Search

The robustness of topological properties, such as quantized currents, generally depends on the existence of gaps surrounding the relevant energy levels or on symmetry-forbidden transitions. Here, we observe quantized currents that survive the addition of bounded local disorder beyond the closing of the relevant instantaneous energy gaps in a driven Aubry-Andr\'e-Harper chain, a prototypical model of quasiperiodic systems. We explain the robustness using a local picture in \textit{configuration-space} based on Landau-Zener transitions, which rests on the Anderson localisation of the eigenstates. Moreover, we propose a protocol, directly realizable in for instance cold atoms or photonic experiments, which leverages this stability to prepare topological many-body states with high Chern numbers and opens new experimental avenues for the study of both the integer and fractional quantum Hall effects., Comment: 12 pages, 8 figures. Slightly extended discussion on the effect of pumping rate. Added further connections to literature on mobility gaps. Additional minor edits

In the curved spacetime of a black hole, quantum physics gives rise to distinctive effects such as Hawking radiation. Here, we present a scheme for an analogue quantum simulation of (1 + 1)- dimensional black holes using ultracold atoms in a locally Floquet-driven 1D optical lattice. We show how the effective dynamics of the driven system can generate a position-dependent tunnelling profile that encodes the curved geometry of the black hole. Moreover, we provide a simple and robust scheme to determine the Hawking temperature of the simulated black hole based solely on on-site atom population measurements. Finally, we show how this scheme can be directly applied to simulate (2 + 1)D black holes by utilising 2D optical lattices. By incorporating the effect of atom-atom interactions, our simulator can probe the scrambling of quantum information which is a fundamental property of black holes.

This document presents a summary of the 2023 Terrestrial Very-Long-Baseline Atom Interferometry Workshop hosted by CERN. The workshop brought together experts from around the world to discuss the exciting developments in large-scale atom interferometer (AI) prototypes and their potential for detecting ultralight dark matter and gravitational waves. The primary objective of the workshop was to lay the groundwork for an international TVLBAI proto-collaboration. This collaboration aims to unite researchers from different institutions to strategize and secure funding for terrestrial large-scale AI projects. The ultimate goal is to create a roadmap detailing the design and technology choices for one or more km-scale detectors, which will be operational in the mid-2030s. The key sections of this report present the physics case and technical challenges, together with a comprehensive overview of the discussions at the workshop together with the main conclusions., Comment: Summary of the Terrestrial Very-Long-Baseline Atom Interferometry Workshop held at CERN: https://indico.cern.ch/event/1208783/

Ultracold atoms in optical lattices have emerged as powerful quantum simulators of translationally invariant systems with many applications in e.g.\ strongly-correlated and topological systems. However, the ability to locally tune all Hamiltonian parameters remains an outstanding goal that would enable the simulation of a wider range of quantum phenomena. Motivated by recent advances in quantum gas microscopes and optical tweezers, we here show theoretically how local control over individual tunnelling links in an optical lattice can be achieved by incorporating local time-periodic potentials. We propose to periodically modulate the on-site energy of individual lattice sites and employ Floquet theory to demonstrate how this provides full individual control over the tunnelling amplitudes in one dimension. We provide various example configurations realising interesting topological models such as extended Su-Schrieffer-Heeger models that would be challenging to realise by other means. Extending to two dimensions, we demonstrate that local periodic driving in a Lieb lattice engineers a 2D network with fully controllable tunnelling magnitudes. In a three-site plaquette, we show full simultaneous control over the relative tunnelling amplitudes and the gauge-invariant flux piercing the plaquette, providing a clear stepping stone to building a fully programmable 2D tight-binding model. We also explicitly demonstrate how utilise our technique to generate a magnetic field gradient in 2D. This local modulation scheme is applicable to many different lattice geometries., Comment: 17 pages, 14 figures

Atom interferometers measure quantum interference patterns in the wave functions of cold atoms that follow superpositions of different space-time trajectories. These can be sensitive to phase shifts induced by fundamental physics processes such as interactions with ultralight dark matter or the passage of gravitational waves. The capabilities of large-scale atom interferometers are illustrated by their estimated sensitivities to the possible interactions of ultralight dark matter with electrons and photons, and to gravitational waves in the frequency range around 1 Hz, intermediate between the peak sensitivities of the LIGO and LISA experiments. Atom interferometers can probe ultralight scalar couplings with much greater sensitivity than is currently available from probes of the Equivalence Principle. Their sensitivity to mid-frequency gravitational waves may open a window on mergers of masses intermediate between those discovered by the LIGO and Virgo experiments and the supermassive black holes present in the cores of galaxies, as well as fundamental physics processes in the early Universe such as first-order phase transitions and the evolution of networks of cosmic strings., Comment: 24 pages, 14 Figures

