QUANTUM STATISTICS OF A 2-MODE SU(1,1) INTERFEROMETER

A comprehensive formalism for a two-mode SU(1,1) interferometer (a non degenerate parametric amplifier, a degenerate four-wave mixer, or a ph ase-conjugating mirror) is presented. The device changes the quantum s tate of the two incident modes by an SU(1,1) transformation. Apart fro m phase shiftings, the quadrature wave functions are Lorentz transform ed. A transformation formula in the Fock space of the two modes is der ived. Hybrids of s and -s quasiprobability distributions are changed b y the inverse-mode transformation. It is related to quantum noise in p hase conjugation. Linear amplification caused by Gaussian reservoirs c orresponds exactly to a heuristic nondegenerate-parametric-amplifier m odel. It allows a simple geometrical explanation for the sensitivity o f squeezing or quantum superposition with respect to phase-sensitive a mplification.