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IEEE Transactions on Magnetics

Harmonic generation and half flux quantum periodicity in the RF-SQUID

P. Fernandez, C. Salvo, R. Parodi, Antonio Sergio Siri, Renzo Vaccarone

Published Jan 1, 1979• 2 citations
Publisher

Abstract

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.

DOI
10.1109/tmag.1979.1060150

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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.
Shapiro steps in an RF-field-driven dc-SQUID (RFDS), where an RF signal is coupled to the SQUID loop magnetically, are numerically investigated. We calculate the current–voltage characteristics of RFDSs under no dc offset flux, which show the enhancement of the even-order Shapiro steps. First, the maximum second (the lowest even-order) step height is evaluated as a function of the normalized frequency Ω. In the case of the inductance parameter βL ≥ 1.0, the maximum second step height is maintained at a certain value in the low frequency region. In the case of βL < 1.0, on the other hand, the maximum step height decreases in the low frequency region of Ω < 0.10. The dependence of the current positions of the step upon the RF signal amplitude shows that the voltage transition at the non-superconductive area between the superconducting interference lobes limits the upper current position of the step.
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.
The dc SQUID had been presented for use in the rf SQUID instead of a weak link. The new device, referred to as “double SQUID”, possesses a large output signal (hundreds of microvolts) in operating in a hysteretic mode. For making an operating mode a double SQUID is coupled to a circuit traditional for rf SQUIDs containing a tank circuit and an rf current pumping generator. The magnetic flux being measured is recognized by the dc SQUID quantization loop which results in changing its critical current. As a result the height of the flat part of the tank circuit I–V characteristics coupled to a double SQUID is modulated. It is this modulation that is the SQUID output signal. The experimental investigations of the double SQUID showed the validity of the assumptions under consideration. Output signals up to 690 μV, noise spectral density ≈2×10−5ϕ0/ Hz 1/2 (ϕ0 is the flux quantum) and energy resolution ≈1.4×10−29 J/Hz have been obtained.
We present numerical investigation of the RF properties of a double-junction SQUID model, which is referred to as an RF-field-driven double-junction SQUID (RFDS). The RFDS generates large current steps, the order of which can be controlled by external dc field. We simulate the current-voltage characteristics of the RFDS in the normalized frequency range from 0.065 to 5.0. In comparison with the results for a single junction, the step heights of the RFDS are much larger for the low frequency region; e.g. the first step of the RFDS becomes nine times larger than that of a single junction when a dc flux of 0.5 0 is applied ( 0 is a flux quantum). For the high frequency region, the step height of the RFDS is comparable to that of a single junction. The results suggest that the RFDS should be applicable as a wide-band RF detector.
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).
The output voltage of a dc superconducting quantum interference device (SQUID) containing a resistive section Rs oscillates at a frequency νq =Vs/ φ0 (φ0=flux quantum) when a current controlled voltage Vs is maintained across Rs. These oscillations have been observed from ∼10−1 to 1011 Hz, using Rs values ranging from ∼10−10 to ∼10−3 Ω in low inductance (∼10−10 H) point contact SQUID loops. At high frequencies, they manifest themselves in the dc current-voltage characteristics by inducing extra current steps.