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Quantum Optics Journal of the European Optical Society Part B

Q-function for the Jaynes-Cummings model with an additional Kerr medium

M J Werner, H. Risken

Published Jun 1, 1991• 38 citations
Publisher

Abstract

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.

DOI
10.1088/0954-8998/3/3/005

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Arab Journal of Basic and Applied Sciences•Jan 1, 2009•0 citations
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.
A cavity-damped Jaynes-Cummings model with a Kerr-like medium filling the cavity is investigated in the rotating-wave approximation. We introduce six operators with respect to the light field whose equations of motion are transformed to six coupled partial differential equations using the s-parametrized quasiprobability distributions of Cahill and Glauber [Phys. Rev. 177, 1882 (1969)]. Equations of motion for expansion coefficients of the distribution functions are solved by a Runge-Kutta procedure for vector tridiagonal relations. Starting with an initial coherent state for the cavity field and the atom in its upper state, we find that revivals of the atomic inversion are more pronounced for a given damping constant compared to the case of no Kerr medium. Also, quadrature squeezing is less affected by weak cavity damping and thermal noise compared to the standard Jaynes-Cummings model. The effect of damping on interesting non-Gaussian structures is also discussed.
he effect of the counter-rotating terms in the Jaynes-Cummings model is investigated with an extended coherent-state approach. The counter-rotating terms greatly modify the vacuum Rabi splitting. Two peaks with different heights in the weak coupling regime and more than two peaks in the intermediate coupling regime are predicted. The collapses and revivals in the evolution of the atomic population inversion disappear in the intermediate coupling regime, but reappear in the strong coupling regime. This reappearance is similar to that under the rotating-wave approximation, attributed to the summation of periodic cosine functions of the evolution.
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.
We study the interaction of a four level-atom with a single mode in a cavity, involving intensity dependent coupling with additional a kirr-like medium. The wave function is obtained when the atom is initially in superposition of its upper and ground states and the field in coherent state. We evaluate the Mandel Q parameter, phase probability distribution and the field entropy. The influence of the Kerr medium, the detuning and the presence of the intensity dependent coupling on their evolution was discussed.