An<i>SU</i>(2)⊗<i>SU</i>(2) Jaynes–Cummings model with a maximum energy level

Ruiz, A. Martín; Frank, A.; Urrutia, L. F.

doi:10.1088/0031-8949/89/04/045103

Cited by 3 publications

(3 citation statements)

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“…Let us keep k finite and investigate the physical properties of the extended Dicke model (9). It is worth underlying that in a foregoing investigation we introduced the k-extended Jaynes-Cumming model (in the dipole and rotating wave approximations), which remains exactly solvable with the new SU(2) ⊗ SU(2) dynamical algebra [16]. There we showed that the temporal evolution of both the atomic and field quantum properties (e.g.…”

Section: The K-dicke Modelmentioning

confidence: 96%

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Quantum phase transition of two-level atoms interacting with a finite radiation field

Quezada,

Martín-Ruiz,

Frank

2019

Preprint

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We introduce a group-theoretical extension of the Dicke model which describes an ensemble of two-level atoms interacting with a finite radiation field. The later is described by a spin model which exhibits the main properties of the Kerr medium, and whose main feature is that it possesses a maximum number of excitations. We use the energy surface minimization method to demonstrate that the extended Dicke model exhibits a quantum phase transition, and we analyse its dependence upon the maximum number of excitations of the model. Our analysis is carried out via three methods: through mean-field analysis (i.e. by using the tensor product of coherent states), by using parity-preserving symmetry-adapted states (using the critical values obtained in the meanfield analysis and numerically minimizing the energy surface) and by means of the exact quantum solution (i.e. by numerically diagonalizing the Hamiltonian). Possible connections with the qpdeformed algebras are also discussed.

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Section: The K-dicke Modelmentioning

confidence: 96%

“…for the photon sector, which contracts to the Heisenberg-Weyl coherent state |α in the large k-representation limit [16,29]. Here, η = tan(ψ/2)e iϕ , ψ ∈ [0, π) and ϕ ∈ [0, 2π).…”

Section: Mean Field Analysismentioning

confidence: 99%

Quantum phase transition of two-level atoms interacting with a finite radiation field

Quezada,

Martín-Ruiz,

Frank

2019

Preprint

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“…The JCM depicts a two-level quantum system (a spin or a qubit) interacting with a single bosonic mode of radiation. Despite its solvability [2,4,9], the model remains realistic enough to stimulate research in diverse fields, encompassing applied group theory [9][10][11], investigations related to quantum integrability [12,13], and extending to quantum information processing [14][15][16]. This text further explores a specific application of the Jaynes-Cummings model for detecting non-orthogonal quantum states, as proposed in Ref.…”

Section: Introductionmentioning

confidence: 99%

Pure Decoherence of the Jaynes–Cummings Model: Initial Entanglement with the Environment, Spin Oscillations and Detection of Non-Orthogonal States

Dajka

2024

Symmetry

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A model based on pure decoherence for the Jaynes–Cummings spin–boson system, coupled through its integral of motion to an infinite bosonic bath, is proposed and examined. The properties of the spin oscillation process suggest an initial entanglement between the environment and the spin–boson degrees of freedom. The study demonstrates that the potential applicability of the Jaynes–Cummings model in detecting non-orthogonal bosonic states is preserved in the presence of pure decoherence.

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Quantum phase transition of two-level atoms interacting with a finite radiation field

Quezada

Martín-Ruiz

Frank

2020

Journal of Mathematical Physics

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We introduce a group-theoretical extension of the Dicke model, which describes an ensemble of two-level atoms interacting with a finite radiation field. The latter is described by a spin model whose main feature is that it possesses a maximum number of excitations. The approach adopted here leads to a nonlinear extension of the Dicke model that takes into account both the intensity dependent coupling between the atoms and the radiation field and an additional nonlinear Kerr-like or Pösch–Teller-like oscillator term, depending on the degree of nonlinearity. We use the energy surface minimization method to demonstrate that the extended Dicke model exhibits a quantum phase transition, and we analyze its dependence upon the maximum number of excitations of the model. Our analysis is carried out via three methods: through mean-field analysis (i.e., by using the tensor product of coherent states), by using parity-preserving symmetry-adapted states (using the critical values obtained in the mean-field analysis and numerically minimizing the energy surface), and by means of the exact quantum solution (i.e., by numerically diagonalizing the Hamiltonian). Possible connections with the qp-deformed algebras are also discussed.

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AnSU(2)⊗SU(2) Jaynes–Cummings model with a maximum energy level

Cited by 3 publications

References 50 publications

Quantum phase transition of two-level atoms interacting with a finite radiation field

Quantum phase transition of two-level atoms interacting with a finite radiation field

Pure Decoherence of the Jaynes–Cummings Model: Initial Entanglement with the Environment, Spin Oscillations and Detection of Non-Orthogonal States

Quantum phase transition of two-level atoms interacting with a finite radiation field

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