Floquet theory of Cooper pair pumping

TL;DR

This paper develops a comprehensive Floquet theory framework for analyzing charge transfer in superconducting nanocircuits, applicable in both adiabatic and non-adiabatic regimes, including environmental effects, and demonstrates its application to a Cooper pair sluice.

Contribution

It introduces a generalized Floquet-based formula for Cooper pair pumping that accounts for non-adiabatic dynamics and environmental influences, extending previous models.

Findings

Reproduces known adiabatic pumping results

Provides new insights into non-adiabatic pumping behavior

Offers a transparent Floquet-based expression for transferred charge

Abstract

In this work we derive a general formula for the charge pumped in a superconducting nanocircuit. Our expression generalizes previous results in several ways, it is applicable both in the adiabatic and in the non-adiabatic regimes and it takes into account also the effect of an external environment. More specifically, by applying Floquet theory to Cooper pair pumping, we show that under a cyclic evolution the total charge transferred through the circuit is proportional to the derivative of the associated Floquet quasi-energy with respect to the superconducting phase difference. In the presence of an external environment the expression for the transferred charge acquires a transparent form in the Floquet representation. It is given by the weighted sum of the charge transferred in each Floquet state, the weights being the diagonal components of the stationary density matrix of the system expressed in the Floquet basis. In order to test the power of this formulation we apply it to the study of pumping in a Cooper pair sluice. We reproduce the known results in the adiabatic regime and we show new data in the non-adiabatic case.