ECAMP 15

Continuous time crystals, i.e., nonequilibrium phases with a spontaneously broken continuous time-translational symmetry, have been studied and recently observed in the long-time dynamics of open quantum systems. In particular, experimental studies of strongly interacting thermal Rydberg gases have established that continuous time crystals (CTC) can emerge under the simultaneous optical driving of more than a single interacting Rydberg state [1].
Motivated by these results, we discuss in this talk the dynamics in lattices of interacting Rydberg atoms, under optical two-photon driving with a standard three-level ladder configuration. While the emergence of continuous time-crystal phases in open quantum system as typically based on an underlying mean-field phenomenology, we focus here on their formation under conditions that do not a priory justify a simplified meanfield treatment [2]. Using complementary numerical methods we find two distinct time-crystal phases that cannot be described within mean-field theory. Remarkably, one of these quantum continuous time crystals (qCTCs) emerges only in the presence of quantum fluctuations. Our findings extend explorations of continuous time-translational symmetry breaking in dissipative systems beyond the classical phenomenology of periodic orbits in a low-dimensional nonlinear system. Possible experiments to observe the predicted qCTC phases in tweezer arrays of neutral atoms are also discussed.

[1] X. Wu, Z. Wang, F. Yang et al., Dissipative time crystal in a strongly interacting Rydberg gas, Nature Physics 20, 1389 (2024)
[2] F. Russo and T. Pohl, Quantum Dissipative Continuous Time Crystals, arXiv:2503.16141 (2025)