vanishing of the order parameter in a point of the phase diagram where no transition occurs. Motivated by such a misleading calculation, we develop two different degenerate perturbative methods to solve the degeneracy-related problems. Firstly, we develop a degenerate perturbative method based on Brillouin-Wigner perturbation theory to tackle the zero-temperature case. Afterwards, we develop another degenerate perturbative method based on a projection operator formalism to deal with the finite-temperature regime. Both methods have the common feature of separating the Hilbert subspace where the degeneracies are contained in from the complementary one. Therefore, such a separation of the Hilbert subspaces fixes the degeneracy-related problems and provides us a framework to obtain physically consistent results for the condensate density near the phase boundary. Moreover, we study the one-dimensional repulsively interacting Bose gas under harmonic confinement, with special attention to the asymptotic behavior of the momentum distribution, which is an universal k4 decay characterized by the Tan´s contact. The latter constitutes a direct signature of the short-range correlations in such an interacting system and provides valuable insights about the role of the interparticle interactions. From the known solutions of the system composed of two particles, we are able to acquire important knowledge about the manifestation of the interaction, e.g., the cusp condition that implies the vanishing of the many-body wave function whenever two particles meet. Then, we investigate the system constituted of N interacting particles in the strongly interacting limit, also known as Tonks-Girardeau gas. In such a regime, the strong interparticle interaction makes the bosons behave similarly to the ideal Fermi gas, an effect known as fermionization,. Because of the difficulty in analytically solving the system for N particles at finite interaction, the Tonks-Girardeau regime provides, through the fermionization of the bosons, a favorable scenario to probe the Tan´s contact. Therefore, within such a regime, we are able to provide an analytical formula for the Tan´s contact in terms of the single-particle orbitals of the harmonic oscillator. Furthermore, we analyze the scaling properties of the Tan´s contact in terms of the number of particles N in the high-temperature regime as well as in the strongly interacting regime. Finally, we compare our analytical calculations of the Tan´s contact to quantum Monte Carlo simulations and discuss some fundamental differences between the canonical and the grand-canonical ensembles. Átomos bosônicos confinados em redes ópticas são descritos pelo modelo de Bose-Hubbard e podem existir em duas diferentes fases, isolante de Mott ou superfluido, dependendo da força dos parâmetros do sistema, tais como a interação local entre partículas e o parâmetro de salto. Diferentemente das transições de fase clássicas, a transição entre isolante de Mott e superfluido pode ocorrer mesmo a temperatura zero, impulsionada por flutuações quânticas, caracterizando uma transição de fase quântica. Para o sistema homogêneo, podemos aproximar as excitações de partículas a um campo médio ao longo do tempo, fornecendo um Hamiltoniano local, o que torna possível a avaliação de propriedades físicas a partir de um único sítio da rede. A partir da teoria de Landau de transições de fase de segunda ordem, é possível expandir o potencial termodinâmico em uma série de potências em termos do parâmetro de order, dando origem ao diagrama de fase. Como a densidade de condensado passa de um valor finito para um valor nulo quando o sistema transita de superfluido para isolante de Mott, este pode ser considerado como sendo o parâmetro de ordem do sistema. Nas proximidades da fronteira de fase, é possível considerar o termo de salto como uma perturbação, uma vez que este contém o parâmetro de ordem. Daí, pode-se aplicar teoria de perturbação para calcular quantidades físicas importantes, como a densidade de condensado. No entanto, devido a degenerescências que existem entre dois lóbulos de Mott adjacentes, teoria de perturbação não degenerada falha em fornecer resultados significativos para a densidade de condensado: esta prevê uma transição de fase devido ao desaparecimento do parâmetro de order em um ponto do diagrama de fase onde nenhuma transição ocorre. Motivados por esse cálculo enganoso, desenvolvemos dois métodos perturbativos degenerados diferentes para resolver os problemas relacionados às degenerescências. Em primeiro lugar, desenvolvemos um método perturbativo degenerado baseado em teoria de perturbação de Brillouin-Wigner para solucionar o sistema a temperatura zero. Posteriormente, desenvolvemos outro método perturbativo degenerado baseado em um formalismo de operadores de projeção para lidar com o regime a temperatura finita. Ambos os métodos têm a característica comum de separar o subespaço de Hilbert onde as degenerescências estão contidas de seu complementar. Portanto, essa separação dos subespaços de Hilbert corrige os problemas relacionados às degenerescências e nos fornece uma estrutura para obter resultados fisicamente consistentes para a densidade de condensado próximo à fronteira da fase. Além disso, estudamos o gás de Bose unidimensional com interação repulsiva entre partículas sob confinamento harmônico, com especial atenção ao comportamento assintótico da distribuição de momento, que é um decaimento universal de k4 caracterizado pelo contato de Tan. Este último constitui uma assinatura direta das correlações de curto alcance em tal sistema interagente e fornece informações valiosas sobre o papel das interações entre partículas. A partir das conhecidas soluções do sistema composto de duas partículas, somos capazes de adquirir conhecimentos importantes sobre a manifestação da interação, e.g., a condição de cúspide que implica no desaparecimento da função de onda de muitos corpos sempre que duas partículas se encontram. Em seguida, investigamos o sistema constituído de N partículas fortemente interagentes, também conhecido como gás de Tonks-Girardeau. Nesse regime, a forte interação entre partículas faz com que os bósons se comportem de maneira semelhante ao gás ideal de Fermi, um efeito conhecido como fermionização. Devido à dificuldade em resolver analiticamente o sistema com N partículas com interação finita, o regime de Tonks-Girardeau fornece, através da fermionização dos bósons, um cenário favorável para o estudo do contato de Tan. Portanto, dentro de tal regime, somos capazes de fornecer uma fórmula analítica para o contato do Tan em termos dos orbitais de uma única partícula do oscilador harmônico. Além disso, analisamos as propriedades de escalonamento do contato do Tan em termos do número de partículas N nos regimes de altas temperaturas e fortes interações. Finalmente, comparamos nossos cálculos analíticos do contato de Tan a simulações de Monte Carlo quântico e discutimos algumas diferenças fundamentais entre os conjuntos canônico e macrocanônico.

