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 , 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 et al.
We calculate the current-voltage (IV) characteristics of a Josephson-junction array with long-range interactions. The array consists of two sets of equally spaced parallel superconducting wires placed at right angles. A Josephson junction is formed at every point wherever the wires cross. We treat each such junction as an overdamped resistively shunted junction, and each wire segment between two junctions as a similar resistively shunted junction with a much higher critical current. The IV characteristics are obtained by solving the coupled Josephson equations numerically. We find that, for a sufficiently large number of wires, the critical current saturates at a finite value because of the wire inductance, in excellent agreement with experiment. The calculated IV characteristics also show a striking hysteresis, even though each of the individual junctions is nonhysteretic. The hysteresis results from a global redistribution of current flow on the upper and lower voltage branches, and is also in excellent agreement with experiment.
We describe a mean-field theory for phase transitions in a Josephson junction array consisting of two sets of parallel wire networks, arranged at right angles and coupled together by Josephson interactions. In contrast to earlier treatments, we include the variation of the superconducting phase along the individual wires; such variation is always present if the wires have finite thickness and are sufficiently long. The mean-field result is obtained by treating the individual wires exactly and the coupling between them within the mean-field approximation. For a perpendicular applied magnetic field of strength f ϭp/q flux quanta per plaquette ͑where p and q are mutually prime integers͒, we find that the mean-field transition temperature T c ( f )ϷT c (0)q Ϫb with bϭ1/4. By contrast, a mean-field theory which neglects phase variation along the array predicts bϭ1/2, and gives a T c which diverges in the thermodynamic limit. The model with phase variations agrees somewhat better with experiment on large arrays than does the approximation which neglects phase variations.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.