Mesoscopic theory of the Josephson junction

TL;DR

This paper develops a mesoscopic theoretical framework for Josephson junctions, enhancing the understanding of their quantum properties and providing a basis for precise superconducting circuit engineering at nanoscales.

Contribution

It introduces a mesoscopic theory derived from scalar electrodynamics that captures spatial variations and relates qubit parameters to physical properties.

Findings

Reproduces Josephson relations with a second harmonic term.

Provides spatially resolved descriptions of superconducting fields.

Derives charge qubit Hamiltonian from first principles.

Abstract

We derive a mesoscopic theory of the Josephson junction from non-relativistic scalar electrodynamics. Our theory reproduces the Josephson relations with the canonical current phase relation acquiring a weak second harmonic term, and it improves the standard lumped-element descriptions employed in circuit quantum electrodynamics by providing spatial resolution of the superconducting order parameter and electromagnetic field. By providing an ab initio derivation of the charge qubit Hamiltonian that relates traditionally free qubit parameters to geometric and material properties, we progress toward the quantum engineering of superconducting circuits at the subnanometer scale.