Abstract: Time crystals (TCs) broadly refer to the spontaneous breaking of time translation symmetry in quantum systems paralleling the similar concept of spatial symmetry breaking evidenced in crystalline matter. In this context, so-called discrete time crystals (DTCs) have been demonstrated in diverse physical systems including cold atoms, magnons in superfluid 3He, nuclear spins, photonic devices, and quantum computer qubits. DTC behavior is typically evidenced by the emergence of period doubling upon a time-dependent external drive. Very recently also continuous time crystals (CTCs) have been proposed in open quantum systems perturbed from their equilibrium with a time-independent drive [1]. We reveal, through both ultra-high resolution spectroscopy and time-resolved spatial first-order coherence function g(1)(r,t) experiments, that the exciton-polariton ground state in a trap can develop a non-linear self-sustained dynamics, intimately affected by mechanics in ways that expose characteristics of both CTCs and DTCs [2]. In contrast to other realizations, here the TC phases can be controlled by the power of continuous-wave non-resonant optical drive exciting the condensate, and by the optomechanical interactions with phonons [3]. Those phases are, for increasing power, (i) Larmor -like precession of pseudo-spins - a limit-cycle signature of continuous TC, (ii) locking of the frequency of precession to self-sustained coherent phonons - stabilized TC, (iii) doubling of TC’s period by phonons - a DTC with continuous excitation. Non-Hermiticity, non-linearity, dissipative coupling between the polariton pseudo-spin states, and non-adiabatic coupling to a dynamical reservoir, are shown to be important ingredients for the observation of the spontaneous breaking of time-symmetry in such a many-body quantum system. Prospects for the realization of coupled polariton time-crystals, and their optomechanical control, will be also discussed.

[1] P. Kongkhambut et al, Science 377, 670 (2022). 

[2] I. Carraro-Haddad et al, Science 384, 995 (2024). 

[3] A. S. Kuznetsov et al, Nature Communications 14, 5470 (2023).