PHASE-SENSITIVE RESERVOIR MODELED BY BEAM-SPLITTERS

The superposition of input fields in a lossless beam splitter is studi ed in the Schrodinger picture by using the convolution of the positive P representations, and the convolution law for these representations is extended to other quasiprobability functions such as the Wigner and Q functions. We show that the reservoir can be modeled by an infinite array of beam splitters, and we use the convolution law and this mode l to derive the Fokker-Planck equation for a system coupled with a pha se-sensitive reservoir. Solving this equation shows that a phase-sensi tive attenuation and amplification can be described by the superpositi on of two independent quantum fields, one of which is the initial sign al field and the other the squeezed thermal noise field representing t he reservoir.