We show that a quantum Otto cycle in which the medium, an interacting ultracold gas, is driven between a superfluid and an insulating phase can outperform similar single particle cycles. The presence of an energy gap between the two phases can be used to improve performance, while the interplay between lattice forces and the particle distribution can lead to a many-body cooperative effect. Since finite time driving of this cycle can create unwanted non-equilibrium dynamics which can significantly impair the performance of the engine cycle, we also design an approximate shortcut to adiabaticity for the many-body state that can be used to achieve an efficient Otto cycle around a critical point., Includes Supplementary Materials

We compute the fluctuations of the number of bosons with a given momentum for the Tonks-Girardeau gas at zero temperature. We show that correlations between opposite momenta, which is an important fingerprint of long range order in weakly interacting Bose systems, are suppressed and that the full distribution of the number of bosons with non zero momentum is exponential. The distribution of the quasi-condensate is however quasi Gaussian. Experimental relevance of our findings for recent cold atoms experiments are discussed., Comment: 10 pages, 4 figures

We study the out-of-equilibrium dynamics of a finite-temperature harmonically trapped Tonks-Girardeau gas induced by periodic modulation of the trap frequency. We give explicit exact solutions for the real-space density and momentum distributions of this interacting many-body system and characterize the stability diagram of the dynamics by mapping the many-body solution to the solution and stability diagram of Mathieu's differential equation. The mapping allows one to deduce the exact structure of parametric resonances in the parameter space characterized by the driving amplitude and frequency of the modulation. Furthermore, we analyze the same problem within the finite-temperature hydrodynamic approach and show that the respective solutions to the hydrodynamic equations can be mapped to the same Mathieu equation. Accordingly, the stability diagram and the structure of resonances following from the hydrodynamic approach is exactly the same as those obtained from the exact many-body solution., 15 pages, 8 figures

