Keldysh approach to periodically driven systems with a fermionic bath: non-equilibrium steady state, proximity effect and dissipation

TL;DR

This paper investigates a periodically driven metallic system coupled to a superconducting bath, analyzing non-equilibrium steady states, proximity effects, and dissipation using Keldysh formalism, with implications for spectroscopic measurements.

Contribution

It introduces a non-perturbative Keldysh approach to study driven systems with fermionic baths, revealing steady-state properties and distribution functions.

Findings

Modified density of states due to proximity effect

Non-equilibrium distribution functions calculated

Observable tunneling spectra predicted

Abstract

We study properties of a periodically driven system coupled to a thermal bath. As a nontrivial example, we consider periodically driven metallic system coupled to a superconducting bath. The effect of the superconductor on the driven system is two-fold: it (a) modifies density of states in the metal via the proximity effect and (b) acts as a thermal bath for light-excited quasi-particles. Using Keldysh formalism, we calculate, nonpertubatively in the system-bath coupling, the steady-state properties of the system and obtain non-equilibrium distribution function. The latter allows one to calculate observable quantities which can be spectroscopically measured in tunneling experiments.