Effect of cross-type bias in a two-dimensional array of short Josephson junctions

We carry out a quantum-mechanical analysis of a small Josephson junction coupled to a single-mode resonant cavity. We find that the eigenstates of the combined junction-cavity system are strongly entangled only when the gate voltage applied at one of the superconducting islands is tuned to certain special values. One such value corresponds to the resonant absorption of a single photon by Cooper pairs in the junction. Another special value corresponds to a two-photon absorption process. Near the single-photon resonant absorption, the system is accurately described by a simplified model in which only the lowest two levels of the Josephson junction are retained in the Hamiltonian matrix. We noticed that this approximation does not work very well as the number of photons in the resonator increases. Our system shows also the phenomenon of "collapse and revival" under suitable initial conditions, and our full numerical solution agrees with the two level approximation result.

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“…Thus, a rather different approach, such as those described in Refs. [17][18][19][20][21] is called for.…”

Section: Discussionmentioning

confidence: 99%

Eigenstates of a small Josephson junction coupled to a resonant cavity

Al-Saidi

Stroud

2001

Phys. Rev. B

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“…1͒ and vertically, i.e., all junctions in the array must be made to enter the voltage state. 28 Similar thinking led Filatrella, Pedersen, and Wiesenfeld 14 to study a 2ϫ2 array with identical junctions using what they described as a cross-type biasing. In contrast to the current injection scheme of Fig.…”

Section: Introductionmentioning

confidence: 96%

“…[1][2][3][4][5][6][7][8] Theoretical studies have begun to determine under what conditions and for what ranges of circuit parameters coherent emission should be possible from such arrays. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] These arrays are also of interest as paradigms of nonlinear dynamical systems with many degrees of freedom. [24][25][26][27] Of particular interest have been the so-called phaselocked states of such arrays.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional arrays of Josephson junctions in a magnetic field: A stability analysis of synchronized states

Trees

Stroud

1999

Phys. Rev. B

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We report the results of a Floquet analysis of two-dimensional arrays of resistively and capacitively shunted Josephson junctions in an external transverse magnetic field. The Floquet analysis indicates stable phase locking of the active junctions over a finite range of values of the bias current and junction capacitance, even in the absence of an external load. This stable phase locking is robust against critical current disorder, up to at least a Ϯ25% rms spread in critical currents.

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“…[13][14][15][16] As test beds for both theoretical and experimental studies of synchronization of disordered oscillator systems, JJ arrays serve an important purpose, but in addition there has been interest for some time in arrays as sources of coherent microwave radiation. [17][18][19][20][21][22][23][24][25][26][27][28][29][30] The experiments by Barbara and co-workers 31 demonstrated that two-dimensional, underdamped arrays in a high-Q resonance cavity formed by the array itself and a ground plane could emit coherent mm-wavelength radiation at power levels much higher than seen before. The main criteria for the high detected ac power output was a sharp resonance of the cavity and a coupling mechanism between the cavity and the individual JJs.…”

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confidence: 99%

Nanomechanical-resonator-induced synchronization in Josephson junction arrays

2005

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We show that a serial array of N nonuniform, underdamped Josephson junctions coupled piezoelectrically to a nanoelectromechanical ͑NEM͒ oscillator results in phase locking of the junctions. Our approach is based on a semiclassical solution to a set of coupled differential equations that were generated by the Heisenberg operator equations, which in turn are based on a model Hamiltonian that includes the following effects: the charging and Josephson energies of the junctions, dissipation in the junctions, the effect of a dc bias current, an undamped simple harmonic oscillator ͑representing the NEM͒, and an interaction energy ͑due to the piezoelectric effect͒ between the NEM and the junctions. Phase locking of the junctions is signaled by a step in the current-voltage ͑I-V͒ curve. We find the phase-locked states are ͑neutrally͒ stable at the bottom and top of the step but not for bias currents in the middle of the step. Using harmonic balance, we are able to calculate an analytical expression for the location of the resonance step, v step , in the I-V curve. Because of the multistability of the underdamped junctions, it is possible, with a judicious choice of initial conditions and bias current, to set a desired number N a ഛ N of junctions on the resonance step, with N − N a junctions in the zero-voltage state. We are also able to show that, when N a junctions are in the phase-locked configuration, the time-averaged energy of the NEM oscillator scales like N a 2 .

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Effect of cross-type bias in a two-dimensional array of short Josephson junctions

Abstract: We investigate numerically the effect of cross-type bias on two-dimensional arrays of short Josephson junctions. We have demonstrated that, for the simplest circuit, this type of bias is able to phase lock the junctions yielding a substantial improvement over ordinary biasing schemes.

Cited by 10 publications

References 19 publications

Eigenstates of a small Josephson junction coupled to a resonant cavity

Eigenstates of a small Josephson junction coupled to a resonant cavity

Two-dimensional arrays of Josephson junctions in a magnetic field: A stability analysis of synchronized states

Nanomechanical-resonator-induced synchronization in Josephson junction arrays

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