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PLoS ONE

Energetics of an rf SQUID Coupled to Two Thermal Reservoirs

Bartłomiej Gardas, J. Łuczka, Andrzej Ptok, Jerzy Dajka

Published Dec 7, 2015• 1 citation
Publisher

Abstract

We study energetics of a Josephson tunnel junction connecting a superconducting loop pierced by an external magnetic flux (an rf SQUID) and coupled to two independent thermal reservoirs of different temperature. In the framework of the theory of quantum dissipative systems, we analyze energy currents in stationary states. The stationary energy flow can be periodically modulated by the external magnetic flux exemplifying the rf SQUID as a quantum heat interferometer. We also consider the transient regime and identify three distinct regimes: monotonic decay, damped oscillations and pulse-type behavior of energy currents. The first two regimes can be controlled by the external magnetic flux while the last regime is robust against its variation.

DOI
10.1371/journal.pone.0143912

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We study energetics of a Josephson tunnel junction connecting a superconducting loop pierced by an external magnetic flux (an rf SQUID) and coupled to two independent thermal reservoirs of different temperature. In the framework of the theory of quantum dissipative systems, we analyze energy currents in stationary states. The stationary energy flow can be periodically modulated by the external magnetic flux exemplifying the rf SQUID as a quantum heat interferometer. We also consider the transient regime and identify three distinct regimes: monotonic decay, damped oscillations and pulse-type behavior of energy currents. The first two regimes can be controlled by the external magnetic flux while the last regime is robust against its variation.
At low temperature and low damping, the magnetic flux of a rf Superconducting QUantum Interference Device (SQUID) acts as a macroscopic quantum variable whose dynamic is described by a double well potential. A rf SQUID consists of a superconducting loop interrupted by a thin insulating barrier, known as a Josephson junction. The modified rf SQUID design discussed in this thesis has independent, in situ, controls that allow varying the barrier height between the potential wells and their relative tilt. This high level of control of the potential together with the capability to implement an experimental setup optimized to reduce coupling to external sources of noise, made this system ideal not only for tests of quantum transition at a macroscopic level, but also as a scalable solid state device for quantum computation. A variety of measurements of quantum phenomena are reported in this thesis, including microwave level spectroscopy, coherent oscillations, and macroscopic resonant tunneling (MRT). These measurements are compared with theoretical models to study the possible sources of decoherence in a rf SQUID qubit. The analysis confirmed that the main source of decoherence is not due to coupling to the external environment, but it can be linked to intrinsic low frequency flux noise. Work from many groups over the last several years has shown that the performance of a superconductive qubit is limited by coupling to spurious defects in the materials used for the device fabrication. In this work we analyze the possibility of using the MRT as a tool for future studies of effects of materials and fabrication process in the realization of improved qubits, and we also explore the feasibility for measurements of quantum phenomena that involve fast pulsing of the potential barrier height.
The standard operation of a dc SQUID leads to oscillatory electric fields that emit electromagnetic radiation. We estimate the effect that this radiation could have on the measured sample. A stationary SQUID could be advantageous if the oscillation contribution to back action on the measured sample has to be avoided. We study a superconducting loop that encloses a magnetic flux, connected to a superconducting and to a normal electrode, when a fixed electric current between the electrodes flows across the loop. The considered circuit does not contain Josephson junctions. We find that in a very broad range of parameters the current flow converges to a stationary regime, i.e. the densities of normal current and of supercurrent become functions of position only, independent of time. The potential difference between the electrodes depends on the magnetic flux, so that measuring this voltage would provide information on the enclosed flux. The influence of thermal noise was estimated. The sizes of the voltage and of the power dissipation could be appropriate for the design of a practical fluxmeter. We found narrow ranges of flux at which the voltage varies sharply with the flux.
The standard operation of a dc SQUID leads to oscillatory electric fields that emit electromagnetic radiation and can change the state of the measured sample. A stationary SQUID could be advantageous when back action on the measured sample has to be avoided. We study a superconducting loop that encloses a magnetic flux, connected to a superconducting and to a normal electrode, when a fixed electric current between the electrodes flows through the loop. The considered circuit does not contain Josephson junctions. We find that in a very broad range of parameters the current flow converges to a stationary regime. The potential difference between the electrodes depends on the magnetic flux, so that measuring this voltage would provide information on the enclosed flux. The influence of thermal noise was estimated. The sizes of the voltage and of the power dissipation could be appropriate for the design of a practical fluxmeter. We found narrow ranges of flux at which the voltage varies sharply with the flux.
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 on experiments performed on a system consisting of a double SQUID (Superconducting Quantum Interference Device) built with gradiometer geometry. Two single-turn coils provide two independent control fluxes: one of these allows biasing the device and tilting the potential, while the other changes the barrier height of the potential. When the dynamics of the inner dc SQUID can be neglected, the free energy of the double SQUID, as a function of the internal magnetic flux, is just the corrugated parabola of an rf SQUID whose local minima represent metastable states for the system. Our analysis instead is substantially concerned with the interesting phenomenology generated by the static configurations of an internal two-junction interferometer and by the tunability of the internal loop inductance. Two readout systems are employed to thoroughly characterize the dynamics of our system. We investigate the dynamical response at temperatures low enough (tens of mK) to minimize the effects of thermal fluctuations concentrating the analysis on the aspects that could be relevant for macroscopic quantum coherence and computing. The results indicate that from the finite inductance of the inner loop originates a potential well generating competing processes with the tunneling between the two main wells of the rf-SQUID potential.
We study a superconducting loop that encloses a magnetic flux, connected to a superconducting and to a normal electrode, when a fixed electric current between the electrodes flows through the loop. The considered circuit does not contain Josephson junctions. We find that in a very broad range of parameters the current flow converges to a stationary regime. The potential difference between the electrodes depends on the magnetic flux, so that measuring this voltage would provide information on the enclosed flux. The sizes of the voltage and of the power dissipation could be appropriate for the design of a practical fluxmeter. We found narrow ranges of flux at which the voltage varies sharply with the flux.