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arXiv:2403.03800 · PRX Quantum

Direct Microwave Spectroscopy of Andreev Bound States in Planar Ge Josephson Junctions

Manuel Hinderling, Sofieke C. ten Kate, Marco Coraiola, D. Z. Haxell, M. Stiefel, Matthias Mergenthaler, Stephan Paredes, Stephen W. Bedell, Deividas Sabonis, Fabrizio Nichele

Published Sep 27, 2024• 15 citations
arXivHTMLPDF

Abstract

We demonstrate microwave measurements of the Andreev-bound-state (ABS) spectrum in planar Josephson junctions (JJs) defined in Ge high-mobility two-dimensional hole gases contacted by superconducting platinum germanosilicide ( Pt Si Ge ). The JJs and readout circuitry are located on separate chips and inductively coupled via flip-chip bonding. For a device with 350-nm junction length, the spectroscopic signatures were consistent with the short-junction limit, with an induced superconducting gap Δ ∗ ≈ 48 μ eV and transmission τ ≈ 0.94 . The interaction between the highest-transmission ABS and the resonator was well described by a Jaynes-Cummings model with a vacuum Rabi splitting of approximately 6 MHz. A device with a junction length of 1 μ m showed an ABS spectrum consistent with a long-junction model. Time-resolved monitoring of the readout resonator in the dispersive regime revealed gate-voltage tunable-junction parity fluctuations on the time scale of seconds. Our work indicates a viable path toward hybrid quantum devices based on planar Ge . Published by the American Physical Society 2024

