Effect of quantum fluctuations on even-odd energy difference in a Cooper-pair box

TL;DR

This paper investigates how quantum charge fluctuations influence the energy difference between even and odd charge states in a small superconducting island, revealing a conductance-dependent renormalization effect.

Contribution

It provides a detailed analysis of the impact of quantum charge fluctuations on the energy spectrum of a Cooper-pair box, highlighting the conductance dependence of energy renormalization.

Findings

Quantum charge fluctuations significantly affect the even-odd energy difference.

Renormalization of activation energy increases with junction conductance g_T.

Strong effects observed when g_T >> 1.

Abstract

We study the effect of quantum charge fluctuations on the even-odd energy difference for a small superconducting island (Cooper-pair box) connected to a large finite-size superconductor by a tunnel junction. Even-odd energy difference is important for understanding the quasiparticle "poisoning" effect, and determines the activation energy of a trapped quasiparticle in the Cooper-pair box. We find that renormalization of the activation energy due to quantum charge fluctuations depends on the dimensionless normal-state conductance of the junction g_T, and becomes strong at g_T >> 1.