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Physical review. B, Condensed matter

Direct observation of a threshold for coherent radiation in unshunted Josephson-junction arrays with ground planes

Branimir Vasilić, Paola Barbara, S. V. Shitov, Christopher J. Lobb

Published Apr 23, 2002• 18 citations
Publisher

Abstract

Previous experiments [Barbara et al., Phys. Rev. Lett. 82, 1963 (1999); Vasili\ifmmode \acute{c}\else \'{c}\fi{} et al., Appl. Phys. Lett. 78, 1137 (2001)] showed that two-dimensional, unshunted Josephson-junction arrays emit radiation coherently when a threshold number of junctions is switched to a radiating state. Here, we report low-power radiation being emitted when the number of radiating junctions is smaller than the threshold number. We show that in this regime the output power is incoherent, i.e., the array behavior is qualitatively different from the coherent regime.

DOI
10.1103/physrevb.65.180503

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Previous experiments [Barbara et al., Phys. Rev. Lett. 82, 1963 (1999); Vasili\ifmmode \acute{c}\else '{c}\fi{} et al., Appl. Phys. Lett. 78, 1137 (2001)] showed that two-dimensional, unshunted Josephson-junction arrays emit radiation coherently when a threshold number of junctions is switched to a radiating state. Here, we report low-power radiation being emitted when the number of radiating junctions is smaller than the threshold number. We show that in this regime the output power is incoherent, i.e., the array behavior is qualitatively different from the coherent regime.
We report measurements of mm-wavelength radiation from two-dimensional arrays of underdamped Josephson junctions. All of our samples emit coherently in a novel synchronized state, which is triggered by a resonance in the array structure. Measurements of the detected power as a function of the number NNN of active junctions show a threshold, suggesting population inversion. Above threshold, the power scales with N2{N}^{2}N2 up to an array size bigger than the free-space radiation wavelength. The highest measured conversion efficiency from dc to ac power is about 17%. Our data are consistent with stimulated emission causing coherence and cannot be explained by existing classical coupling mechanisms.
The authors have detected coherent emission from two-dimensional (2D) arrays of superconductor-insulator-superconductor (SIS) Josephson junctions. 2D arrays emit coherent radiation over a frequency range of 60 to 210 GHz, when coupled to detector junctions through DC-blocking capacitors. The detector junctions exhibit Shapiro steps at frequencies corresponding to the voltage across single-array junctions. The maximum power from a 10-by-10 junction-array coupled to a detector junction occurs at 150 GHz and is estimated to be 0.4 mu W, based on simulations of the detector circuit. By varying the number of array junctions, the array geometry, the junction critical current, and the coupling circuit, they have begun determining the essential conditions for observing coherent emission.
We have investigated two-dimensional arrays of overdamped Josephson junctions that have been fabricated in Nb/Al/sub 2/O/sub 3//Nb-technology, together with microwave coupling structures. Different arrays have shown to emit coherent microwave radiation by using microwave-coupled on-chip detectors. Low-temperature scanning electron microscopy is used to study the coupling of the microwave radiation to an on-chip load. From the appearance of Shapiro steps in the current vs. voltage curves of detector junctions for different degrees of disorder in the array-junctions, margins of the spread in the critical currents of the Josephson junctions for coherent oscillation can be drawn.
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,{N}^{2},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.