The present paper establishes the photonic superguiding theory in polar crystals with a high nonlinearity. In quantum theory it is shown that photons can sense an attractive effective interaction by exchange of virtual optical phonons. Such an interaction leads to the superguiding state. In the standing-wave superguiding state, the photons with opposite wave vectors and spins are bound into pairs. In the traveling-wave superguiding state, a propagating photon pair consists of a combination of two photons with opposite transverse wave vectors and spins. We study the particle properties of the photonic superguiding state, the most important property being that the system of photon pairs evolves without scattering attenuations. Quantum fluctuations of the standing-wave superguiding state exceed the vacuum fluctuations while the traveling-wave superguiding state has the squeezing property. We also investigate the wave properties of the photonic superguiding state. It is found that the polar crystals with a high nonlinearity are self-defocusing media. In the standing-wave superguiding state, the system of photon pairs exists in the form of quantized vortices. In the traveling-wave superguiding state, the system of photon pairs exists in the form of quantized temporal solitons.

• Received 11 August 1994

DOI:https://doi.org/10.1103/PhysRevA.51.675