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Europhysics Letters (EPL)

Dynamical localization of interacting ultracold atomic kicked rotors

A. Marino, Gianpaolo Torre, R. Citro

Published Oct 24, 2019• 4 citations
Publisher

Abstract

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.

DOI
10.1209/0295-5075/127/50008

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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.
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 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.
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.
In this work, we study finite-time effects in ultracold atomic systems by considering time-dependent modulations with variable waveforms and durations. These two characteristics can be controlled by adjusting only a single parameter. For arbitrarily short pulses, our model recovers the paradigmatic kicked rotor while maintaining the impulse transmitted per period and unit amplitude constant. Furthermore, we demonstrate that finite-time effects have a profound impact on dynamical localization, a result that cannot be captured by the δ-kicked-rotor model. Through a detailed analysis of the effects of different modulation amplitudes, periods, and waveforms, we identify the conditions for which dynamical localization is significantly enhanced. We show that the strength of dynamical localization increases sharply as the system approaches the δ-kicked-rotor limiting case. Moreover, we establish the existence of an optimal value of the period that maximizes dynamical localization for given values of the amplitude and shape parameter.
Atom-optics kicked rotor represents an experimentally reliable version of the paradigmatic quantum kicked rotor system. In this system, a periodic sequence of kicks are imparted to the cold atomic cloud. After a short initial diffusive phase the cloud settles down to a stationary state due to the onset of dynamical localization. In this paper, to explore the interplay between localized and diffusive phases, we experimentally implement a modification to this system in which the sign of the kick sequence is flipped after every M kicks. This is achieved in our experiment by allowing free evolution for half the Talbot time after every M kicks. Depending on the value of M, this modified system displays a combination of enhanced diffusion followed by asymptotic localization. This is explained as resulting from two competing processes-localization induced by standard kicked rotor type kicks, and diffusion induced by the half Talbot time evolution. The experimental and numerical simulations agree with one another. The evolving states display localized but nonexponential wave function profiles. This provides another route to quantum control in the kicked rotor class of systems.