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arXiv:cond-mat/0501565 · Physical Review Letters

Resonant Nonlinear Quantum Transport for a Periodically Kicked Bose Condensate

Sandro Wimberger, R. Mannella, O. Morsch, E. Arimondo

Published Apr 8, 2005• 60 citations
arXivHTMLPDF

Abstract

Our realistic numerical results show that the fundamental and higher-order quantum resonances of the delta-kicked rotor are observable in state-of-the-art experiments with a Bose condensate in a shallow harmonic trap, kicked by a spatially periodic optical lattice. For stronger confinement, interaction-induced destruction of the resonant motion of the kicked harmonic oscillator is predicted.

DOI
10.1103/physrevlett.94.130404

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Our realistic numerical results show that the fundamental and higher-order quantum resonances of the delta-kicked rotor are observable in state-of-the-art experiments with a Bose condensate in a shallow harmonic trap, kicked by a spatially periodic optical lattice. For stronger confinement, interaction-induced destruction of the resonant motion of the kicked harmonic oscillator is predicted.
We experimentally investigate the atom-optical $\ensuremath{\delta}$-kicked harmonic oscillator for the case of nonlinearity due to collisional interactions present in a Bose-Einstein condensate. A Bose condensate of rubidium atoms tightly confined in a static harmonic magnetic trap is exposed to a one-dimensional optical standing-wave potential that is pulsed on periodically. We focus on the quantum antiresonance case for which the classical periodic behavior is simple and well understood. We show that after a small number of kicks the dynamics are dominated by dephasing of matter wave interference due to the finite width of the condensate's initial momentum distribution. In addition, we demonstrate that the nonlinear mean-field interaction in a typical harmonically confined Bose condensate is not sufficient to give rise to chaotic behavior.
Scope and Method of Study: A purpose of this research was to study the scaling behavior of resonances of a periodically kicked quantum system. Specifically, a model known as a quantum delta-kicked rotor (QDKR) was implemented with a 87 Rb Bose-Einstein Condensate. Two variants of this system, a quantum delta-kicked accelerator (QDKA) and a quantum ratchet, were also realized experimentally and used to study quantum transport. Furthermore, experiments were undertaken to introduce mean-field interactions in these systems through an Optical Feshbach resonance.
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.
We have observed high-order quantum resonances in a realization of the quantum delta-kicked rotor, using Bose-condensed Na atoms subjected to a pulsed standing wave of laser light. These resonances occur for pulse intervals that are rational fractions of the Talbot time, and are characterized by ballistic momentum transfer to the atoms. The condensate's narrow momentum distribution not only permits the observation of the quantum resonances at 3/4 and 1/3 of the Talbot time, but also allows us to study scaling laws for the resonance width in quasimomentum and pulse interval.
We report measurements of the early-time momentum diffusion for the atom-optical delta-kicked rotor. In this experiment a Bose-Einstein condensate provides a source of ultracold atoms with an ultranarrow initial momentum distribution, which is then subjected to periodic pulses (or "kicks") using an intense far-detuned optical standing wave. We characterize the effect of varying the effective Planck's constant for the system, while keeping all other parameters fixed. The observed behavior includes both quantum resonances (ballistic energy growth) and antiresonances (re-establishment of the initial state). Our experimental results are compared with theoretical predictions.