Berry connection from many-body wave functions and superconductivity: Circuit quantization for superconducting qubits and absence of a dissipative quantum phase transition in Josephson junctions

TL;DR

This paper introduces a new superconductivity theory based on Berry phases from many-body wave functions, impacting circuit quantization and explaining the absence of dissipative quantum phase transitions in Josephson junctions.

Contribution

It applies a Berry phase-based theory to circuit quantization, removing the need for phase-charge duality and explaining phenomena like Shapiro steps without normal current.

Findings

Absence of dissipative quantum phase transition in Josephson junctions explained

Charge-decaying term leads to compact phase description

Shapiro steps occur without normal current

Abstract

The new superconductivity theory that attributes the $U(1)$ superconductivity phase to a Berry phase arising from many-body wave functions is applied to the circuit quantization for superconducting qubits. The phase-charge duality required for the occurrence of superconductivity in the standard theory becomes irrelevant in the new theory, and the absence of a dissipative quantum phase transition in Josephson junctions is explained. It is shown that a charge-decaying term leads to the compact phase description, and the appearance of Shapiro steps is explained without introducing normal current.