Model for a Josephson junction array coupled to a resonant cavity

TL;DR

This paper presents a Hamiltonian model for a Josephson junction array coupled to a resonant cavity, demonstrating a transition to coherent emission as the number of junctions increases, aligning with recent experimental observations.

Contribution

It introduces a simple Hamiltonian and mean-field theory to describe coherence transition in Josephson arrays coupled to a photon mode, matching experimental results.

Findings

Transition from incoherence to coherence as N increases

Photon energy scales with N^2 above threshold

Model aligns with recent experimental data

Abstract

We describe a simple Hamiltonian for an underdamped Josephson array coupled to a single photon mode in a resonant cavity. Using a Hartree-like mean-field theory, we show that, for any given strength of coupling between the photon field and the Josephson junctions, there is a transition from incoherence to coherence as a function of N, the number of Josephson junctions in the array. Above that value of N, the energy in the photon field is proportional to N^2, indicative of coherent emission. Both of these features agree with recent experiments by Barbara et al. The experimentally observed voltage steps may require an explicit solution of the dynamical equations.