Cavity Quantum Eliashberg Enhancement of Superconductivity

Abstract

Driving a conventional superconductor with an appropriately tuned classical electromagnetic field can lead to an enhancement of superconductivity via a redistribution of the quasiparticles into a more favorable non-equilibrium distribution -a phenomenon known as the Eliashberg effect. Here we theoretically consider coupling a two-dimensional superconducting film to the quantized electromagnetic modes of a microwave resonator cavity. As in the classical Eliashberg case, we use a kinetic equation to study the effect of the fluctuating, dynamical electromagnetic field on the Bogoliubov quasiparticles. We find that when the photon and quasiparticle systems are out of thermal equilibrium, a redistribution of quasiparticles into a more favorable non-equilibrium steadystate occurs, thereby enhancing superconductivity in the sample. We predict that by tailoring the cavity environment (e.g. the photon occupation and spectral functions), enhancement can be observed in a variety of parameter regimes, offering a large degree of tunability.It has been known since the late 1960's that subjecting a superconductor to strong microwave radiation can lead to an enhancement of superconductivity [1,2]. The explanation of this was first provided by Eliashberg et. al. [3][4][5], who showed that the irradiation yields a nonthermal distribution of the Bogoliubov excitations with an effectively colder band edge. The degree of enhancement can be obtained by using standard BCS theory with a non-thermal quasiparticle distribution function. In the subsequent decades, Eliashberg's theoretical explanation for this effect has been extended and applied to a variety of other systems [6][7][8][9][10][11][12].In recent years there has been a renewed interest in non-equilibrium superconductivity motivated in-part by a number of "pump-probe" experiments which have found that materials subjected to intense THz pulses exhibit transient superconducting properties up to very high sample temperatures [13][14][15]. Understanding these transient states has led to a variety of theoretical models which go beyond the quasiparticle redistribution effect [16][17][18][19][20][21].All of these systems concern the interaction between quantum matter and a classical external field. Particularly interesting and novel however, is the effect that a fluctuating quantum gauge field has on quantum matter. Indeed, it has been a long-standing focus in the field of cavity-quantum-electrodynamics to realize the dynamical quantum nature of the electromagnetic field through the use of resonant electromagnetic cavities [22][23][24][25][26]. Recently there have been many advances in this area including the realization of exciton-polariton condensates [27,28], states formed from hybridizing cavity photons and semiconductor excitons. This paper extends some of these concepts to superconducting systems with an eye on cavity-induced Eliashberg-type enhancement of superconductivity. The central observation is that even in a non-equilibrium steady-state the BCS self-consistency equationc...

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