A dissipative time crystal with or without $\mathbb Z_2$ symmetry breaking

Cristóbal Lledó, Marzena H. Szymańska

Published 2020-04-06Version 1

We study an emergent semiclassical time crystal composed of two interacting driven-dissipative bosonic modes. The systems has a discrete $\mathbb Z_2$ spatial symmetry which, depending on the strength of the drive, can be broken in the time-crystalline phase or it cannot. An exact semiclassical mean-field analysis, numerical simulations in the quantum regime, and the spectral analysis of the Liouvillian are combined to show the emergence of the time crystal and to prove its robustness against quantum fluctuations.