Stability of the discrete time-crystalline order in spin-optomechanical and open cavity QED systems

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.

8 pages

References in corpus (12)

• Two-Dimensional Material Nanophotonics
• Opto-mechanical transducers for long-distance quantum communication
• Discrete Time-Crystalline Order in Cavity and Circuit QED Systems
• Observation of a many-body-localized discrete time crystal with a programmable spin-based quantum simulator
• Dynamical quantum phase transitions in the dissipative Lipkin-Meshkov-Glick model and proposed realization in optical cavity QED
• High-contrast plasmonic-enhanced shallow spin defects in hexagonal boron nitride for quantum sensing
• Review of cavity optomechanical cooling
• Highly sensitive optical sensor for precision measurement of electrical charges based on optomechanically induced difference-sideband generation
• Light-mediated strong coupling between a mechanical oscillator and atomic spins one meter apart
• Reversible modifications of linear dispersion - graphene between boron nitride monolayers
• Hybrid opto-mechanical systems with nitrogen-vacancy centers
• Symmetry-breaking dynamics of the finite-size Lipkin-Meshkov-Glick model near ground state

Cited by in corpus (1)

• Quantum sensing and imaging with spin defects in hexagonal boron nitride