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The Journal of Chemical Physics

On the determination of Green's functions involved in a description of resonance fluorescence

Robert L. Fulton

Published Jul 1, 1974• 0 citations
Publisher
DOI
10.1063/1.1681664

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A superoperator non-equilibrium Green’s function formalism is presented for computing nonlinear optical processes involving any combination of classical and quantum optical modes. Closed correlation-function expressions based on superoperator time-ordering are derived for the combined effects of causal response and non-causal spontaneous fluctuations. Coherent three wave mixing (sum frequency generation and parametric down conversion) involving one and two quantum optical modes, respectively, are compared with their incoherent counterparts: two-photon-induced fluorescence and two-photon-emitted fluorescence.
We have studied the fluorescence spectra arising from the interaction of a three-level atom with two strong electromagnetic fields whose initially populated modes are equal to the two atomic transition frequencies, respectively. The Green's function formalism has been used to calculate the excitation spectrum of the system. An expression for the spectral function describing the excitation spectrum of the system has been derived in a closed form in the limit of high photon densities. Numerical computation of the expression for the spectral function indicates that at each transition frequency there may exist either one pair or two pairs or three pairs of sidebands, in addition to the central peak, depending upon the relative strength of the Rabi frequencies involved.