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Acta Physica Sinica

Quantum-resonance ratchet in a kicked Bose-Einstein condensate

Chunlei Qu, Zhao Qing, 北京理工大学理学院物理系，北京 100081

Published Jan 1, 2009• 1 citation
Publisher

Abstract

The dynamical evolution of a periodically kicked Bose-Einstein condensate was investigated by simulation. Emphasis was placed on the influence of the nonlinear interaction between atoms on the quantum-resonance ratchet effect. It was found that weak nonlinear interaction reduces the ratchet effect while the strong nonlinear interaction causes the ratchet current to disappear or even reversed. The ratchet effect under high-order quantum resonance conditions was further studied. The ratchet effect is not obvious in this case and can be easily destroyed by the noise of the kicking potential period.

DOI
10.7498/aps.58.4390

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The dynamical evolution of a periodically kicked Bose-Einstein condensate was investigated by simulation. Emphasis was placed on the influence of the nonlinear interaction between atoms on the quantum-resonance ratchet effect. It was found that weak nonlinear interaction reduces the ratchet effect while the strong nonlinear interaction causes the ratchet current to disappear or even reversed. The ratchet effect under high-order quantum resonance conditions was further studied. The ratchet effect is not obvious in this case and can be easily destroyed by the noise of the kicking potential period.
We investigate the effect of the nonlinear interaction on the quantum resonance ratchet for the periodically kicked Bose-Einstein condensate that is realized on a ring. In the noninteracting case, the wave packet spreads asymmetrically in momentum space, leading to a directed current. We show that for the weak nonlinear interaction, the probability density distribution in momentum space has two peaks which linearly shift to ward positive and negative momentum, respectively. The force periodically acting on each peak is a constant with time evolution. The competition between the motions of the two parts of cold atoms leads to the reduce or the revival of the momentum current. For the strong nonlinearity, the momentum distribution has only one peak which does not shift with time. The force on this peak is almost zero with time evolution, thus the directed current varnishes.
A theory of quantum ratchets for a particle periodically kicked by a general periodic potential under quantum-resonance conditions is developed for arbitrary values of the conserved quasimomentum β. A special case of this theory is experimentally realized using a Bose–Einstein condensate (BEC) exposed to a pulsed standing light wave. While this case corresponds to completely symmetric potential and initial wave-packet, a purely quantum ratchet effect still arises from the generic noncoincidence of the symmetry centers of these two entities. The experimental results agree well with the theory after taking properly into account the finite quasimomentum width of the BEC. This width causes a suppression of the ratchet acceleration occurring for "resonant" β, so that the mean momentum saturates to a finite ratchet velocity, strongly pronounced relative to that for nonresonant β.
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.
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.
Quantum-resonance ratchets associated with the kicked particle are experimentally realized for arbitrary quasimomentum using a Bose-Einstein condensate (BEC) exposed to a pulsed standing light wave. The ratchet effect for general quasimomentum arises even though both the standing-wave potential and the initial state of the BEC have a point symmetry. The experimental results agree well with theoretical ones which take into account the finite quasimomentum width of the BEC. In particular, this width is shown to cause a suppression of the ratchet acceleration for exactly resonant quasimomentum, leading to a saturation of the directed current.
We study the response of a Bose-Einstein Condensate in a δ-kicked optical lattice ratchet potential, with δ-kicked interactions, at quantum resonances. Our results reveal a strong dependency on the kicking strength K and the interaction parameter g˜. A critical curve in the (K,g˜)-space separating quasi-periodicity from full chaos shows that full chaos can be easily achieved for stronger interactions. In the full chaos regime, large currents including current reversals are generated and the current spectrum symmetry is broken. Outside the stability window, |g˜|≤1, the directed transport is no longer guaranteed. Experiments are possible thanks to recent progress in optical lattices and the possibility of time-modulating Feshbach-resonance.