Chaos in the Dicke model: quantum and semiclassical analysis

Bastarrachea-Magnani, Miguel A.; López-del-Carpio, B.; Lerma-Hernández, Sergio; Hirsch, Jorge G.

doi:10.1088/0031-8949/90/6/068015

Cited by 51 publications

(49 citation statements)

References 51 publications

(62 reference statements)

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“…Finally, for energies larger than ω 0 , the whole Bloch sphere becomes accessible. So, as mentioned, the QPT separates the system into a normal and a superradiant phase, with the latter having three regions separated by the ESQPTs [13,46,47], as well as a great richness of regularity and chaos.…”

Section: B the Classical Hamiltonianmentioning

confidence: 89%

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Delocalization and quantum chaos in atom-field systems

et al. 2016

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Employing efficient diagonalization techniques, we perform a detailed quantitative study of the regular and chaotic regions in phase space in the simplest non-integrable atom-field system, the Dicke model. A close correlation between the classical Lyapunov exponents and the quantum Participation Ratio of coherent states on the eigenenergy basis is exhibited for different points in the phase space. It is also shown that the Participation Ratio scales linearly with the number of atoms in chaotic regions, and with its square root in the regular ones.

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Section: B the Classical Hamiltonianmentioning

confidence: 89%

“…They are marked by the ESQPT [13,34,46], sudden changes in the slope of the density of states. For energies in the interval ∈ [ 0 (γ), −ω 0 ] the surface of constant energy is formed by two disconnected lobes, which merges as the energy reaches = −ω 0 .…”

Section: B the Classical Hamiltonianmentioning

confidence: 99%

Delocalization and quantum chaos in atom-field systems

et al. 2016

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“…It was proven useful in various models (see Ref. [45] and references therein) including the Dicke model [22,38]. A general Peres lattice shows expectation values P i = ψ i |P |ψ i of a selected observable P in individual energy eigenstates |ψ i (enumerated by integer i) arranged into lattices with energy E i on one of the axes.…”

Section: Quantum Phasesmentioning

confidence: 99%

Quantum phases and entanglement properties of an extended Dicke model

2017

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We study a simple model describing superradiance in a system of two-level atoms interacting with a single-mode bosonic field. The model permits a continuous crossover between integrable and partially chaotic regimes and shows a complex thermodynamic and quantum phase structure. Several types of excited-state quantum phase transitions separate quantum phases that are characterized by specific energy dependences of various observables and by different atom-field and atom-atom entanglement properties. We observe an approximate revival of some states from the weak atom-field coupling limit in the strong coupling regime.

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“…While the Dicke Hamiltonian is non-integrable, the Tavis-Cummings Hamiltonian is its integrable version due the rotating-wave approximation (RWA). The Dicke model is interesting not only because its experimental realizations, but also thanks to its critical phenomena: the superradiant thermal phase transition [20], the wellknown superradiant QPT, related with quantum chaos and entanglement [21], and the presence of (dynamic and static) ESQPTs [22,23,24,25]. The Dicke model is a suited toy model to explore the connection between thermodynamics and the spectrum of quantum systems.…”

Section: Introductionmentioning

confidence: 99%

Thermal and quantum phase transitions in atom-field systems: a microcanonical analysis

Bastarrachea-Magnani¹,

Lerma-Hernández²,

Hirsch³

2016

J. Stat. Mech.

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Abstract. The thermodynamical properties of a generalized Dicke model are calculated and related with the critical properties of its energy spectrum, namely the quantum phase transitions (QPT) and excited state quantum phase transitions (ESQPT). The thermal properties are calculated both in the canonical and the microcanonical ensembles. The latter deduction allows for an explicit description of the relation between thermal and energy spectrum properties. While in an isolated system the subspaces with different pseudo spin are disconnected, and the whole energy spectrum is accesible, in the thermal ensamble the situation is radically different. The multiplicity of the lowest energy states for each pseudo spin completely dominates the thermal behavior, making the set of degenerate states with the smallest pseudo spin at a given energy the only ones playing a role in the thermal properties, making the positive energy states thermally inaccesible. Their quantum phase transitions, from a normal to a superradiant phase, are closely associated with the thermal transition. The other critical phenomena, the ESQPTs occurring at excited energies, have no manifestation in the thermodynamics, although their effects could be seen in finite sizes corrections. A new superradiant phase is found, which only exists in the generalized model, and can be relevant in finite size systems.

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Chaos in the Dicke model: quantum and semiclassical analysis

Cited by 51 publications

References 51 publications

Delocalization and quantum chaos in atom-field systems

Delocalization and quantum chaos in atom-field systems

Quantum phases and entanglement properties of an extended Dicke model

Thermal and quantum phase transitions in atom-field systems: a microcanonical analysis

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