Theory of parametric resonance for discrete time crystals in fully-connected spin-cavity systems
arXiv:2402.03729 · doi:10.1103/PhysRevA.109.042212
Abstract
We pinpoint the conditions necessary for discrete time crystal (DTC) formation in fully connected spin-cavity systems from the perspective of parametric resonance by mapping these systems onto oscillator like models. We elucidate the role of nonlinearity and dissipation by mapping the periodically driven open Dicke model onto effective linear and nonlinear oscillator models, while we analyze the effect of global symmetry breaking using the Lipkin-Meshkov-Glick model with tunable anisotropy. We show that the system's nonlinearity restrains the dynamics from becoming unbounded when driven resonantly. On the other hand, dissipation keeps the oscillation amplitude of the period-doubling instability fixed, which is a key feature of DTCs. The presence of global symmetry breaking in the absence of driving is found to be crucial in the parametric resonant activation of period-doubling response. We provide analytic predictions for the resonant frequencies and amplitudes leading to DTC formation for both systems using their respective oscillator models.
15 pages, 8 figures
References in corpus (64)
- Floquet Time Crystals
- On the phase structure of driven quantum systems
- Quantum Time Crystals
- Chaos and the Quantum Phase Transition in the Dicke Model
- Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system
- Absence of Quantum Time Crystals
- Observation of a dissipative time crystal
- Discrete Time-Crystalline Order in Cavity and Circuit QED Systems
- Floquet time crystal in the Lipkin-Meshkov-Glick model
- Faraday patterns in Bose-Einstein condensates
- Dynamics of Nonequilibrium Dicke Models
- Observation of a continuous time crystal
- 1D Many-body localized Floquet systems II: Symmetry-Broken phases
- Observation of a space-time crystal in a superfluid quantum gas
- Nonequilibrium Quantum Phase Transitions in the Dicke Model
- Superlattice Patterns in Surface Waves
- Dynamical quantum phase transitions in the dissipative Lipkin-Meshkov-Glick model and proposed realization in optical cavity QED
- Dissipation Induced Structural Instability and Chiral Dynamics in a Quantum Gas
- Dicke time crystals in driven-dissipative quantum many-body systems
- Classical Discrete Time Crystals
- Amplitude equations and pattern selection in Faraday waves
- Limit cycle phase in driven-dissipative spin systems
- Self-organised Limit-Cycles, Chaos and Phase-Slippage with a Superfluid inside an Optical Resonator
- Emergent limit cycles and time crystal dynamics in an atom-cavity system
- Higher-order and fractional discrete time crystals in clean long-range interacting systems
- Classical many-body time crystals
- Period- discrete time crystals and quasicrystals with ultracold bosons
- On time crystallinity in dissipative Floquet systems
- Parametric Excitation of a Bose-Einstein Condensate: From Faraday Waves to Granulation
- Exactness of mean-field equations for open Dicke models with an application to pattern retrieval dynamics
- Collective spin systems in dispersive optical cavity QED: Quantum phase transitions and entanglement
- Defining Time Crystals via Representation Theory
- Dynamical many-body phases of the parametrically driven, dissipative Dicke model
- Square Patterns and Quasi-patterns in Weakly Damped Faraday Waves
- Measurement Induced Continuous Time Crystals
- Parametric instabilities of interacting bosons in periodically-driven 1D optical lattices
- Emergent parametric resonances and time-crystal phases in driven BCS systems
- Realization of a periodically driven open three-level Dicke model
- Mode softening in time-crystalline transitions of open quantum systems
- Creating big time crystals with ultracold atoms
- Quantum correlations and limit cycles in the driven-dissipative Heisenberg lattice
- AC-driven Quantum Phase Transition in the Lipkin-Meshkov-Glick Model
- Parametrically driven-dissipative three-level Dicke model
- Simulating the Lipkin-Meshkov-Glick model in a hybrid quantum system
- A dissipative time crystal with or without symmetry breaking
- Exact resummation of the Holstein-Primakoff expansion and differential equation approach to operator square-roots
- Phase diagram and optimal control for n-tupling discrete time crystal
- Entangled time-crystal phase in an open quantum light-matter system
- Discrete time crystals in many-body quantum chaos
- Driven-dissipative time crystalline phases in a two-mode bosonic system with Kerr nonlinearity
- Quantum fluctuations and correlations in open quantum Dicke models
- Floquet time crystals in driven spin systems with all-to-all -body interactions
- Dissipative time crystal in an atom-cavity system: Influence of trap and competing interactions
- Higgs time crystal in a high- superconductor
- Dynamical phases transitions in periodically driven Bardeen-Cooper-Schrieffer systems
- Realization of an inherent time crystal in a dissipative many-body system
- Self-organized Limit Cycles in Red-detuned Atom-cavity Systems
- Anharmonic classical time crystals: A coresonance pattern formation mechanism
- Entanglement and parametric resonance in driven quantum systems
- Nonequilibrium phases of ultracold bosons with cavity-induced dynamic gauge fields
- Bridging closed and dissipative discrete time crystals in spin systems with infinite-range interactions
- Non-Gaussian dynamics of quantum fluctuations and mean-field limit in open quantum central spin systems
- Emergence of a tunable crystalline order in a Floquet-Bloch system from a parametric instability
- Complex localization mechanisms in networks of coupled oscillators: two case studies