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arXiv:2405.13642 · Physical Review Letters

Direct Measurement of a sin ( 2 φ ) Current Phase Relation in a Graphene Superconducting Quantum Interference Device

Simon Messelot, Nicolás Aparicio, Elie de Seze, Eric Eyraud, Johann Coraux, Kenji Watanabe, Takashi Taniguchi, Julien Renard

Published Sep 5, 2024• 18 citations
arXivHTMLPDF

Abstract

In a Josephson junction, the current phase relation relates the phase variation of the superconducting order parameter φ, between the two superconducting leads connected through a weak link, to the dissipationless current. This relation is the fingerprint of the junction. It is usually dominated by a sin(φ) harmonic, however, its precise knowledge is necessary to design superconducting quantum circuits with tailored properties. Here, we directly measure the current phase relation of a superconducting quantum interference device made with gate-tunable graphene Josephson junctions and we show that it can behave as a sin(2φ) Josephson element, free of the traditionally dominant sin(φ) harmonic. Such element will be instrumental for the development of superconducting quantum bits protected from decoherence.

DOI
10.1103/physrevlett.133.106001

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In a Josephson junction, the current phase relation relates the phase variation of the superconducting order parameter φ, between the two superconducting leads connected through a weak link, to the dissipationless current. This relation is the fingerprint of the junction. It is usually dominated by a sin(φ) harmonic, however, its precise knowledge is necessary to design superconducting quantum circuits with tailored properties. Here, we directly measure the current phase relation of a superconducting quantum interference device made with gate-tunable graphene Josephson junctions and we show that it can behave as a sin(2φ) Josephson element, free of the traditionally dominant sin(φ) harmonic. Such element will be instrumental for the development of superconducting quantum bits protected from decoherence.
Abstract Hybrid superconductor-semiconductor Josephson field-effect transistors (JoFETs) function as Josephson junctions with a gate-tunable critical current. Additionally, they can feature a non- sinusoidal current-phase relation (CPR) containing multiple harmonics of the superconducting phase difference, a so-far underutilized property. In this work, we exploit this multi-harmonicity to create a Josephson circuit element with an almost perfectly π-periodic CPR, indicative of a largely dominant charge-4e supercurrent transport. Such a Josephson element was recently proposed as the basic building block of a protected superconducting qubit. Here, it is realized using a superconducting quantum interference device (SQUID) with low-inductance aluminum arms and two nominally identical JoFETs. The latter are fabricated from a SiGe/Ge/SiGe quantum-well heterostructure embedding a high-mobility two-dimensional hole gas. By carefully adjusting the JoFET gate voltages and finely tuning the magnetic flux through the SQUID close to half a flux quantum, we achieve a regime where the sin(2φ) component accounts for more than 95 % of the total supercurrent. This result demonstrates a new promising route for the realization of superconducting qubits with enhanced coherence properties.
We present measurements of DC superconducting quantum interference devices based on Nb/graphene/Nb Josephson junctions. The superconducting proximity effect in graphene can be used to build Josephson junctions whose critical current can be controlled by field-effect gates. These junctions combine the tunability of semiconductor Josephson junctions with the high critical currents and low contact resistances of metal SNS junctions. By using local gates, the SQUID junction critical currents can be modified individually and this allows the sensitivity and symmetry of the SQUID to be controlled in-situ. We compare the critical current of the SQUID with simulations that include a non-sinusoidal current phase relation in the junctions, as expected for ballistic graphene junctions. We also investigate the transfer function of the device in both symmetric and asymmetric configurations and find a highest transfer function of 300 μV/Φ0. Graphene Josephson junctions have the potential to add functionality to existing technologies; for example, to make SQUID magnetometers with tunable sensitivity or superconducting qubits with fast electrical control.
