Absorption spectrum of an atom strongly coupled to a high-temperature reservoir

Abstract

We study the absorption spectrum of a weak probe field near resonant to an atomic transition, the upper level of which is strongly coupled to a third level by the interaction with a Lorentzian bosonic reservoir, such as, e.g., a mode of a high-$Q$ cavity or a local vibration in a solid. The reservoir coupling is approximated by the interaction with a classical complex Gaussian-Markovian random process (control field), which is justified when the reservoir temperature exceeds significantly the mode frequency or when the high-$Q$ cavity is pumped by broadband incoherent radiation. The present theory is applicable also when the control field is chaotic laser light. We assume that the rms control-field Rabi frequency ${V}_{0}$ is much greater than the field detuning ${\ensuremath{\Delta}}_{c}$, which, in turn, is much greater than the material relaxation constants. We reveal and describe analytically all qualitatively different regimes of the spectrum modification and obtain their validity conditions. The analytical results are verified by numerical calculations using the exact continued-fraction solution. The analytical formulas obtained allow one to perform fast computer calculations for arbitrarily small values of the reservoir (control-field) bandwidth $\ensuremath{\nu}$, in contrast to the known numerical methods, which require sharply increasing computational resources with a decrease of $\ensuremath{\nu}$. In the most interesting case $\ensuremath{\nu}⪡{V}_{0}$, the spectrum consists of two peaks, the nonvanishing bandwidth and material relaxation affecting mainly the dip between the peaks. The results obtained in the static limit (i.e., a very narrow reservoir) are independent of the reservoir band shape. We reveal reservoir-induced transparency (RIT)---i.e., absorption reduction due to the reservoir coupling. Moreover, two unexpected, remarkable features are uncovered in a range of intermediate values of $\ensuremath{\nu}$ and ${V}_{0}$, ${\ensuremath{\Gamma}}^{2}\ensuremath{\mid}{\ensuremath{\Delta}}_{c}\ensuremath{\mid}⪡{V}_{0}^{2}\ensuremath{\nu}⪡{\ensuremath{\mid}{\ensuremath{\Delta}}_{c}\ensuremath{\mid}}^{3}$ ($\ensuremath{\Gamma}$ is the spectral width in the absence of the control field): an extra peak in the dip and a resonance-absorption decrease by a half (i.e., an increase of RIT) relative to the static limit. The existence of the above spectral features depends on the statistical details of the control-field temporal behavior.