Abstract
Discrete time crystals (DTC) have been demonstrated experimentally in several different quantum systems in the past few years. Spin couplings and cavity losses have been shown to play crucial roles for realizing DTC order in open many-body systems out of equilibrium. Recently, it has been proposed that eternal and transient DTC can be present with an open Floquet setup in the thermodynamic limit and in the deep quantum regime with few qubits, respectively. In this work, we consider the effects of spin damping and spin dephasing on the DTC order in spin-optomechanical and open cavity systems in which the spins can be all-to-all coupled. In the thermodynamic limit, it is shown that the existence of dephasing can destroy the coherence of the system and finally lead the system to its trivial steady state. Without dephasing, eternal DTC is displayed in the weak damping regime, which may be destroyed by increasing the all-to-all spin coupling or the spin damping. By contrast, the all-to-all coupling is constructive to the DTC in the moderate damping regime. We also focus on a model which can be experimentally realized by a suspended hexagonal boron nitride (hBN) membrane with a few spin color centers under microwave drive and Floquet magnetic field. Signatures of transient DTC behavior are demonstrated in both weak and moderate dissipation regimes without spin dephasing. Relevant experimental parameters are also discussed for realizing transient DTC order in such an hBN optomechanical system.
Highlights
In recent years, periodically driven (Floquet) quantum many-body systems have attracted considerable attention since they are crucial for understanding new non-equilibriumFloquet many-body localization (MBL) [1] phase and may have potential applications in quantum metrology [2]
One example of a non-equilibrium Floquet-MBL phase is the discrete time-crystalline (DTC) order [3,4,5], which is different from a continuous time crystal [6,7,8,9] and is characterized by the breaking of discrete time-translation symmetry (TTS) [10]
We consider the DTC behaviors in an open Floquet system as N qubits in a cavity via switching on and off of the spin-cavity coupling. It describes a cavity QED model with a large ensemble of trapped spins while, in the deep quantum regime, it characterizes an optomechanical model as a suspended hexagonal boron nitride (hBN) monolayer membrane with a few spin defects under a microwave drive and a Floquet magnetic field (Figure 1)
Summary
Periodically driven (Floquet) quantum many-body systems have attracted considerable attention since they are crucial for understanding new non-equilibrium. As the DTC order has been found in N atoms in a lossy cavity [19,20,21], it is interesting to explore the DTC in such spin-optomechanical systems with incoherent noise (spin damping or dephasing). We consider the DTC behaviors in an open Floquet system as N qubits in a (mechanical) cavity via switching on and off of the spin-cavity coupling. It describes a cavity QED model with a large ensemble of trapped spins while, in the deep quantum regime (with few qubits), it characterizes an optomechanical model as a suspended hBN monolayer membrane with a few spin defects under a microwave drive and a Floquet magnetic field (Figure 1). Both spin and cavity losses are considered
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