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 $Γ_s |Ω|^2/Δ^2$, where $Γ_s$ is the spontaneous decay rate, $Ω$ is the laser transition coupling, and $Δ$ 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.

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