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 $\lambda$. 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 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 $\lambda$ and with it the interplay between chaos and nonequilibrium quantum matter in a real experiment.

中文翻译：

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玻色-爱因斯坦凝聚物的混沌诱导相干损失

玻色子量子多体系统的平均场极限由（主要是）非线性运动方程描述，在经典粒子混沌的精神下，该方程可能会表现出非常大的混沌，即希尔伯特空间中轨迹的指数分离与Lyapunov指数为正的比率 $\lambda$。现在的问题是$\lambda$即使在有限的粒子数下，也将其自身烙印到潜在的量子多体系统的可测量观测值上。使用在浅势势图中扩展的玻色-爱因斯坦凝聚物作为玻色子量子多体系统的范例，我们证明了该系统以指数级的快速速率失去了其相干性。此外，我们表明速率是由与混沌平均场动力学相关的李雅普诺夫指数给出的。最后，我们证明了这种混沌引起的相干性损失将其自身烙印到飞行后总密度中干涉条纹的可见性上，从而为测量提供了可能性$\lambda$ 在真实的实验中，它与混沌和非平衡量子物质之间的相互作用。