Model for a Josephson junction array coupled to a resonant cavity

J. Kent Harbaugh; D. Stroud

doi:10.1103/PhysRevB.61.14765

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Model for a Josephson junction array coupled to a resonant cavity

J. Kent Harbaugh, D. Stroud

DOI 10.1103/PhysRevB.61.14765 · Physical Review B

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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 N2, suggestive of coherent emission. These features remain even when the junction parameters have some random variation from junction to junction, as expected in a real array. Both of these features agree with recent experiments by Barbara and co-workers.