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Physical Review A

Effects of the relative coupling constants on the dynamic properties of a two-atom system

Song Tong-Qiang, Jian Feng, Wenzheng Wang, Jing-zhi Xu

Published Mar 1, 1995• 21 citations
Publisher

Abstract

The collapse-revival phenomenon of Rabi oscillations and the pure-state evolutions of the atomic as well as the field states in the Raman interaction of a pair of effective two-level atoms with a single-mode quantized radiation field are studied with an analytic method. The effects of the relative values of the two-atom--field coupling constants on them are also analyzed.

DOI
10.1103/physreva.51.2648

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The collapse-revival phenomenon of Rabi oscillations and the pure-state evolutions of the atomic as well as the field states in the Raman interaction of a pair of effective two-level atoms with a single-mode quantized radiation field are studied with an analytic method. The effects of the relative values of the two-atom--field coupling constants on them are also analyzed.
In the preceding chapters concerning the interaction of a radiation field with matter, we assumed the field to be classical. In many situations this assumption is valid. There are, however, many instances where a classical field fails to explain experimentally observed results and a quantized description of the field is required. This is, for example, true of spontaneous emission in an atomic system which was described phenomenologically in Chapter 5. For a rigorous treatment of the atomic level decay in free space, we need to consider the interaction of the atom with the vacuum modes of the universe. Even in the simplest system involving the interaction of a single-mode radiation field with a single two-level atom, the predictions for the dynamics of the atom are quite different in the semiclassical theory and the fully quantum theory. In the absence of the decay process, the semiclassical theory predicts Rabi oscillations for the atomic inversion whereas the quantum theory predicts certain collapse and revival phenomena due to the quantum aspects of the field. These interesting quantum field theoretical predictions have been experimentally verified. In this chapter we discuss the interaction of the quantized radiation field with the two-level atomic system described by a Hamiltonian in the dipole and the rotating-wave approximations. For a single-mode field it reduces to a particularly simple form. This is a very interesting Hamiltonian in quantum optics for several reasons. First, it can be solved exactly for arbitrary coupling constants and exhibits some true quantum dynamical effects such as collapse followed by periodic revivals of the atomic inversion.
The two-photon absorption process is studied by considering the interaction of a quantized single-mode field with an effective two-level atom through intermediate states. The equations of motion of the coupled atom–field probability amplitudes for the effective two-level atom are obtained after adiabatically eliminating the intermediate states. These equations are then solved in the rotating-wave approximation. The time constants associated with the Rabi oscillation, collapse, and revival of the atomic inversion are derived, and the photon statistics are discussed with special reference to photon antibunching.
The Raman interaction of a pair of two-level atoms with the radiation field is studied. The emission spectra for two interacting processes are calculated in which either two atoms couple to the field with different constants or with the same constant but at the same time the dipole-dipole interaction between two atoms being included in the consideration. The effect of the relative value of two atom-field coupling constants and also that of atomic dipole-dipo-le interaction on the emission spectra are analyzed.