Recurrences in an isolated quantum many-body system

The evolution of an isolated quantum system is unitary. If the system becomes large and its constituents interact one is not able to follow the evolution of the complex many body eigenstates. A system out of equilibrium it will ‘relax’ for practical observables [1]. The steady state reached can be described by a Generalized Gibbs Ensemble [2]. In our present study [3] we ask the question if, under which conditions the initial coherence can be revived.

In general the complexity of interacting many-body systems prevent the observation of recurrences of quantum states for all but the smallest systems, even if completely isolated from the environement. For large systems one cannot access the full complexity of the quantum states and the requirements to observe a recurrence in experiments reduces to being close to the initial state with respect to the employed observable. Selecting an observable connected to the collective excitations in one-dimensional super-fluids, we demonstrate recurrences of coherence and long range order in an interacting quantum many-body system containing thousands of particles. This opens up a new window into the dynamics of large quantum systems even after they reached a transient thermal-like state.

In the context of Quantum Thermodynamics and building Quantum Machines our experiments offer a direct way for designing a reservoir, that can either look Markovian and classical, and at later time strongly non-Markovian, remembering all the quantum correlations written into it by the last operation of the quantum machine.

[1] M. Gring et al., Science, 337, 1318 (2012); T. Langen et al., Nature Physics, 9, 640–643 (2013).
[2] T. Langen et al., Science 348, 207-211 (2015).
[3] B. Rauer et al. arXiv:1705.08231