Time factorization of the higher-order intensity correlation functions in the theory of resonance fluorescence

Abstract

The intensity correlation functions $\mathrm{Tr}\left\{\rho \mathrm{}\right(0\left)\mathrm{}{s}^{+}\mathrm{}\right(t\left)\mathrm{}{s}^{+}\right(t+{\tau }_1\left)\cdots s^{+}\right(t+{\Sigma }_{i=1\mathrm{}}^n{\tau }_i\left)s^{-}\right(t+{\Sigma }_{i=1\mathrm{}}^n{\tau }_i\left)\cdots s^{-}\right(t+{\tau }_1\left)s^{-}\mathrm{}\right(t\left)\right\}$ associated with a two-level atom undergoing Markovian dynamics [$s^{\pm }\mathrm{}\left(t\right)\mathrm{}$ being the spin-½ operators for the atom] are shown to factorize in the form $f\left(t\right)\mathrm{}{\Pi }_{i=1\mathrm{}}^{n}g\left({\tau }_i\right)$ with $f\left(t\right)\mathrm{}$ [$g\left(t\right)\mathrm{}$] giving the probability of finding the atom in the excited state when initially it is in the state $\rho \mathrm{}\left(0\right)\mathrm{}$ [ground state].