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arXiv:1302.0588

Jaynes-Cummings model in a finite Kerr medium

A. Martín Ruiz, Alejandro Frank, Luis F. Urrutia

Published Feb 4, 2013• 0 citations
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Abstract

We introduce a spin model which exhibits the main properties of a Kerr medium to describe an intensity dependent coupling between a two-level atom and the radiation field. We select a unitary irreducible representation of the su(2) Lie algebra such that the number of excitations of the field is bounded from above. We analyze the behavior of both the atomic and the field quantum properties and its dependence on the maximal number of excitations.

DOI
10.48550/arxiv.1302.0588

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We introduce a spin model which exhibits the main properties of a Kerr medium to describe an intensity dependent coupling between a two-level atom and the radiation field. We select a unitary irreducible representation of the su(2) Lie algebra such that the number of excitations of the field is bounded from above. We analyze the behavior of both the atomic and the field quantum properties and its dependence on the maximal number of excitations.
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The system under consideration consists of a two-level atom coupled an optical field in k-photon Jaynes-Cummings model with a Kerr medium.The time evolution of field entropy squeezing and population inversion of the atom for three and four-photon transitions was discussed.The influence of Kerr medium on field entropy squeezing and population inversion of the atom was also analyzed.The results show that the field entropy squeezing and population inversion of the atom are sensitive to effect of Kerr medium.
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.
The dynamics of the Q-function for a two-level system coupled to one-cavity mode (Jaynes-Cummings model) in the presence of a Kerr-like medium is investigated. Starting the field mode in a coherent state and the atom in its upper state, the Q-function splits into distinct distribution functions as in the case of the Jaynes-Cummings model. In addition to this splitting the Kerr medium introduces an additional rotation and broadening of the counter-rotating contributions to the Q-function. It is further shown that the discrete superpositions of coherent states produced by the Kerr medium split into additional peaks is due to atomic coupling.