Out-of-equilibrium many-body physics is the fascinating study of complex systems that are subjected to driving, dissipation, or both. Through such procedures it is possible to generate exciting new dynamical phases of matter that have no static counterpart. In this thesis, we investigate the interplay between driving and dissipation in several paradigmatic many-body quantum systems. In particular, we analyze the impact of nonequilibrium phenomena on the stability of topological matter and light-matter interactions. We begin by addressing how to characterize the topological criticality of lower-dimensional systems whose parameters are periodically driven in time. We first introduce a curvature renormalization group method that extends the notions of Landau criticality to the realm of topological phase transitions. We show how this framework presents a simple and efficient way to map out topological phase diagrams of static and Floquet systems in any dimension. Furthermore, we illustrate its ability to precisely capture topological critical phenomena. We then apply it to prototypical static and Floquet topological systems to extract correlation lengths, critical exponents, scaling laws, and universality classes. In one dimension, we apply this methodology to the periodically driven Kitaev chain hosting Majorana end modes. As an interlude, we also examine the consequences of multifrequency driving, and reveal that it can be used as a valuable tool to dynamically control the number and the stability of the topological modes. In two dimensions, we analyze a Floquet-Chern insulator and the periodically driven Kitaev model on the honeycomb lattice. We also establish that periodic driving can induce very exotic topological semimetal phases hosting nodal loop gap closures. We demonstrate that the corresponding phase transitions belong to a different universality class than the ones described by Dirac low-energy theories, but both can coexist at multicritical points. We then discuss the physical origin of nodal loop gap closures and establish that they emerge as a consequence of enhanced symmetries introduced by the driving scheme. We separately analyze symmetry protection and provide concrete examples of how to induce it in both static and driven settings. In realistic settings, one has to often deal with open systems. To incorporate dissipation in our analysis, we re-examine the periodically driven Kitaev chain additionally subjected to a coupling with end reservoirs. In this context we discover that the Floquet-Majorana edge modes survive despite dissipation, and have strong signatures in stroboscopic observables that can reliably track their appearance and disappearance in different phases. Another challenge of contemporary physics is to understand the role of many-body interactions in driven-dissipative settings. As a first step in this direction, we present a very efficient numerical algorithm — the MultiConfigurational Time-Dependent Hartree method — tailored at reliably simulating the time-evolution of interacting many-body quantum systems. We illustrate its applications to several systems of ultracold atoms coupled with the radiation field of optical cavities that host intriguing light-matter phases stabilized by dissipation, such as superradiant phases, Mott insulating phases, and Tonks-Girardeau phases. We highlight how to calculate density distributions, correlation functions, and various order parameters for such setups, and how to simulate realistic single-shot experiments. We conclude this thesis by presenting a brief outlook on unresolved issues and new intriguing questions that have surfaced throughout our study.

The scaling of the largest eigenvalue $\lambda_0$ of the one-body density matrix of a system with respect to its particle number $N$ defines an exponent $\mathcal{C}$ and a coefficient $\mathcal{B}$ via the asymptotic relation $\lambda_0 \sim \mathcal{B}\,N^{\mathcal{C}}$. The case $\mathcal{C}=1$ corresponds to off-diagonal long-range order. For a one-dimensional homogeneous Tonks-Girardeau gas, a well known result also confirmed by bosonization gives instead $\mathcal{C}=1/2$. Here we investigate the inhomogeneous case, initially addressing the behaviour of $\mathcal{C}$ in presence of a general external trapping potential $V$. We argue that the value $\mathcal{C}= 1/2$ characterises the hard-core system independently of the nature of the potential $V$. We then define the exponents $\gamma$ and $\beta$ which describe the scaling with $N$ of the peak of the momentum distribution and the natural orbital corresponding to $\lambda_0$ respectively, and we derive the scaling relation $\gamma + 2\beta= \mathcal{C}$. Taking as a specific case the power-law potential $V(x)\propto x^{2n}$, we give analytical formulas for $\gamma$ and $\beta$ as functions of $n$. Analytical predictions for the coefficient $\mathcal{B}$ are also obtained. These formulas are derived exploiting a recent field theoretical formulation and checked against numerical results. The agreement is excellent., Comment: 14 pages, 5 figures

We investigate the properties of a Tonks-Girardeau gas in the presence of a one-dimensional lattice potential. Such a system is known to exhibit a pinning transition when the lattice is commensurate with the particle density, leading to the formation of an insulating state even at infinitesimally small lattice depths. Here we examine the properties of the gas at all lattices depths and, in addition to the static properties, also consider the non-adiabatic dynamics induced by the sudden motion of the lattice potential with a constant speed. Our work provides a continuum counterpart to the work done in discrete lattice models., 24 pages, 12 figures

