Higgs gap modes in superconducting circuit quantisation

TL;DR

This paper develops a quantum circuit approach to analyze Higgs modes in superconductors, deriving analytical expressions for their properties and validating them numerically, advancing understanding of gap dynamics in mesoscopic systems.

Contribution

It extends a projective circuit quantisation method to include superconducting Higgs modes, providing analytical and numerical insights into their properties and anharmonic corrections.

Findings

Analytical expressions for Higgs mass and oscillation frequency.

Numerical validation of analytical results.

Comparison of anharmonic corrections with previous models.

Abstract

We extend a recently developed projective circuit quantisation approach to incorporate superconducting Higgs modes associated to gap dynamics. This approach starts from a microscopic fermionic Hamiltonian for mesoscopic superconductors, and projects the system onto its low-energy "BCS" Hilbert space. We derive analytical results for the superconducting Higgs mass, "spring" constant, and oscillation frequency of the gap dynamics, which we validate numerically. We compute anharmonic corrections to the Higgs frequency for higher excitations of small superconducting islands, and compare our results to previous long-wavelength calculations.