Although we have chosen to consider the canonically conjugate roles of magnetic flux and charge in a thick superconducting ring containing a weak link, this quantum mechanical description can be carried over to the case of a superconducting weak link enclosed in a normal metal ring. The concept still holds that for small enough cross sections flux can be transferred quantum mechanically back and forth across the weak link in units of ±Φ0,
±2Φ0…±nΦ0. Thus equation [29], which yields the ground-state charge-band energy, is not dependent on the weak link being contained within a
superconducting ring. Magnetic flux is still confined when the ring is normal, at least on a time scale short compared with the circuit time constant of the ring (Λ/R, where R is the resistance of the normal section).
We have started to investigate the rf behaviour of niobium point-contact weak links incorporated in normal copper rings. We find that these hybrid rings, operated at frequencies between 17 and 30 MHz, display perfectly good SQUID charge mode VOUT versus IIN characteristics which are split in
the usual way by a static bias displacement charge (Qx). We have not observed flux mode behaviour in these hybrid rings. The obvious difference
between the normal copper and superconducting niobium ring devices is that for the former the Qx-bias cannot be generated by currents of too small a
modulation frequency. When the inverse of this frequency becomes comparable with Λ/R, the time-dependent bias fluxΦx, which is required to generate
Qx, simply leaks out through the copper ring and does not cut across the weak link.
As an example of the behaviour of hybrid rings we show in Figure 7.14 the result of our first attempt to monitor directly the ground-state charge band of the superconducting niobium weak link. We plot the mean square noise voltage across the tank circuit coupled to the ring as a function of increasing bias displacement charge with no rf current drive applied to the tank circuit and, from [31], observe the second derivative pattern versus Qx
with the weak link operating in the ground-state band. This is the charge mode analogue of the noise spectroscopy technique used to plot the flux-mode magnetic susceptibility ( equation [19], Figures 7.6 and 7.7) as a function of external applied flux Φx. The susceptibility spikes in Figure
7.14, which were recorded using a linearly increasing and decreasing (triangular modulation) Qx at a frequency of 3 kHz, are somewhat truncated in height
due to band-width limitations in the charge-mode receiver system. Nevertheless, the power of the noise spectroscopy technique and the correspondence between flux-mode and charge-mode susceptibility data (Figure 7.6(a) and Figure 7.14) are obvious.
Figure 7.14 Plot of mean square noise voltage as a function of linearly increasing triangular modulation frequency to generate set at 3 kHz; frequency band-pass for measurement 10 kHz to 100 kHz; T=1.5 K; periodicity=q/C.
Conclusions
We have attempted to provide a systematic description of weak link ring devices treated as single macroscopic quantum objects. We have demonstrated that within this description even these simple objects display a remarkably rich macroscopic quantum-mechanical structure. However, the usefulness of these devices in any future study of quantum mechanics itself, and its relationship to relativity, is an area still to be explored.
Acknowledgments
I would like to thank my friends and fellow researchers at the University of Sussex, Drs R.J.Prance, J.E.Mutton, H.Prance and T.P. Spiller for making all this work possible. I am also grateful to Dr R. Nest of the University of Copenhagen for his much appreciated collaboration with us and to Professor A.Widom of Northeastern for his unique contribution to this subject. Our special thanks to Dr J.
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