Frank W. J. Hekking performed his PhD work on "Aspects of Electron Transport in Semiconductor Nanostructures" at the TU Delft in 1992. He then worked as a postdoc at the University of Karlsruhe, the University of Minnesota, the Cavendish Laboratory at the University of Cambridge, and the Ruhr University at Bochum. In 1999 he joined the LPMMC (Laboratoire de Physique et Mod\' elisation des Milieux Condens\' es) in Grenoble and was appointed Professor at the Universit\' e Joseph Fourier and afterwards Universit\' e Grenoble Alpes. Frank Hekking was nominated as a member of the Institut Universitaire de France, for the periods 2002-2007 and 2012-2017. This review provides an overview of his scientific contributions to several fields of mesoscopic electron transport and superconductivity as well as atomic gases, and is organized along sections describing the different themes., We acknowledge the financial support of the Fondation Nanosciences Grenoble, the LabEx LANEF (ANR-10-LABX-51-01), the Center for Theoretical Physics in Grenoble, the University Grenoble Alpes. Funding information The recent activity of Frank Hekking was founded by Institut Universitaire de France, the ANR SuperRing (ANR-15-CE30-0012-02), the ANR QPS-NanoWires (ANR-15-CE30-0021-02).

We calculate the spatial distributions and the dynamics of a few-body two-component strongly interacting Bose gas confined to an effectively one-dimensional trapping potential. We describe the densities for each component in the trap for different interaction and population imbalances. We calculate the time evolution of the system and show that, for a certain ratio of interactions, the minority population travels through the system as an effective wave packet., 8 pages, 2 figures

Quantum state preparation is vital to quantum computation and quantum information processing tasks. In adiabatic state preparation, the target state is theoretically obtained with nearly perfect fidelity if the control parameter is tuned slowly enough. As this, however, leads to slow dynamics, it is often desirable to be able to do processes faster. In this work, we employ two global optimization methods to estimate the quantum speed limit for few-fermion systems confined in a one-dimensional harmonic trap. Such systems can be produced experimentally in a well controlled manner. We determine the optimized control fields and achieve a reduction in the ramping time of more than a factor of four compared to linear ramping. We also investigate how robust the fidelity is to small variations of the control fields away from the optimized shapes., 8 pages, 5 figures, 1 table

We analyse the breathing-mode oscillations of a harmonically quenched Tonks-Giradeau (TG) gas using an exact finite-temperature dynamical theory. We predict a striking collective manifestation of impenetrability---a collective many-body bounce effect. The effect, while being invisible in the evolution of the in-situ density profile of the gas, can be revealed through a nontrivial periodic narrowing of its momentum distribution, taking place at twice the rate of the fundamental breathing-mode frequency. We identify physical regimes for observing the many-body bounce and construct the respective nonequilibrium phase diagram as a function of the quench strength and the initial temperature of the gas. We also develop a finite-temperature hydrodynamic theory of the TG gas, wherein the many-body bounce is explained by an increased thermodynamic pressure of the gas during the isentropic compression, which acts as a potential barrier at the inner turning points of the breathing cycle., Comment: 5 pages, 4 figures, and Supplemental Material. arXiv admin note: substantial text overlap with arXiv:1608.08720

This paper introduces a model for a few repulsively interacting particles trapped in a one-dimensional harmonic well and provides exact solutions for the three-particle case. This model is a hybrid of two other well-known systems, the Calogero model and the contact-interaction model, and coincides with them in limiting cases. However, those models have purely two-body interactions whereas this model has intrinsically few-body interactions. Comparing these three models provides clarifying distinctions among the properties of symmetry, separability, and integrability. The model's analytic solutions provide a useful basis to improve approximation schemes, especially near the unitary limit of hard-core contact interactions.

