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Physical Review A

Comment on "Theory of collective resonance fluorescence in strong driving fields"

JOSIP SEKE

Published Sep 1, 1984• 2 citations
Publisher

Abstract

In a recent paper by Compagno and Persico a factorization for three-operator expectation values was used. In connection with this factorization the result obtained in that paper is discussed for the relative variance of the population-inversion operator in the pure superfluorescence, and we propose a new approximation procedure.
DOI
10.1103/physreva.30.1543

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It is argued that the findings of a recent reanalysis by Compagno and Persico [Phys. Rev. A 57, 1595 (1998)] of the Bohr-Rosenfeld procedure for the measurement of a single space-time-averaged component of the electromagnetic field are incorrect when the field measurement time is shorter than that required for light to traverse the measurement's test body. To this end, the time-averaged ``self-force'' on the test body, assumed for simplicity to be of a spherical shape, is evaluated in terms of a one-dimensional quadrature for the general trajectory allowed for the test body by Compagno and Persico, and in closed form for the limiting steplike trajectory used by Bohr and Rosenfeld.
Summary form only given. In this work we suggest and discuss the method of collective atomic-field operators for the resonance fluorescence of two-level atom with the transition frequency near the band gap edge. The method is based on the formal diagonalization of the interaction Hamiltonian in the absence of driving. In the absence of driving the method also allows to obtain the exact solution for the case when there are two photons in the field. We show that due to closeness to the gap edge the collective operators are weakly coupled. This allows to develop an effective approximation applicable when the problem is strongly non-Markovian, i.e. when in the absence of driving the effect of "freezing" of upper-level atomic population takes place. Then the dynamics of all but one collective operators becomes similar to the bosonic one. Only the dynamics of this one collective operators is nonlinear. We show that in this case a perturbation theory could be developed using as a small parameter a respective coupling strength between this one collective operator and others. In fact, the method of collective operators gives possibility to develop a perturbation theory "tailored" especially for the essentially non-Markovian problem. We derive a condition of applicability for this theory. Essentially, it is the condition of weak excitation of all collective atom-field "modes" corresponding to the collective operators with dynamics similar to the bosonic one. For the moderate intensities of the driving field even an approximation of independent collective operators gives good results. In the limit of weak driving field a simple analytic approximation is developed. As comparison shows, this approximation allows to describe a basic features of atomic population dynamics even for the cases when the driving field could not any more be considered weak.