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Journal of Applied Physics

Shapiro steps on current-voltage curves of dc SQUIDs

C. Vanneste, C. C., W. J. Gallagher, Alan W. Kleinsasser, Stanley I. Raider, Robert L. Sandstrom

Published Jul 1, 1988• 46 citations
Publisher

Abstract

We have studied in detail the current-voltage (I-V) curves of dc SQUIDs in the presence of rf fields in the frequency range 2–18 GHz. Strong voltage locking at half-integral as well as the usual integral Shapiro step spacing is observed when the applied dc-magnetic flux is close to half-integral numbers of flux quanta. Numerical simulations are in excellent agreement with the experimental I-V curves. The half-integral steps are found to be associated with the flip-flop between two adjacent fluxoid states of the SQUID synchronized to the rf field.

DOI
10.1063/1.341471

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We have studied in detail the current-voltage (I-V) curves of dc SQUIDs in the presence of rf fields in the frequency range 2–18 GHz. Strong voltage locking at half-integral as well as the usual integral Shapiro step spacing is observed when the applied dc-magnetic flux is close to half-integral numbers of flux quanta. Numerical simulations are in excellent agreement with the experimental I-V curves. The half-integral steps are found to be associated with the flip-flop between two adjacent fluxoid states of the SQUID synchronized to the rf field.
A high-Tc dc superconducting quantum interference device (SQUID) with three Josephson junctions (JJs) in series in each of its arms has been fabricated. Its Shapiro steps were studied using microwave (rf) radiation of 10 GHz and weak magnetic fields. The appearance of giant Shapiro steps and of some of half-integer steps was observed. Separation between the adjacent Shapiro steps could be tuned by rf magnetic fields and small external dc magnetic fields. This phenomenon was analyzed by phase locking the JJs in the SQUID.
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.
The current height of RF-induced voltage steps in nonhysteretic single Josephson junctions is usually a small fraction of the critical current. It is demonstrated that when a resistively shunted DC superconducting quantum interference device (SQUID) is subjected to an RF magnetic flux, a voltage step with a large current height is obtained. In contrast to weak selection rules for single Josephson junctions, strong selection of the step harmonic number occurs in a shunted DC SQUID for appropriate choice of RF amplitude and DC flux offset, with odd harmonic numbers selected by half-integer flux quantum offsets and even harmonic numbers by integer flux quantum offsets. This pronounced effect has immediate implications for voltage standards and fast, high-precision digital-to-analog converters.>
We have been studying an RF-Field-driven DC SQUID (RFDS) that exhibits RF-induced-current-steps larger than those of single junctions at lower normalized frequency and a strong selection rule for the step orders which depends on the external DC magnetic field. In RFDS, even order steps are dominant in the absence of DC magnetic field. Contrarily, a DC magnetic field of a half flux quantum dominantly enhances odd order steps. Therefore the output of an RFDS can be switched between two voltage levels corresponding to the RF-induced-step by an external DC field input for a certain bias condition. We carried out numerical simulations to characterize the switching properties of the RFDS for various bias conditions, including RF circulating currents and DC bias current.
Shapiro voltage steps at voltages V n = nV 0 occur in the voltage-current characteristics of a superconducting film with a periodic pinning potential in the presence of rf radiation. We report on their experimental observation in a superconducting film with a square lattice of perforated microholes (antidots) and on numerical simulations showing the Shapiro steps in the voltage-current characteristics of the dc flux transformer. For the square antidot lattice, the ratio VQ/V of the step height to the applied rf frequency depends on the antidot lattice period d, while in the flux transformer geometry this ratio can be tuned by the magnetic field. This tuneability of the resolution makes the flux transformer a good candidate for applications (e.g. broad-band radiation detection).
We demonstrate a zero-crossing Shapiro step in a three-junction SQUID (3J-SQUID) coupled with two phase-shifted RF signals. The operation is based on periodic flux quantum transitions in the 3J-SQUID under the zero- and negatively-biasing conditions. A test circuit is fabricated using a Nb/AlO/sub x//Nb junction technology. When we feed RF signals up to 10.5 GHz, we observe a Shapiro step crossing the zero-current axis at the voltage position of the 1st order. The experimental current-voltage characteristics are quantitatively reproduced by simulation. Zero-crossing conditions for the DC offset flux and the RF power are obtained experimentally, which is also confirmed by simulation. A programmable Josephson voltage standard is discussed as one of the possible applications.