Pair-amplitude dynamics in strongly-coupled superconductor-quantum dot hybrids

TL;DR

This paper investigates the time-dependent behavior of pair amplitudes in a superconductor-quantum dot hybrid system, revealing oscillations and decay patterns influenced by coupling strengths and external driving, with implications for experimental detection.

Contribution

It introduces a real-time diagrammatic method to analyze pair amplitude dynamics in strongly-coupled superconductor-quantum dot hybrids, including effects of periodic driving.

Findings

Pair amplitude exhibits oscillations after a quench with frequency set by superconductor coupling.

Pair amplitude decays exponentially with a time scale determined by normal metal coupling.

Oscillations occur under periodic driving in both adiabatic and fast limits.

Abstract

We consider a three-terminal system consisting of a quantum dot strongly coupled to two superconducting reservoirs in the infinite gap limit and weakly coupled to a normal metal. Using a real-time diagrammatic approach, we calculate the dynamics of the proximity-induced pair amplitude on the quantum dot. We find that after a quench the pair amplitude shows pronounced oscillations with a frequency determined by the coupling to the superconductors. In addition, it decays exponentially on a time scale set by the coupling to the normal metal. Strong oscillations of the pair amplitude occur also when the system is periodically driven both in the adiabatic and fast-driving limit. We relate the dynamics of the pair amplitude to the Josephson and Andreev current through the dot to demonstrate that it is an experimentally accessible quantity.