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Physical review. B, Condensed matter

Cavity-mode excitation in a Josephson tunnel junction

Jhy-Jiun Chang, J. T. Chen

Published Sep 1, 1980• 15 citations
Publisher

Abstract

Using Takanaka's theory of the zero-field dc-current steps of a Josephson tunnel junction, we have studied the effect of the junction $Q$ 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.

DOI
10.1103/physrevb.22.2392

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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\ensuremathνceV=h\frac{{\ensuremath{\nu}}_{c}}{e}V=he\ensuremathνc​​, where \ensuremathνc{\ensuremath{\nu}}_{c}\ensuremathνc​ 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.
We have investigated theoretically the amplitudes of RF- induced constant voltage steps in two-dimensional Josephson tunnel junctions, using both a first-order approximation and a numerical it- eration procedure to calculate the current density distribution in the junction. We use a planar resonator model to analyze the electromag- netic field in the microwave-driven junction. Integrating the local Jo- sephson current density over the junction area yields the total dc current on a chosen Shapiro step. Numerical calculations of the Sha- piro step amplitudes in two-dimensional resonant junctions show a qualitatively different behavior from that in one-dimensional resonant junctions. Depending on the dominant resonant mode, the microwave power dependence of the step amplitude gives a smooth curve without zeros. This behavior is advantageous for biasing the Josephson junc- tion in its maximum step amplitude. The main difference between the results of the first-order approximation and the full theory is that- using the iteration procedure-the Shapiro steps in resonant junctions become asymmetric with respect to the quasi-particle curve. This is due to consideration of the losses and the internal Josephson currents in the numerical iteration procedure of the full theory.
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.
A new parametric mode in a Josephson tunnel junction biased in the zero-voltage mode is suggested. It is a nondegenerate parametric excitation where the junction plasma resonance represents the input circuit, and a junction geometrical resonance represents the idler circuit. This nondegenerate mode has been observed in analog experiments. In a real junction the realization of this mode of operation depends on the coupling between the plasma resonance and the geometrical resonance, and it is argued that without an external dc magnetic field the even geometrical resonances are most favorable for such a coupling.
This paper investigates the physical nature of a series of step structures or oscillations present in a Josephson current within one magnetic flux quantum when either a Josephson junction, a double junction squId, or a single junction superconducting ring is placed inside a high Q cavity under the condition in which the Josephson frequency is equal to the resonance frequency of the cavity. The frequency effect of the feedback field produces a series of induced current steps in the Josephson junction or the two-junction squId when ..omega.. = ..omega../sub r/. The oscillating electromagnetic field excited by the junction current acts on the junction itself. A series of new current step structures occur within one magnetic flux phi/sub 0/ quantum, since the amplitude of the feedback field is modulated by an applied magnetic field as the modulation of the amplitude of the feedback field is coupled to that of the radiation. For the superconducting ring containing a single junction, as n..omega.. = ..omega../sub r/, the feedback radiation of the stationary electromagnetic wave will give rise to a constrained oscillation of the supercurrent with a period smaller than that of the superconducting current oscillation phi/sub 0/.
Josephson junctions connected to high Q microstriplines display current-steps which we attribute to standing wave resonances. The step voltages of the resonances depend on sample geometry and correspond to frequencies at which the loaded microstrip is resonant. The voltages of the resonances are insensitive to applied magnetic field and junction current density. Current step amplitudes scale with the zero-voltage critical current, and are largest for zero applied magnetic field. The strength of these resonant steps has important implications for biasing weakly damped Josephson junction circuits. In addition, the resonances are a useful tool for measuring microstrip properties.
We point out that by placing a large Josephson junction in high Q-value cavity whose rth eigen mode is excited by the Josephson frequency ω0=2cV0/h, the oscillating electromagnetic field will act on the juntion and one must recognize that the space part of the eigen mode of the field are not the same on the junction. We have obained theoretical result which is different from paper [2] and shows how the step structure current vary with the magnetic field. The match condition for eigen mode of the feedback field from the cavity and electromagnetic field radiated by Josephson junction has been worked out. Finally, the physical reason for the absence of step structure with period less than φ0 is given.