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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 PtSiGe. The JJs and readout circuitry are located on separate chips and inductively coupled via flip-chip bonding. For a device with $350~\mathrm{nm}$ junction length, spectroscopic signatures were consistent with the short-junction limit, with an induced superconducting gap $\Delta^{*}\approx48~\mathrm{\mu eV}$ and transmission $\tau \approx 0.94$. 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 $6~\mathrm{MHz}$. A device with junction length of $1~\mu m$ 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 timescale of seconds. Our work indicates a viable path towards hybrid quantum devices based on planar Ge.

We investigate the direction-dependent switching current in a flux-tunable four-terminal Josephson junction defined in an InAs/Al two-dimensional heterostructure. The device exhibits the Josephson diode effect, with switching currents that depend on the sign of the bias current. The superconducting diode efficiency, reaching a maximum of $|\eta|\approx34\%$, is widely tunable - both in amplitude and sign - as a function of magnetic fluxes and gate voltages. Our observations are supported by a circuit model of three parallel Josephson junctions with non-sinusoidal current-phase relation. With respect to conventional Josephson interferometers, phase-tunable multiterminal Josephson junctions enable large diode efficiencies in structurally symmetric devices, where local magnetic fluxes break both time-reversal and spatial-inversion symmetries. Our work establishes a pathway to develop Josephson diodes with wide-range tunability and that do not rely on exotic materials or externally applied magnetic fields.

Properties of superconducting devices depend sensitively on the parity (even or odd) of the quasiparticles they contain. Encoding quantum information in the parity degree of freedom is central in several emerging solid-state qubit architectures. Yet, accurate, non-destructive, and time-resolved parity measurement is a challenging and long-standing 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. 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 and non-destructive parity readout. We resolved even and odd parity states with signal-to-noise ratio SNR $\approx3$ with an integration time of $20~\mu$s and detection fidelity exceeding 98%. Real-time parity measurement showed state lifetime extending into millisecond range. Our approach will lead to better understanding of coherence-limiting mechanisms in superconducting quantum hardware and provide novel readout schemes for hybrid qubits.

Harnessing spin and parity degrees of freedom is of fundamental importance for the realization of emergent quantum devices. Nanostructures embedded in superconductor--semiconductor hybrid materials offer novel and yet unexplored routes for addressing and manipulating fermionic modes. Here we spectroscopically probe the two-dimensional band structure of Andreev bound states in a phase-controlled hybrid three-terminal Josephson junction. Andreev bands reveal spin-degeneracy breaking, with level splitting in excess of 9 GHz, and zero-energy crossings associated to ground state fermion parity transitions, in agreement with theoretical predictions. Both effects occur without the need of external magnetic fields or sizable charging energies and are tuned locally by controlling superconducting phase differences. Our results highlight the potential of multiterminal hybrid devices for engineering quantum states.

We perform supercurrent and tunneling spectroscopy measurements on gate-tunable InAs/Al Josephson junctions (JJs) in an in-plane magnetic field, and report on phase shifts in the current-phase relation measured with respect to an absolute phase reference. The impact of orbital effects is investigated by studying multiple devices with different superconducting lead sizes. At low fields, we observe gate-dependent phase shifts of up to ${\varphi_{0}=0.5\pi}$ which are consistent with a Zeeman field coupling to highly-transmissive Andreev bound states via Rashba spin-orbit interaction. A distinct phase shift emerges at larger fields, concomitant with a switching current minimum and the closing and reopening of the superconducting gap. These signatures of an induced phase transition, which might resemble a topological transition, scale with the superconducting lead size, demonstrating the crucial role of orbital effects. Our results elucidate the interplay of Zeeman, spin-orbit and orbital effects in InAs/Al JJs, giving new understanding to phase transitions in hybrid JJs and their applications in quantum computing and superconducting electronics.

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 a nonlocal Josephson effect, and the implementation of a $\varphi_0$-junction which is tunable both electrostatically and magnetically. The anomalous phase shift was larger for shorter distances between the JJs and vanished for distances much longer than the superconducting coherence length. Results are consistent with the hybridization of ABSs, 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.

