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Modern Physics Letters B

MACROSCOPIC QUANTUM TUNNELING IN A SUPERCONDUCTING RING CONTAINING A WEAK SUPERCONDUCTING JUNCTION

Antonio Luis Extremera

Published Oct 20, 1992• 0 citations
Publisher

Abstract

Macroscopic quantum effects in SQUIDs are discussed. An equation describing the behavior of the superconducting ring in the harmonic approximation is reduced to the standard form of Mathieu’s equation. For well-defined flux states, good agreement with exact theoretical calculations and experimental results is found near the minimum energy regions. We establish the effective dissipation dependence on tunneling rate via the “instanton” or “bounce” action. WKB-type approximations enable us to obtain the quantum decay rate for a metastable state in the anharmonic (quartic) potential.

DOI
10.1142/s0217984992001204

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Macroscopic quantum effects in SQUIDs are discussed. An equation describing the behavior of the superconducting ring in the harmonic approximation is reduced to the standard form of Mathieu’s equation. For well-defined flux states, good agreement with exact theoretical calculations and experimental results is found near the minimum energy regions. We establish the effective dissipation dependence on tunneling rate via the “instanton” or “bounce” action. WKB-type approximations enable us to obtain the quantum decay rate for a metastable state in the anharmonic (quartic) potential.
We study macroscopic properties of a system of weakly interacting neutral bosons confined in a ring-shaped potential with a Josephson junction. We derive an effective low energy action for this system and evaluate its properties. In particular, we find that the system possesses a set of metastable current-carrying states and evaluate the rates of transitions between these states due to macroscopic quantum tunneling and thermal activation mechanism. Finally, we discuss signatures of different metastable states in the time-of-flight images and argue that the effect is observable within currently available experimental technique.
Macroscopic quantum tunneling (MQT) for a single fluxon moving along a long Josephson junction is studied theoretically. To introduce a fluxon-pinning force, we consider inhomogeneities made by modifying thickness of an insulating layer locally. Two different situations are studied: one is the quantum tunneling from a metastable state caused by a single inhomogeneity, and the other is the quantum tunneling in a two-state system made by two inhomogeneities. In the quantum tunneling from a metastable state, the decay rate is estimated within the WKB approximation. Dissipation effects on a fluxon dynamics are taken into account by the Caldeira-Leggett theory. We propose a device to observe quantum tunneling of a fluxon experimentally. Required experimental resolutions to observe MQT of a fluxon seem attainable within the presently available micro-fabrication technique. For the two-state system, we study quantum resonance between two stable states, i.e., macroscopic quantum coherence (MQC). From the estimate for dissipation coefficients due to quasiparticle tunneling, the observation of MQC appears to be possible within the Caldeira-Leggett theory.
The mechanisms of the decay of metastable current states in the superconducting loop of an rf SQUID in the hysteresis state are studied. Clamped point contacts are used as the Josephson weak link. The first derivative of the radio-frequency IVC dVT/dIRF, which gives the dependence of the decay probability density on the amplitude of the oscillations of the magnetic flux in the ring, was measured experimentally. Studies of the temperature dependence of the width of the probability distribution in the interval from 4.2 to 0.5 K show that for most high-resistance Nb–Nb, Nb–Ag–Nb contacts the quantum mechanisms of decay become dominant at a temperature of the order of 2 K. The experimentally measured parameters of the decay probability distribution in the quantum limit are compared with the theoretical values calculated based on the theory of macroscopic quantum tunneling in the limit of strong and weak dissipation. The experimental magnitude of the width of the probability density as well as the characteristic quantum temperature exceed the theoretical values, which can be explained by the deviation of the current-phase dependence of the contact from a sinusoidal dependence. In addition, some contacts apparently correspond to the case of an intermediate magnitude of dissipation. When the frequency of the rf oscillations changed from 30 to 6 MHz, the width of the distribution remained unchanged, which follows from the theory of quantum tunneling decay of the metastable current state in the loop in the limit of strong damping. At low temperatures (T ∼ 50 K) and for a sufficiently small damping coefficient, anomalous peaks were observed in the probability density with an amplitude of the rf oscillations significantly smaller than the critical magnitude of the magnetic flux in the loop.
We report experiments on energy level quantization in Nb/AlOx/Nb Josephson junctions while measurements on SQUIDs are in progress. Data on the presence of energy level quantization are shown at temperatures above the classical-quantum regime crossover temperature. This has been possible by extending the measurements of the rate of the escape from the zero-voltage state at higher sweep bias rate in order to induce non-stationary conditions in the energy potential describing the junction dynamics. Data are compatible with extremely low "effective" dissipation in our system. Theoretical predictions on quantum effects related to the presence of non-stationary conditions in the potential associated to a rf SQUID are reported in view of new possible experiments.
The problem of macroscopic quantum coherence in superconducting systems is studied theoretically. A two-level model of a SQUID with phonon-field coupling is considered. The probability of a transition, induced by a periodic perturbation, occurring between the lowest states of the two-well potential, describing the phase dependence of the energy in the SQUID, is calculated for a particular region of this coupling. Use is made of the conformity between this model and the resonance-level model. We also consider the strong-viscosity limit. It is shown that in this case the two-level model cannot be used to describe quantum interferometers.