Fluorescence and absorption by a two-level atom in a bichromatic field with one strong and one weak component

Abstract

We analyze the fluorescence and absorption spectra of a two-level atom driven by a bichromatic field with frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$, separated by ${\mathrm{\ensuremath{\omega}}}_{2}$-${\mathrm{\ensuremath{\omega}}}_{1}$=2\ensuremath{\delta}, and Rabi frequencies (at resonance) 2${\mathrm{\ensuremath{\Omega}}}_{1}$ and 2${\mathrm{\ensuremath{\Omega}}}_{2}$ such that their ratio \ensuremath{\alpha}=${\mathrm{\ensuremath{\Omega}}}_{2}$/${\mathrm{\ensuremath{\Omega}}}_{1}$1. We focus on the case of ${\mathrm{\ensuremath{\omega}}}_{1}$ close to the atomic frequency ${\mathrm{\ensuremath{\omega}}}_{0}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$ near the Rabi sideband frequency ${\mathrm{\ensuremath{\omega}}}_{1}$+2${\mathrm{\ensuremath{\Omega}}}_{1}$; the detunings are denoted by ${\mathrm{\ensuremath{\Delta}}}_{1}$=${\mathrm{\ensuremath{\omega}}}_{0}$-${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\Delta}}}_{2}$=${\mathrm{\ensuremath{\omega}}}_{1}$+2${\mathrm{\ensuremath{\Omega}}}_{1}$-${\mathrm{\ensuremath{\omega}}}_{2}$. We find that the spectra depend critically on the detuning ${\mathrm{\ensuremath{\Delta}}}_{2}$: For large ${\mathrm{\ensuremath{\Delta}}}_{2}$, the fluorescence spectrum consists of the well known Mollow triplet, centered at ${\mathrm{\ensuremath{\omega}}}_{1}$; for smaller (but nonzero) ${\mathrm{\ensuremath{\Delta}}}_{2}$, the spectrum is composed of a triplet at ${\mathrm{\ensuremath{\omega}}}_{1}$ together with doublets near the sideband frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$\ifmmode\pm\else\textpm\fi{}2${\mathrm{\ensuremath{\Omega}}}_{1}$. However, when ${\mathrm{\ensuremath{\Delta}}}_{2}$=0 (and \ensuremath{\alpha}\ensuremath{\ll}1), the spectrum consists of a doublet centered at ${\mathrm{\ensuremath{\omega}}}_{1}$ and triplets at ${\mathrm{\ensuremath{\omega}}}_{1}$\ifmmode\pm\else\textpm\fi{}2${\mathrm{\ensuremath{\Omega}}}_{1}$: there is then no fluorescence at ${\mathrm{\ensuremath{\omega}}}_{1}$. As \ensuremath{\alpha} increases, additional triplet structures appear in the spectrum at frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$\ifmmode\pm\else\textpm\fi{}2n${\mathrm{\ensuremath{\Omega}}}_{1}$ with intensities proportional to ${\mathrm{\ensuremath{\alpha}}}^{2(\mathit{n}\mathrm{\ensuremath{-}}1)}$, n\ensuremath{\gtrsim}1, and a line reappears at ${\mathrm{\ensuremath{\omega}}}_{1}$, with intensity proportional to ${\mathrm{\ensuremath{\alpha}}}^{4}$. The absorption by the system of a weak probe beam is also strongly dependent on the detuning, and the spectrum is composed of emission-dispersion-absorption features located near ${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{1}$\ifmmode\pm\else\textpm\fi{}2n${\mathrm{\ensuremath{\Omega}}}_{1}$. An analysis in the dressed-atom picture is presented which explains the physical origin of all these features, in both fluorescence and absorption. \textcopyright{} 1996 The American Physical Society.