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APS

Interacting ultracold atomic kicked rotors: loss of dynamical localization

Pinquan Qin, Alexei Andreanov, Hee Chul Park, Sergej Flach A

Published Mar 1, 2017• 0 citations
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Abstract

We study the fate of dynamical localization of two quantum kicked rotors with contact interaction, which relates to experimental realizations of the rotors with ultra-cold atomic gases. A single kicked rotor is known to exhibit dynamical localization, which 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/k4. This is in contrast to the center-of-mass momentum K for which the amplitudes excited by U decay superexponentially fast with K. Therefore dynamical localization is preserved for the center-of-mass momentum, but destroyed for the relative momentum for any nonzero strength of interaction.

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We study the fate of dynamical localization of two quantum kicked rotors with contact interaction, which relates to experimental realizations of the rotors with ultra-cold atomic gases. A single kicked rotor is known to exhibit dynamical localization, which 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/k4. This is in contrast to the center-of-mass momentum K for which the amplitudes excited by U decay superexponentially fast with K. Therefore dynamical localization is preserved for the center-of-mass momentum, but destroyed for the relative momentum for any nonzero strength of interaction.
Abstract We study the fate of dynamical localization of two quantum kicked rotors with contact interaction, which relates to experimental realizations of the rotors with ultra-cold atomic gases. A single kicked rotor is known to exhibit dynamical localization, which 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/k4. This is in contrast to the center-of-mass momentum K for which the amplitudes excited by U decay superexponentially fast with K. Therefore dynamical localization is preserved for the center-of-mass momentum, but destroyed for the relative momentum for any nonzero strength of interaction.
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 kkk of a pair of interacting rotors in a non-analytic way. Consequently the evolution operator UUU is exciting large relative momenta with amplitudes which decay only as a power law 1/k41/k^41/k4. This is in contrast to the center-of-mass momentum KKK for which the amplitudes excited by UUU decay superexponentially fast. Therefore dynamical localization is preserved for the center-of-mass momentum, but destroyed for the relative momentum for any nonzero strength of interaction.
We study a system of two atomic quantum kicked rotors with hard-core interaction. This system shows different dynamical behavior depending on the value of the kick period. In particular, we find that for periods close to resonance, the system shows a crossover from quantum resonance to dynamical localization. We characterize this crossover by the analysis of momenta distribution and density probability function in the configuration space, and discuss the role of the hard-core interaction on the dynamical localization by comparing it to the free-bosons case. In particular we note that dynamical localization of the center of mass persists even in the presence of strong interaction among the atoms. Some experimental proposals are also discussed.
The quantum kicked rotor is well known to display dynamical localization in the noninteracting 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 times. However, contrary to the noninteracting limit, the momentum distribution $\mathrm{\ensuremath{\Pi}}(k)$ of the bosons is not exponentially localized, but decays as C/k4\mathcal{C}/{k}^{4}C/k4, as expected for interacting quantum particles, with Tan's contact C\mathcal{C}C which remains finite at long times. We discuss how our results will impact the experimental study of kicked interacting bosons.
A periodically driven rotor is a prototypical model that exhibits a transition to chaos in the classical regime and dynamical localization (related to Anderson localization) in the quantum regime. In a recent work [Phys. Rev. B 94, 085120 (2016)], A. C. Keser et al. considered a many-body generalization of coupled quantum kicked rotors, and showed that in the special integrable linear case, dynamical localization survives interactions. By analogy with many-body localization, the phenomenon was dubbed dynamical many-body localization. In the present work, we study nonintegrable models of single and coupled quantum relativistic kicked rotors (QRKRs) that bridge the gap between the conventional quadratic rotors and the integrable linear models. For a single QRKR, we supplement the recent analysis of the angular-momentum-space dynamics with a study of the spin dynamics. Our analysis of two and three coupled QRKRs along with the proved localization in the many-body linear model indicate that dynamical localization exists in few-body systems. Moreover, the relation between QRKR and linear rotor models implies that dynamical many-body localization can exist in generic, nonintegrable many-body systems. And localization can generally result from a complicated interplay between Anderson mechanism and limiting integrability, since the many-body linear model is a high-angular-momentum limit of many-body QRKRs. We also analyze the dynamics of two coupled QRKRs in the highly unusual superballistic regime and find that the resonance conditions are relaxed due to interactions. Finally, we propose experimental realizations of the QRKR model in cold atoms in optical lattices.
The quantum kicked rotor is a paradigmatic model system in quantum physics. As a driven quantum system, it features dynamical localization, specifically Anderson localization in momentum space. However, the interacting many-body kicked rotor is believed to break localization. Here, we present evidence for many-body dynamical localization for the Lieb-Liniger version of the many-body quantum kicked rotor. After some initial evolution, the momentum distribution of interacting quantum-degenerate bosonic atoms in one-dimensional geometry, kicked hundreds of times by means of a pulsed sinusoidal potential, stops spreading. Our results shed light on the boundary between the classical, chaotic world and the realm of quantum physics.