The combined effect of disorder and interactions is central to the richness of condensed matter physics and can lead to novel quantum states such as the Bose glass phase in disordered bosonic systems. Here, we report on the experimental realisation of the two-dimensional Bose glass using ultra-cold atoms in an eight-fold symmetric quasicrystalline optical lattice. By probing the coherence properties of the system, we observe a Bose glass to superfluid transition and map out the phase diagram in the weakly interacting regime. Moreover, we reveal the non-ergodic nature of the Bose glass by probing the capability to restore coherence. Our observations are in good agreement with recent quantum Monte Carlo predictions and pave the way for experimentally testing the connection between the Bose glass, many-body localisation, and glassy dynamics more generally.

Quasicrystals are long-range ordered, yet not periodic, and thereby present a fascinating challenge for condensed matter physics, as one cannot resort to the usual toolbox based on Bloch's theorem. Here, we present a numerical method for constructing the Hubbard Hamiltonian of non-periodic potentials without making use of Bloch's theorem and apply it to the case of an eightfold rotationally symmetric 2D optical quasicrystal that was recently realized using cold atoms. We construct maximally localised Wannier functions and use them to extract on-site energies, tunneling amplitudes, and interaction energies. In addition, we introduce a configuration-space representation, where sites are ordered in terms of shape and local environment, that leads to a compact description of the infinite-size quasicrystal in which all Hamiltonian parameters can be expressed as smooth functions. This configuration-space picture allows one to construct arbitrarily large tight-binding graphs for numerical many-body calculations and enables new analytic arguments on the topological structure and many-body physics of these models, for instance the conclusion that this quasicrystal will host unit-filling Mott insulators in the thermodynamic limit., Comment: 9 pages, 12 figures, plus appendix; minor changes

We study the effect of spatially correlated classical noise on both Anderson and many-body localization of a disordered fermionic chain. By analyzing the evolution of the particle density imbalance following a quench from an initial charge density wave state, we find prominent signatures of localization also in the presence of the time-dependent noise, even though the system eventually relaxes to the infinite temperature state. In particular, for sufficiently strong static disorder we observe the onset of metastability, which becomes more prominent the stronger the spatial correlations of the noise. In this regime we find that the imbalance decays as a stretched-exponential - a behavior characteristic of glassy systems. We identify a simple scaling behavior of the relevant relaxation times in terms of the static disorder and of the noise correlation length. We discuss how our results could be exploited to extract information about the localization length in experimental setups., Comment: 6 pages, 3 figures; v2 close to published version

We summarize the discussions at a virtual Community Workshop on Cold Atoms in Space concerning the status of cold atom technologies, the prospective scientific and societal opportunities offered by their deployment in space, and the developments needed before cold atoms could be operated in space. The cold atom technologies discussed include atomic clocks, quantum gravimeters and accelerometers, and atom interferometers. Prospective applications include metrology, geodesy and measurement of terrestrial mass change due to, e.g., climate change, and fundamental science experiments such as tests of the equivalence principle, searches for dark matter, measurements of gravitational waves and tests of quantum mechanics. We review the current status of cold atom technologies and outline the requirements for their space qualification, including the development paths and the corresponding technical milestones, and identifying possible pathfinder missions to pave the way for missions to exploit the full potential of cold atoms in space. Finally, we present a first draft of a possible road-map for achieving these goals, that we propose for discussion by the interested cold atom, Earth Observation, fundamental physics and other prospective scientific user communities, together with ESA and national space and research funding agencies., Comment: Summary of the Community Workshop on Cold Atoms in Space and corresponding Road-map: https://indico.cern.ch/event/1064855/

Discontinuous quantum phase transitions and the associated metastability play central roles in diverse areas of physics ranging from ferromagnetism to false vacuum decay in the early universe. Using strongly-interacting ultracold atoms in an optical lattice, we realize a driven many-body system whose quantum phase transition can be tuned from continuous to discontinuous. Resonant shaking of a one-dimensional optical lattice hybridizes the lowest two Bloch bands, driving a novel transition from a Mott insulator to a $\pi$-superfluid, i.e., a superfluid state with staggered phase order. For weak shaking amplitudes, this transition is discontinuous (first-order) and the system can remain frozen in a metastable state, whereas for strong shaking, it undergoes a continuous transition toward a $\pi$-superfluid. Our observations of this metastability and hysteresis are in good quantitative agreement with numerical simulations and pave the way for exploring the crucial role of quantum fluctuations in discontinuous transitions., Comment: 5 pages, 4 figures + Supplementary

