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arXiv:2302.09192 · Nature Physics

Observation of Josephson harmonics in tunnel junctions

Dennis Willsch, Dennis Rieger, Patrick Winkel, Madita Willsch, Christian Dickel, Jonas Krause, Yoichi Ando, Raphaël Lescanne, Zaki Leghtas, Nicholas T. Bronn, Pratiti Deb, Olivia Lanes, Zlatko Minev, Benedikt Dennig, Simon Geisert, Simon Günzler, Soeren Ihssen, Patrick Paluch, Thomas J.G. Reisinger, Roudy Hanna, Jin Hee Bae, Peter Schüffelgen, Detlev Grützmacher, Luiza Buimagă-Iarinca, Cristian Morari, Wolfgang Wernsdorfer, David Peter Divincenzo, Kristel F. L. Michielsen, Gianluigi Catelani, Ioan M. Pop

Published Feb 14, 2024• 73 citations
arXivHTMLPDF

Abstract

Abstract Approaches to developing large-scale superconducting quantum processors must cope with the numerous microscopic degrees of freedom that are ubiquitous in solid-state devices. State-of-the-art superconducting qubits employ aluminium oxide (AlO x ) tunnel Josephson junctions as the sources of nonlinearity necessary to perform quantum operations. Analyses of these junctions typically assume an idealized, purely sinusoidal current–phase relation. However, this relation is expected to hold only in the limit of vanishingly low-transparency channels in the AlO x barrier. Here we show that the standard current–phase relation fails to accurately describe the energy spectra of transmon artificial atoms across various samples and laboratories. Instead, a mesoscopic model of tunnelling through an inhomogeneous AlO x barrier predicts percent-level contributions from higher Josephson harmonics. By including these in the transmon Hamiltonian, we obtain orders of magnitude better agreement between the computed and measured energy spectra. The presence and impact of Josephson harmonics has important implications for developing AlO x -based quantum technologies including quantum computers and parametric amplifiers. As an example, we show that engineered Josephson harmonics can reduce the charge dispersion and associated errors in transmon qubits by an order of magnitude while preserving their anharmonicity.

