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

Lewis-Swan, Robert J.; Muleady, Sean R.; Barberena, Diego; Bollinger, John J.; Rey, Ana María

doi:10.1103/physrevresearch.3.l022020

Cited by 22 publications

(11 citation statements)

References 59 publications

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“…In fact, recent investigations have pointed out the generation of robust spin squeezing in phase II [305]. Understanding the dynamics of entanglement across a DPT is a fascinating new direction [306,307]. Is entanglement maximum at the critical point?…”

Section: Discussionmentioning

confidence: 99%

Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments

Marino¹,

Eckstein²,

Foster³

et al. 2022

Preprint

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We overview the concept of dynamical phase transitions in isolated quantum systems quenched out of equilibrium. We focus on non-equilibrium transitions characterized by an order parameter, which features qualitatively distinct temporal behaviour on the two sides of a certain dynamical critical point. Dynamical phase transitions are currently mostly understood as long-lived prethermal phenomena in a regime where inelastic collisions are incapable to thermalize the system. The latter enables the dynamics to substain phases that explicitly break detailed balance and therefore cannot be encompassed by traditional thermodynamics. Our presentation covers both cold atoms as well as condensed matter systems. We revisit a broad plethora of platforms exhibiting pre-thermal DPTs, which become theoretically tractable in a certain limit, such as for a large number of particles, large number of order parameter components, or large spatial dimension. The systems we explore include, among others, quantum magnets with collective interactions, φ 4 quantum field theories, and Fermi-Hubbard models. A section dedicated to experimental explorations of DPTs in condensed matter and AMO systems connects this large variety of theoretical models.

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Section: Discussionmentioning

confidence: 99%

Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments

Marino¹,

Eckstein²,

Foster³

et al. 2022

Preprint

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“…This Letter provides a powerful framework to identify a broad class of ESQPTs dynamically, as the number of constants of motion abruptly changes at the corresponding critical energy. This should entail important consequences for nonequilibrium processes crossing an ESQPT due to the change of conserved charges [15,52] and also for the steady states resulting from dynamical phase transitions [23,75]. A consequence of the noncommutativity of Ĉ and Π is the possibility to build equilibrium states in which the information about both the population of each symmetric well and the quantum coherence between them is recorded.…”

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confidence: 99%

Constant of Motion Identifying Excited-State Quantum Phases

Corps

Relaño

2021

Phys. Rev. Lett.

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We propose that a broad class of excited-state quantum phase transitions (ESQPTs) gives rise to two different excited-state quantum phases. These phases are identified by means of an operator Ĉ, which is a constant of motion in only one of them. Hence, the ESQPT critical energy splits the spectrum into one phase where the equilibrium expectation values of physical observables crucially depend on this constant of motion and another phase where the energy is the only relevant thermodynamic magnitude. The trademark feature of this operator is that it has two different eigenvalues AE1, and, therefore, it acts as a discrete symmetry in the first of these two phases. This scenario is observed in systems with and without an additional discrete symmetry; in the first case, Ĉ explains the change from degenerate doublets to nondegenerate eigenlevels upon crossing the critical line. We present stringent numerical evidence in the Rabi and Dicke models, suggesting that this result is exact in the thermodynamic limit, with finite-size corrections that decrease as a power law.

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“…Not only for one-degree-of-freedom models with pairs of hyperbolic fixed points, but also in models with more degrees of freedom where hyperbolic fixed points appears when the integrability of the models is broken and they move toward a chaotic regime [37]. The results presented here could also be relevant in the study of dynamical phase transitions [38], where avoided crossings and closeness to hyperbolic fixed points could influence the dynamics of non-stationary states in a similar way as we identified here for coherent states in the Lipkin-Meshkov-Glick model. This expression can be written as…”

Section: Discussionmentioning

confidence: 80%

Avoided crossings and dynamical tunneling close to excited-state quantum phase transitions

Nader,

González-Rodríguez,

Lerma-Hernández

2021

Preprint

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Using the Wherl entropy, we study the delocalization in phase-space of energy eigenstates in the vicinity of avoided crossing in the Lipkin-Meshkov-Glick model. These avoided crossing, appearing at intermediate energies in a certain parameter region of the model, originate classically from pairs of trajectories lying in different phase space regions, which contrary to the low energy regime, are not connected by the discrete parity symmetry of the model. As coupling parameters are varied, a sudden increase of the Wherl entropy is observed for eigenstates close to the critical energy of the excited-state quantum phase transition (ESQPT). This allows to detect when an avoided crossing is accompanied by a superposition of the pair of classical trajectories in the Husimi functions of eigenstates. This superposition yields an enhancement of dynamical tunneling, which is observed by considering initial Bloch states that evolve partially into the partner region of the paired classical trajectories, thus breaking the quantum-classical correspondence in the evolution of observables.

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

Cited by 22 publications

References 59 publications

Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments

Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments

Constant of Motion Identifying Excited-State Quantum Phases

Avoided crossings and dynamical tunneling close to excited-state quantum phase transitions

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