Strong interaction between a two-level atom and the whispering-gallery modes of a dielectric microsphere: Quantum-mechanical consideration

The interaction is considered between a two-level atom and the continuum of electric field modes falling within the profile of one of the resonance modes of a dielectric microsphere (a whispering gallery mode). Subject to minimal assumptions, simple equations are obtained on first principles, which describe the spectral properties of the one-photon continuum and the relaxation processes occurring therein. If the initial state of the atom is excited, a doublet structure is formed in the emitted photon spectrum, provided that the interaction is strong enough. If it is the microsphere that is excited at the initial instant, the excited photon spectrum depends substantially on the excitation method used. When excitation is optimal, the atom is effectively excited, and a Rabi-doublet is then formed in the fluorescence spectrum. When the excitation conditions are other than optimal, the spectrum becomes of triplet character, and when the deviation from the optimal excitation conditions is strong enough, the atom practically fails to get excited, and the fluorescence spectrum is of singlet type. A considerable part of the results obtained is of a general nature and can easily be applied to other cases of strong interaction between atoms and resonators.