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Quantum Optics Journal of the European Optical Society Part B

Phase properties of the field interacting with a three-level atom. II. Two-mode case

Ho Trung Dung, R. Tanaś, A.S. Shumovsky

Published Oct 1, 1991• 7 citations
Publisher

Abstract

For pt.1, see ibid., p.241, 1991. The authors consider phase properties of the field in the two-mode three-level problem. Phase properties of each individual mode as well as their joint probability distribution and correlation function are studied. They find that phase properties of the field reflect the collapses and revivals of the level occupation probabilities in most situations. However, there exist exceptions, for example, in the case of Raman scattering, which allows them to conclude that the collapses and revivals of the atomic population can be completely decorrelated from the phase of the field. This takes place when the field mode is fed by the photons emitted spontaneously from a real atomic level, which affects the field occupation numbers but not its phase.

DOI
10.1088/0954-8998/3/5/002

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For pt.1, see ibid., p.241, 1991. The authors consider phase properties of the field in the two-mode three-level problem. Phase properties of each individual mode as well as their joint probability distribution and correlation function are studied. They find that phase properties of the field reflect the collapses and revivals of the level occupation probabilities in most situations. However, there exist exceptions, for example, in the case of Raman scattering, which allows them to conclude that the collapses and revivals of the atomic population can be completely decorrelated from the phase of the field. This takes place when the field mode is fed by the photons emitted spontaneously from a real atomic level, which affects the field occupation numbers but not its phase.
Single-photon J-C model (or two-level J-C model) composed of a two-level atom and single-mode field has been studied for many years. Recently, this model was expanded into two–photon J–C model (or three-level J–C model) composed of a three-level atom and single-mode field, which has the potential to produce antibunched field[1] and even squeezed field. A main property of the J-C model is the collapse and revival phenomenon, which has experimentally in single-photon J-C model been proved[2] last year. In the collapse period, average photon number and atomic populations keep constant, as if no interaction between the atom and field exists. We would like to ask if other properties of the field change little in the collapse period and there is really no interaction.
This paper presents some results on aspects of the two-level atom interacting with a single-mode with the privileged field mode being in the squeezed displaced Fock state (SDFS). The exact results are employed to perform a careful investigation of the temporal evolution of the atomic inversion, entropy and phase distribution. It is shown that the interference between component states leads to non-classical oscillations in the photon number distribution. At the revival time the field is again in the pure state. We have briefly discussed the collapses and revivals of the atomic inversion by studing the evolution of the Q function of the cavity field. We also established the connection between the field entropy and the collapses and revivals of the atomic inversion. We find that the phase probability distribution of the field reflects the collapses and revivals of the level occupation probabilities in most situations. The interaction brings about the symmetrical splitting of the phase probability distribution. The general conclusions reached are illustrated by numerical results.