In hybrid Josephson junctions with three or more superconducting terminals coupled to a semiconducting region, Andreev bound states may form unconventional energy band structures, or Andreev matter, which are engineered by controlling superconducting phase differences. Here we report tunnelling spectroscopy measurements of three-terminal Josephson junctions realised in an InAs/Al heterostructure. The three terminals are connected to form two loops, enabling independent control over two phase differences and access to a synthetic Andreev band structure in the two-dimensional phase space. Our results demonstrate a phase-controlled Andreev molecule, originating from two discrete Andreev levels that spatially overlap and hybridise. Signatures of hybridisation are observed in the form of avoided crossings in the spectrum and band structure anisotropies in the phase space, all explained by a numerical model. Future extensions of this work could focus on addressing spin-resolved energy levels, ground state fermion parity transitions and Weyl bands in multiterminal geometries.

We demonstrate a flip-chip-based approach to microwave measurements of Andreev bound states in a gate-tunable planar Josephson junction using inductively-coupled superconducting low-loss resonators. By means of electrostatic gating, we present control of both the density and transmission of Andreev bound states. Phase biasing of the device shifted the resonator frequency, consistent with the modulation of supercurrent in the junction. Two-tone spectroscopy measurements revealed an isolated Andreev bound state consistent with an average induced superconducting gap of $184~\mathrm{\mu eV}$ and a gate-tunable transmission approaching $0.98$. Our results represent the feasibility of using the flip-chip technique to address and study Andreev bound states in planar Josephson junctions, and they give a promising path towards microwave applications with superconductor-semiconductor two-dimensional materials.

Light-matter interaction enables engineering of non-equilibrium quantum systems. In condensed matter, spatially and temporally cyclic Hamiltonians are expected to generate energy-periodic Floquet states, with properties inaccessible at thermal equilibrium. A recent work explored the tunnelling conductance of a planar Josephson junction under microwave irradiation, and interpreted replicas of conductance features as evidence of steady Floquet-Andreev states. Here we realise a similar device in a hybrid superconducting-semiconducting heterostructure, which utilises a tunnelling probe with gate-tunable transparency and allows simultaneous measurements of Andreev spectrum and current-phase relation of the planar Josephson junction. We show that, in our devices, spectral replicas in sub-gap conductance emerging under microwave irradiation are caused by photon assisted tunnelling of electrons into Andreev states. The current-phase relation under microwave irradiation is also explained by the interaction of Andreev states with microwave photons, without the need to invoke Floquet states. The techniques outlined in this study establish a baseline to distinguish photon assisted tunnelling from Floquet-Andreev states in mesoscopic devices, a crucial development towards understanding light-matter coupling in hybrid nanostructures.

We experimentally investigate the stochastic phase dynamics of planar Josephson junctions (JJs) and superconducting quantum interference devices (SQUIDs) defined in epitaxial InAs/Al heterostructures, and characterized by a large ratio of Josephson energy to charging energy. We observe a crossover from a regime of macroscopic quantum tunneling to one of phase diffusion as a function of temperature, where the transition temperature $T^{*}$ is gate-tunable. The switching probability distributions are shown to be consistent with a small shunt capacitance and moderate damping, resulting in a switching current which is a small fraction of the critical current. Phase locking between two JJs leads to a difference in switching current between that of a JJ measured in isolation and that of the same JJ measured in an asymmetric SQUID loop. In the case of the loop, $T^*$ is also tuned by a magnetic flux.

Recent experiments suggest the possibility to tune superconductivity in metallic nanowires by application of modest gate voltages. It is largely debated whether the effect is due to an electric field at the superconductor surface or small currents of high-energy electrons. We shed light on this matter by studying the suppression of superconductivity in sample geometries where the roles of electric field and electron-current flow can be clearly separated. Our results show that suppression of superconductivity does not depend on the presence or absence of an electric field at the surface of the nanowire, but requires a current of high-energy electrons. The suppression is most efficient when electrons are injected into the nanowire, but similar results are obtained also when electrons are passed between two remote electrodes at a distance $d$ to the nanowire (with $d$ in excess of $1~\mathrm{\mu m}$). In the latter case, high-energy electrons decay into phonons which propagate through the substrate and affect superconductivity in the nanowire by generating quasiparticles. We show that this process involves a non-thermal phonon distribution, with marked differences from the loss of superconductivity due to Joule heating near the nanowire or an increase in the bath temperature.