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arXiv:1404.3602 · Physical Review Letters

Flux-Dependent Crossover between Quantum and Classical Behavior in a dc SQUID

S. Butz, Alexey K. Feofanov, Kirill G. Fedorov, Hannes Rotzinger, A. U. Thomann, Brigitte Mackrodt, R. Dolata, V. B. Geshkenbeǐn, G. Blatter, Alexey Vladimirovich Ustinov

Published Dec 11, 2014• 7 citations
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Abstract

In a coupled system of one classical and one quantum mechanical degree of freedom, the quantum degree of freedom can facilitate the escape of the whole system. Such unusual escape characteristics have been theoretically predicted as the "Münchhausen effect." We implement such a system by shunting one of the two junctions of a dc SQUID with an additional capacitance. In our experiments, we detect a crossover between quantum and classical escape processes related to the direction of escape. We find that, under varying external magnetic flux, macroscopic quantum tunneling periodically alternates with thermally activated escape, a hallmark of the "Münchhausen effect."

DOI
10.1103/physrevlett.113.247005

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In a coupled system of one classical and one quantum mechanical degree of freedom, the quantum degree of freedom can facilitate the escape of the whole system. Such unusual escape characteristics have been theoretically predicted as the "Münchhausen effect." We implement such a system by shunting one of the two junctions of a dc SQUID with an additional capacitance. In our experiments, we detect a crossover between quantum and classical escape processes related to the direction of escape. We find that, under varying external magnetic flux, macroscopic quantum tunneling periodically alternates with thermally activated escape, a hallmark of the "Münchhausen effect."
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.>
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)]].
A classical system cannot escape out of a metastable state at zero temperature. However, a composite system made from both classical and quantum degrees of freedom may drag itself out of the metastable state by a sequential process. The sequence starts with the tunneling of the quantum component which then triggers a distortion of the trapping potential holding the classical part. Provided this distortion is large enough to turn the metastable state into an unstable one, the classical component can escape. We show that such a composite system can be conveniently studied and implemented in a dc superconducting quantum interference device (SQUID) featuring asymmetric dynamical parameters. We determine the dynamical phase diagram of this system for various choices of junction parameters and system preparations.
Experiments are described that demonstrate the quantum behavior of a macroscopic degree of freedom, namely the phase difference \ensuremath{\delta} across a current-biased Josephson tunnel junction. The behavior of \ensuremath{\delta} was deduced from measurements of the escape rate \ensuremath{\Gamma} of the junction from its zero-voltage state. The relevant parameters of the junction, that is, its critical current and shunting admittance, were determined in situ in the thermal regime from the dependence of \ensuremath{\Gamma} on bias current and from resonant activation in the presence of microwaves. It was found that the shunting capacitance was dominated by the self-capacitance of the junction while the shunting conductance was dominated by the bias circuitry. For an underdamped junction in the quantum regime, \ensuremath{\Gamma} became independent of temperature at low temperatures with a value that, with no adjustable parameters, was in excellent agreement with predictions for macroscopic quantum tunneling at T=0. When the critical current was reduced with a magnetic field so that the junction remained in the thermal regime at low temperatures, \ensuremath{\Gamma} followed the predictions of the thermal model, thereby showing the influence of extraneous noise to be negligible. In a further series of experiments, the existence of quantized energy levels in the potential well of the junction was demonstrated spectroscopically. The positions of the energy levels agreed quantitatively with quantum-mechanical predictions involving junction parameters measured in the thermal regime. The relative heights and widths of the resonances are in reasonable agreement with the predictions of a simple model.
We have studied the temperature dependence of escape phenomena in various underdamped Josephson junctions (JJs). The junctions had different Josephson coupling energies E J which were relatively small, but larger than the charging energy E C . Upon increasing the temperature T , we first observe the usual cross-over between macroscopic quantum tunnelling and thermally activated (TA) behaviour at temperatures k B T ∼ ℏω p , where ω p is the plasma frequency of the junction. Increasing T further, the width of the switching current distribution has, counterintuitively, a non-monotonic temperature dependence. This can be explained by the novel cross-over from TA behaviour to underdamped phase diffusion. We show that this cross-over is expected to occur at temperatures such that k B T ∼ E J (1 − 4/π Q ) 3 /2, where Q is the quality factor of the junction at the plasma frequency, in agreement with experiment. Our findings can be compared with detailed model calculations which take into account dissipation and level quantization in a metastable well. Particular attention is paid to the sample with the smallest E J , which shows extensive phase diffusion even at the lowest temperatures. This sample consists of a dc-SQUID and a single JJ close to each other, such that the SQUID acts as a tunable inductive protection for the single junction from fluctuations of a dissipative environment. By varying the flux through the dc-SQUID, we present, for the first time, experimental evidence of the escape of a JJ from the phase diffusion regime to the free running state in a tunable environment. We also show that in the zero voltage state the losses mainly occur at frequencies near the plasma resonance.