Coherent state description of the ground state in the Tavis–Cummings model and its quantum phase transitions

Castaños, Octavio; López‐Peña, R.; Nahmad-Achar, Eduardo; Hirsch, Jorge G.; López‐Moreno, Enrique; Vitela, Javier E.

doi:10.1088/0031-8949/79/06/065405

Cited by 41 publications

(51 citation statements)

References 29 publications

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“…Their symmetrized solutions have been thoroughly studied in [16,17]. For the Dicke Hamiltonian, it is necessary to restrict consideration to rotations by an angle φ 0 = 0,π for the Hamiltonian to remain invariant.…”

Section: Dicke Hamiltonian and Symmetry-adapted Statesmentioning

confidence: 99%

Superradiant phase in field-matter interactions

et al. 2011

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We show that semiclassical states adapted to the symmetry of the Hamiltonian are an excellent approximation to the exact quantum solution of the ground and first excited states of the Dicke model. Their overlap with the exact quantum states is very close to 1 except in a close vicinity of the quantum phase transition. Furthermore, they have analytic forms in terms of the model parameters and allow us to calculate analytically the expectation values of field and matter observables. Some of these differ considerably from results obtained via the standard coherent states and by means of Holstein-Primakoff series expansion of the Dicke Hamiltonian. Comparison with exact solutions obtained numerically supports our results. In particular, it is shown that the expectation values of the number of photons and of the number of excited atoms have no singularities at the phase transition. We comment on why other authors have previously found otherwise.

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Section: Dicke Hamiltonian and Symmetry-adapted Statesmentioning

confidence: 99%

Superradiant phase in field-matter interactions

et al. 2011

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“…Since the number of bosons is not limited, the range of possible energies is only lower bounded. The secondorder QPT, according to the Ehrenfest classification, appears as a discontinuity on the second derivative of the semiclassical ground state energy 0 (γ), which can be expressed as [21,24,45] …”

Section: B the Classical Hamiltonianmentioning

confidence: 99%

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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“…To obtain analytical expressions, the variational procedure described in [11] is employed. We use as a trial state the direct product of coherent states in each subspace: Heisenberg-Weyl states |α for the photon sector [12,13] and SU (2) or spin states |ζ for the particle sector [14,15], i.e., |α, ζ = |α ⊗ |ζ .…”

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confidence: 99%

No singularities in observables at the phase transition in the Dicke model

et al. 2011

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The Dicke Hamiltonian describes the simplest quantum system with atoms interacting with photons: N two-level atoms inside a perfectly reflecting cavity, which allows only one electromagnetic mode. It has also been successfully employed to describe superconducting circuits that behave as artificial atoms coupled to a resonator. The system exhibits a transition to a superradiant phase at zero temperature. When the interaction strength reaches its critical value, both the number of photons and atoms in excited states in the cavity, together with their fluctuations, exhibit a sudden increase from zero. By employing symmetry-adapted coherent states, it is shown that these properties scale with the number of atoms, their reported divergences at the critical point represent the limit when this number goes to infinity, and, in this limit, they remain divergent in the superradiant phase. Analytical expressions are presented for all observables of interest, for any number of atoms. Comparisons with exact numerical solutions strongly support the results.

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Coherent state description of the ground state in the Tavis–Cummings model and its quantum phase transitions

Cited by 41 publications

References 29 publications

Superradiant phase in field-matter interactions

Superradiant phase in field-matter interactions

Delocalization and quantum chaos in atom-field systems

No singularities in observables at the phase transition in the Dicke model

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