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Applied Physics Letters

Voltage-flux bistability in damped direct current SQUIDs

Ian Atkin, E. Abraham, Colin M. Pegrum

Published Aug 26, 1996• 1 citation
Publisher

Abstract

We present an analysis and numerical study of a dc superconducting quantum interference device (SQUID) with a damped loop inductance. We find a previously unreported regime of voltage-flux bistability due to the damping resistor when the SQUID is biased below the zero-field critical current. We determine the region where this phenomenon can be found in the parameter space defined by the damping resistance and the inductance parameter. We show that switching between the bistable states can be controlled by external flux pulses and by adding thermal noise to the model, we have determined the maximum noise level at which the bistability can be seen.

DOI
10.1063/1.117401

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We present an analysis and numerical study of a dc superconducting quantum interference device (SQUID) with a damped loop inductance. We find a previously unreported regime of voltage-flux bistability due to the damping resistor when the SQUID is biased below the zero-field critical current. We determine the region where this phenomenon can be found in the parameter space defined by the damping resistance and the inductance parameter. We show that switching between the bistable states can be controlled by external flux pulses and by adding thermal noise to the model, we have determined the maximum noise level at which the bistability can be seen.
We have fabricated and characterized the noise performance of well-coupled Nb-Pb alloy edge junction dc superconducting quantum interference devices (SQUIDs) with a resistively shunted inductance. The extra damping resistor removes the resonances in the current-voltage characteristics resulting in a very low value of the extrinsic energy sensitivity in flux-locked-loop operation. Numerical simulations, with the junction capacitance included, indicate that the damping resistance does not degrade noise performance until it is significantly less than the junction-shunting resistance. We also tested different SQUID designs and demonstrated that a large SQUID inductance, proposed earlier to be desirable when resistively shunted, can seriously affect the low-frequency flux noise.
Noise characteristics of a dc SQUID with an inductance shunted by a damping resistance are studied numerically. It is shown that the damping resistance improves considerably the resolution of the SQUID in the case of large β, where β=2LI0/Φ0, I0 is a critical current, L is a loop inductance and Φ0 is the flux quantum. The energy resolutions for β=4 and β=10 are only about 2 and 4 times larger than that for β=1, respectively. Furthermore, the ranges of both the bias current and the external flux, where good resolution is obtained, become very wide compared with the conventional SQUID. Therefore, the SQUID with the damping resistance can be used for large β (or L) without the significant degradation of the resolution, and will much improve the coupling properties between the SQUID and the input circuitry. The numerical simulation results are also compared with analytical ones, and a reasonable agreement is obtained.
We experimentally studied weakly damped superconducting quantum interference devices (SQUIDs) shunted by an external resistor Rs and operated in either current- or voltage-bias mode. The SQUID parameters, such as the flux-to-voltage transfer coefficient ∂V/∂Φ and the dynamic resistance Rd, are reduced due to Rs, while the SQUID intrinsic noise remains unchanged. The reduced parameters can be enhanced again by using voltage feedback circuitry. Furthermore, Rs can be used to damp the SQUID in order to avoid the appearance of hysteresis or oscillation in SQUID characteristics. SQUID shunted by small Rs is always operated in mixed-bias mode.
Direct current-superconducting quantum interference devices (SQUIDs) characterized by asymmetric Josephson junctions have never been used for applications. In order to demonstrate their potential advantages, a throughout numerical analysis of different asymmetric configurations has been carried out. A damping resistance has been included in the SQUID circuit and the thermal noise associated with junction and damping resistances has been considered in the numerical model. Magnetic modulations and flux noise spectral densities have been computed as a function of many parameters (bias current, asymmetry, SQUID inductance, and damping resistance) and the performance of symmetric and asymmetric devices have been compared. The results show that, by properly optimizing the SQUID design, asymmetric SQUIDs are characterized by higher magnetic flux to voltage transfer coefficient and lower flux noise. As a result, asymmetric configurations can be very useful in all the applications where high sensitivity is required.
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.
We experimentally studied two important parameters of helium-cooled superconducting quantum interference devices (SQUIDs) in the voltage bias mode: the dynamic resistance Rd and the flux-to-current transfer coefficient ∂i/∂Φ, with different junction shunt resistors RJ. We investigated a voltage-biased SQUID using the direct readout current-to-voltage converter scheme involving an operational amplifier. At higher RJ, the flux-to-voltage conversion coefficient ∂V/∂Φ becomes sufficiently large to effectively suppress the room-temperature amplifier's noise without any need for additional feedback circuits. The McCumber parameter limits the rise of ∂V/∂Φ. We discuss the performance of voltage-biased SQUIDs at different effective McCumber parameters.