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arXiv:2212.02657

Superconducting diode from flux biased Josephson junction arrays

Rafael Haenel, Oguzhan Can

Published Dec 5, 2022• 5 citations
arXivHTMLPDF

Abstract

We propose a realization of the superconducting diode effect in flux biased superconducting circuits of Josephson junctions. So far the observation of the superconducting diode effect has been limited to rather exotic material platforms. In theoretical proposals, it relied on a non-sinusoidal form of the current phase relation of Josephson junctions. Here, we show how the diode effect can be engineered in superconducting circuits without any such requirements. The only necessary ingredients are standard sinusoidal Josephson junctions and flux bias lines that are readily available in scalable industrial silicon-chip based superconducting design processes.

DOI
10.48550/arxiv.2212.02657

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We propose a realization of the superconducting diode effect in flux biased superconducting circuits of Josephson junctions. So far the observation of the superconducting diode effect has been limited to rather exotic material platforms. In theoretical proposals, it relied on a non-sinusoidal form of the current phase relation of Josephson junctions. Here, we show how the diode effect can be engineered in superconducting circuits without any such requirements. The only necessary ingredients are standard sinusoidal Josephson junctions and flux bias lines that are readily available in scalable industrial silicon-chip based superconducting design processes.
A Josephson diode is a superconducting circuit element that enables non-reciprocal transport, allowing a dissipationless supercurrent to preferentially flow in a single direction. Existing methods for achieving the required symmetry breaking mostly rely on specifically-designed materials or carefully-engineered circuits composed of multiple Josephson junctions. Here, we demonstrate that applying a biharmonic drive to a conventional superconducting tunnel-junction induces a diode effect through harmonic mixing processes that shift the supercurrent region. We show that, in a conventional tunnel junction, unity efficiency is achievable while maintaining a large supercurrent. Moreover, the relative phase between the two driving tones determines the directionality of the diode, which can be tuned in situ.
Abstract A Josephson diode is a superconducting circuit element that enables non-reciprocal transport, allowing a dissipationless supercurrent to preferentially flow in a single direction. Existing methods for achieving the required symmetry breaking mostly rely on specifically-designed materials or carefully-engineered circuits composed of multiple Josephson junctions. Here, we investigate the diode effect induced by applying a biharmonic drive to a conventional superconducting tunnel-junction. In the slow-driving regime, the effect is straightforward to understand in a simple adiabatic picture, providing insight in the tunability of the magnitude and directionality of the diode effect through the drive parameters. We then focus on the fast-driving regime, where we show how the more complex physics underlying the dynamics of the junction can be approximated as a cascaded two-tone mixing process. We derive analytic expressions for the diode efficiency as a function of drive parameters in the limit of small driving amplitudes.
In a SQUID tuned away from half-integer flux (in units of the superconducting flux quantum), the concurrence of multiple Josephson harmonics and an asymmetry between the junctions leads to the Josephson diode effect -- a nonreciprocal current-voltage characteristic manifested as an asymmetry of critical currents at opposite polarities. We predict a dual version of this effect in a gate-tunable Cooper pair transistor placed in series with a highly resistive environment. When tuned away from half-integer gate charge (in units of the Cooper pair charge) it shows an asymmetry of critical voltages at opposite polarities -- a dual diode effect we refer to as the Bloch diode effect. It arises from an asymmetry in the dispersion of the transistor's Bloch bands. A highly resistive environment can be realized with a Josephson junction array, suggesting that such a diode could be implemented using conventional superconducting quantum circuits.
We propose a scheme for a cavity quantum electrodynamics (QED) architecture for a current-biased superconducting flux qubit with three Josephson junctions. The qubit operation is performed by using a bias current coming from the current mode of the circuit resonator. If the phase differences of junctions are to be coupled with the bias current, the Josephson junctions should be arranged in an asymmetric way in the qubit loop. Our QED scheme provides a strong coupling between the flux qubit and the transmission line resonator of the circuit.
Current-biased Josephson junctions exhibit hysteretic transitions between dissipative and superconducting states as characterized by switching and retrapping currents. Here, we develop a theory for diodelike effects in the switching and retrapping currents of weakly damped Josephson junctions. We find that while the diodelike behavior of switching currents is rooted in asymmetric current-phase relations, nonreciprocal retrapping currents originate in asymmetric quasiparticle currents. These different origins also imply distinctly different symmetry requirements. We illustrate our results by a microscopic model for junctions involving a single magnetic atom. Our theory provides significant guidance in identifying the microscopic origin of nonreciprocities in Josephson junctions.
The development of nonlinear and frequency-tunable superconducting microwave circuits for operation in large magnetic fields is of high relevance for hybrid quantum systems such as spin resonance spectrometers, microwave quantum magnonics, dark matter axion detectors or flux-mediated optomechanics. With these exciting perspectives in mind, we investigate niobium-based circuits with integrated nano-constriction quantum interferometers in magnetic in-plane fields of up to several hundred mT. Our experiments reveal an unexpected and pronounced field-induced asymmetry in the bias-flux response of the circuits, which is demonstrated to originate from a field-induced Josephson-diode effect within the nano-constrictions and which enhances the circuit figures of merit in a magnetic field. An intuitive macroscopic Josephson-diode model attributes the effect to inhomogeneous constriction properties and provides us with the diode current-phase relation as a function of the in-plane field. Finally, we demonstrate that in the diode-state the circuit Kerr nonlinearity is bimodal in frequency, not only eliminating alternative explanations for the bias-flux-asymmetries but also being potentially useful for quantum circuit applications. Overall, our report underlines the potential of niobium nano-constriction circuits for high-field hybrid quantum systems, provides a conceptually simple explanation for the diode effect in superconducting nano-structures, and reveals the untapped potential of combining Josephson nano-diodes with microwave quantum circuits.