Regular Article

Nonlinear coupling of photons via a collective mode of transparent superconductor^★,★★

¹ Laboratoire Aimé Cotton, CNRS (UPR 3321), Bâtiment 505, 91405 Orsay Cedex, France
² Institute for Information Transmission Problems of the Russian Academy of Science, Bolshoy Karetny per. 19, Moscow 127994, Russia
³ Laboratoire J.-V. Poncelet CNRS (UMI 2615) Bolshoi Vlassievsky per. 11, Moscow 119002, Russia

^a e-mail: akulinvladimir@gmail.com

Received: 9 July 2018
Received in final form: 18 October 2018
Published online: 10 January 2019

Abstract

At the first glance, the expression “transparent superconductor” may seem an oxymoron. Still, the first principle calculations [A. Nakanishi, H. Katayama-Yoshida, Solid State Commun. 152, 24 (2012)] and experiments [A. Kumatani, T. Ohsawa, R. Shimizu, Y. Takagi, S. Shiaki, T. Hitosugi, Appl. Phys. Lett. 101, 123103 (2012)] 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 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 ponderomotive energy is proportional to the ratio of the charge squared to the mass of the “collective particle” interacting with radiation, e²∕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 μ-scale of the tube diameter and the cm-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.