In response to quantum optical fields, pairs of molecules generate coherent nonlinear spectroscopy signals. Homodyne signals are given by sums over terms each being a product of Liouville space pathways of the pair of molecules times the corresponding optical field correlation function. For classical fields all field correlation functions may be factorized and become identical products of field amplitudes. The signal is then given by the absolute square of a susceptibility which in turn is a sum over pathways of a single molecule. The molecular pathways of different molecules in the pair are uncorrelated in this case ( each path of a given molecule can be accompanied by any path of the other). However, entangled photons create an entanglement between the molecular pathways. We use the superoperator nonequlibrium Green's functions formalism to demonstrate the signatures of this pathway-entanglement in the difference frequency generation signal. Comparison is made with an analogous incoherent two-photon fluorescence signal. (C) 2009 Optical Society of America

Multi-exciton Green’s functions and scattering matrices in many fermion systems are calculated using a quasiparticle approach based on a generalized Bethe–Salpeter equation. The simulation protocol only requires numerical diagonalization of the single-exciton manifold. Using coboson algebra all many-body effects are recast in terms of two tetradic exciton–exciton interactions: direct Coulomb scattering and Pauli exchange. The tedious equations-of-motion derivations and calculations of multi-exciton manifolds are avoided. The approach is applied to calculate the third- and fifth-order signals generated by sequences of femtosecond optical pulses. Several coherent fifth order optical signals that directly probe three-exciton states and their projections on double and single-exciton states are predicted.