Dissipation and quantum phase transitions of a pair of Josephson junctions

TL;DR

This paper investigates the quantum phase transitions and dissipation effects in a system of two Josephson junctions coupled to a superconducting grain, revealing five distinct phases and a novel superconducting state with unique coherence properties.

Contribution

It introduces a detailed analysis of a two-junction system showing five quantum phases, including a new superconducting state, and explores the critical behavior controlled by an intermediate coupling fixed point.

Findings

Identification of five quantum phases, including a novel superconducting state.

Discovery of a continuous variation of critical exponents at the transition.

Analysis of phase diagram using sine-Gordon models and Coulomb gases.

Abstract

A model system consisting of a mesoscopic superconducting grain coupled by Josephson junctions to two macroscopic superconducting electrodes is studied. We focus on the effects of ohmic dissipation caused by resistive shunts and superconducting-normal charge relaxation within the grain. As the temperature is lowered, the behavior crosses over from uncoupled Josephson junctions, similar to situations analyzed previously, to strongly interacting junctions. The crossover temperature is related to the energy-level spacing of the grain and is of the order of the inverse escape time from the grain. In the limit of zero temperature, the two-junction system exhibits five distinct quantum phases, including a novel superconducting state with localized Cooper pairs on the grain but phase coherence between the leads due to Cooper pair cotunneling processes. In contrast to a single junction, the transition from the fully superconducting to fully normal phases is found to be controlled by an intermediate coupling fixed point whose critical exponents vary continuously as the resistances are changed. The model is analyzed via two component sine-Gordon models and related Coulomb gases that provide effective low temperature descriptions in both the weak and the strong Josephson coupling limits. The complicated phase diagram is consistent with symmetries of the two component sine-Gordon models, which include weak to strong coupling duality and permutation triality. Experimental consequences of the results and potential implications for superconductor to normal transitions in thin wires and films are discussed briefly.