Justification of the canonical quantization of the Josephson effect

TL;DR

This paper rigorously justifies the canonical quantization approach for Josephson effect-based quantum devices, identifying the conditions under which it is valid and quantifying the lowest energy corrections.

Contribution

It provides a rigorous validation of the canonical quantization method for Josephson devices and determines the parameter range for its applicability.

Findings

Canonical quantization is valid within specific parameter ranges.

Derived the lowest corrections to the Josephson energy.

Established conditions for the validity of the quantization approach.

Abstract

Quantum devices based on Josephson effect in superconductors are usually described by a Hamiltonian obtained by commonly used canonical quantization. However, this recipe has not been yet rigorously justified. We show that this approach is indeed correct in certain range of parameters. We find the condition of the validity of such quantization and the lowest corrections to the Josephson energy.