New formalism for two-photon quantum optics. I. Quadrature phases and squeezed states

This paper introduces a new formalism for analyzing two-photon devices (e.g., parametric amplifiers and phase-conjugate mirrors), in which photons in the output modes are created or destroyed two at a time. The key property of a two-photon device is that it excites pairs of output modes independently. Thus our new formalism deals with two modes at a time; a continuum multimode description can be built by integrating over independently excited pairs of modes. For a pair of modes at frequencies Ω±ε, we define (i) quadrature-phase amplitudes, which are complex-amplitude operators for modulation at frequency ε of waves ‘‘cos[Ω(t-x/c)]’’ and ‘‘sin[Ω(t-x/c)]’’ and (ii) two-mode squeezed states, which are the output states of an ideal two-photon device. The quadrature-phase amplitudes and the two-mode squeezed states serve as the building blocks for our formalism; their properties and their physical interpretation are extensively investigated.