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IEEE Transactions on Applied Superconductivity

Signal properties of radio frequency SQUID with a finite amplitude of the second harmonic in the current-phase relationship

Evgeni V. Il’ichev, Ya. S. Greenberg, R.P.J. IJsselsteijn, V. Schultze, Hans E. Hoenig, H.‐G. Meyer

Published Mar 1, 2001• 0 citations
Publisher

Abstract

The signal properties of radio frequency (rf) SQUIDs with a finite amplitude of the second harmonic in the current-phase relationship have been theoretically and experimentally investigated. Both amplitude as well as phase detection has been considered in order to readout the SQUID's output signal. We observed peculiarities of the rf SQUID response of a SQUID with YBCO 45 degree grain boundary Josephson junction. We found that the current-phase relationship contains a finite amplitude of the second harmonic. Comparison of the theoretical and experimental results is given. It is shown that the sign of the amplitude of the second harmonic can be determined from the shape of experimental curves, and the value of this amplitude is defined by the positions of extrema of these curves.

DOI
10.1109/77.919543

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The signal properties of radio frequency (rf) SQUIDs with a finite amplitude of the second harmonic in the current-phase relationship have been theoretically and experimentally investigated. Both amplitude as well as phase detection has been considered in order to readout the SQUID's output signal. We observed peculiarities of the rf SQUID response of a SQUID with YBCO 45 degree grain boundary Josephson junction. We found that the current-phase relationship contains a finite amplitude of the second harmonic. Comparison of the theoretical and experimental results is given. It is shown that the sign of the amplitude of the second harmonic can be determined from the shape of experimental curves, and the value of this amplitude is defined by the positions of extrema of these curves.
The signal properties of radio frequency (rf) (SQUIDs) based on YBa2Cu3O7−x symmetrical 30° and asymmetrical 45° grain-boundary Josephson junctions have been experimentally investigated. Both amplitude as well as phase detection have been used to read out the SQUID output signal. Comparison of the SQUID output signals to each other is given. It is shown that peculiarities of the rf SQUID response of SQUIDs with a 45° grain-boundary Josephson junction are consistent with an unconventional current-phase relation (CPR) of the Josephson junction, namely, the CPR contains a finite amplitude of the second harmonic.
We measured the amplitude–frequency characteristics of radio frequency superconducting quantum interference devices (rf SQUIDs) over a temperature range between 65 and 79 K. Using the expressions derived from the recently developed rf SQUID theory, valid also at large thermal fluctuations, we determined from these data the basic parameters of high-transition-temperature superconductor (HTS) rf SQUIDs. These parameters were: (a) the high-frequency coupling coefficient between the rf SQUID and the tank circuit resonator, k, (b) the SQUIDs hysteretic parameter, β, (c) the critical current of the Josephson junction, Ic, (d) its normal resistance, Rn, and (e) its noise parameter, Γ. We found a good agreement with the values of β(Ic) and Rn determined directly after destructively opening the SQUID loop. In accordance with the theoretical predictions, our experimental results show that at large thermal fluctuation levels (T≅77 K), rf SQUIDs with large loop inductance operate in nonhysteretic mode up to β values exceeding 3. Furthermore, we have shown that the optimal energy sensitivity is attained in the nonhysteretic mode at a value of β distinctly higher than 1. A quantitative comparison of white noise predicted by the theory with that obtained from the experiment showed a reasonable agreement. We also discussed the contribution of the phase information to the SQUID’s signal and noise at optimum operation conditions, when a mixer was used as a signal detector.
We have studied the basic characteristics of a radio frequency superconducting quantum interference device (rf SQUID) involving two Josephson junctions connected in series, the case for the widely used grain boundary junction (GBJ) rf SQUID. It is found that the SQUID properties are determined mainly by the weaker junction when the critical current of the weaker junction is much lower than that of the other junction. Otherwise, the effect of the other junction is not negligible. We also find that only when the hysteresis parameter β is less than 1−α, where α is the critical current ratio of the two junctions, will the SQUID operate in the nonhysteretic mode.
We studied the RF driven SQUID by a numeric simulation and experimentally. The amplitude and the phase of the RF voltage vs RF driving current and DC flux has been obtained both with the SQUID working in the conventional mode and in a new operating mode based on the 2nd harmonic generation in the system. A spectral analysis has been carried out and we report the characteristics of harmonic and subharmonic generation. For the even harmonic components, and in particular for the second one on which the proposed method is based, the VRFvs IRFstaircase pattern is replaced by a series of peaks. We find that the position of the peaks does not depend on the DC flux level and so they result in a stable marker for RF level measurements. The 2nd harmonic output, as a function of DC flux, shows a triangular behaviour with VRF= 0 at\phi_{DC} = n \phi_{0}/2. The dependence of VRFon φDCis at least as high as in the conventional operating mode. We have experimentally verified the harmonic generation and the half flux quantum periodicity up to the 4th harmonic. The signal amplitude was enough to allow flux-locked-loop operation.
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.
Conventional rf SQUIDs (superconducting quantum interference devices) consist of a superconducting loop interrupted by one weak link, and when read out via a tank circuit they produce output signals in the order of a few tens of microvolts. When the single weak link is replaced by a dc SQUID (a superconducting loop with two junctions) a so-called double quantization loop SQUID is formed. In this paper it is shown theoretically, and supported experimentally with thin-film devices of three different designs, that the general behaviour can be explained by a simplified picture of the fixed critical current of the single junction of the rf SQUID being replaced by an effective critical current of a dc SQUID loop that is varied by the applied magnetic flux (i.e., we have a rf SQUID with a variable β parameter). A more detailed analysis of the experimental data and the theory of this novel device reveals its interesting nonlinear character and shows the deviations from this simple picture. It is demonstrated experimentally that output signals in the order of ≥1 mV can be obtained with a suitable read-out mode for the tank circuit, a clear advantage when compared to conventional rf SQUIDs. With respect to dc SQUIDs, the coupling to integrated planar input coils will be unproblematic since no microwave resonances should occur in the structures.