Luttinger liquid theory is a powerful and widely applicable framework for modelling one-dimensional many-body quantum systems. Within this framework, one supposes that the macroscopic behaviour of such systems is entirely determined by two phenomenological parameters, g(2) and g(4). While there exists an intuitive and seemingly sensible physical interpretation of these parameters in terms of the scattering of the system's constituent particles, g(2) and g(4) are traditionally either fixed by experiment or calculated using heavy-duty numerical techniques, rather than inferred using scattering theory, and for this reason the interpretation remains untested. By applying Luttinger liquid theory in a simple setting, we show that a widely-held and repeatedly-stated belief, namely that the intrabranch terms appearing in Luttinger's model originate from microscopic intrabranch interactions, is a misconception. We begin with the microscopic model of an interacting one-dimensional, spin-polarized Fermi gas, which we systematically transform into a Luttinger model by introducing an effective interaction, linearizing the dispersion, and renormalizing. By this method, we are able to show that the usual interpretation of g(4) as a measure of intrabranch scattering implies that it must vanish in the dilute limit. Since this runs contrary to conservation of particle number, we conclude that g(4) cannot be related to intrabranch scattering. Rather, we show that g(4) interactions must be included in the effective model in order to compensate for the deleterious effect that introducing an effective interaction has upon the model's energetics. We explicitly calculate an approximation to this correction for our simple system, and find that it agrees with the value of g(4) found in the literature. We therefore propose a new fermionic Hamiltonian which agrees with the traditional model after bosonisation, but which better reflects the underlying microscopic physics.

We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of many body system ---including entanglement and correlations--- and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for (quasi) one-dimensional systems. By linearizing around a stationary solution, we furthermore derive an associated generalization of the Bogoliubov -- de Gennes equations. This framework is applied to compute the steady state response amplitude to a periodic perturbation of the potential., Comment: 4.{\epsilon} pages + references and 4 pages supplementary material (small revisions + extended discussion of periodic potential example)

Energy level splitting from the unitary limit of contact interactions to the near unitary limit for a few identical atoms in an effectively one-dimensional well can be understood as an example of symmetry breaking. At the unitary limit in addition to particle permutation symmetry there is a larger symmetry corresponding to exchanging the $N!$ possible orderings of $N$ particles. In the near unitary limit, this larger symmetry is broken, and different shapes of traps break the symmetry to different degrees. This brief note exploits these symmetries to present a useful, geometric analogy with graph theory and build an algebraic framework for calculating energy splitting in the near unitary limit., 6 pages, 1 figure, accepted in Few-Body Systems

We study the dynamics of a one-dimensional system composed of a bosonic background and one impurity in single- and double-well trapping geometries. In the limit of strong interactions, this system can be modeled by a spin chain where the exchange coefficients are determined by the geometry of the trap. We observe non-trivial dynamics when the repulsion between the impurity and the background is dominant. In this regime, the system exhibits oscillations that resemble the dynamics of a Josephson junction. Furthermore, the double-well geometry allows for an enhancement in the tunneling as compared to the single-well case., Comment: 20 pages, 9 figures

