Generation of nonclassical light in parametric amplification of counterpropagating waves in consecutive interactions

A quantum theory of consecutive interactions of counterpropagating waves with multiple frequencies ω, 2ω, and 3ω is developed. Parametric processes of high- and low-frequency amplification of ω and 3ω waves are studied in the approximation of an undepleted 2ω pump field. Fluctuations of quadrature components, statistics of photons, and correlation between fluctuations of photon numbers are considered at these frequencies.