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Physical Review A

Dynamics of anM-level atom interacting with cavity fields: Effects of the level number on quantum collapse and revival

Fuli Li, D. L. Lin, Thomas F. George, Xiao-shen Li

Published Aug 1, 1989• 18 citations
Publisher

Abstract

A quantum-mechanical theory is developed to treat the interaction of a multilevel atom with cavity fields of arbitrary detunings. The Hilbert space spanned by the energy eigenvectors is divided into subspaces specified by eigenvalues of the total excitation number, which is a constant of motion. Since the total Hamiltonian does not connect states in different subspaces, it can be diagonalized in each subspace independently. The time evolutions of the level occupation probabilities and the mean photon number are investigated numerically, and their variations with the atomic level number and the initial photon number are discussed. Their relation with the field squeezing is also discussed.

DOI
10.1103/physreva.40.1394

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Modern Physics Letters B•Nov 10, 2008•6 citations
A quantum-mechanical theory is developed to treat the interaction of a multilevel atom with cavity fields of arbitrary detunings. The Hilbert space spanned by the energy eigenvectors is divided into subspaces specified by eigenvalues of the total excitation number, which is a constant of motion. Since the total Hamiltonian does not connect states in different subspaces, it can be diagonalized in each subspace independently. The time evolutions of the level occupation probabilities and the mean photon number are investigated numerically, and their variations with the atomic level number and the initial photon number are discussed. Their relation with the field squeezing is also discussed.
A model is presented to investigate the problem of interaction between an N-level atom and N-1 modes of the field. The model includes detuning. Constants of motion are obtained. The evolution operator is calculated, and the probability distribution function for the photon numbers is computed for different initial atomic states. The characteristic functions are computed. Different statistical quantities concerning the photons or the atomic system are given. The case of a three-level atom and two modes is considered for its different configurations. The phenomenon of collapses and revivals is discussed for squeezed light, and the effect of squeezing is shown in this phenomenon.
We assume that an N -level moving atom interacts with an ( N − 1) mode electromagnetic cavity field. The model includes the detuning and the intensity-dependent coupling. The constants of motion and the wave function for the atomic system is obtained. Some statistical aspects of the considered atomic system such as momentum increment and momentum diffusion have been calculated. The influence of the initial mean photon number, the detuning parameter and the intensity dependent coupling on the momentum increment are investigated when the atom is initially in excited state and the field is in a squeezed state. It is found that the momentum of the atom is unchanged for large initial mean photon number.
We study the interaction of a moving four-level atom with a single mode cavity field. Involving intensity dependent coupling, the atom-field wave function and the reduced density matrix of the field are obtained when the atom is initially prepared in a coherent superposition of the upper and ground states and the field is initially in a coherent state. The influence of the intensity dependent atom-field coupling and of the detuning on the collapse and revival phenomenon of the time evolution of statistical aspects, such as the mean photon number, the second-order correlation function of the field, the momentum increment and momentum diffusion, are investigated. It is found that, for the nonresonant case, the detuning between the field and the atom has a significant influence which leads to increasing the collapse time with decreasing amplitude. Numerical computations and discussion of the results are presented.
The atomic system on which we focus is a single four-level atom interacting with two-mode cavity fields. We obtain the wavefunction when the atom is initially in an excited state. The result presented in this context is employed to discuss the collapses–revivals phenomenon, the photon statistics and frequency sum squeezing phenomenon. The influence of the detuning on these phenomena are investigated for two four-level atomic systems. We found that the presence of the detuning leads to an increase of the collapse time while the amount of squeezing decreases. Also, the photon statistics is affected by the existence of the detuning parameters where the anti-bunching effect appears.