Microscopic theory of photo-assisted electronic transport in normal-metal/BCS-superconductor junctions

TL;DR

This paper develops a microscopic theory for photo-assisted electronic transport in normal-metal/BCS-superconductor junctions, analyzing current and noise under various voltage drives, revealing conditions for minimal noise and perfect Cooper pair transmission.

Contribution

It introduces a comprehensive microscopic approach to study photo-assisted transport in superconductor junctions, including regimes of different gap sizes and drive frequencies, and explores on-demand Cooper pair sources.

Findings

Minimal excess noise with Lorentzian drives at small gaps.

Perfect Cooper pair transmission with half-quantized levitons at large gaps.

Identification of regimes where Andreev reflection dominates.

Abstract

We investigate photo assisted electronic transport in a normal-metal/BCS-superconductor junction with a microscopic Hamiltonian approach, for several types of periodic voltage drives applied on the normal-metal side. The time-dependent current and the photo-assisted noise are computed to all orders of the tunneling Hamiltonian using a Keldysh-Nambu-Floquet approach. An excess noise analysis allows one to determine to what extent pure electronic excitations with a small number of electrons per period can be generated by the different drives. When the superconducting gap is small compared to the drive frequency, the junction behaves like a normal-metal junction and minimal excess noise is reached for Lorentzian voltage drives carrying an integer charge (levitons). In the opposite regime of a large-gap, the excess noise vanishes for half-quantized levitons, giving rise to the perfect transmission of a Cooper pair on the superconducting side. This microscopic approach also allows us to address the intermediate regime, when the drive frequency is comparable to the gap, allowing us to study the non-trivial interplay between Andreev reflection and quasiparticle-transfer processes. Our analysis also shows the appearance of Tien-Gordon-type relations connecting the current and noise in the AC-driven junction to their DC counterpart, which we investigate in details. Finally, the possibility to build a reliable on-demand source of Cooper pairs with this setup is examined using realistic experimental parameters.