DOI
10.1038/s41567-024-02400-8

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Abstract Approaches to developing large-scale superconducting quantum processors must cope with the numerous microscopic degrees of freedom that are ubiquitous in solid-state devices. State-of-the-art superconducting qubits employ aluminium oxide (AlO x ) tunnel Josephson junctions as the sources of nonlinearity necessary to perform quantum operations. Analyses of these junctions typically assume an idealized, purely sinusoidal current–phase relation. However, this relation is expected to hold only in the limit of vanishingly low-transparency channels in the AlO x barrier. Here we show that the standard current–phase relation fails to accurately describe the energy spectra of transmon artificial atoms across various samples and laboratories. Instead, a mesoscopic model of tunnelling through an inhomogeneous AlO x barrier predicts percent-level contributions from higher Josephson harmonics. By including these in the transmon Hamiltonian, we obtain orders of magnitude better agreement between the computed and measured energy spectra. The presence and impact of Josephson harmonics has important implications for developing AlO x -based quantum technologies including quantum computers and parametric amplifiers. As an example, we show that engineered Josephson harmonics can reduce the charge dispersion and associated errors in transmon qubits by an order of magnitude while preserving their anharmonicity.
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Quantum computing based on superconducting qubits requires the understanding and control of the materials, device architecture, and operation. However, the materials for the central circuit element, the Josephson junction, have mostly been focused on using the AlO x tunnel barrier. Here, we demonstrate Josephson junctions and superconducting qubits employing two-dimensional materials as the tunnel barrier. We batch-fabricate and design the critical Josephson current of these devices via layer-by-layer stacking N layers of MoS 2 on the large scale. Based on such junctions, MoS 2 transmon qubits are engineered and characterized in a bulk superconducting microwave resonator for the first time. Our work allows Josephson junctions to access the diverse material properties of two-dimensional materials that include a wide range of electrical and magnetic properties, which can be used to study the effects of different material properties in superconducting qubits and to engineer novel quantum circuit elements in the future.
Josephson junctions are the central nonlinear element of superconducting qubits, yet their standard description is reached through a chain of approximations. We propose a purely quantum-mechanical model of the junction, formulated directly in Hilbert space: a charged particle moves on a one-dimensional loop, and the junction is a point at which the wave function obeys self-adjoint boundary conditions, labelled by a coupling strength λλλ, which controls the transparency of the junction, and a phase jump δδδ, which plays the role of the superconducting phase difference. For a loop with a single junction we solve the spectral problem and show that the ground-state momentum expectation, identified with the supercurrent, factorises exactly as ⟨p^0⟩=Ic(δ,λ)sin⁡δ\langle\hat{p}_0\rangle = I_c(δ,λ)\sinδ⟨p^​0​⟩=Ic​(δ,λ)sinδ. For opaque junctions IcI_cIc​ becomes independent of δδδ and the first Josephson relation I=Icsin⁡δI=I_c\sinδI=Ic​sinδ is recovered; for strongly attractive coupling, where the ground state is bound to the junction, the sin⁡δ\sinδsinδ law is also recovered, but with an exponentially suppressed amplitude. For more transparent junctions, however, the model \emph{predicts} deviations from the pure sin⁡δ\sinδsinδ law: IcI_cIc​ acquires a dependence on δδδ already at order λ−2λ^{-2}λ−2, compatible with the higher Josephson harmonics recently found necessary to describe superconducting qubit spectra, and a fully transparent contact yields a current linear in δδδ. When the phase varies in time, a gauge transformation shows that the voltage drop across the junction is proportional to δ˙\dotδδ˙, so that the second Josephson relation emerges without being imposed. The boundary-condition approach thus reproduces both Josephson relations from first principles and predicts corrections to them, offering a route towards higher-fidelity models of superconducting qubits.
Flux-tunable transmon incorporating a van der Waals superconductor via an Al/AlOx_xx​/4Hb-TaS2_22​ Josephson junction
Incorporating van der Waals (vdW) superconductors into Josephson elements extends circuit-QED beyond conventional Al/AlOx_xx​/Al tunnel junctions and enables microwave probes of unconventional condensates and subgap excitations. In this work, we realize a flux-tunable transmon whose nonlinear inductive element is an Al/AlOx_xx​/4Hb-TaS2_22​ Josephson junction. The tunnel barrier is formed by sequential deposition and full in-situ oxidation of ultrathin Al layers on an exfoliated 4Hb-TaS2_22​ flake, followed by deposition of a top Al electrode, yielding a robust, repeatable hybrid junction process compatible with standard transmon fabrication. Embedding the device in a three-dimensional copper cavity, we observe a SQUID-like flux-dependent spectrum that is quantitatively reproduced by a standard dressed transmon--cavity Hamiltonian, from which we extract parameters in the transmon regime. Across measured devices we obtain sub-microsecond energy relaxation (T1T_1T1​ from 0.080.080.08 to 0.69 μ0.69~μ0.69 μs), while Ramsey measurements indicate dephasing faster than our 161616 ns time resolution. We also find a pronounced discrepancy between the Josephson energy inferred from spectroscopy and that expected from the Ambegaokar--Baratoff relation using room-temperature junction resistances, pointing to nontrivial junction physics in the hybrid Al/AlOx_xx​/4Hb-TaS2_22​ system. Although we do not resolve material-specific subgap modes in the present geometry, this work establishes a practical route to integrating 4Hb-TaS2_22​ into coherent quantum circuits and provides a baseline for future edge-sensitive designs aimed at enhancing coupling to boundary and subgap degrees of freedom in vdW superconductors.
Here we report normal-state conductance measurements of three different types of superconducting tunnel junctions that are being used or proposed for quantum computing applications: p-Al/a-AlO/p-Al, e-Re/e-AlO/p-Al, and e-V/e-MgO/p-V, where p stands for polycrystalline, e for epitaxial, and a for amorphous. All three junctions exhibited significant deviations from the parabolic behavior predicted by the WKB approximation models. In the p-Al/a-AlO/p-Al junction, we observed enhancement of tunneling conductances at voltages matching harmonics of Al–O stretching modes. On the other hand, such Al–O vibration modes were missing in the epitaxial e-Re/e-AlO/p-Al junction. This suggests that absence or existence of the Al–O stretching mode might be related to the crystallinity of the AlO tunnel barrier and the interface between the electrode and the barrier. In the e-V/e-MgO/p-V junction, which is one of the candidate systems for future superconducting qubits, we observed suppression of the density of states at zero bias. This implies that the interface is electronically disordered, presumably due to oxidation of the vanadium surface underneath the MgO barrier, even if the interface was structurally well ordered, suggesting that the e-V/e-MgO/p-V junction will not be suitable for qubit applications in its present form. This also demonstrates that the normal-state conductance measurement can be effectively used to screen out low quality samples in the search for better superconducting tunnel junctions.
The performance of various superconducting devices operating at ultra-low temperatures is impaired by the presence of non-equilibrium quasiparticles. Inelastic quasiparticle (QP) tunneling across Josephson junctions in superconducting qubits results in decoherence and spurious excitations and, notably, can trigger correlated errors that severely impede quantum error correction. In this work, we use "gap engineering" to suppress the tunneling of low-energy quasiparticles in Al-based transmon qubits, a leading building block for superconducting quantum processors. By implementing potential barriers for QP, we strongly suppress QP tunneling across the junction and preserve charge parity for over 10310^3103 seconds. The suppression of QP tunneling also results in a reduction in the qubit energy relaxation rates. The demonstrated approach to gap engineering can be easily implemented in all Al-based circuits with Josephson junctions.