Interaction-driven breakdown of dynamical localization in a kicked quantum gas
Alec Cao, Roshan Sajjad, Hector Mas, Ethan Q. Simmons, Jeremy L. Tanlimco, Eber Nolasco-Martinez, Toshihiko Shimasaki, H. Esat Kondakci, Victor Galitski, David M. Weld
Quantum interference can terminate energy growth in a continually kicked system, via a single-particle ergodicity-breaking mechanism known as dynamical localization. The effect of many-body interactions on dynamically localized states, while important to a fundamental understanding of quantum decoherence, has remained unexplored despite a quarter-century of experimental studies. We report the experimental realization of a tunably-interacting kicked quantum rotor ensemble using a Bose-Einstein condensate in a pulsed optical lattice. We observe signatures of a prethermal localized plateau, followed for interacting samples by interaction-induced anomalous diffusion with an exponent near one half. Echo-type time reversal experiments establish the role of interactions in destroying reversibility. These results quantitatively elucidate the dynamical transition to many-body quantum chaos, advance our understanding of quantum anomalous diffusion, and delimit some possibilities for protecting quantum information in interacting driven systems.
We provide evidence that a clean kicked Bose-Hubbard model exhibits a many-body dynamically localized phase. This phase shows ergodicity breaking up to the largest sizes we were able to consider. We argue that this property persists in the limit of large size. The Floquet states violate eigenstate thermalization and then the asymptotic value of local observables depends on the initial state and is not thermal. This implies that the system does not generically heat up to infinite temperature, for almost all the initial states. Differently from many-body localization here the entanglement entrop…
The kicked rotor system is a textbook example of how classical and quantum dynamics can drastically differ. The energy of a classical particle confined to a ring and kicked periodically will increase linearly in time whereas in the quantum version the energy saturates after a finite number of kicks. The quantum system undergoes Anderson localization in the angular-momentum space. Conventional wisdom says that in a many-particle system with short-range interactions the localization will be destroyed due to the coupling of widely separated momentum states. Here we provide evidence that for an in…
We study experimentally a quantum kicked rotor with broken parity symmetry, supporting a ratchet effect due to the presence of a classical accelerator mode. We show that the short-time dynamics is very well described by the classical dynamics, characterized by a strongly asymmetric momentum distribution with directed motion on one side, and an anomalous diffusion on the other. At longer times, quantum effects lead to dynamical localization, causing an asymptotic resymmetrization of the wave function.
Multifractal states offer a "third way" for quantum matter, neither fully localized nor ergodic, exhibiting singular continuous spectra, self-similar wavefunctions, and transport and entanglement scaling exponents intermediate between extended and localized states. While multifractality in equilibrium systems generally requires fine-tuning to a critical point, externally driven quantum matter can exhibit multifractal states with no equilibrium counterpart. We report the experimental observation of multifractal matter and anomalous localization in a kicked Aubry-André-Harper quasicrystal. Our c…
We study the fate of dynamical localization of two quantum kicked rotors with contact interaction. This interaction mimics experimental realizations with ultracold atomic gases. Dynamical localization for a single rotor takes place in momentum space. The contact interaction affects the evolution of the relative momentum $k$ of a pair of interacting rotors in a non-analytic way. Consequently the evolution operator $U$ is exciting large relative momenta with amplitudes which decay only as a power law $1/k^4$. This is in contrast to the center-of-mass momentum $K$ for which the amplitudes excited…
We study the effect of many-body quantum interference on the dynamics of coupled periodically kicked systems whose classical dynamics is chaotic and shows an unbounded energy increase. We specifically focus on a $N$ coupled kicked rotors model: we find that the interplay of quantumness and interactions dramatically modifies the system dynamics inducing a transition between energy saturation and unbounded energy increase. We discuss this phenomenon both numerically and analytically, through a mapping onto a $N$-dimensional Anderson model. The thermodynamic limit $N\to\infty$, in particular, alw…
