Absorption And Dispersion Of A Single Atom In A Driven Cavity

The dispersion and absorption are a pair of fundamental properties of optical medium. Ordinary optical medium contains macroscopic quantity of atoms. Because of the average effect, semiclassical theory of light-matter interaction is accurate. However, for the system of a single atom inside a driven cavity, semiclassical theory is invalid. Light-matter interaction is in two limits: the limit in which the matter is reduced to a single atomic transition and the limit in which the single photon saturates the atom. The quantum correlations between the atom and the cavity field are no longer neglectable, therefor, both the atom and the cavity must be treated quantum mechanically.Firstly, we consider the mode of a single atom damped by normal vacuum in a resonantly driven cavity, we examine the absorption and dispersion of the atom to the weak probe field by using the exact numerical method without any approximation except for an appropriate truncation. It is shown that the spectrum exhibits the well-known Mollow structure for the strong driving and the weak coupling, and the well resolved two-peaked structure for the weak driving and the strong coupling. In particular, the broad one-, two- and tree-peaked structures have been predicted for the intermediate driving and coupling. The physical reason for above different lineshapes is explained in terms of dressed states.Secondly, we consider the mode of a single atom damped by squeezed vacuum in a resonantly driven cavity. We address the problem in the bad cavity limit. Analytical expressions for the absorption spectra are obtained by using the adiabatic approximation and Fokker-Plank equation method. When the driving is in the weak field limit, only the squeezing parameter has effect on the response of the atom to the probe. The squeezed vacuum narrow and depress the absorption peak. While when the driving is strong, the lineshapes of the spectra depend both on the squeezing parameter and on the relative phase between the driving field and the squeezed vacuum. Lastly we examine the absorption and dispersion spectra in a cavity with arbitrary loss rate by using numerical method.