With a large portfolio of elemental quantum components, superconducting quantum circuits have contributed to dramatic advances in microwave quantum optics. Of these elements, quantum-limited parametric amplifiers have proven to be essential for low noise readout of quantum systems whose energy range is intrinsically low (tens of µeV). They are also used to generate non classical states of light that can be a resource for quantum enhanced detection. Superconducting parametric amplifiers, like quantum bits, typically utilize a Josephson junction as a source of magnetically tunable and dissipation-free nonlinearity. The magnetic control is not an industry standard for devices and starts already to be an issue in large scale circuits. In recent years, efforts have been made to introduce semiconductor weak links as electrically tunable nonlinear elements, with demonstrations of microwave resonators and quantum bits using semiconductor nanowires, a two dimensional electron gas, carbon nanotubes and graphene. However, given the challenge of balancing nonlinearity, dissipation, participation, and energy scale, parametric amplifiers have not yet been implemented with a semiconductor weak link. The work presented in this PhD thesis demonstrates the design, fabrication and performances of a parametric amplifier leveraging a graphene Josephson junction.The graphene is encapsulated in between hBN flakes in order to improve its quality. Using such high quality junctions, we demonstrate amplification with 20 dB gain which is the milestone for overcoming noise of the classical amplifiers in the rest of the amplification chain. The Josephson parametric amplifier being based on a resonant structure (around 6 GHz) suffers from the gain bandwidth product limiting the amplification to a few MegaHertz frequency range. The use of a side gate to electrically tune the graphene gives control of the Josephson junction inductance and thus the resonant frequency of the amplifier. We demonstrate a near 1 GHz tunability of the amplification frequency with the use of a side gate which is as good as the tunability offered by using a magnetic flux on a SQUID for similar amplifier designs. Moreover, graphene has shown to exhibit nonlinear loss under a strong microwave irradiation arising because of dynamics in the Andreev states. Dissipation is known to add intrinsic noise on quantum amplifiers and could be a problem for quantum limited parametric amplification. We demonstrate that despite the presence of nonlinear loss, graphene based Josephson parametric amplifiers can reach near quantum limited amplification. A two photon loss model was used to describe the behaviour of the device but we show that a more complex model is required in order to take into account the nonlinear dissipation and the non-sinusoidal current phase relation. We also studied the dynamic range and showed that the graphene based Josephson parametric amplifier can reach a 1 dB compression point of -123 dBm which is as good as single tunnel junctions based parametric amplifiers. Our results expand the toolset for electrically tunable superconducting quantum circuits and offer new opportunities for the development of quantum technologies such as quantum computing, quantum sensing and fundamental science.
Gate-tunable Josephson junctions embedded in a microwave environment provide a promising platform to in situ engineer and optimize novel superconducting quantum circuits. The key quantity for the circuit design is the phase-dependent complex admittance of the junction, which can be probed by sensing a radio frequency SQUID with a tank circuit. Here, we investigate a graphene-based Josephson junction as a prototype gate-tunable element enclosed in a SQUID loop that is inductively coupled to a superconducting resonator operating at 3 GHz. With a concise circuit model that describes the dispersive and dissipative response of the coupled system, we extract the phase-dependent junction admittance corrected for self-screening of the SQUID loop. We decompose the admittance into the current-phase relation and the phase-dependent loss, and as these quantities are dictated by the spectrum and population dynamics of the supercurrent-carrying Andreev bound states, we gain insight to the underlying microscopic transport mechanisms in the junction. We theoretically reproduce the experimental results by considering a short, diffusive junction model that takes into account the interaction between the Andreev spectrum and the electromagnetic environment, from which we estimate lifetimes on the order of $\ensuremath{\sim}10$ ps for nonequilibrium populations.
The development of superconducting electronics requires careful characterization of the components that makeup electronic circuits. Superconducting weak links are the building blocks of most superconducting electronic components and are characterized by highly nonlinear current-to-phase relations (CPRs), which are often not perfectly known. Recent research has found that the Josephson diode effect (JDE) can be related to the high harmonic content of the current-to-phase relation of the weak links embedded in superconducting interferometers. This makes the JDE a natural tool for exploring the harmonic content of weak links beyond single-harmonic CPR. In this study, we present the theoretical model and experimental characterization of a double-loop superconducting quantum interference device (DL-SQUID) that embeds all-metallic superconductor-normal metal-superconductor junctions. The proposed device exhibits the JDE due to the interference of the supercurrents of three weak links in parallel, and this feature can be adjusted through two magnetic fluxes, which act as experimental knobs. We carry out a theoretical study of the device in terms of the relative weight of the interferometer arms and the experimental characterization concerning flux tunability and temperature.