Radio-frequency method for characterization of superconducting weak links

Robert Rifkin

Jason F. Ralph, Terrence D. Clark, Robert J. Prance +2 more

We use a discrete-field model for the quantum evolution of distributed superconducting circuits to calculate the effective capacitance for a radio-frequency-SQUID magnetometer: a large-capacitance superconducting ring containing an ultra-small-capacitance weak link. We demonstrate that the self-capacitance of the weak link can dominate the behaviour of the circuit.

William H. Howard, Y. H. Kao

A. Baratoff, James A. Blackburn, Brian B. Schwartz

Philippe Lethuillier

The electrical equations of a resonant circuit fed with a radio-frequency current and inductively coupled to a weakly superconducting loop have been derived. The current-voltage characteristic of the rf superconducting quantum interference device can then be calculated and studied as a function of the junction resistance or of the resonance frequency, enabling its behavior to be better understood. As shown by Kurkijärvi, the large positive slope of the steps and the rounding of the characteristic result from thermal noise. However, in order to explain quantitatively the experimental results concerning, namely, point contact weak links which are generally oxidized or which have several contact points, it is useful to remark that the connection between the two superconductors constituting the Josephson junction may be made from n resistive paths. The mean thermal energy of the fluctuating flux is then close to nkbT instead of kbT if the inductances linking the contact points are large enough, that is, on the order of 10−11 H.

Arnold H. Silver, James Edward Zimmerman

Voltage biasing of a single superconducting weak link results in coherent electromagnetic oscillation at the frequency $\ensuremath{\nu}=\frac{V}{{\ensuremath{\Phi}}_{0}}$; simultaneous voltage biasing of two weak links in a superconducting ring produces two strongly coupled oscillators at the same frequency. The electromagnetic phase difference is the difference in the gauge-invariant quantum phases across the two contacts. Because of the quantization of the superconducting ring, this phase difference is $\frac{2\ensuremath{\pi}〈\ensuremath{\Phi}〉}{{\ensuremath{\Phi}}_{0}}$, where $〈\ensuremath{\Phi}〉$ is the time-averaged magnetic flux in the superconducting circuit and ${\ensuremath{\Phi}}_{0}$ is the flux quantum. We can characterize the coupled system in terms of normal modes, and we have experimentally observed these modes of oscillation at 30 MHz. This provides a means of understanding the earlier observations of quantum interference in the resistive state.