A compact correlation-function expansion is developed for $n$-order optical susceptibilities in the frequency domain using the Keldysh-Schwinger loop. By not keeping track of the relative time ordering of bra and ket interactions at the two branches of the loop, the resulting expressions contain only $n+1$ basic terms, compared to the $2^n$ terms required for a fully-time-ordered density matrix description. Superoperator Green’s function expressions for ${\chi }^{\left(n\right)}$ derived using both expansions reflect different types of interferences between pathways. These are demonstrated for correlation-induced resonances in four-wave-mixing signals.

• Received 29 May 2007

DOI:https://doi.org/10.1103/PhysRevA.77.023801