Optical Spectra of a Two-Level Atom inside an Optical Parametric Oscillator

Perry Rice, Pranaw Rungta**, and Robert J. Brecha (U. Dayton)
Phys. Rev. A 62, 33802 (2000)

We calculate the transmitted and fluorescent spectra of a two-level atom inside an optical parametric oscillator. Sub-natural linewidths and vacuum-Rabi spliting are obtained

Since the generation of squeezed light has become possible, interest has turned to possible applications, and the effects of squeezed light on optical systems. Gardiner¹, and Carmichael, Lane, and Walls² have considered the effects of an atom which is immersed in squeezed light. It is found that the Lorentzian lineshape became a sum of two Lorentzians, one which narrowed as the amount of squeezing was increased, and another which broadened. It was recognized by these authors and others that it was impossible to squeeze all of the modes of the radiation field that the atom interacted with, and that an optical cavity would be needed. There have been a number of papers dealing with such a situation. Recently, Xiao and Jin3 proposed placing two-level atoms inside an optical parametric oscillator, as the light inside such a cavity is indeed squeezed. They obtained results for the transmitted spectrum which showed vacuum-Rabi splitting under conditions of strong atom-field coupling, and sub-natural linewidths, results similar to those of a single atom in a driven optical cavity4. The system considered by Xiao and Jin is also bistable.

The basic model that we consider in this paper is a single two-level atom inside an optical parametric oscillator. We calculate the optical spectrum, and spectrum of squeezing, of both the transmitted and fluorescent light. Results are presented for arbitrary cavity and atomic lifetimes in the limiting case of weak intracavity fields, i.e. on the lower branch. In addition, we explore the treatment of this problem in a formalism using a truncated basis state involving zero-, one- and two-photon states, obtaining results to lowest order in the intracavity field strength at the subharmonic frequency, which is resonant with the atom. It is found that for large atom-field coupling, a vacuum-Rabi splitting is observed, and that these peaks may be sub-natural under certain conditions. Non-Lorentzian behavior is discussed, and we also make comparisons to the many-atom results of Xiao and Jin, commenting on the coupled-oscillator model used there.