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Journal of Physics F Metal Physics

The response of RF superconducting quantum interferometers, particularly those containing resistive sections, to magnetic flux modulation

J G Park

Published Jun 1, 1973• 4 citations
Publisher

Abstract

The response of a double hole RF SQUID to modulation by magnetic flux phi e introduced into one of the holes is first considered. The output voltage v 0 is a periodic function of phi e but it is shown that one would expect the period not to be equal to the flux quantum phi 0 itself but to some multiple of it. The flux in either hole of the SQUID may be calculated by imagining the weak link broken and the RF drive removed: one period of the v 0 variation is produced by a change in phi e sufficient to change the flux in either hole (averaged over one RF cycle), due both to current in the coil and to current induced on the inside wall of the SQUID, by phi 0 . This principle is applied to a double hole SQUID modified by the replacement of part of one wall by a block of normal metal (an R SQUID). Explicit expressions for the response to modulation, which is frequency dependent, are derived in the limit of low frequency, and more generally, at any frequency, for an R SQUID in which both the holes and the modulation coil are long in comparison with their diameter. The size of the superconducting screen which must surround the R SQUID, if only to avoid interference from other magnetic fields in the laboratory, is shown to play an important part in determining the response at low frequencies. The spectrum of noise currents is also calculated.

DOI
10.1088/0305-4608/3/6/012

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IEEE Transactions on Applied Superconductivity•Jun 1, 1999•17 citations
The response of a double hole RF SQUID to modulation by magnetic flux phi e introduced into one of the holes is first considered. The output voltage v 0 is a periodic function of phi e but it is shown that one would expect the period not to be equal to the flux quantum phi 0 itself but to some multiple of it. The flux in either hole of the SQUID may be calculated by imagining the weak link broken and the RF drive removed: one period of the v 0 variation is produced by a change in phi e sufficient to change the flux in either hole (averaged over one RF cycle), due both to current in the coil and to current induced on the inside wall of the SQUID, by phi 0 . This principle is applied to a double hole SQUID modified by the replacement of part of one wall by a block of normal metal (an R SQUID). Explicit expressions for the response to modulation, which is frequency dependent, are derived in the limit of low frequency, and more generally, at any frequency, for an R SQUID in which both the holes and the modulation coil are long in comparison with their diameter. The size of the superconducting screen which must surround the R SQUID, if only to avoid interference from other magnetic fields in the laboratory, is shown to play an important part in determining the response at low frequencies. The spectrum of noise currents is also calculated.
It is theoretically explained that a response of a superconducting quantum interference device (SQUID) is periodically dependent on total magnetic flux coupling to the SQUID ring (Φ) and its period is a flux quantum (Φ(o)=h/2e, where h and e, respectively, express Planck's constant and elementary charge). For example, the voltage of an electromagnetically oscillated rf-SQUID or a current biased dc-SQUID is thought to be periodically dependent on Φ with a period of Φ(o). In this paper, we propose an accurate method to check the periodicity of a SQUID response by using a set of sensing coils covered with a superconducting sheath. As a demonstration, we measured periodicity of a commercially available thin-film type rf-SQUID response in magnetic flux ranging up to approximately 4300Φ(o). Its flux dependence was periodic below about 3400Φ(o).
Superconducting quantum interference devices (SQUIDs) are among the most sensitive detectors for out-of-plane magnetic field components. However, due to their periodic response with short modulation period M=1Φ0M = 1 Φ_0M=1Φ0​, determined by the magnetic flux quantum Φ0≈2.068×10−15 WbΦ_0 \approx 2.068\times 10^{-15}\,\mathrm{Wb}Φ0​≈2.068×10−15Wb, it is difficult to infer the value of the magnetic flux unambiguously, especially in case the magnetic flux enclosed in the SQUID loop changes by many flux quanta. Here, we demonstrate that by introducing a second degree of freedom in the form of a second SQUID, we substantially enhance the modulation period MMM of our device without sacrificing sensitivity. As a proof of concept, we implement our idea by embedding two asymmetric direct current SQUIDs into a common tank circuit. By measuring the reflection coefficient of the device, we extract the two lowest energy eigenfrequencies as a function of the external magnetic flux created by a superconducting field coil, from which we experimentally deduce a modulation period M≥15Φ0M \geq 15 Φ_0M≥15Φ0​, as well as the magnetic offset-field B0=22 nTB_0 = 22\,\mathrm{nT}B0​=22nT present in our experiment.
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/.
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.
Using a superconducting ring containing a Nb point contact inductively coupled to a resonant circuit fed with an rf current source, (typical rf SQUID configuration) we have measured the tank voltage as a function of frequency in the regimeLI_{c}< \Phi_{0}/2\pi. ForLI_{c} \ll \Phi_{0}/2\pi, the curves of tank voltage versus drive current for various values of external flux\Phi_{x}through the ring agree with the calculations of Hansma. For higher critical currents, there is an asymmetry in these curves for frequencies above and below ω0, the resonant frequency of the circuit. Calculations using an expanded theory including the effects of a conductanceG_{o}(1+\alpha \cos \phi)and of screening flux give good agreement with the data. In principle α can be determined from these measurements, however the\cos \phiterm and the screening flux produce qualitatively similar effects. A quantitative determination of α requires a precise knowledge of Go/Ic. Using values of Goand Icfrom independent impedance measurements, the data yield a negative value of α in agreement with another experiment.
This paper demonstrates a design of a planar multi-turn flux transformer integrated with a superconducting labyrinth resonator serving as the planar tank circuit for a radio frequency (rf) superconducting quantum interference device (SQUID) magnetometer. All structures were patterned from 200 nm-thick epitaxial YBa/sub 2/Cu/sub 3/O/sub 7/ (YBCO) films grown on 10/spl times/10 mm/sup 2/ LaAlO/sub 3/ substrates. A double-hole washer SQUID had one hole coupled to the input coil of the labyrinth resonator and the other hole coupled to the input coil of the multi-turn flux transformer using a flip-chip configuration to form a magnetometer. This resonator has a good high-frequency coupling to the double-hole rf SQUID, thus securing its optimum operation. For the voltage-to-flux (transfer function) coefficient, a value of 300-500 /spl mu/V//spl Phi//sub 0/ was obtained. A SQUID magnetometer with an inductance of 210 pH exhibited white flux noise of 11.5 /spl mu//spl Phi//sub 0///spl radic/Hz at 77 K. This corresponded to a white magnetic field noise of 11.5 fT//spl radic/Hz.