Boundary Field Theory Approach to the Renormalization of SQUID Devices

TL;DR

This paper models the quantum behavior of Josephson SQUID devices using a boundary sine Gordon framework, unifying descriptions of multi-junction devices and reproducing known results for single junction SQUIDs.

Contribution

It introduces a boundary field theory approach to analyze SQUID devices, providing new insights and connections to quantum impurity problems, and extends the analysis to multi-junction configurations.

Findings

Reproduces known results for rf-SQUIDs.

Analyzes regimes for two-junction SQUIDs.

Derives current-voltage characteristics consistent with established models.

Abstract

We show that the quantum properties of some Josephson SQUID devices are described by a boundary sine Gordon model. Our approach naturally describes multi-junction SQUID devices and, when applied to a single junction SQUID (the rf-SQUID), it reproduces the known results of Glazman and Hekking. We provide a detailed analysis of the regimes accessible to an rf-SQUID and to a two-Josephson junction SQUID device (the dc-SQUID). We then compute the normal component of the current-response of a SQUID device to an externally applied voltage and show that the equation describing the current-voltage characteristic function reduces to well-known results when the infrared cutoff is suitably chosen. Our approach helps in establishing new and interesting connections between superconducting devices, quantum brownian motion, fermionic quantum wires and, more generally, quantum impurity problems.