Ac Stark shift of a two-photon transition induced by a model stochastic field

Abstract

We have investigated the ac Stark shift of a two-photon transition induced by a model stochastic field by using a Monte Carlo technique. The model field has a stochastic single mode, which can possess both colored amplitude and colored frequency fluctuations. The stochastic field’s modification of the ac Stark shift is quantified by a parameter M, which is the ratio of the Stark shift in the model stochastic field to the Stark shift that would be obtained in a phase-diffusion field of equivalent linewidth (i.e., a field with frequency fluctuations but no amplitude fluctuations). In the regime of weak fields, below saturation of the bound-bound transition, we find that M is greater than unity: the Stark shift is enhanced by the stochastic field. Moreover, in this regime M is an increasing function of the field’s degree of photon bunching. In strong fields, where the bound–bound transition is nearly saturated, the enhancement of the Stark shift is diminished, so much so that in extremely strong fields M is actually less than unity. Our calculations indicate that the ac Stark shift’s modification occurs through two distinct processes, depending on the strength of the field. In weak fields enhancement of a multiphoton transition’s Stark shift is influenced primarily by the intrinsic correlation between ac-Stark-shift fluctuations and Rabi-frequency fluctuations. In strong fields the fluctuating Stark shifts give rise to an asymmetric resonance line shape in a fashion analogous to inhomogeneous broadening. The line shape’s peak position then has a sublinear dependence on the stochastic field’s intensity, and this yields a diminished value of M.