Quasicrystals are long-range ordered but not periodic, representing an interesting middle ground between order and disorder. We experimentally and numerically study the ground state of non- and weakly-interacting bosons in an eightfold symmetric quasicrystalline optical lattice. We find extended states for weak lattices but observe a localisation transition at a lattice depth of $V_0=1.78(2)\,E_{\mathrm{rec}}$ for the non-interacting system. We identify this transition by measuring the timescale required for adiabatic loading into the lattice, which diverges at the critical lattice depth for localisation. Gross-Pitaevskii simulations show that in interacting systems the transition is shifted to deeper lattices, as expected from superfluid order counteracting localisation. Our experimental results are consistent with such a mean-field shift. Quasiperiodic potentials, lacking conventional rare regions, provide the ideal testing ground to realise many-body localisation in 2D.

We introduce a two-dimensional generalisation of the quasiperiodic Aubry-Andr\'e model. Even though this model exhibits the same duality relation as the one-dimensional version, its localisation properties are found to be substantially more complex. In particular, partially extended single-particle states appear for arbitrarily strong quasiperiodic modulation. They are concentrated on a network of low-disorder lattice lines, while the rest of the lattice hosts localised states. This spatial separation protects the localised states from delocalisation, so no mobility edge emerges in the spectrum. Instead, localised and partially extended states are interspersed, giving rise to an unusual type of mixed spectrum and enabling complex dynamics even in the absence of interactions. A striking example is ballistic transport across the low-disorder lines while the rest of the system remains localised. This behaviour is robust against disorder and other weak perturbations. Our model is thus directly amenable to experimental studies and promises fascinating many-body localisation properties., Comment: 10 pages, 8 figures, published version

Quasicrystals are long-range ordered and yet non-periodic. This interplay results in a wealth of intriguing physical phenomena, such as the inheritance of topological properties from higher dimensions, and the presence of non-trivial structure on all scales. Here we report on the first experimental demonstration of an eightfold rotationally symmetric optical lattice, realising a two-dimensional quasicrystalline potential for ultracold atoms. Using matter-wave diffraction we observe the self-similarity of this quasicrystalline structure, in close analogy to the very first discovery of quasicrystals using electron diffraction. The diffraction dynamics on short timescales constitutes a continuous-time quantum walk on a homogeneous four-dimensional tight-binding lattice. These measurements pave the way for quantum simulations in fractal structures and higher dimensions.

We have investigated scaling properties of the Aubry-Andr\'e model and related one-dimensional quasiperiodic Hamiltonians near their localisation transitions. We find numerically that the scaling of characteristic energies near the ground state, usually captured by a single dynamical exponent, does not obey a power law relation. Instead, the scaling behaviour depends strongly on the correlation length in a manner governed by the continued fraction expansion of the irrational number $\beta$ describing incommensurability in the system. This dependence is, however, found to be universal between a range of models sharing the same value of $\beta$. For the Aubry-Andr\'e model, we explain this behaviour in terms of a discrete renormalisation group protocol which predicts rich critical behaviour. This result is complemented by studies of the expansion dynamics of a wave packet under the Aubry-Andr\'e model at the critical point. Anomalous diffusion exponents are derived in terms of multifractal (R\'enyi) dimensions of the critical spectrum; non-power-law universality similar to that found in ground state dynamics is observed between a range of critical tight-binding Hamiltonians., Comment: 18 pages, 13 figures

Periodic driving of optical lattices has enabled the creation of novel bandstructures not realizable in static lattice systems, such as topological bands for neutral particles. However, especially driven systems of interacting bosonic particles often suffer from strong heating. We have systematically studied heating in an interacting Bose-Einstein condensate in a driven one-dimensional optical lattice. We find interaction-dependent heating rates that depend both on the scattering length and the driving strength and identify the underlying resonant intra- and interband scattering processes. By comparing experimental data and theory, we find that for driving frequencies well above the trap depth, the heating rate is dramatically reduced by the fact that resonantly scattered atoms leave the trap before dissipating their energy into the system. This mechanism of Floquet evaporative cooling offers a powerful strategy to minimize heating in Floquet engineered quantum gases., Comment: 5 pages + Appendix

