Four-wave mixing in a Bloch two-level system with incoherent laser light having a Lorentzian spectral density: Analytic solution and a diagrammatic approach

Degenerate four-wave mixing using broadband, non-transform-limited (incoherent) laser light having a Lorentzian spectral density is treated analytically for a Bloch two-level system. We consider the configuration in which an incoherent beam from a Lorentzian source is split into two beams having distinct k vectors, k and k'. The twin beam along k' has been subjected to a controllable delay, tau, relative to k. These twin beams, focused into the sample of interest, generate new fourth fields, the signal at k(s)=2k-k' being examined here as a function of tau. A set of factorized time correlation (FTC) diagrams is introduced to organize the calculation and to yield both analytic expressions as well as physical insight. Not only is the signal not symmetric in tau but the signal can peak at tau not equal 0 even in the absence of inhomogeneous broadening. Finally, the physical insights and the use of the FTC diagrams are extended to rationalize several other incoherent light spectroscopies.