Comment on “Discrepancies in the resonance-fluorescence spectrum calculated with two methods”

Abstract

There are two alternative methods used in the literature to calculate the incoherent part of the spectrum of light scattered by an atomic system. In the first, one calculates the spectrum of the total light scattered by the system and obtains the incoherent part by subtracting the coherent part. In the second method, one introduces the fluctuation operators and obtains the incoherent part of the spectrum by taking the Fourier transform of the two-time correlation function of the fluctuation operators. These two methods have been recognized for years as completely equivalent for evaluating the incoherent part of the spectrum. In a recent paper, Xu et al. [Phys. Rev. A 78, 013407 (2008)] showed that there are discrepancies between the incoherent parts of the stationary spectrum of a three-level $\ensuremath{\Lambda}$-type system calculated with these two methods. The predicted discrepancies can be severe that over a wide range of the Rabi frequencies and atomic decay rates, the spectrum calculated with the variance method can have negative values. In this Comment, we show that there are no discrepancies between these two methods. We show the equivalence of these two methods that leads to the same incoherent spectra which are positive for all frequencies independent of values of the parameters involved. We also identify the source of the discrepancy, that is, in an incorrect treatment of the incoherent part of the spectrum calculated with the two-time correlation function of the fluctuation operators.