Nonlinear spectroscopy with time- and frequency-gated photon counting: A superoperator diagrammatic approach

We present a diagrammatic technique for calculating quantum-detected nonlinear optical signals using loop diagrams that act in the joint matter plus field space. This formalism, which is based on time-ordered superoperators keeps track of the entangled matter plus field state, making it most suitable for spectroscopy applications. Photon counting is recast as a time and frequency convolution of a bare signal, which is given by a correlation function of matter, and a gating spectrogram.