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

Abstract

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