A New Formalism for Two-Photon Quantum Optics
In this paper we describe a new formalism for analyzing a particular class of nonlinear optical devices. We call these devices two-photon devices because they operate as follows: several modes of the electromagnetic field are coupled via a nonlinearity in some material; two of the modes are the device’s “signal” modes, the rest are “pump” modes; photons are created or destroyed in the signal modes two at a time. Examples include parametric amplifiers and four-wave mixers. Two-photon devices are to be contrasted with one-photon devices, such as the laser, in which photons are created or destroyed in the signal mode one at a time. The formalism used in one-photon optics uses variables and quantum states suited to describing the output of a one-photon device.
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