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Physical Review A

Nonresonant interaction of a three-level atom with cavity fields. I. General formalism and level occupation probabilities

Xiao-shen Li, D. L. Lin, Chang-De Gong

Published Dec 1, 1987• 71 citations
Publisher

Abstract

We present a general formalism of the theory of a three-level atom interacting with one-mode or two-mode cavity fields of arbitrary detunings. The dynamic behavior of the mean atomic level occupation probabilities are investigated numerically as functions of time and detuning parameters. A number of novel phenomena are discovered and discussed.

DOI
10.1103/physreva.36.5209

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We present a general formalism of the theory of a three-level atom interacting with one-mode or two-mode cavity fields of arbitrary detunings. The dynamic behavior of the mean atomic level occupation probabilities are investigated numerically as functions of time and detuning parameters. A number of novel phenomena are discovered and discussed.
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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.
In this paper, the problem of a three-level atom interacting with a single mode of the quantized electromagnetic cavity field is considered. The considered theoretical model describes the distinct configurations of a three-level atom. Also, this model includes a detuning and arbitrary forms of both the field and the intensity-dependent atom-field coupling. We obtain the general forms for both the constants of motion and the wavefunction when the atom is initially prepared in one of its states. We use this model for computing a number of statistical aspects of the three-level system. As an illustration, we use the model for studying the time evolution of the second-order correlation function when the atom is initially in an upper state and the field is considered in a coherent state.