Superfluidity of coherent light in self-focusing nonlinear waveguides

We establish the superfluidity theory of coherent light in waveguides made of nonlinear polar crystals. It is found that the pairing state of photons in a nonlinear polar crystal is the photonic superfluid state. The photon-photon interaction potential is an attractive effective interaction by exchange of virtual optical phonons. In the traveling-wave pairing state of photons, the photon number is conserved, which is similar to the Bose-Einstein condensation (BEC) state of photons. In analogy to the BCS-BEC crossover theory of superconductivity, we derive a set of coupled order parameter and number equations, which determine the solution of the traveling-wave superfluid state of photons. This solution gives the critical velocity of light in a self-focusing nonlinear waveguide. The most important property of the photonic superfluid state is that the system of photon pairs evolves without scattering attenuations.