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Superconductor Science and Technology

Numerical investigation for the frequency dependence of Shapiro steps in an RF-field-driven SQUID

Yoshinao Mizugaki

Published Nov 5, 2003• 2 citations
Publisher

Abstract

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.

DOI
10.1088/0953-2048/16/12/012

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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.
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.
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.
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We demonstrate a zero-crossing Shapiro step in an asymmetric two-junction superconducting quantum interference device (SQUID) driven by one sinusoidal RF signal. The operation is based on the imbalanced evolution of the junction phases due to the tilted interference diagrams. A test circuit was fabricated using Nb/AlO x /Nb junction technology. When we applied an RF signal of 10 GHz, we observed a Shapiro step crossing the zero-current axis at the voltage position of the first order. The polarity of the step voltage was switched by a DC control flux to the SQUID loop. The experimental current–voltage curves were quantitatively reproduced by simulation.
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 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.