Nonlinear coupling of photons via a collective mode of transparent superconductor

Abstract

At the first glance, the expression "transparent superconductor" may seem an oxymoron. Still, the first principle calculations and experiments show that the materials that behave as superconductors at low frequencies and do not absorb in the optical domain may exist. Virtual excitation of the collective electronic modes of such superconductors in a magnetic field appears as an efficient way to realize the nonlinear interaction of light at the level of two single photons. The essence of the effect is in the fact that the pondermotor energy is proportional to the ratio of the charge squared to the mass of the "collective particle" interacting with radiation, $e^2/m$, and therefore, for a "particle" representing a collective motion of many electrons, it scales linearly-, and its second-order correction quadratically with the number of the electrons involved. This general situation is analyzed in detail in the framework of a simple model of a fiber tube waveguide equipped with a clean superconductor layer. It turns out that for realistic parameters, at the micron-scale of the tube diameter and the centimeter-scale of the fiber length, such a system is capable of performing the logic gate operation on the polarization variables of a pair of optical photons.