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IEEE Transactions on Applied Superconductivity

Numerical Demonstration of Relaxation Oscillation in a Resistive Superconducting Quantum Interference Device With Two Nonhysteretic Josephson Junctions

Yoshinao Mizugaki

Published Aug 10, 2010• 6 citations
Publisher

Abstract

The author numerically demonstrates that a resistive superconducting quantum interference device (RSQUID) with two nonhysteretic Josephson junctions works as a relaxation oscillator. Sequential switching of the Josephson junctions transfers positive and negative flux quanta in the RSQUID loop one by one. Differently from a conventional two-junction superconducting quantum interference device, the dissipative RSQUID loop does not maintain the quantized flux, and hence, finite flux can be accumulated in the RSQUID loop during sequential switching of the Josephson junctions. When the accumulated flux reaches a critical value, the corresponding loop current prevents subsequent junction switching. That is, the oscillation stops. After the loop current decays, sequential switching of the junctions resumes. In addition to the waveforms of relaxation oscillation, dependence of relaxation oscillation on device parameters is presented.

DOI
10.1109/tasc.2010.2060333

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The author numerically demonstrates that a resistive superconducting quantum interference device (RSQUID) with two nonhysteretic Josephson junctions works as a relaxation oscillator. Sequential switching of the Josephson junctions transfers positive and negative flux quanta in the RSQUID loop one by one. Differently from a conventional two-junction superconducting quantum interference device, the dissipative RSQUID loop does not maintain the quantized flux, and hence, finite flux can be accumulated in the RSQUID loop during sequential switching of the Josephson junctions. When the accumulated flux reaches a critical value, the corresponding loop current prevents subsequent junction switching. That is, the oscillation stops. After the loop current decays, sequential switching of the junctions resumes. In addition to the waveforms of relaxation oscillation, dependence of relaxation oscillation on device parameters is presented.
The author numerically demonstrates several features of blocking oscillation in resistive superconducting quantum interference devices (RSQUIDs) including two Josephson junctions. The key for the blocking oscillation is a combination of discrete and continuous flux transfer into/from the RSQUID loop. The discrete flux transfer takes place through the Josephson junctions, while the dissipative element (resistor) in the loop allows the continuous flux transfer. Three features of the blocking oscillation are presented by numerical simulation. Firstly, switching events alternately occur in the two junctions. Next, a finite average voltage is induced in the RSQUID, when the blocking oscillation is synchronized with an external rf signal. Finally, blocking oscillation modes including several intermittent periods are generated in coupled-RSQUIDs.
Partly resistive superconducting quantum interference devices (RSQUIDs) are used in noise thermometry in the liquid helium temperature range. Here we analyze one type of RSQUID that has not been thoroughly investigated until now: the direct current biased with two Josephson junctions and a resistive part connected in series with the junctions and closed by a superconducting ring. The resistive shunted model of the Josephson junctions is used for the analysis. Two cases of the RSQUID ring inductance were analyzed: (i) negligibly small and (ii) small but finite inductance. The expressions for the low frequency output signal, the current–voltage (I–V) characteristics, and the current flowing through the resistive part are obtained. In the dependence of the output frequency versus the dc current passed through the resistive part often an offset is observed experimentally. This phenomenon can be explained as an influence of an asymmetry in the critical currents of the junctions.
Blocking oscillation (BO) is a unique operation mode of resistive superconducting quantum interference devices (RSQUIDs). The author presents experimental measurements of periodic BO by means of the average voltage method. Test circuits are fabricated using a Nb/AlO x /Nb integration process. The input/output voltage ratio in an RSQUID, of which the output is connected to a Josephson transmission line (JTL), becomes 2 under appropriate operation conditions. Since the voltage ratio is exactly proportional to the input/output switching frequency ratio, the results demonstrate the periodic BO, in which the numbers of switching during one period are 2 and 1 in the input and output junction, respectively.
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Recent experiments on superconducting flux qubits, consisting of a superconducting loop interrupted by Josephson junctions, have demonstrated quantum coherence between two different quantum states. The state of the qubit is measured with a superconducting quantum interference device (SQUID). Such measurements require the SQUID to have high resolution while exerting minimal backaction on the qubit. By designing shunts across the SQUID junctions appropriately, one can improve the measurement resolution without increasing the backaction significantly. Using a path-integral approach to analyze the Caldeira-Leggett model, we calculate the narrowing of the distribution of the switching events from the zero-voltage state of the SQUID for arbitrary shunt admittances, focusing on shunts consisting of a capacitance Cs{C}_{s}Cs​ and resistance Rs{R}_{s}Rs​ in series. To test this model, we fabricated a dc SQUID in which each junction is shunted with a thin-film interdigitated capacitor in series with a resistor, and measured the switching distribution as a function of temperature and applied magnetic flux. After accounting for the damping due to the SQUID leads, we found good agreement between the measured escape rates and the predictions of our model. We analyze the backaction of a shunted symmetric SQUID on a flux qubit. For the given parameters of our SQUID and realistic parameters for a flux qubit, at the degeneracy point we find a relaxation time of $113\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$, which limits the decoherence time to $226\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$. Based on our analysis of the escape process, we determine that a SQUID with purely capacitive shunts should have narrow switching distributions and no dissipation.