In a many-body localized (MBL) quantum system, the ergodic hypothesis breaks down completely, giving rise to a fundamentally new many-body phase. Whether and under which conditions MBL can occur in higher dimensions remains an outstanding challenge both for experiments and theory. Here, we experimentally explore the relaxation dynamics of an interacting gas of fermionic potassium atoms loaded in a two-dimensional optical lattice with different quasi-periodic potentials along the two directions. We observe a dramatic slowing down of the relaxation for intermediate disorder strengths and attribute this partially to configurational rare-region effects. Beyond a critical disorder strength, we see negligible relaxation on experimentally accessible timescales, indicating a possible transition into a two-dimensional MBL phase. Our experiments reveal a distinct interplay of interactions, disorder, and dimensionality and provide insights into regimes where controlled theoretical approaches are scarce., Comment: 5 pages, 4 figures. Comments and suggestions welcome

In the presence of sufficiently strong disorder or quasiperiodic fields, an interacting many-body system can fail to thermalize and become many-body localized. The associated transition is of particular interest, since it occurs not only in the ground state but over an extended range of energy densities. So far, theoretical studies of the transition have focused mainly on the case of true-random disorder. In this work, we experimentally and numerically investigate the regime close to the many-body localization transition in quasiperiodic systems. We find slow relaxation of the density imbalance close to the transition, strikingly similar to the behavior near the transition in true-random systems. This dynamics is found to continuously slow down upon approaching the transition and allows for an estimate of the transition point. We discuss possible microscopic origins of these slow dynamics.

In the presence of disorder, an interacting closed quantum system can undergo many-body localization (MBL) and fail to thermalize. However, over long times even weak couplings to any thermal environment will necessarily thermalize the system and erase all signatures of MBL. This presents a challenge for experimental investigations of MBL, since no realistic system can ever be fully closed. In this work, we experimentally explore the thermalization dynamics of a localized system in the presence of controlled dissipation. Specifically, we find that photon scattering results in a stretched exponential decay of an initial density pattern with a rate that depends linearly on the scattering rate. We find that the resulting susceptibility increases significantly close to the phase transition point. In this regime, which is inaccessible to current numerical studies, we also find a strong dependence on interactions. Our work provides a basis for systematic studies of MBL in open systems and opens a route towards extrapolation of closed system properties from experiments., Comment: 5+7 pages, 9 figures

We experimentally study a periodically driven many-body localized system realized by interacting fermions in a one-dimensional quasi-disordered optical lattice. By preparing the system in a far-from-equilibrium state and monitoring the remains of an imprinted density pattern, we identify a localized phase at high drive frequencies and an ergodic phase at low ones. These two distinct phases are separated by a dynamical phase transition which depends on both the drive frequency and the drive strength. Our observations are quantitatively supported by numerical simulations and are directly connected to the change in the statistical properties of the effective Floquet Hamiltonian., Comment: 4 pages main text + 4 pages supplementary mat

Topology and geometry are essential to our understanding of modern physics, underlying many foundational concepts from high energy theories, quantum information, and condensed matter physics. In condensed matter systems, a wide range of phenomena stem from the geometry of the band eigenstates, which is encoded in the matrix-valued Wilson line for general multi-band systems. Using an ultracold gas of Rb atoms loaded in a honeycomb optical lattice, we realize strong-force dynamics in Bloch bands that are described by Wilson lines and observe an evolution in the band populations that directly reveals the band geometry. Our technique enables a full determination of band eigenstates, Berry curvature, and topological invariants, including single- and multi-band Chern and $Z_2$ numbers., Comment: 5+9 pages, final ublished version

We experimentally study the effects of coupling one-dimensional Many-Body Localized (MBL) systems with identical disorder. Using a gas of ultracold fermions in an optical lattice, we artifically prepare an initial charge density wave in an array of 1D tubes with quasi-random onsite disorder and monitor the subsequent dynamics over several thousand tunneling times. We find a strikingly different behavior between MBL and Anderson Localization. While the non-interacting Anderson case remains localized, in the interacting case any coupling between the tubes leads to a delocalization of the entire system., Comment: 4+3 pages, 5+4 figures final version using stretched exponential fits to improve fit quality

We experimentally observe many-body localization of interacting fermions in a one-dimensional quasi-random optical lattice. We identify the many-body localization transition through the relaxation dynamics of an initially-prepared charge density wave. For sufficiently weak disorder the time evolution appears ergodic and thermalizing, erasing all remnants of the initial order. In contrast, above a critical disorder strength a significant portion of the initial ordering persists, thereby serving as an effective order parameter for localization. The stationary density wave order and the critical disorder value show a distinctive dependence on the interaction strength, in agreement with numerical simulations. We connect this dependence to the ubiquitous logarithmic growth of entanglement entropy characterizing the generic many-body localized phase., Comment: 6 pages, 6 figures + supplementary information