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

TL;DR

This paper refutes recent claims of discrepancies between two methods for calculating the incoherent spectrum of light scattered by atoms, demonstrating their equivalence and the positivity of the spectrum across parameters.

Contribution

It shows that the two methods are equivalent and produce positive spectra, correcting previous assertions of discrepancies and unphysical negative values.

Findings

The two methods yield identical incoherent spectra.

The spectra are positive for all frequencies and parameters.

Numerical calculations support the analytical proof.

Abstract

There are two alternative methods used in 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 two completely equivalent for evaluating the incoherent part of the spectrum. In a recent paper Qing Xu et al. [Phys. Rev. A 78, 013407 (2008)] have shown that there are discrepancies between the incoherent parts of the stationary spectrum of a three-level Lambda-type system calculated with these two methods. The predicted discrepancies can be severe that over a wide rage of the Rabi frequencies and atomic decay rates, the spectrum calculated with the variance method can have negative values. This is obviously unphysical result since the fluorescence spectrum is a positively defined quantity. It represents the frequency distribution of light incoherently scattered by the atomic system. Therefore, the calculated spectrum should be positive for all frequencies independent of values of the Rabi frequencies and the damping rates. In this comment, we show that there are no discrepancies between these two methods. The equivalence of these two alternative methods leads to the same incoherent spectra that are positive for all frequencies independent of values of the parameters involved. The analytical analysis is supported by simple numerical calculations.