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arXiv:cond-mat/0306660 · Physical Review Letters

Transition to Instability in a Kicked Bose-Einstein Condensate

Chuanwei Zhang, Jie Liu, Mark G. Raizen, Qian Niu

Published Feb 3, 2004• 90 citations
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Abstract

A periodically kicked ring of a Bose-Einstein condensate is considered as a nonlinear generalization of the quantum kicked rotor. For weak interactions between atoms, periodic motion (antiresonance) becomes quasiperiodic (quantum beating) but remains stable. There exists a critical strength of interactions beyond which quasiperiodic motion becomes chaotic, resulting in an instability of the condensate manifested by exponential growth in the number of noncondensed atoms. Similar behavior is observed for dynamically localized states (essentially quasiperiodic motions), where stability remains for weak interactions but is destroyed by strong interactions.

DOI
10.1103/physrevlett.92.054101

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A periodically kicked ring of a Bose-Einstein condensate is considered as a nonlinear generalization of the quantum kicked rotor. For weak interactions between atoms, periodic motion (antiresonance) becomes quasiperiodic (quantum beating) but remains stable. There exists a critical strength of interactions beyond which quasiperiodic motion becomes chaotic, resulting in an instability of the condensate manifested by exponential growth in the number of noncondensed atoms. Similar behavior is observed for dynamically localized states (essentially quasiperiodic motions), where stability remains for weak interactions but is destroyed by strong interactions.
A periodically kicked ring of a Bose-Einstein condensate is considered as a nonlinear generalization of the quantum kicked rotor, where the nonlinearity stems from the mean-field interactions between the condensed atoms. For weak interactions, periodic motion (antiresonance) becomes quasiperiodic (quantum beating) but remains stable. There exists a critical strength of interactions beyond which quasiperiodic motion becomes chaotic, resulting in an instability of the condensate manifested by exponential growth in the number of noncondensed atoms. In the stable regime, the system remains predominantly in the two lowest energy states and may be mapped onto a spin model, from which we obtain an analytic expression for the beat frequency and discuss the route to instability. We numerically explore a parameter regime for the occurrence of instability and reveal the characteristic density profile for both condensed and noncondensed atoms. The Arnold diffusion to higher energy levels is found to be responsible for the transition to instability. Similar behavior is observed for dynamically localized states (essentially quasiperiodic motions), where stability remains for weak interactions but is destroyed by strong interactions.
Bose-Einstein condensates subject to short pulses (``kicks'') from standing waves of light represent a nonlinear analog of the well-known chaos paradigm, the quantum kicked rotor. Previous studies of the onset of dynamical instability (i.e., exponential proliferation of noncondensate particles) suggested that the transition to instability might be associated with a transition to chaos. Here we conclude instead that instability is due to resonant driving of Bogoliubov modes. We investigate the Bogoliubov spectrum for both the quantum kicked rotor (QKR) and a variant, the double kicked rotor (QKR-2). We present an analytical model, valid in the limit of weak impulses which correctly gives the scaling properties of the resonances and yields good agreement with mean-field numerics.
We study the dynamics of a Bose-Einstein condensate in the quasiperiodic kicked rotor described by a Gross-Pitaevskii equation confined in a toroidal trap. As the interactions are increased, Bogoliubov excitations appear and deplete the condensate; we characterize this instability by considering the population of the first Bogoliubov mode, and we show that it does not prevent, for small enough interaction strengths, the observation of the quasi--insulator-to-metal transition that replaces the Anderson transition of the noninteracting case. However, the predicted subdiffusion in momentum space is not observed in the stable region within experimentally accessible times. For higher interaction strengths, the condensate may be strongly depleted before this dynamical regimes set in.
We study the dynamics of Bogoliubov excitations of a Bose-Einstein condensate in the quasiperiodic kicked rotor. In the weakly interacting regime, the condensate is stable and both the condensate and the excitations undergo a phase transition from a quasilocalized to a diffusive regime. The corresponding critical exponents are identical for the condensate and the excitations, and compare very well with the value ν≈1.6ν\approx1.6ν≈1.6 for non-interacting particles.
We investigate the quantum dynamics of a periodically kicked Bose-Einstein condensate (BEC) confined in a one-dimensional (1D) box both numerically and theoretically, emphasizing on the phenomena of quantum resonance and antiresonance. The quantum resonant behavior of BEC is different from the single particle case but the antiresonance condition (Tau = 2pi and alpha = 0) is not affected by the atomic interaction. For the antiresonance case, the nonlinearity (atom interaction) causes the transition between oscillation and quantum beating. For the quantum resonance case, because of the coherence of BEC, the energy increase is oscillating and the rate is dramatically affected by the many-body interaction. We also discuss the relation between the quantum resonant behavior and the Kolmogorov-Arnold-Moser (KAM) or non-KAM property of the corresponding classical system.
We investigate the dynamics of kicked pseudo-spin-1/2 Bose–Einstein condensates (BECs) with spin–orbit coupling (SOC) in a tightly confined toroidal trap. The system exhibits different dynamical behaviors depending on the competition among SOC, kick strength, kick period and interatomic interaction. For weak kick strength, with the increase of SOC the density profiles of two components evolve from overlapped symmetric distributions into staggered antisymmetric distributions, and the evolution of energy experiences a transition from quasiperiodic motion to modulated quantum beating. For large kick strength, when the SOC strength increases, the overlapped symmetric density distributions become staggered irregular patterns, and the energy evolution undergoes a transition from quasiperiodic motion to dynamical localization. Furthermore, in the case of weak SOC, the increase of kick period leads to a transition of the system from quantum beating to Rabi oscillation, while for the case of strong SOC the system demonstrates complex quasiperiodic motion.