Proximity effect in asymmetric-gap superconducting bilayers and regularization of transition rates

TL;DR

This paper investigates how the proximity effect in asymmetric-gap superconducting bilayers can regularize the divergent density of states and transition rates, leading to smoother physical responses in superconducting qubits.

Contribution

It provides analytical approximations for the density of states in asymmetric superconducting bilayers and demonstrates how the proximity effect regularizes divergences in qubit transition rates.

Findings

Density of states smearing increases with gap asymmetry

Proximity effect regularizes divergence in transition rates

Smoothening of qubit frequency shift discontinuity

Abstract

The standard mean-field treatment of low-temperature superconductors leads to a square-root divergent density of states at the gap value. This feature can lead to unphysical logarithmic divergences in various quantities, such as currents and qubit transition rates. We revisit their possible regularization based on the proximity effect between two superconducting films with different gaps. We derive analytical approximations for the density of states in each superconducting film. We find that the smearing of the density of states grows with the gap asymmetry. As a concrete example, we discuss the regularization of transition rates in qubits with frequency close to resonance with the gap asymmetry between the two films, and the consequent smoothening of the jump discontinuity in the qubit frequency shift.