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Journal of the Optical Society of America B

Interaction of two two-level atoms with a single-mode quantized radiation field

M. S. Iqbal, S. Mahmood, M. S. K. Razmi, Muhammad Suhail Zubairy

Published Jun 1, 1988• 55 citations
Publisher

Abstract

Interactions of two two-level atoms with a single-mode quantized radiation field are studied, and exact expressions for the atom-field probability amplitudes in the rotating-wave approximation are presented. These solutions are employed in the study of the quantum collapse and revivals of the atomic coherence.
DOI
10.1364/josab.5.001312

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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.
An exact solution for the problem of two two-level atoms interacting with a single-mode detuned quantized radiation field is presented. On resonance, an asymptotic result is derived for large coherent initial fields. It is shown that when the atoms are initially prepared in one of the semiclassical eigenstates, the atom-plus-field wavefunction remains almost factored into an atomic and a field part throughout the interaction. Under certain conditions, the atomic part evolves into a unique pure state at half-revival time. The effects of the cavity detuning on the dynamics of the atomic level occupation probabilities and emission spectra are studied. It is found, for non-symmetrical excitation, that far off-resonance the field acts like a virtual level by means of which the energy is transferred between the atoms. Due to non-zero detuning, nine-peaked spectra are observed and are given a clear explanation from the dressed-state viewpoint. It is established that in the case of symmetrical excitation, the intensity of the emission spectrum is two times larger than that in the case of non-symmetrical excitation.