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Physical Review A

Comment on “Resonance-fluorescence and absorption spectra of a two-level atom driven by a strong bichromatic field”

David L. Aronstein, Ryan S. Bennink, Robert W. Boyd, Carlos R. Stroud

Published Jun 17, 2002• 22 citations
Publisher

Abstract

We identify discrepancies between two published predictions of the resonance fluorescence from a two-level atom driven by a strong bichromatic field [J. Opt. Soc. Am. B $8,$ 1163 (1991) and Phys. Rev. A $48,$ 3092 (1993)]. These discrepancies are shown to arise from subtleties in extracting the time-averaged resonance fluorescence from the expansions used to solve the optical Bloch equations. We construct a solution to these equations that corrects the results of the latter reference and reconciles the two predictions.

DOI
10.1103/physreva.65.067401

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We identify discrepancies between two published predictions of the resonance fluorescence from a two-level atom driven by a strong bichromatic field [J. Opt. Soc. Am. B 8,8,8, 1163 (1991) and Phys. Rev. A 48,48,48, 3092 (1993)]. These discrepancies are shown to arise from subtleties in extracting the time-averaged resonance fluorescence from the expansions used to solve the optical Bloch equations. We construct a solution to these equations that corrects the results of the latter reference and reconciles the two predictions.
We examine the radiative properties of a two-level atom driven by a strong bichromatic field with frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$=${\mathrm{\ensuremath{\omega}}}_{0}$-${\mathrm{\ensuremath{\delta}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$=${\mathrm{\ensuremath{\omega}}}_{0}$+${\mathrm{\ensuremath{\delta}}}_{2}$, which can be asymmetrically placed about the atomic transition frequency ${\mathrm{\ensuremath{\omega}}}_{0}$ and can have different Rabi frequencies ${\mathrm{\ensuremath{\Omega}}}_{1}$ and ${\mathrm{\ensuremath{\Omega}}}_{2}$. Applying the optical Bloch equations for the bichromatic excitation, we derive an infinite set of equations of motion for the time evolution of the atomic variables. The equations are solved numerically by matrix inversion and Laplace transforms. Using the quantum regression theorem, we then solve for the steady-state total fluorescence intensity, and the resonance-fluorescence and absorption spectra. The spectra are found to depend on the frequency difference 2\ensuremath{\delta}=${\mathrm{\ensuremath{\delta}}}_{1}$+${\mathrm{\ensuremath{\delta}}}_{2}$, the average detuning \ensuremath{\Delta}=${\mathrm{\ensuremath{\omega}}}_{0}$-1/2(${\mathrm{\ensuremath{\omega}}}_{1}$+${\mathrm{\ensuremath{\omega}}}_{2}$), and the Rabi frequencies of the driving fields. For ${\mathrm{\ensuremath{\Omega}}}_{1}$=${\mathrm{\ensuremath{\Omega}}}_{2}$=\ensuremath{\Omega}, the total fluorescent intensity displays a series of maxima for \ensuremath{\Delta}=\ifmmode\pm\else\textpm\fi{}n\ensuremath{\delta}\ensuremath{\mp}${\mathrm{\ensuremath{\Omega}}}^{2}$/4\ensuremath{\delta}, where the n are the odd integers. The intensity-dependent shift from the resonances n\ensuremath{\delta} is explained as an analog of the generalized Bloch-Siegert shift. The resonance-fluorescence spectrum for \ensuremath{\Delta}\ensuremath{\ne}0 appears to contain more peaks than that for \ensuremath{\Delta}=0.This is due to the splitting of the central peak and the even sidebands into doublets. The absorption spectrum of a weak-probe beam for \ensuremath{\Delta}=0 and equal Rabi frequencies consists of a symmetric series of dispersionlike sidebands separated from ${\mathrm{\ensuremath{\omega}}}_{0}$ by integer multiples of \ensuremath{\delta}, together with a central absorption peak at ${\mathrm{\ensuremath{\omega}}}_{0}$, whose amplitude oscillates with \ensuremath{\Omega}. For \ensuremath{\Delta}\ensuremath{\ne}0 and/or ${\mathrm{\ensuremath{\Omega}}}_{1}$\ensuremath{\ne}${\mathrm{\ensuremath{\Omega}}}_{2}$, the odd sidebands remain dispersionlike, while the central peak and the even sidebands split into absorption-emission doublets. A simple physical interpretation of the spectral features is given in terms of the dressed-atom model.
The discrepancies in the power spectrum of the light scattered by a coherently driven three-level atom are identified with the help of two methods [see, A. S. Manka et al., Phys. Rev. A 43, 3748 (1991); M. R. Ferguson et al., Phys. Rev. A 54, 2379 (1996)]. Moreover, the most prominent differences are the negative values as well as the greatly distorted profile in the spectrum. It is shown that the inhomogeneity or homogeneity of the two-time correlation Bloch vector equation is responsible for such discrepancies.
An experiment was performed recently [Y. Zhu, A. Lezama, Q. Wu, and T. W. Mossberg (unpublished)] in which a two-level atom of transition frequency \ensuremath{\Omega} was placed in a bichromatic laser field with frequencies \ensuremath{\Omega}\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta}, of sufficient intensity to produce dynamic Stark splitting. The observed fluorescence spectrum differed qualitatively in almost all its details from the well-known Mollow triplet [B. R. Mollow, Phys. Rev. 188, 1969 (1969)]. In this article, we use a dressed-atom model to explain the observed results.