Abstract
We investigate the emergence of a time crystal (TC) in a driven dissipative many-body spin array. In this system the interplay between incoherent spin pumping and collective emission stabilizes a synchronized non-equilibrium steady state which in the thermodynamic limit features a self-generated time-periodic pattern imposed by collective elastic interactions. In contrast to prior realizations where the time symmetry is already broken by an external drive, here it is only spontaneously broken by the elastic exchange interactions and manifest in the two-time correlation spectrum. Employing a combination of exact numerical calculations and a second-order cumulant expansion, we investigate the impact of many-body correlations on the TC formation and establish a connection between the regime where it is stable and where the system features a slow growth rate of the mutual information. This observation allows us to conclude that the TC studied here is an emergent semi-classical out-of-equilibrium state of matter. We also confirm the rigidity of the TC to single-particle dephasing. Finally, we discuss an experimental implementation using long lived dipoles in an optical cavity.
Highlights
Experimental progress in the control and preparation of quantum cold gases [1] has opened a new era in which non-equilibrium phenomena have a central role
In contrast to prior realizations where the time symmetry is already broken by an external drive, here it is only spontaneously broken by the elastic exchange interactions and manifest in the two-time correlation spectrum
Employing a combination of exact numerical calculations and a second-order cumulant expansion, we investigate the impact of many-body correlations on the time crystal (TC) formation and establish a connection between the regime where it is stable and where the system features a slow growth rate of the mutual information
Summary
Experimental progress in the control and preparation of quantum cold gases [1] has opened a new era in which non-equilibrium phenomena have a central role. Non-equilibrium steady state which in the thermodynamic limit features a self-generated time-periodic pattern imposed by collective elastic interactions.
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