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arXiv:0808.1892 · Journal of Physics A Mathematical and Theoretical

Higher order Josephson effects

Roman V. Buniy, Thomas W Kephart

Published May 11, 2010• 3 citations
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Abstract

Gaussian linking of superconducting loops containing Josephson junctions with enclosed magnetic fields give rise to interference shifts in the phase that modulates the current carried through the loop, proportional to the magnitude of the enclosed flux. We generalize these results to higher order linking of a superconducting loop with several magnetic solenoids, and show there may be interference shifts proportional to the product of two or more fluxes.

DOI
10.1088/1751-8113/43/22/225301

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Gaussian linking of superconducting loops containing Josephson junctions with enclosed magnetic fields give rise to interference shifts in the phase that modulates the current carried through the loop, proportional to the magnitude of the enclosed flux. We generalize these results to higher order linking of a superconducting loop with several magnetic solenoids, and show there may be interference shifts proportional to the product of two or more fluxes.
We consider a superconducting loop with two weak links that encloses a magnetic flux. The weak links are unequal and are treated as Josephson junctions with non-sinusoidal phase dependence. We devise a model that takes into account the fluctuation of the critical currents, due to the fluctuations of the order parameter in the weak links. These fluctuations are important near the onset of superconductivity; in this regime they may significantly weaken and eventually disconnect the superconducting loop. As a consequence of these fluctuations and of the resistive noise in the junctions, the average dc voltage does not vanish. Our model can be easily extended to provide a qualitative description of a recent experiment.
This paper investigates the physical nature of a series of step structures or oscillations present in a Josephson current within one magnetic flux quantum when either a Josephson junction, a double junction squId, or a single junction superconducting ring is placed inside a high Q cavity under the condition in which the Josephson frequency is equal to the resonance frequency of the cavity. The frequency effect of the feedback field produces a series of induced current steps in the Josephson junction or the two-junction squId when ..omega.. = ..omega../sub r/. The oscillating electromagnetic field excited by the junction current acts on the junction itself. A series of new current step structures occur within one magnetic flux phi/sub 0/ quantum, since the amplitude of the feedback field is modulated by an applied magnetic field as the modulation of the amplitude of the feedback field is coupled to that of the radiation. For the superconducting ring containing a single junction, as n..omega.. = ..omega../sub r/, the feedback radiation of the stationary electromagnetic wave will give rise to a constrained oscillation of the supercurrent with a period smaller than that of the superconducting current oscillation phi/sub 0/.
The mutual coherent interaction of Josephson junctions in a multi-junction superconducting loop (MSL) in the limit of zero-loop inductance is theoretically investigated. For the loop containing 2 M junctions there are M coherent states corresponding to different values of effective flux ϕ eff in the loop. The stability analysis using the method of Floquet exponents shows the highest stability for the state with ϕ eff = 1/2. In this state, the MSL behaves like an oscillating magnetic dipole. The optimum stability is reached for the normalised bias current i b ≃ 2.5 and the McCumber parameter β C ≃ 0.5.
Pair-quasiparticle interference current has a measurable effect on the tuning characteristics of a superconducting interferometer operating in the nonhysteretic regime: $\ensuremath{\epsilon}\ensuremath{\equiv}(\frac{2\ensuremath{\pi}}{{\ensuremath{\Phi}}_{0}}){L}_{R}{I}_{c}<1$ where ${\ensuremath{\Phi}}_{0}=\frac{h}{2e}$, LR{L}_{R}LR​ is the inductance of the interferometer ring, and Ic{I}_{c}Ic​ is the critical current of the interferometer's weak link. In the limit $\ensuremath{\epsilon}\ensuremath{\ll}1$ the interferometer will have a zero crossing in its magnetic flux sensitivity versus frequency characteristic that is above, on, or below resonance depending whether the coefficient of the interference current term is positive, zero, or negative, respectively. For larger $\ensuremath{\epsilon}$, screening currents will also shift the zero crossing. Results for the magnitude of this additional shift are presented and discussed.
In superconducting quantum interference devices (SQUIDs), the superconducting diode effect may be generated by interference of multiple harmonic components in the current-phase relationships (CPRs) of different branches forming SQUID loops. Through the inclusion of two gate-tunable Josephson junctions in series in each interference branch of a double-loop SQUID, we demonstrate independent control over both the harmonic content and the amplitude of three interfering CPRs, facilitating significant improvement in the maximum diode efficiency. Through optimized gate-controlled tuning of individual Josephson energies, diode efficiency exceeding 50% is demonstrated. Flux-dependent oscillations show quantitative agreement with a simple model of SQUID operation.