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Journal of Physics B Atomic and Molecular Physics

A quantum-mechanical master-equation treatment of the dynamical Stark effect

H. J. Carmichael, Daniel F. Walls

Published Oct 21, 1976• 7 citations
Publisher
DOI
10.1088/0022-3700/9/15/524

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The description begins with an operator master equation for the atom plus incident field. Reduced atomic matrix elements are derived for arbitrary field strengths. First- and second-order correlation functions in the scattered field are also obtained and discussed in relation to the scattered spectrum and intensity-fluctuation measurements. This formalism has the appealing feature that all information is readily available from the one set of four coupled equations. The deficiencies in both the one-photon approximation and the semiclassical perspective are established in a natural and transparent fashion.
This paper presents new results on aspects of the two-photon laser. A semiclassical investigation of threshold behaviour reveals that the atom-field coupling is already so strong at threshold that a non-perturbative treatment of the dynamics is necessary. A master equation is derived on the basis of an effective Hamiltonian generalized in that it includes the effect of an overall two-photon detuning, the effect of ionization of the upper atomic level and the effect of dynamic Stark shifts. From the diagonal elements of the master equation, a Fokker-Planck equation is obtained and shown to yield a general analytical expression for the photon distribution which is found to simplify considerably in special cases. The agreement with the result obtained through numerical solution of the master equation itself is very good. It is further shown that a detuning from two-photon resonance and a significant Stark shift lead to sub-Poissonian statistics. Finally, time-dependent solutions for the photon distribution under an injected coherent state are presented.