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Applied Physics Letters

Thermally induced vortex-to-vortex transitions in a superconducting quantum interference device

M. Naor, Claudia D. Tesche, M. B. Ketchen

Published Jul 15, 1982• 21 citations
Publisher

Abstract

Thermally induced vortex-to-vortex transitions between the zero-quantum vortex state and one- flux-quantum vortex state of a symmetric two-junction dc superconducting quantum interference device (SQUID) have been observed. The characterization of transitions of this type is an essential part of the modeling of Josephson junction logic and memory devices. The transition rates, measured as a function of bias current, applied flux, and temperature, are in excellent agreement with rates predicted by a thermal activation model for two-junction SQUID’s.

DOI
10.1063/1.93462

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Thermally induced vortex-to-vortex transitions between the zero-quantum vortex state and one- flux-quantum vortex state of a symmetric two-junction dc superconducting quantum interference device (SQUID) have been observed. The characterization of transitions of this type is an essential part of the modeling of Josephson junction logic and memory devices. The transition rates, measured as a function of bias current, applied flux, and temperature, are in excellent agreement with rates predicted by a thermal activation model for two-junction SQUID’s.
We have measured the thermally-activated escape rate out of the zero-voltage state of hysteretic dc superconducting quantum interference devices (SQUID's) at 4.2 K. We found evidence that the zero-voltage state of these SQUID's is in general not unique, but can correspond instead to several metastable states. Each of these substates is associated with a given number of flux quanta trapped in the super-conducting loop of the SQUID's. The existence of this multiplicity is a direct consequence of the two-dimensional character of the dc-SQUID dynamics. For a fixed external magnetic flux, each zero-voltage substate is characterized by a particular value of the critical current, the expression of which can be derived from the double-cosine tilted two-dimensional SQUID potential. Experimentally, we observed multiple peaks in the switching-current distribution. Each peak was assigned to a given zero-voltage substate and we measured the dependence of the associated critical currents on the external magnetic flux. A procedure was developed in order to select a given substate among the multiplicity of the zero-voltage state. This allowed a precise measurement of the lifetime of one preselected zero-voltage substate as a function of the barrier height. Good agreement with two-dimensional transition-state theory was obtained.
The authors report measurements of the transition rate from zero-voltage metastable minima in the two-dimensional potential of a DC SQUID (superconducting quantum interference device) as a function of applied flux and temperature. A crossover is observed from thermally activated escape to macroscopic quantum tunneling at a critical temperature that is a strong function of the bias flux. The macroscopic quantum tunneling rate is substantially reduced by damping, which also broadens the crossover region. The authors unexpectedly observed thermal rates that are significantly suppressed from those predicted by the classical two-dimensional thermal activation model, as if the potential barrier for activation were effectively enhanced. They discuss possible explanations for this result, based on the interaction of the macroscopic degrees of freedom in the device and energy level quantization effects.>
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.
Superconducting quantum circuits (SQCs) are being explored as model systems for scalable quantum computing architectures. Josephson junctions are extensively used in superconducting quantum interference devices (SQUIDs) and in persistent-current qubit systems. Noise excitations, however, have a critical influence on their dynamics. Thus, the primary focus of this research was to investigate the effects of thermal ac-tivation on the superconducting properties of Josephson junctions. Specifically, ther-mal noise tends to result in a range of switching currents, values less than the critical current at which a junction switches from the superconducting to the normal state. First, a general review of superconductivity concepts is given, including a treatment of the Josephson phenomena. Next, I describe some of my work on characterizing the current-voltage traces of Josephson junctions tested at 4 K with a Multi-Chip Probe (MCP). Then, I describe thermal activation theory and examine the equations useful for modeling switching current distributions. The Josephson junctions of a SQUID with a ramped bias current were tested for numerous temperatures T < 4.5 K (and
Thermal noise induced switching of Josephson logic devices is studied, both theoretically and experimentally. The results are critical for the design of the operating bias points for these devices. An analysis of the relevant energy contours shows that a three-junction superconducting quantum interference device has the same noise switching rate as a point junction with the same maximum critical current. Experimental results, for the dependence of the thermal noise induced switching rate on the gate current bias ratio, are in very good agreement with the theory.
A dc superconducting quantum interference device (SQUID) consisting of a symmetric ring circuit with four Josephson junctions and two independent external currents I1{I}_{1}I1​ and I2{I}_{2}I2​, which enter the circuit at different points, has a phase boundary between the fully superconducting and the normal states that is different from that of a conventional SQUID. The control current I2{I}_{2}I2​ modifies the magnetic flux (\ensuremath{\varphi}) periodicity and the value of the maximum measuring current I1m{I}_{1m}I1m​(\ensuremath{\varphi}). For values of I2{I}_{2}I2​>Ic{I}_{c}Ic​ (critical current of Josephson junction) the fully resistive state exists over flux intervals centered around (n+(1/2)${\ensuremath{\varphi}}_{0}$, where n is an integer and ${\ensuremath{\varphi}}_{0}$ is the fluxoid quantum. A superconducting circuit without Josephson junctions is suggested which should have a phase boundary similar to that found here. Minimization procedures which are usually employed in analyzing SQUID's are discussed.