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

The ac Stark shift in the presence of spontaneous decay is typically considered to induce an effective dephasing with a scattering rate equal to $ \Gamma_s |\Omega|^2/\Delta^2 $, where $ \Gamma_s $ is the spontaneous decay rate, $ \Omega $ is the laser transition coupling, and $ \Delta $ is the detuning. We show that under realistic circumstances this dephasing rate may be strongly modifed 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.