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The dynamical properties in the nonlinear Jaynes-Cummings model

YX Huang, Y Wang, Zhan Zhan

Published Oct 1, 2002• 0 citations
OpenAlex

Abstract

The properties of state evolution of the atom, field, and atom-field systems in the intensity-dependent coupling Jaynes-Cummings Model with an additional Kerr medium are investigated by using the distance between density operators. The effects of nonlinearity interaction of Kerr medium and the average photon number of initial coherent field on the dynamical behaviour of the quantum system are discussed in comparison with the one-photon Jaynes-Cummings model with an additional Kerr medium.

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The properties of state evolution of the atom, field, and atom-field systems in the intensity-dependent coupling Jaynes-Cummings Model with an additional Kerr medium are investigated by using the distance between density operators. The effects of nonlinearity interaction of Kerr medium and the average photon number of initial coherent field on the dynamical behaviour of the quantum system are discussed in comparison with the one-photon Jaynes-Cummings model with an additional Kerr medium.
The atom-field entanglement properties in the intensity-dependent coupling Jaynes-Cummings model with an additional Kerr medium are investigated by using negative eigenvalues ofthe partial transposition matrix of the density matrix.The influences of Kerr medium and initial fieldon atom-field entanglement degree are discussed.The results show that the time evolution of atom-field entanglement degree has the periodicity,for different preparations.The period depends on thestrengthes of the field-atom coupling and field-medium interaction,with the increase of thestrengthes,the period becomes smaller.The initial state of the field plays an important role in the atom-field entanglement degree.
Dynamics of entanglement due to intensity-dependent interaction between a two-level atom and a single-mode electromagnetic field in a Kerr medium is studied. The form of the interaction is such that the Hamiltonian evolution is exactly solvable. The Hamiltonian is shown to be a deformed Jaynes-Cummings model admitting a closed, symmetric algebra. Dynamics of population inversion and atom-field entanglement are studied taking the initial state of the field to be either a coherent state or a squeezed vacuum. Analysis is extended to the case of a two-mode cavity field interacting with a two-level atom. For the two-mode case, the initial field is a pair coherent state or a two-mode squeezed vacuum. Effects due to nonlinearity, intensity-dependent interaction and detuning on the dynamics are discussed and compared with those of the single-mode case.
A generalization of the time-dependent Jaynes–Cummings Hamiltonian is considered including nonlinear terms in the field and/or an intensity-dependent coupling term. Using algebraic methods we find the corresponding time evolution operator of the problem as a product of exponential operators. Also, we study the effect of the atomic motion in the cavity on its quantum state. We found that, when the atom is vibrating classically with a small amplitude A0 (in comparison with the effective length of the cavity L), i.e. A0 ≪ L, the effects of the atom’s motion are negligible but when A0 ∼ L/4, the state of the atom changes drastically. Our study is devoted to a Jaynes–Cummings Hamiltonian with an additional Kerr medium.
In this paper a two-photon Jaynes-Cummings model interacting with a Kerr-like medium is studied. It is assumed that the electromagnetic field is in different states such as coherent, squeezed vacuum and pair coherent, and that the atom is initially in the excited state. The temporal evolution of the population of the excited level, and the second-order coherence function are studied. The results obtained show that this system has some similarities with the two-mode Stark system. Two photon entanglement are analysed at different initial conditions.