Nonlinearity and temperature dependence of drive-induced shifts in a thermal environment

Drive-induced shifts, such as ac Stark shift and Bloch-Siegert shift, are routinely used in various

spectroscopies. These shifts are experimentally known to show dispersive Lorentzian behavior as a function

of its characteristic frequencies in optical pumping experiments. However, the drive-induced Stark shifts,

as calculated using Floquet or dressed atom approaches, does not show the above nonlinear behavior. To this

end, we theoretically investigated the drive-induced shifts using a previously reported

fluctuation-regulated quantum master equation [A. Chakrabarti and R. Bhattacharyya, Phys. Rev. A 97, 063837

(2018)]. The shifts are obtained as closed-form expressions over the entire detuning range of the drive. The

predicted shifts match satisfactorily with the known experimental data of the light shifts. We shall show that the

calculated shifts are Kramers-Kronig pair of the drive-induced dissipation in conformity with experimental

findings. Moreover, we also show that at low temperatures, i.e., for less thermal fluctuations, our results

asymptotically match with the known theoretical form of the shifts. In the high-temperature regime, we

predict that the shifts decrease in magnitude and are inversely proportional to the square of the

temperature.