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Quantum Optics Journal of the European Optical Society Part B

Interaction of two two-level atoms with two-photon transitions with a cavity radiation field

Igor Jex

Published Dec 1, 1990• 14 citations
Publisher

Abstract

Presents the interaction of two two-level atoms with two-photon transitions with a single mode of the quantized radiation field. Following the work of Iqbal J. Opt. Soc. Am B, vol.5, p.1312 (1987) and co-workers the exact solution of the field-atom dynamic in the rotating-wave approximation is found. Based on this solution the collapse-revival phenomenon in this model is studied in detail.

DOI
10.1088/0954-8998/2/6/003

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•Jan 1, 2004•0 citations
Presents the interaction of two two-level atoms with two-photon transitions with a single mode of the quantized radiation field. Following the work of Iqbal J. Opt. Soc. Am B, vol.5, p.1312 (1987) and co-workers the exact solution of the field-atom dynamic in the rotating-wave approximation is found. Based on this solution the collapse-revival phenomenon in this model is studied in detail.
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.
We investigate the atomic inversion dynamics when a multilevel atom interacts with a two-mode quantized radiation field in a Raman-type process. By utilizing the rotating-wave approximation and adiabatically eliminating all but two of the atomic levels, we derive a nonlinear-interaction Hamiltonian for this system. Working in the Schr\"odinger picture, we obtain numerical results that depend on the width and average photon number of the field statistics. Varying these photon statistics allows us to uncover secondary revivals that arise due to the complicated double sum over the two field modes that appear in the solutions. The origin of this phenomenon is described analytically.