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arXiv:cond-mat/0202380

(Quantum) Chaos in BECs

S. A. Gardiner

Published Feb 21, 2002• 1 citation
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Abstract

I consider general connections between chaotic and quantum chaotics dynamics in single particles, and the effect of adding comparable ``chaos-inducing'' potentials to a Bose-condensed system, considering in particular concepts of integrability and the effect of particle loss from the condensate mode.
DOI
10.48550/arxiv.cond-mat/0202380

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The mean-field limit of a bosonic quantum many-body system is described by (mostly) nonlinear equations of motion which may exhibit chaos very much in the spirit of classical particle chaos, i.e., by an exponential separation of trajectories in Hilbert space with a rate given by a positive Lyapunov exponent $\ensuremath{\lambda}$. The question now is whether $\ensuremath{\lambda}$ imprints itself onto measurable observables of the underlying quantum many-body system even at finite particle numbers. Using a Bose-Einstein condensate expanding in a shallow potential landscape as a paradigmatic example for a bosonic quantum many-body system, we show that the system loses its coherence at an exponentially fast rate. Furthermore, we show that the rate is given by the Lyapunov exponent associated with the chaotic mean-field dynamics. Finally, we demonstrate that this chaos-induced loss of coherence imprints itself onto the visibility of interference fringes in the total density after time of flight, thus, opening the possibility to measure $\ensuremath{\lambda}$ and with it the interplay between chaos and nonequilibrium quantum matter in a real experiment.
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