The quantum kicked rotor is well-known to display dynamical localization in the non-interacting limit. In the interacting case, while the mean-field (Gross-Pitaevskii) approximation displays a destruction of dynamical localization, its fate remains debated beyond mean-field. Here we study the kicked Lieb-Liniger model in the few-body limit. We show that for any interaction strength, two kicked interacting bosons always dynamically localize, in the sense that the energy of the system saturates at long time. However, contrary to the non-interacting limit, the momentum distribution $Π(k)$ of the …
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 succesful …
Finite-time effects in periodically kicked systems
Universidad Politécnica de Madrid（马德里理工大学）；Universidad de Extremadura（埃斯特雷马杜拉大学）；Instituto de Computación Científica Avanzada (ICCAEx)（高级科学计算研究所 (ICCAEx)）；Universidad Autónoma de Madrid（马德里自治大学）
We study the dynamics of the many-body atomic kicked rotor with interactions at the mean-field level, governed by the Gross-Pitaevskii equation. We show that dynamical localization is destroyed by the interaction, and replaced by a subdiffusive behavior. In contrast to results previously obtained from a simplified version of the Gross-Pitaevskii equation, the subdiffusive exponent does not appear to be universal. By studying the phase of the mean-field wave function, we propose a new approximation that describes correctly the dynamics at experimentally relevant times close to the start of subd…
Periodic drives are a common tool to control physical systems, but have a limited applicability because time-dependent drives generically lead to heating. How to prevent the heating is a fundamental question with important practical implications. We address this question by analyzing a chain of coupled kicked rotors, and find two situations in which the heating rate can be arbitrarily small: (i) linear stability, for initial conditions close to a fixed point, and (ii) marginal localization, for drives with large frequencies and small amplitudes. In both cases, we find that the dynamics shows u…
The quantum kicked rotor is well-known for displaying dynamical (Anderson) localization. It has recently been shown that a periodically kicked Tonks gas will always localize and converge to a finite energy steady-state. This steady-state has been described as being effectively thermal with an effective temperature that depends on the parameters of the kick. Here we study a generalization to a quasi-periodic driving with three frequencies which, without interactions, has a metal-insulator Anderson transition. We show that a quasi-periodically kicked Tonks gas goes through a dynamical many-body …
We map the infinite-range coupled quantum kicked rotors over an infinite-range coupled interacting bosonic model. In this way we can apply exact diagonalization up to quite large system sizes and confirm that the system tends to ergodicity in the large-size limit. In the thermodynamic limit the system is described by a set of coupled Gross-Pitaevskij equations equivalent to an effective nonlinear single-rotor Hamiltonian. These equations give rise to a power-law increase in time of the energy with exponent $γ\sim 2/3$ in a wide range of parameters. We explain this finding by means of a master-…
Anderson localization is the ubiquitous phenomenon of inhibition of transport of classical and quantum waves in a disordered medium. In dimension one, it is well known that all states are localized, implying that the distribution of an initially narrow wave-packet released in a disordered potential will, at long time, decay exponentially on the scale of the localization length. However, the exact shape of the stationary localized distribution differs from a purely exponential profile and has been computed almost fifty years ago by Gogolin. Using the atomic quantum kicked rotor, a paradigmatic …
Dynamical localization is the analog of Anderson localization in momentum space, where the system's energy saturates and the single-particle wave-functions are exponentially localized in momentum space. In the presence of interactions, in the context of a periodically kicked Bose gas, it has been argued that dynamical localization persists. Focusing on the Tonks (strongly interacting) regime, we show that the many-body dynamically localized phase is effectively thermal, a clear deviation from the breaking of ergodicity observed in standard many-body localized systems. We relate the effective t…
Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles（布鲁塞尔自由大学非线性现象与复杂系统中心）；International Solvay Institutes（国际索尔维研究所）；Laboratoire Kastler Brossel, Sorbonne Université（索邦大学卡斯特勒-布罗塞尔实验室）；Laboratoire Collisions Agrégats Réactivité, Université de Toulouse（图卢兹大学碰撞聚集体反应实验室）；INPHYNI, Université Côte d’Azur（蔚蓝海岸大学INPHYNI实验室）；Laboratoire de Physique Théorique, Université de Toulouse（图卢兹大学理论物理实验室）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）
