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.
Highlights
Molecular, and optical (AMO) quantum simulators are driving a surge in the investigation of dynamical phase transitions (DPTs) and associated nonequilibrium phases of matter [1,2,3,4,5,6]
Richer nonintegrable models have been pursued in trapped ion systems [22], but the associated complexity of the quantum dynamics limited the theoretical analysis of the DPT to small system sizes and prevented a rigorous scaling analysis
Following recent works linking DPTs to coexisting excited-state quantum phase transitions (QPTs) (EQPTs) [20,36,44], we find different dynamical critical points in the spin and boson-dominated regimes that reflect the presence of distinct EQPTs in these limits
Summary
Molecular, and optical (AMO) quantum simulators are driving a surge in the investigation of dynamical phase transitions (DPTs) and associated nonequilibrium phases of matter [1,2,3,4,5,6]. It is highly desirable to find and study DPTs in nonintegrable models featuring novel nonequilibrium phenomena that are both implementable in tunable quantum simulators and theoretically tractable under controllable approximations. We advance this direction by studying a DPT in the iconic Dicke model [23,24,25], which describes the collective coupling of many spins to a single harmonic oscillator. We investigate the DPT in analytically tractable spin- and bosondominated limits, as well as a nonintegrable regime where near-resonant coupling of spin and bosons leads to chaotic dynamical phases seen in other non-integrable systems [7,8].
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