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Physical review. B, Condensed matter

Thermal activation of a hysteretic dc superconducting quantum interference device from its different zero-voltage states

Valérie Lefèvre-Seguin, Emmanuel Turlot, C. Urbina, Daniel Esteve, Michel Devoret

Published Sep 1, 1992• 60 citations

Abstract

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.

DOI: 10.1103/physrevb.46.5507

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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.

Abstract This work investigates the distribution of flux states of hysteretic dc superconducting quantum interference devices (SQUIDs) obtained from standard current ramp measurement at 2.50 and 0.35 K. Each flux state corresponds to a specific number of flux quanta trapped in the superconducting loop, associated with a metastable state in the two-dimensional potential energy of the hysteretic SQUID. The flux states can be distinguished by the multiple switching currents. The observed distribution is different from the distribution caused only by thermal excitation at a specific temperature. There are notable systematic deviations between the measurement results of three samples and the standard Boltzmann distribution, which can be clearly identified from the ratios between the proportions of different flux states. A formula resembling the Boltzmann distribution, involving multiple effective temperatures, is proposed to provide a better fit to the measured results. The finding suggests that the observed distribution of flux states is established during the SQUID’s transition from the dissipative state to the zero-voltage state, and multiple equivalent temperatures may be involved in the process.

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.>

We studied the escape process from the zero-voltage state to the running state in hysteretic dc-SQUIDs made with trilayer Nb-AlOx-Nb junctions. We analyze the experimental results, according to the thermal activation model, for devices having similar parameters except for the dimensionless inductance β L , which however is always very small. The interest in hysteretic dc-SQUIDs is in the possibility of using them to perform non-invasive measurements of the flux states in rf-SQUIDs: this achievement would be very important both in tests of macroscopic quantum properties of SQUIDs and in measurements on a class of quantum bits that has been recently proposed, based on magnetic flux states in SQUIDs.

We study the metastable response of a highly hysteretic dc superconducting quantum interference device (SQUID) made of a niobium loop interrupted by two nanobridges. We excite the SQUID with an alternating current and with direct magnetic flux, and find different stability zones forming diamond-like structures in the measured voltage across the SQUID. When such a SQUID is embedded in a transmission line resonator, similar diamond structures are observed in the reflection pattern of the resonator. We calculate the dc-SQUID stability diagram in the plane of the exciting control parameters, both analytically and numerically. In addition, we obtain numerical simulations of the SQUID equations of motion, taking into account temperature variations and nonsinusoidal current-phase relation of the nanobridges. Good agreement is found between experimental and theoretical results.

A hysteretic dc-superconducting quantum interference device (SQUID) is used to trace the flux characteristic of a tunable rf-SQUID, the basic element for the realization of superconducting flux qubits. This allows important simplifications of circuitry and electronics in developing devices for quantum computing, by eliminating the necessity of more complex magnetometers. A hysteretic dc-SQUID is usually operated as a comparator, distinguishing only which one of two adjacent flux states is occupied by the rf-SQUID. The necessary sensitivity, moreover, is usually reached only at temperatures in the mK range. However, by exploiting the statistical properties of the current–voltage curve in the region where the switching from the zero-voltage state occurs, it is possible to obtain an accurate tracing of the input flux, even at a relatively high temperature (a few Kelvin). In our case, the input signal is given by the internal flux of a tunable rf-SQUID, the building block of a flux qubit.

The escape probability out of the superconducting state of a hysteretic dc SQUID has been measured at different values of the applied magnetic flux. At low temperatures, the escape current and the width of the probability distribution are temperature independent but they depend on flux. Experimental results do not fit the usual one-dimensional macroscopic quantum tunneling (MQT) law but are perfectly accounted for by the two-dimensional MQT behavior as we propose here. Near zero flux, our data confirms the recent MQT observation in a dc SQUID [Phys. Rev. Lett. 89, 98301 (2002)]].