Discrete Time Crystals in the Absence of Manifest Symmetries or Disorder in Open Quantum Systems

Abstract

We establish a link between metastability and a discrete time-crystalline phase in a periodically driven open quantum system. The mechanism we highlight requires neither the system to display any microscopic symmetry nor the presence of disorder, but relies instead on the emergence of a metastable regime. We investigate this in detail in an open quantum spin system, which is a canonical model for the exploration of collective phenomena in strongly interacting dissipative Rydberg gases. Here, a semi-classical approach reveals the emergence of a robust discrete time-crystalline phase in the thermodynamic limit in which metastability, dissipation, and inter-particle interactions play a crucial role. We perform numerical simulations in order to investigate the dependence on the range of interactions, from all-to-all to short ranged, and the scaling with system size of the lifetime of the time crystal.arXiv:1807.10161v3 [cond-mat.stat-mech]

Discrete time-crystalline order in Bose–Hubbard model with dissipation

“…This corresponds to the case where a metastable state in the undriven system exists, it is necessary to have DTC. We further find that even the undriven system is not in the self-trapping regime, the periodic drive can also turn the system to a DTC, this interesting result is quite different from the earlier studies, for example in [13] the appearance of DTC requires meta-stable states in the undriven system. In addition, we show that period-n (n>2) DTC can be realized in large rings based on two-site systems considered here.…”

“…The extension of DTC to open quantum system with drive and dissipation attracts widespread research interest recently. Concrete models [12,13] shown that the DTC order can exist in open system with appropriately engineered drive and dissipation. This prediction was confirmed by the authors of [12] who shown that the modified Dicke model with the help of sufficiently strong atom-photon coupling and photon loss can exhibit time crystalline structure, and the same prediction was reported in [13] that a dissipative Rydberg model is also possible to possess time crystal order.…”

“…Reference [12] utilizes this feature and drives the system in the superradiant phase to entail sub-harmonic dynamical responses. The sub-harmonic response of [13] originates from the coexistence of two phases connected by first-order phase transition in dissipative Rydberg gas. Though the physical realizations of these two proposals are different, both of them feature period-doubling n=2 and the appearance of DTC in these proposals relies on the existence of meta-stable state of the undriven system.…”

Dicke time crystals in driven-dissipative quantum many-body systems

“…In this quest for phases of quantum matter without equilibrium counterpart, time crystals (TCs) represent a promising candidate for a novel form of dynamical order out-of-equilibrium. In TCs, observables dynamically entrain at a frequency subharmonic of the one imposed by an external periodic drive [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], and they have been currently realized with trapped ions [19] and solid state systems [20][21][22]. In most previous studies, TCs are realized in closed interacting quantum many-body systems, which are prone to heating towards an infinite temperature state under the action of periodic drive [23,24], therefore, a slowdown of energy absorption is customarily entailed via a disorder induced many-body localized phase [25][26][27][28], or by fast driving [8,[29][30][31][32][33].…”

Dissipative time crystal in an asymmetric nonlinear photonic dimer

“…The open nature is common to a vast class of modern experimental platforms in quantum science and technology, such as photonic systems [4], ultracold atoms [5-9], optomechanical systems [10][11][12][13] or superconducting circuits [14][15][16], for which driving and losses are omnipresent. Open quantum systems also display emergent physics, in particular dissipative phase transitions and topological phases [40][41][42][43][44][45].Several studies have highlighted the possibility for a continuous-wave driven-dissipative quantum system to reach a non-stationary state in the long time limit in which undamped oscillations arise spontaneously [46][47][48][49][50][51][52]. This phenomenon has been dubbed as boundary or dissipative time crystal (DTC), in analogy with the time crystals in some Hamiltonian systems [53].…”