Suppression of the ac-Stark-shift scattering rate due to non-Markovian behavior

Abstract

The ac Stark shift in the presence of spontaneous decay is typically considered to induce an effective dephasing with a scattering rate equal to ${\mathrm{\ensuremath{\Gamma}}}_{s}{|\mathrm{\ensuremath{\Omega}}|}^{2}/{\mathrm{\ensuremath{\Delta}}}^{2}$, where ${\mathrm{\ensuremath{\Gamma}}}_{s}$ is the spontaneous decay rate, $\mathrm{\ensuremath{\Omega}}$ is the laser transition coupling, and $\mathrm{\ensuremath{\Delta}}$ is the detuning. We show that under realistic circumstances this dephasing rate may be strongly modified due to non-Markovian behavior. The non-Markovian behavior arises due to an effective modification of the light-atom coupling in the presence of the ac-Stark-shift laser. An analytical formula for the non-Markovian ac-Stark-shift-induced dephasing is derived. We obtain that for narrow laser linewidths the effective dephasing rate is suppressed by a factor of ${Q}^{2}$, where $Q$ is the quality factor of the laser.