Model for a Josephson junction array coupled to a resonant cavity

Harbaugh, J. Kent; Stroud, D.

doi:10.1103/physrevb.61.14765

Cited by 15 publications

(20 citation statements)

References 22 publications

(22 reference statements)

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“…This transition is the dynamic analog of that analyzed by an equilibrium mean-field theory in Ref. [24]. Finally, in Fig.…”

Section: Numerical Resultsmentioning

confidence: 97%

“…The coupling of propagating modes in Josephson ladders and other structures to electromagnetic radiation has also been studied theoretically 22,23 . A simple Hamiltonian to treat the equilibrium properties of a one-dimensional, voltagedriven array in the weak-coupling regime has recently been proposed and studied within a mean-field approximation which should be very accurate in the limit of large numbers of junctions 24 . Within this approach, it was found that the array developed coherence only above a threshold number of junctions, in agreement with experiment.…”

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confidence: 99%

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Dynamics of a Josephson array in a resonant cavity

Almaas

Stroud

2002

Phys. Rev. B

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We derive dynamical equations for a Josephson array coupled to a resonant cavity by applying the Heisenberg equations of motion to a model Hamiltonian described by us earlier [Phys. Rev. B 63, 144522 (2001); Phys. Rev. B 64, 179902 (E)]. By means of a canonical transformation, we also show that, in the absence of an applied current and dissipation, our model reduces to one described by Shnirman et al [Phys. Rev. Lett. 79, 2371(1997] for coupled qubits, and that it corresponds to a capacitive coupling between the array and the cavity mode. From extensive numerical solutions of the model in one dimension, we find that the array locks into a coherent, periodic state above a critical number of active junctions, that the current-voltage characteristics of the array have self-induced resonant steps (SIRS's), that when Na active junctions are synchronized on a SIRS, the energy emitted into the resonant cavity is quadratic in Na, and that when a fixed number of junctions is biased on a SIRS, the energy is linear in the input power. All these results are in agreement with recent experiments. By choosing the initial conditions carefully, we can drive the array into any of a variety of different integer SIRS's. We tentatively identify terms in the equations of motion which give rise to both the SIRS's and the coherence threshold. We also find higher-order integer SIRS's and fractional SIRS's in some simulations. We conclude that a resonant cavity can produce threshold behavior and SIRS's even in a one-dimensional array with appropriate experimental parameters, and that the experimental data, including the coherent emission, can be understood from classical equations of motion.

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“…This transition is the dynamic analog of that analyzed by an equilibrium mean-field theory in Ref. [24]. Finally, in Fig.…”

Section: Numerical Resultsmentioning

confidence: 97%

mentioning

confidence: 99%

Dynamics of a Josephson array in a resonant cavity

Almaas

Stroud

2002

Phys. Rev. B

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“…[17][18][19][20][21][22][23][24] In the past three years researchers have introduced different 1D models [21][22][23][24] to describe the operation of our 2D arrays. 6,8 The emphasis in these works was on explaining the high power outputs of the 2D arrays.…”

Section: Comparison To Other Modelsmentioning

confidence: 99%

Observation and a model for resonances in one-dimensional unshunted Josephson-junction arrays with ground planes

et al. 2003

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We present data from one-dimensional unshunted Josephson-junction arrays with ground planes, showing resonant behavior for certain values of the critical current. Due to the hysteresis of the current-voltage characteristics, the number of junction that oscillate on resonance can be controlled. The resonant frequency decreases as more junctions are switched onto the resonance and increases as the array length is increased. We develop a transmission-line model of the arrays that reproduces these experimental observations. We also examine the microscopic origin of this model and compare it to existing models in the literature.

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“…They interpreted their results as analogous to lasing, with gain due to stimulated Josephson tunnelling. Subsequently, Stroud et al showed that many of the experimental observations could be reproduced by classical treatments [24,25,26,27] of models similar to (9).…”

Section: Discussionmentioning

confidence: 99%

Phase-locking in quantum and classical oscillators: polariton condensates, lasers, and arrays of Josephson junctions

Eastham¹,

Szymańska²,

Littlewood³

2003

Solid State Communications

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We connect three phenomena in which a coherent electromagnetic field could be generated: polariton condensation, phase-locking in arrays of underdamped Josephson junctions, and lasing. All these phenomena have been described using Dicke-type models of spins coupled to a single photon mode. These descriptions may be distinguished by whether the spins are quantum or classical, and whether they are strongly or weakly damped.

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Model for a Josephson junction array coupled to a resonant cavity

Cited by 15 publications

References 22 publications

Dynamics of a Josephson array in a resonant cavity

Dynamics of a Josephson array in a resonant cavity

Observation and a model for resonances in one-dimensional unshunted Josephson-junction arrays with ground planes

Phase-locking in quantum and classical oscillators: polariton condensates, lasers, and arrays of Josephson junctions

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