Characterizing the dynamical phase diagram of the Dicke model via classical and quantum probes

Abstract

We theoretically study the dynamical phase diagram of the Dicke model in both classical and quantum limits using large, experimentally relevant system sizes. Our analysis elucidates that the model features dynamical critical points that are distinct from previously investigated excited-state equilibrium transitions. Moreover, our numerical calculations demonstrate that mean-field features of the dynamics remain valid in the exact quantum dynamics, but we also find that in regimes where quantum effects dominate signatures of the dynamical phases and chaos can persist in purely quantum metrics such as entanglement and correlations. Our predictions can be verified in current quantum simulators of the Dicke model including arrays of trapped ions.

5+8 pages, 4+5 figures. Accepted version

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• Identifying and harnessing dynamical phase transitions for quantum-enhanced sensing
• Inverted harmonic oscillator dynamics of the nonequilibrium phase transition in the Dicke model
• Avoided crossings and dynamical tunneling close to excited-state quantum phase transitions
• Superradiant Phase Transition in the Strong Coupling Regime
• Engineering Dynamical Phase Diagrams with Driven Lattices in Spinor Gases
• Quantum multifractality as a probe of phase space in the Dicke model
• Relaxation time as a control parameter for exploring dynamical phase diagrams
• Control of dynamical phase transitions and non-ergodic relaxation via spinor phases
• Energy cat states induced by a parity-breaking excited-state quantum phase transition
• Chaos, thermalization and breakdown of quantum-classical correspondence in a collective many-body system
• Characterizing dynamical phase transitions in a spinor Bose-Einstein condensate via quantum and semiclassical analyses