Many intriguing phenomena in modern physics are rooted in the coupling of electric charge to magnetic fields. However, it mostly includes quantum many-body systems, which makes these systems hard to address both experimentally—because of the rather extreme conditions they usually require, and theoretically—because of the exponential dependence of the required classical computer memory on the number of quantum system constituents. The solution is found by following Feynman’s idea of the so-called quantum simulators. Namely, as new methods for synthetic magnetism are developed, controllable systems of neutral atoms and photons are governed to realize and simulate various fascinating phenomena, which are typically emergent only in elusive states of matter. The contribution of the work presented in this thesis is twofold. The first part focuses on the role of synthetic magnetism in the research of topological phases [1, 2]. The latter are nowadays causing a lot of excitement, due to their fascinating emergent behavior, which opens the way for diverse technological applications. By taking advantage of tunable synthetic magnetic fields, we point out how topological phases that otherwise rely on complicated space groups and are thus hardly obtainable, can be realized in simple lattice geometries. Namely, we show that Weyl points, and all of the related phenomena, can be experimentally addressed in an experimentally viable ultracold atomic lattice with laser assisted tunneling [1]. We also consider the realization and detection of a state with fractional statistic in an ultracold atomic gas. We demonstrate how standard methods and understanding have to be taken with caution when studying topological matter via quantum simulation and synthetic magnetism. Specifically, we point out that the momentum distribution, one of the key signatures of quantum states of matter, is not a proper observable for a system of anyons [2]. As a substitute, we propose to use the asymptotic single-particle density after expansion of anyons in free space from the state. The second part of the thesis discusses our proposals of new methods for introducing synthetic magnetism in atomic and photonic systems [3–7]. We show that drawing analogies between different physical systems can yield new ideas in synthetic magnetism, which enables addressing intriguing topological phases and beyond. Namely, we propose a grating assisted tunneling scheme that introduces tunable synthetic magnetic fields in a photonic lattice [3], inspired by the laser assisted tunneling method for optical lattices. We also introduce an approach for the mapping of light propagation in dielectric structures and ultracold atomic dynamics to intriguing discrete models. By taking advantage of it, we also confirm the applicability of laser assisted tunneling for a Tonks-Girardeau gas in a 1D optical lattice [4]. Finally, we extend the concept of simulation to complex classical, rather than quantum, systems in the presence of magnetism. We propose a method for creating a synthetic Lorentz force in a classical ultracold atomic gas [5], which was recently experimentally realized through a collaboration with an experimental group [6, 7]. Kolektivno ponašanje velikog broja kvantnih cestica dovodi do nekih od najsloženijih i zanimljivih pojava, kao što su supravodljivost, suprafluidnost ili Bose-Einesteinova kondenzacija. Međutim, razumijevanje i predviđanje razvoja kvantnih višečestičnih sustava izuzetno je zahtjevno, cak i u slučajevima kada su svi zakoni koji vladaju jednočestičnim ponašanjem poznati. S jedne strane, eksperimentalna dostupnost zanimljivih pojava u kvantnim sustavima znatno je otežana ekstremnim uvjetima koje takva stanja zahtijevaju (npr. niske temperature). S druge strane, uobičajen pristup prema kojem se višečestični sustavi numerički simuliraju na klasičnim računalima nije primjenjiv u slučajevima u kojima je kvantna priroda sustava izražena. Naime, broj stupnjeva slobode kvantnih sustava cestica eksponencijalno je ovisan o njihovom broju. Računalna memorija koja je potrebna za opisivanje i rješavanje toga sustava, dakle, eksponencijalno raste s brojem cestica u sustavu. Zbog toga je numerički pristup u slučaju kvantnih pojava ograničen na sustave s malim brojem cestica. Richard Feynman je 1982. godine uveo ideju korištenja kontrolabilnih fizikalnih sustava za simuliranje željenih kvantnih pojava [8]. Kao rješenje problema s kojim se klasična računala susreću u slučajevima kvantnih višečestičnih sustava, predložio je koncept kvantnih simulatora. Točnije, Feynman je predložio korištenje visoko kontrolabilnih kvantnih sustava koji su pažljivo prilagođeni na način da u potpunosti oponašaju (simuliraju) željeni kvantni višečestični sustav, te njegove pojave koje bi u protivnom ostale skrivene i nerazjašnjene. U tom kontekstu, posljednjih godina veliku pozornost privlači fleksibilnost ultrahladnih atomskih plinova i fotoničkih sustava [9–13]. Njihova efektivna dimenzionalnost može se kretati od jedne do tri dimenzije. Atomi u ovim rijetkim hladnim plinovima [9, 10] mogu pripadati bozonskoj ili fermionskoj statistici. Zbog raznolike prostorne ovisnosti energije, podrijetlom od okolnih magnetskih polja i laserske svjetlosti, atomi mogu biti zatočeni u harmoničkim, periodičkim ili iskrivljenim potencijalima. Međudjelovanje između atoma moguće je namjestiti korištenjem raspršenja svjetlosti. U botaničkim kristalima [11], ponašanje fotona određeno je strukturom kristalnih vrpci na isti način kao i elektronsko ponašanje u uobičajenim materijalima. Krojenjem dielektričnih struktura kroz koje se svjetlost propagira, fotonima se može oponašati elektrone u raznolikim zanimljivim stanjima. Međutim, i atomi i fotoni električki su neutralne cestice, te kao takve ne mogu izravno reproducirati magnetske pojave. S druge strane, široki raspon intrigantnih pojava u modernoj fizici, kao što su baždarna invarijantnost ili kvantni Hallov i Aharonov-Bohm efekt, proizlaze upravo iz vezanja elektromagnetskih polja i nabijenih cestica. Postoji stoga veliko zanimanje za pronalazak umjetnih (sintetskih) magnetskih polja za atome i fotone, odnosno okruženja u kojem se neutralni atomi i fotoni ponašaju po istim zakonima kao nabijene cestice u magnetskim poljima. U klasičnim sustavima, radi se ponajprije o Loretzovoj sili. U kvantnim sustavima, kao kljucne značajke izdvajaju se pojava geometrijskih faza (Aharonov-Bohm faza [15] i Peierlsova substitucija [16]). Pristup i način stvaranja sintetskog magnetskog/baždarnog polja usko je vezan uz konkretan sustav o kojemu se radi. Prva sintetska magnetska polja za atome dobivena su pri brzoj rotaciji Bose-Einstein-kondenziranih atomskih plinova, korištenjem analogije između Coriolisove i Loretzove sile [17, 18]. U narednim godinama, pokazano je da se umjetna magnetska polja za neutralne atome mogu dobiti iz njihovog međudjelovanja sa svjetlošću u posebno krojenim laserskim poljima [19, 21, 22]. U tom slučaju, mehanizam se temelji na analogiji Aharonov-Bohmove faze [15] pri gibanju nabijene cestice u magnetskom polju, i Berryjeve faze [20] pri adijabatskom gibanju atoma u laserskom polju [19, 21, 22]. U optičkim rešetkama, metode za stvaranje sintetskih magnetskih polja uključuju kompleksne matrične elemente tuneliranja između čvorova rešetke [23–27]. Netrivijalne faze kompleksnih matričnih elemenata tuneliranja atoma, dobivene primjerice trešnjom ili tzv. laserski potpomognutim tuneliranjem, pri tom se interpretiraju kao Peierlsove faze [16]. Sličan pristup, te analogija s Peierlsovim fazama matričnih elemenata tuneliranja, za stvaranje sintetskih magnetskih polja koristi se i u fotonickim sustavima [28–30, 30, 31, 31– 37, 39, 40].

