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Journal of Physics C Solid State Physics

Optical transitions between vibronic states

P. Schwendimann, E. Sigmund

Published Oct 30, 1986• 3 citations
Publisher

Abstract

For an infinite set of initial conditions exact solutions of generalised Rabi equations describing specific optical transitions in a vibronic system are found in the rotating-wave approximation. The influence of the choice for the initial state and the dependence of the solutions on the electron-phonon and the electron-electromagnetic-field coupling strengths as well as on the energies of the coupled subsystems is discussed.

DOI
10.1088/0022-3719/19/30/009

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For an infinite set of initial conditions exact solutions of generalised Rabi equations describing specific optical transitions in a vibronic system are found in the rotating-wave approximation. The influence of the choice for the initial state and the dependence of the solutions on the electron-phonon and the electron-electromagnetic-field coupling strengths as well as on the energies of the coupled subsystems is discussed.
One of the simplest models involving the atom-field interaction is the coupling of a single two-level atom with single-mode optical field. Under the rotating wave approximation, this problem is reduced to a form that can be solved exactly. But the approximation is only valid when the two levels are resonant or nearly resonant with the applied electromagnetic radiation. Here we present an analytical solution without the rotating wave approximation and applicable to general atom-field interaction far away from the resonance. We find that there exists remarkable influence of the initial phase of optical field on the Rabi oscillations and Rabi splitting, and this issue cannot be explored in the context of the rotating wave approximation. Due to the retention of the counter-rotating terms, higher-order harmonic appears during the Rabi splitting. The analytical solution suggests a way to regulate and control the quantum dynamics of a two-level atom and allows for exploring more essential features of the atom-field interaction.
We propose a general perturbative approach to quantum-optical models without the rotating-wave approximation. We show that a generic Hamiltonian describing interaction between two subsystems can be represented as a series of operators corresponding to different transitions between bare energy levels of the whole system. Under certain relations between frequencies of interacting subsystems one of these transitions becomes resonant. The rotating-wave approximation leads to separation of the resonant transition and to appearance of the integral of motion, which makes the problem exactly solvable in this approximation. (Different resonance conditions lead to different integrals of motion.) All of the other terms in these expansion can be considered as a perturbation. They result in dynamic Stark shifts and small corrections to the integrals of motion. All possible resonances are classified, and approximate integrals of motion are found for each resonance. Examples of field-field, field-atom, and atom-atom interactions are considered.