Chaos-induced depletion of a Bose-Einstein condensate

TL;DR

This paper demonstrates that chaos in the mean-field dynamics of a Bose-Einstein condensate causes exponential depletion of the condensate, and this rate can be experimentally measured through interference fringe visibility.

Contribution

It establishes a direct link between classical chaos (Lyapunov exponent) and quantum many-body depletion in a Bose-Einstein condensate, providing a method for experimental measurement.

Findings

Depletion of non-condensed particles grows exponentially with rate given by Lyapunov exponent.

Chaos-induced depletion can be observed via interference fringe visibility.

The work connects classical chaos with quantum many-body dynamics experimentally.

Abstract

The mean-field limit of a bosonic quantum many-body system is described by (mostly) non-linear 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 $\lambda$. The question now is whether $\lambda$ 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 number of non-condensed particles is subject to an exponentially fast increase, i.e. depletion. Furthermore, we show that the rate of exponential depletion is given by the Lyapunov exponent associated with the chaotic mean-field dynamics. Finally, we demonstrate that this chaos-induced depletion is accessible experimentally through the visibility of interference fringes in the total density after time of flight, thus opening the possibility to measure $\lambda$, and with it, the interplay between chaos and non-equilibrium quantum matter, in a real experiment.