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

TLDR

Two‑photon devices excite pairs of output modes independently. This paper introduces a new formalism for analyzing two‑photon devices such as parametric amplifiers and phase‑conjugate mirrors. The formalism treats pairs of modes simultaneously, defining quadrature‑phase amplitudes and two‑mode squeezed states, and extends to a continuum multimode description by integrating over independently excited pairs.

Abstract

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 \ensuremath{\Omega}\ifmmode\pm\else\textpm\fi{}\ensuremath{\epsilon}, we define (i) quadrature-phase amplitudes, which are complex-amplitude operators for modulation at frequency \ensuremath{\epsilon} of waves ``cos[\ensuremath{\Omega}(t-x/c)]'' and ``sin[\ensuremath{\Omega}(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.