The ground-state properties of a one-dimentional, attractively interacting Bose gas are studied at a fixed density. The exact solution obtained shows that an interesting phase transition can occur as the interaction strength is reduced to a vanishingly small value and the size of the system grows to the thermodynamic limit.

We theoretically investigate an ultracold spin-polarized atomic Fermi gas with resonant odd-channel ($p$-wave) interactions trapped in one-dimensional harmonic traps. We solve the Yang-Yang thermodynamic equations based on the exact Bethe ansatz solution, and predict the finite-temperature density profile and breathing mode frequency, by using a local density approximation to take into account the harmonic trapping potential. The system features an exotic super fermionic Tonks-Girardeau (super-fTG) phase, due to the large effective range of the interatomic interactions. We explore the parameter space for such a fascinating super-fTG phase at finite temperature and provide smoking-gun signatures of its existence in both breathing mode frequencies and density profiles. Our results suggest that the super-fTG phase can be readily probed at temperature at about $0.1T_{F}$, where $T_{F}$ is the Fermi temperature. These results are to be confronted with future cold-atom experiments with $^{6}$Li and $^{40}$K atoms., Comment: 6 pages, 4 figures

A scheme for the generation of a Tonks-Girardeau gas of photons with purely dissipative interaction is described. We put forward a master equation approach for the description of stationary light in atomic four-level media and show that, under suitable conditions, two particle decays are the dominant photon loss mechanism. These dissipative two-photon losses increase the interaction strength by at least one order of magnitude as compared to dispersive two-photon processes and can drive the photons into the Tonks-Girardeau regime. Different scenarios for the observation of fermionic correlations between photons in the Tonks-Girardeau gas regime are discussed., Comment: 4 pages, 1 figure

The ground-state properties of one-dimensional electron-spin-polarized hydrogen H-1, deuterium H-2, and tritium 3 Hare obtained by means of quantum Monte Carlo methods. The equations of state of the three isotopes are calculated for a wide range of linear densities. The pair correlation function and the static structure factor are obtained and interpreted within the framework of the Luttinger liquid theory. We report the density dependence of the Luttinger parameter and use it to identify different physical regimes: Bogoliubov Bose gas, super-Tonks-Girardeau gas, and quasi-crystal regimes for bosons; repulsive, attractive Fermi gas, and quasi-crystal regimes for fermions. We find that the tritium isotope is the one with the richest behavior. Our results show unambiguously the relevant role of the isotope mass in the properties of this quantum system.

