On the quantum-mechanical description of Josephson junctions

Lugiato, L. A.; Milani, M.

doi:10.1007/bf02739171

Cited by 9 publications

(10 citation statements)

References 6 publications

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“…This model generalizes one used recently to describe the energetics of such a system [5]. It bears many resemblances to previous dynamical models, which either connect this array to laser action in excitable twolevel atoms [6] or introduce various types of impedance loads to provide global coupling between junctions [7][8][9][10]. In our model, we infer the equations of motion starting from a more conventional Hamiltonian which describes Josephson junctions coupled to a vector potential [11].…”

mentioning

confidence: 93%

“…In order to make these exact relations amenable to numerical computation, we now replace the operators by c-numbers, as should be reasonable when the eigenvalues of n j ≫ 1 [6]. To introduce dissipation into the equations of motion, we may add a term to H of the form…”

mentioning

confidence: 99%

“…This current not only lies well within the bistable region, but also leads to a voltage on the first integer SIRS. The total energyẼ(N a ) (normalized toẼ (6)) for this case is plotted as a function of N a in Fig. 3.…”

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confidence: 99%

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Resonant-cavity-induced phase locking and voltage steps in a Josephson array

Almaas

Stroud

2001

Phys. Rev. B

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We describe a simple dynamical model for an underdamped Josephson junction array coupled to a resonant cavity. From numerical solutions of the model in one dimension, we find that (i) currentvoltage characteristics of the array have self-induced resonant steps (SIRS), (ii) at fixed disorder and coupling strength, the array locks into a coherent, periodic state above a critical number of active Josephson junctions, and (iii) when Na active junctions are synchronized on an SIRS, the energy emitted into the resonant cavity is quadratic with Na. All three features are in agreement with a recent experiment [Barbara et al, Phys. Rev. Lett. 82, 1963].

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confidence: 93%

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confidence: 99%

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Resonant-cavity-induced phase locking and voltage steps in a Josephson array

Almaas

Stroud

2001

Phys. Rev. B

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“…This model generalizes one used recently to describe the energetics of such a system. 5 It bears many resemblances to previous dynamical models, which either connect this array to laser action in excitable two-level atoms 6 or introduce various types of impedance loads to provide global coupling between junctions. [7][8][9][10] In our model, however, we infer the equations of motion starting from a more conventional Hamiltonian which describes Josephson junctions coupled to a vector potential.…”

Section: Introductionmentioning

confidence: 89%

Erratum: Resonant-cavity-induced phase locking and voltage steps in a Josephson array [Phys. Rev. B63, 144522 (2001)]

Almaas¹,

Stroud²

2001

Phys. Rev. B

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We describe a simple dynamical model for an underdamped Josephson junction array coupled to a resonant cavity. From numerical solutions of the model in one dimension, we find that ͑i͒ current-voltage characteristics of the array have self-induced resonant steps ͑SIRS͒, ͑ii͒ at fixed disorder and coupling strength, the array locks into a coherent, periodic state above a critical number of active Josephson junctions, and ͑iii͒ when N a active junctions are synchronized on an SIRS, the energy emitted into the resonant cavity is quadratic with N a . All three features are in agreement with a recent experiment ͓P. Barbara, A. B. Cawthorne, S. V. Shitov, and C.

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“…A simple number-phase-angle (NPA) description can then be used to simplify the mathematical treatment8, based on the commutation relations [Sj, S] Sj Sj] S&j, [S+,S]dJ (8) The time average of < S1 >, < S > and <S zi> can be found from equations 7-8. We shall further assume that <S >, the average of operator of population inversion, is small (implying a strong departure from equilibrium).…”

Section: Total Superdelayed Luminescence E and Initial Photon Count P1mentioning

confidence: 99%