Dynamical Superalgebra of the "Dressed" Jaynes-Cummings Model

Buzano, Carla; Rasetti, Mario; Rastello, María Luisa

doi:10.1103/physrevlett.62.137

Cited by 64 publications

(44 citation statements)

References 9 publications

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“…In other hand, the supergroup theoretical approach to Jaynes-Cummings model has opened the way to relate the exact solvability of this model and representation theory of superalgebras. Indeed the Hamiltonian H JC is an element of the u(1/1) superalgebra [8]. In the absence of coupling (κ = 0) and for exact resonance (ω = ω 0 ), the u(1/1) dynamical superalgebra reduces to sl(1/1) one and the JC model coincides with the supersymmetric harmonic oscillator.…”

Section: Introductionmentioning

confidence: 99%

A GENERALIZED JAYNES–CUMMINGS MODEL: NONLINEAR DYNAMICAL SUPERALGEBRA u(1/1) AND SUPERCOHERENT STATES

Daoud

Douari

2003

Int. J. Mod. Phys. B

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The generalization of the Jaynes-Cummings (GJC) Model is proposed. In this model, the electromagnetic radiation is described by a Hamiltonian generalizing the harmonic oscillator to take into account some nonlinear effects which can occurs in the experimental situations. The dynamical superalgebra and supercoherent states of the related model are explicitly constructed. A relevant quantities (total number of particles, energy and atomic inversion) are computed.

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Section: Introductionmentioning

confidence: 99%

A GENERALIZED JAYNES–CUMMINGS MODEL: NONLINEAR DYNAMICAL SUPERALGEBRA u(1/1) AND SUPERCOHERENT STATES

Daoud

Douari

2003

Int. J. Mod. Phys. B

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“…Applications of the supersymmetric approach to the JC model, including representation theory of superalgebras, have opened large venues for the exact solvability of the model. In fact, as will be demonstrated here, the supersymmetric JC Hamiltonian is an element of the u(1/1) superalgebra [12]. Additionally, shape invariance studies of bound state problems for two-level systems also lead to generalized JC models [11].…”

Section: Introductionmentioning

confidence: 68%

“…It is the lowest in a special superalgebra hierarchy [14]. Moreover, it is isomorphic to u(1/1) Lie superalgebra [12]. Most of earlier work on the analytic solutions of the two-level JC model was limited to the underlying symmetries associated with N = 2 supersymmetry, su (2) or su (1,1) symmetry.…”

Section: Introductionmentioning

confidence: 99%

The supersymmetric Jaynes–Cummings model and its solutions

Alhaidari¹

2006

J. Phys. A: Math. Gen.

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The super-algebraic structure of a generalized version of the Jaynes-Cummings model is investigated. We find that a Z 2 graded extension of the so(2,1) Lie algebra is the underlying symmetry of this model. It is isomorphic to the four-dimensional superalgebra u(1/1) with two odd and two even elements. Differential matrix operators are taken as realization of the elements of the superalgebra to which the model Hamiltonian belongs. Several examples with various choices of superpotentials are presented. The energy spectrum and corresponding wavefunctions are obtained analytically.

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“…Thus, the approach taken in this paper in relating JC model to supersymmetry is different from that of Ref. [32]. Our approach is similar to that of Ref.…”

Section: Jcth From Supersymmetry: General Formulationmentioning

confidence: 97%

“…Hamiltonian is known as "dressed" JC Hamiltonian in the literature [30,32]. Note that a non-hermitian version of the "dressed" JC model is included in the HamiltonianH.…”

Section: B Non-hermitian Non-resonant Jc Model and Other Generalizationsmentioning

confidence: 99%

Exactly solvable non-Hermitian Jaynes–Cummings-type Hamiltonian admitting entirely real spectra from supersymmetry

Ghosh¹

2005

J. Phys. A: Math. Gen.

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It is shown that for a given hermitian Hamiltonian possessing supersymmetry, there is always a non-hermitian Jaynes-Cummings-type Hamiltonian(JCTH) admitting entirely real spectra. The parent supersymmetric Hamiltonian and the corresponding non-hermitian JCTH are simultaneously diagonalizable. The exact eigenstates of these non-hermitian Hamiltonians are constructed algebraically for certain shape-invariant potentials, including a non-hermitian version of the standard Jaynes-Cummings(JC) model for which the parent supersymmetric Hamiltonian is the superoscillator. It is also shown that a non-hermitian version of the several physically motivated generalizations of the JC model admits entirely real spectra. The positive-definite metric operator in the Hilbert space is constructed explicitly along with the introduction of a new inner product structure, so that the eigenstates form a complete set of orthonormal vectors and the time-evolution is unitary.

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Dynamical Superalgebra of the "Dressed" Jaynes-Cummings Model

Cited by 64 publications

References 9 publications

A GENERALIZED JAYNES–CUMMINGS MODEL: NONLINEAR DYNAMICAL SUPERALGEBRA u(1/1) AND SUPERCOHERENT STATES

A GENERALIZED JAYNES–CUMMINGS MODEL: NONLINEAR DYNAMICAL SUPERALGEBRA u(1/1) AND SUPERCOHERENT STATES

The supersymmetric Jaynes–Cummings model and its solutions

Exactly solvable non-Hermitian Jaynes–Cummings-type Hamiltonian admitting entirely real spectra from supersymmetry

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