The topological Kondo (TK) model has been proposed in solid-state quantum devices as a way to realize non-Fermi liquid behaviors in a controllable setting. Another motivation behind the TK model proposal is the demand to demonstrate the quantum dynamical properties of Majorana fermions, which are at the heart of their potential use in topological quantum computation. Here we consider a junction of crossed Tonks-Girardeau gases arranged in a star-geometry (forming a Y -junction), and we perform a theoretical analysis of this system showing that it provides a physical realization of the topological Kondo model in the realm of cold atom systems. Using computer-generated holography, we experimentally implement a Y-junction suitable for atom trapping, with controllable and independent parameters. The junction and the transverse size of the atom waveguides are of the order of 5 micrometers, leading to favorable estimates for the Kondo temperature and for the coupling across the junction. Since our results show that all the required theoretical and experimental ingredients are available, this provides the demonstration of an ultracold atom device that may in principle exhibit the topological Kondo effect., Comment: 20 pages, 3 figures. v2: main text expanded, references added

We describe the dynamical preparation of magnetic states in a strongly interacting two-component Bose gas in a harmonic trap. By mapping this system to an effective spin chain model, we obtain the dynamical spin densities and the fidelities for a few-body system. We show that the spatial profiles transit between ferromagnetic and antiferromagnetic states as the intraspecies interaction parameter is slowly increased., Comment: 6 pages, 7 figures

We consider quantum quenches from an ideal Bose condensate to the Lieb-Liniger model with arbitrary attractive interaction strength. We focus on the properties of the non-equilibrium steady state reached at late times after the quench. Using recently developed methods based on integrability, we obtain an exact description of the stationary state for a large number of bosons. A distinctive feature of this state is the presence of a hierarchy of multi-particle bound states. We determine the dependence of their densities on interaction strength and obtain an exact expression for the stationary value of the local pair correlation $g_2$. We discuss ramifications of our results for cold atom experiments., 6 pages, 3 figures; v2: minor revision and references added

We study static properties and the dynamical structure factor of zero-temperature dilute bosons interacting via a soft-shoulder potential in one dimension. Our approach is fully microscopic and employs state-of-the-art quantum Monte Carlo and analytic continuation techniques. By increasing the interaction strength, our model reproduces the Lieb-Liniger gas, the Tonks-Girardeau and the Hard-Rods models., Comment: 8 pages, 5 figures, published on J. Low. Temp. Phys, Special Issue QFS 2016. Updated with hard-rods regime results obtained with a better initial wavefunction

The ground-state properties of one-dimensional electron-spin-polarized hydrogen 1H, deuterium 2H, and tritium 3H are obtained by means of quantum Monte Carlo methods. The equations of state of the three isotopes are calculated for a wide range of linear densities. The pair correlation function and the static structure factor are obtained and interpreted within the framework of the Luttinger liquid theory. We report the density dependence of the Luttinger parameter and use it to identify different physical regimes: Bogoliubov Bose gas, super- Tonks-Girardeau gas, and quasi-crystal regimes for bosons ; repulsive, attractive Fermi gas, and quasi-crystal regimes for fermions. We find that the tritium isotope is the one with the richest behaviour. Our results show unambiguously the relevant role of the isotope mass in the properties of this quantum system.

The physics of one-dimensional interacting bosonic systems is reviewed. Beginning with results from exactly solvable models and computational approaches, the concept of bosonic Tomonaga-Luttinger liquids relevant for one-dimensional Bose fluids is introduced, and compared with Bose-Einstein condensates existing in dimensions higher than one. The effects of various perturbations on the Tomonaga-Luttinger liquid state are discussed as well as extensions to multicomponent and out of equilibrium situations. Finally, the experimental systems that can be described in terms of models of interacting bosons in one dimension are discussed. © 2011 American Physical Society.