Rigorous derivation of the triple scattering signal from single-atom responses

Abstract

We study coherent backscattering of intense laser light from three immobile two-level atoms using the master-equation approach. The master equation is solved analytically, and the triple scattering spectrum is expressed in quadratures. We show that this solution can be obtained via a self-consistent combination of single-atom spectral responses, and is equivalent to the solution following from the diagrammatic pump-probe approach. We deduce the general expressions for single-atom building blocks which can be used in simulations of multiple inelastic scattering of laser light in the bulk atomic medium.

Diagrammatic treatment of coherent backscattering of intense light by cold atoms with degenerate energy levels

“…Recently, it has been shown that there is a systematic way of obtaining analytical expressions for such blocks in case of an arbitrary number of probe fields [19]. In future work, these expressions will be incorporated into the theory of nonlinear transport by classical scatterers [27] to describe CBS of intense laser light in cold atomic gases [17].…”

“…III E 1, that pairs of circles correspond to the factorized parts of the atomic dipole correlation function, which describe the elastic spectral responses. The number of pairs of circles in the graphical expansion of the building blocks is equal to 2 n , where n is the number of incoming probe fields [19,24]. Apart from the open circles, each of the graphical equations in Figs.…”

“…Now, we will discuss the rules of their self-consistent combination into doublescattering contributions to CBS. For non-degenerate dipole transitions, these rules were elaborated in [19,24].…”

“…Here, a subtlety arises when combining diagrams (c2) and (d2). Such a combination is forbidden since it features a closed loop including two amplitudes cycling between the two circles without an outgoing amplitude [19,24,27]. Excluding the forbidden diagram, we obtain five contributions -(c1)(d1), (c1)(d2), (c2)(d1), (c2)(d3), and (c3)(d2) to the elastic, and three contributions -(c1)(d3), (c3)(d1), and (c3)(d3) -to the inelastic spectrum of CBS.…”

“…Second, it transforms the problem of CBS of intense laser light off a cold atomic cloud into a form that is amenable to Monte-Carlo simulation methods [17]. Third, for double [18] and triple [19] scattering orders the solutions obtained within the pump-probe approach are equivalent to the solutions following from the master equation (where, in the triple scattering case, the recurrent scattering contributions are dropped). Under the assumption that this equivalence always holds in the dilute regime, general analytical expressions have recently been derived for singleatom responses [19].…”