DOI
10.1103/prxquantum.5.030357

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We demonstrate microwave measurements of the Andreev-bound-state (ABS) spectrum in planar Josephson junctions (JJs) defined in Ge high-mobility two-dimensional hole gases contacted by superconducting platinum germanosilicide ( Pt Si Ge ). The JJs and readout circuitry are located on separate chips and inductively coupled via flip-chip bonding. For a device with 350-nm junction length, the spectroscopic signatures were consistent with the short-junction limit, with an induced superconducting gap Δ ∗ ≈ 48 μ eV and transmission τ ≈ 0.94 . The interaction between the highest-transmission ABS and the resonator was well described by a Jaynes-Cummings model with a vacuum Rabi splitting of approximately 6 MHz. A device with a junction length of 1 μ m showed an ABS spectrum consistent with a long-junction model. Time-resolved monitoring of the readout resonator in the dispersive regime revealed gate-voltage tunable-junction parity fluctuations on the time scale of seconds. Our work indicates a viable path toward hybrid quantum devices based on planar Ge . Published by the American Physical Society 2024
Measurement and coherent manipulation of Andreev bound states (ABSs) in planar superconductor-semiconductor heterostructures could enable gate-controllable, small-footprint superconducting spin qubits with long coherence times. So far, readout capabilities and device coherence have been limited by lossy $I\phantom{\rule{0}{0ex}}I\phantom{\rule{0}{0ex}}I\ensuremath{-}V$ substrates, but here researchers overcome this limitation with a flip-chip approach to microwave experiments on ABSs. Superconductor-semiconductor devices and microwave resonators are placed on different chips and inductively coupled via a vacuum gap, enabling high-quality readout without sacrificing device properties.
The properties of superconducting devices depend sensitively on the parity (even or odd) of the quasiparticles that they contain. Encoding quantum information in the parity degree of freedom is central in several emerging solid-state qubit architectures, including in hybrid superconductor-semiconductor devices. In the latter case, accurate, nondestructive, and time-resolved parity measurements are a challenging issue. Here, we report on control and real-time parity measurement in a superconducting island embedded in a superconducting loop and realized in a hybrid two-dimensional heterostructure using a microwave resonator. To avoid microwave losses impeding time-resolved measurements, the device and readout resonator are located on separate chips, connected via flip-chip bonding, and couple inductively through vacuum. The superconducting resonator detects the parity-dependent circuit inductance, allowing for fast parity readout. We have resolved even- and odd-parity states with a signal-to-noise ratio of SNR ≈ 3 for an integration time of 20 μ s and a detection fidelity exceeding 98 % . The real-time parity measurement shows a state lifetime extending into the millisecond range. Our approach will lead to a better understanding of coherence-limiting mechanisms in superconducting quantum hardware and help to advance inductive-readout schemes for hybrid qubits. Published by the American Physical Society 2024
Abstract Josephson junctions based on semiconductor nanowires are potential building blocks for electrically tunable qubit structures, e.g., the gatemon or the Andreev qubit. However, an actual realization requires the thorough investigation of the intrinsic excitation spectrum. Here, we demonstrate the fabrication of low-loss superconducting microwave circuits that combine high quality factors with a well-controlled gate architecture by utilizing a flip-chip approach. This platform is then used to perform single-tone and two-tone experiments on Andreev states in in-situ grown InAs/Al core/half-shell nanowires with shadow mask defined Josephson junctions. In gate-controlled and flux-biased spectroscopic measurements we find clear signatures of single quasiparticle as well as quasiparticle pair transitions between discrete Andreev bound states mediated by photon-absorption. Our experimental findings are supported by simulations that show that the junction resides in the intermediate channel length regime.
High Resolution Image Download MS PowerPoint Slide We perform switching current measurements of planar Josephson junctions (JJs) coupled by a common superconducting electrode with independent control over the two superconducting phase differences. We observe an anomalous phase shift in the current–phase relation of a JJ as a function of gate voltage or phase difference in the second JJ. This demonstrates the nonlocal Josephson effect, and the implementation of a φ 0 -junction which is tunable both electrostatically and magnetically. The anomalous phase shift is larger for shorter distances between the JJs and vanishes for distances much longer than the superconducting coherence length. Results are consistent with the hybridization of Andreev bound states, leading to the formation of an Andreev molecule. Our devices constitute a realization of a tunable superconducting phase source and could enable new coupling schemes for hybrid quantum devices.
The modern understanding of the Josephson effect in mesosopic devices derives from the physics of Andreev bound states, fermionic modes that are localized in a superconducting weak link. Recently, Josephson junctions constructed using semiconducting nanowires have led to the realization of superconducting qubits with gate-tunable Josephson energies. We have used a microwave circuit QED architecture to detect Andreev bound states in such a gate-tunable junction based on an aluminum-proximitized indium arsenide nanowire. We demonstrate coherent manipulation of these bound states, and track the bound-state fermion parity in real time. Individual parity-switching events due to nonequilibrium quasiparticles are observed with a characteristic timescale T_{parity}=160±10 μs. The T_{parity} of a topological nanowire junction sets a lower bound on the bandwidth required for control of Majorana bound states.
Andreev molecule states arise from hybridization of Andreev bound states in different Josephson Junctions. Extensive theoretical and experimental research concentrates on direct coherent electron coupling between the junctions: this implies the distance between the junctions is of the order of superconducting coherence length, that is, short. We propose and discuss the possibility to create Andreev molecules at long (in principle, arbitrary long) distance between the junctions. In this case, the hybridized states are excited quasi-particle singlets and the coupling is provided by an embedding electric circuit. To achieve a strong hybridization, one aligns the energies of the Andreev bound states with associated phase differences. In fact, a recent experiment realizes such setup. With circuit theory we derive the hybridization level splitting and estimate the scale of the effect. Since the phenomenon encompasses excited states, we derive and solve the associated Lindblad equation under condition of persistent resonant excitation. By analyzing the resulting dissipative dynamics we identify relevant regimes where the hybridization and resonant excitation peaks are most pronounced. The low-frequency mutual inductance of the Josephson junctions is an important signature of the molecular state and associated non-local Josephson effect. We demonstrate the peak structures for both mutual and self-inductance, and compute them in various frequency regimes. In an interesting common case the embedding circuit includes an oscillator, which can be used both to enhance hybridization and for state readout with two-tone spectroscopy. We derive and solve Lindblad equations for the conditions of two-tone spectroscopy to demonstrate the the readout of molecular states.