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Physical review. B, Condensed matter

Self-induced steps in a small Josephson junction strongly coupled to a multimode resonator

A. Larsen, Hans Dalsgaard Jensen, J. Mygind

Published May 1, 1991• 31 citations
Publisher

Abstract

An equally spaced series of very large and nearly constant-voltage self-induced singularities has been observed in the dc I-V characteristics of a small Josephson tunnel junction strongly coupled to a resonant section of a superconducting transmission line. The system allows extremely high values of the coupling parameter. The current steps are due to subharmonic parametric excitation of the fundamental mode of the resonator loaded by the junction admittance. Using an applied magnetic field to vary the coupling parameter, we traced out half-integer steps as well as the mode steps known from more weakly coupled systems. Based on a single-resonator model, we explain the exceptional size of the steps by the large content of higher harmonics of the Josephson oscillation sustained by the multiple modes of the resonator. The parameters of the junction and the loaded resonator---measured in situ by using the junction as detector---form a consistent set. The dominant system loss originates in the junction but cannot be ascribed to a relevant conductance.

DOI
10.1103/physrevb.43.10179

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An equally spaced series of very large and nearly constant-voltage self-induced singularities has been observed in the dc I-V characteristics of a small Josephson tunnel junction strongly coupled to a resonant section of a superconducting transmission line. The system allows extremely high values of the coupling parameter. The current steps are due to subharmonic parametric excitation of the fundamental mode of the resonator loaded by the junction admittance. Using an applied magnetic field to vary the coupling parameter, we traced out half-integer steps as well as the mode steps known from more weakly coupled systems. Based on a single-resonator model, we explain the exceptional size of the steps by the large content of higher harmonics of the Josephson oscillation sustained by the multiple modes of the resonator. The parameters of the junction and the loaded resonator---measured in situ by using the junction as detector---form a consistent set. The dominant system loss originates in the junction but cannot be ascribed to a relevant conductance.
Self-pumped parametric excitations and mutual locking in systems of Josephson tunnel junctions coupled to multimode resonators are reported. For the very large values of the coupling parameter, obtained with small Nb-Al/sub 2/O/sub 3/-Nb junctions integrated in superconducting microstrip resonators, the DC I-V characteristic shows an equidistant series of current steps generated by subharmonic pumping of the fundamental resonator mode. This is confirmed by measurement of frequency and linewidth of the emitted Josephson radiation.
The high frequency properties of the one-dimensional transmission line consisting of a parallel array of resistively shunted Josephson tunnel junctions have been studied in the limit of relatively low damping where this nonlinear system exhibits new and interesting phenomena. Here we report on experimental and numerical investigations of a resonant step observed at a voltage corresponding to 600 GHz in the dc current-voltage characteristic of a parallel array of 20 identical small NbAl2O3Nb Josephson junctions interconnected by short sections of superconducting microstrip line. The junctions are mutually phase locked due to collective interaction with the line sections excited close to the half wavelength resonance. The phase locking range can be adjusted by means of an external dc magnetic field and the step size varies periodically with the magnetic field. The largest step corresponds to a superconducting phase difference of π between neighboring junctions.
The high frequency properties of the one-dimensional transmission line consisting of a parallel array of resistively shunted Josephson tunnel junctions have been studied in the limit of relatively low damping where this nonlinear system exhibits new and interesting phenomena. Here we report on experimental investigations of a resonant step observed at a voltage corresponding to 600 GHz in the dc current-voltage characteristic of a parallel array of 20 identical small NbAlO/sub x/Nb Josephson junctions interconnected by short sections of superconducting microstrip line. The junctions are mutually phase locked due to collective interaction with the line sections excited close to the half wavelength resonance. The phase locking range can be adjusted by means of an external dc magnetic field and the step size varies periodically with the magnetic field.>
We have measured the current-voltage characteristic of a small capacitance tunnel junction coupled to a transmission line resonator. We calibrate the resonator using the sharp resonances displayed by the junction in the superconducting state, which corresponds to the pumping of the modes of the resonator by the ac Josephson current. With this calibration, we explain quantitatively the nonlinearity of the junction characteristic in the normal state as being due to the process by which a single electron tunnels by emitting a photon, the basic process of the theory of the effect of the electromagnetic environment on tunneling.
Using Takanaka's theory of the zero-field dc-current steps of a Josephson tunnel junction, we have studied the effect of the junction QQQ factor on the shape of the current step near the first even-order resonant voltage $V=h\frac{{\ensuremath{\nu}}_{c}}{e}$, where ${\ensuremath{\nu}}_{c}$ is the frequency of the fundamental cavity mode. In addition, we have found that the effect of a magnetic field on the step height can be qualitatively explained by modifying Takanaka's theory to include a magnetic-field-dependent term.