Four-level atom dynamics and emission statistics using a quantum jump approach

Abstract

Four-level atom dynamics is studied in a ladder system in the nine parameter space consisting of driving field strengths, detunings and decay constants, ${{\ensuremath{\Omega}}_{1},{\ensuremath{\Omega}}_{2},{\ensuremath{\Omega}}_{3},{\ensuremath{\Delta}}_{1},{\ensuremath{\Delta}}_{2},{\ensuremath{\Delta}}_{3},{\ensuremath{\Gamma}}_{2},{\ensuremath{\Gamma}}_{3},{\ensuremath{\Gamma}}_{4}}$. One can selectively excite or induce two-level behavior between particular levels of ones choice by appropriately tuning the driving field strengths at three-photon resonance. The dynamics may be classified into two main regions of interest (i) small ${\ensuremath{\Omega}}_{2}$ coupling the \ensuremath{\mid}2⟩-\ensuremath{\mid}3⟩ transition and (ii) large ${\ensuremath{\Omega}}_{2}$. In case (i) one sees two-level behavior consisting of adjacent levels and in a particular region in the parameter space, there is an intermittent shelving of the electrons in one of the two subsystems. In case (ii) the levels consist of the ground state and the upper most level. Emission statistics is studied using the delay function approach in both the cases. In case (i), the behavior of the second order correlation function ${g}^{2}(t)$, is similar to that of two-level emission for low ${\ensuremath{\Omega}}_{1}$ coupling the \ensuremath{\mid}1⟩-\ensuremath{\mid}2⟩ transition, and the correlation increases with ${\ensuremath{\Omega}}_{1}$ for smaller time delays. While, in case (ii) when, in addition, ${\ensuremath{\Omega}}_{3}$ coupling the \ensuremath{\mid}3⟩-\ensuremath{\mid}4⟩ transitionis kept low, ${g}^{2}(t)$ shows superpoissonian distribution, which may be attributed to three-photon processes.