Atomic two-photon excitation by an injected squeezed vacuum in a cavity

We study the two-photon excitation rate and the spectrum of a three-level atom in the Xi configuration interacting with a resonant cavity mode which is coupled to a broadband squeezed vacuum through its input-output mirror. We show that the optical Bloch equations in the cavity environment are formally identical to these in free space but, in the bad-cavity limit, with cavity-modified parameters describing the injected squeezed vacuum. It is shown that the two-photon excitation rate (which is proportional to the upper-level population) has two components, one depending linearly and the other quadratically on the squeezed photon number N, in excellent agreement with experiment [Georgiades et at, Phys. Rev. Lett. 75, 3426 (1995)]. The presence of the term quadratic in N is entirely due to the effectively imperfect correlation of the squeezed photon pairs in the bad cavity. We also find that the two-photon excitation spectrum (as measured by the fluorescent emission from the upper level to the intermediate level) exhibits an extremely narrow peak at Line center, under appropriate choices of the bad-cavity parameters. All these results are independent of the squeezed phase.