Dispersive charge sensing is realized in hybrid semiconductor-superconductor nanowires in gate-defined single- and double-island device geometries. Signal-to-noise ratios (SNRs) were measured in both the frequency and time domains. Frequency-domain measurements were carried out as a function of frequency and power and yield a charge sensitivity of 1 × 10–3 e/Hz for an ∼11 MHz measurement bandwidth. Time-domain measurements yield SNR > 1 for a 20 μs integration time. At zero magnetic field, photon-assisted tunneling was detected dispersively in a double-island geometry, indicating coherent hybridization of the two superconducting islands. At an axial magnetic field of 0.6 T, subgap states are detected dispersively, demonstrating the suitability of the method to sensing in the topological regime.
Dispersive charge sensing is realized in hybrid semiconductor-superconductor nanowires in gate-defined single- and double-island device geometries. Signal-to-noise ratios (SNRs) were measured in both the frequency and time domains. Frequency-domain measurements were carried out as a function of frequency and power and yield a charge sensitivity of 1 × 10–3 e/Hz for an ∼11 MHz measurement bandwidth. Time-domain measurements yield SNR > 1 for a 20 μs integration time. At zero magnetic field, photon-assisted tunneling was detected dispersively in a double-island geometry, indicating coherent hybridization of the two superconducting islands. At an axial magnetic field of 0.6 T, subgap states are detected dispersively, demonstrating the suitability of the method to sensing in the topological regime.
Spin and topological-qubit based quantum computers require an easily scalable and highly sensitive method for readout and manipulation, for which Dispersive Gate Sensing (DGS) is a promising candidate [1, 2]. DGS enables sensing of single electron tunneling events in a mesoscopic system by measuring a reflected Radio Frequency (RF) signal from a resonator capacitively coupled to one of the system’s gate electrodes. From the resonator’s perspective, the system is modeled as an effective ‘parametric capacitance’ [3]. Motivated by its viability for qubit readout and control, we measure transport characteristics of a semiconducting-superconducting hybrid charge island system using this method. Doing so, we observe a spin degeneracy modulation of interdot tunnel couplings resulting from hybridization of a dot orbital with a subgap state of the superconductor, measured entirely within Coulomb blockade. Without DC measurement, we also track a subgap state’s energy via voltage intervals between island charge states as a function of field. Subsequently, we attempt to correlate changes in the resonator’s internal dissipation with coherence of tunneling into the superconducting island. In particular, we collapse a superconducting island’s lowest energy state to the Fermi level by applying a magnetic field. Contrary to expectations, internal dissipation in the resonator did not change dramatically with field, in fact decreasing at charge degeneracy points at all field strengths. We corroborate measurements with existing theory, augmented by simple analytical and numerical models demonstrating that coherence factors of superconducting quasiparticle states and the degeneracy of dot orbitals modulate parametric capacitance. A master equation model of finite temperature interdot tunneling is solved, agreeing with experimental evidence that Sisyphus dissipation is negligible when a dot orbital is hybridized with multiple independent quasiparticle states. To be employed in quantum computers, a full understanding of all phenomena contributing to a DGS signal in these hybrid systems is critical. Hence, these results mark a step towards unambiguous readout of Majorana parity in topological qubits [4].
High-fidelity readout of semiconductor-based qubits (in particular, Majorana qubits of the future) could be accomplished by dispersive readout, as already used with superconducting qubits. So far, though, the dispersive signals have been small, and the required integration times much longer than typical qubit coherence times. This work shows that signal amplitude can be vastly increased by strongly coupling a sensing gate to a readout quantum dot. This coupling allows readout of this system in the microsecond regime, which is on par with the state of the art for other qubits. Here the chief limiting factor of the signal-to-noise ratio is tunnel coupling.
We report direct detection of charge tunneling between a quantum dot and a superconducting island through radio-frequency gate sensing. We are able to resolve spin-dependent quasiparticle tunneling as well as two-particle tunneling involving Cooper pairs. The quantum dot can act as an RF-only sensor to characterize the superconductor addition spectrum, enabling us to access subgap states without transport. Our results provide guidance for future dispersive parity measurements of Majorana modes, which can be realized by detecting the parity-dependent tunneling between dots and islands.
Quantum computers can solve some problems exponentially faster than classical computers. Unfortunately, the computational power of quantum computers is currently limited by the number of working qubits. It is difficult to scale up these systems, because qubits are easily affected by noise in their environment. This noise leads to decoherence: loss of the qubit’s encoded information. A possible solution to diminish decoherence is using Majorana box qubits, as these qubits are predicted to be insensitive to local noise. However, this promising type of qubit does not exist yet. With the research described in this thesis, we aim to contribute to the development of Majorana box qubits (MBQs). In these qubits, Majorana zero modes, the basic elements of MBQs, are contained within a superconducting island to suppress Majorana parity fluctuations caused by quasiparticle poisoning. To enable parity readout of the MBQ, these modes are coupled to quantum dots within a nanowire network. To help realize MBQs, we need a better understanding of quasiparticles in superconducting islands, parity-readout techniques, and ways to fabricate nanowire networks. These three aspects are the focus of the experiments presented in this thesis. To study superconducting islands and readout techniques, we used InAs semiconductor nanowires with an epitaxially grown Al shell. Majorana signatures have already been observed in such nanowires. We addressed quasiparticle dynamics in superconducting islands by measuring the gate-charge modulation of the switching current. We found a consistent 2e-periodic modulation at zero magnetic field, and an exponential decrease of parity lifetime with increasing magnetic field. We explored MBQ readout, using a quantum dot level as a proxy for a Majorana zero mode, and measured its charge hybridization with another dot using gate-based readout. We showed that we can rapidly discriminate between two settings with different tunnel couplings, demonstrating the potential of gate-based readout to measure MBQs. And, using gate-based readout, we could study charge-transfer processes occurring in hybrid structures of superconducting islands coupled to quantum dots. Finally, to find a good material platform for nanowire networks, we characterized two two-dimensional systems. We realized quantum point contacts in InSb, which we used to measure the g-factor anisotropy, and effective electron mass in this system. And, we studied the spin-orbit interaction in InAs/GaSb by extracting the difference in density between electrons with different spin orientations. This thesis finishes with a proposal for a series experiments to realize MBQs. These experiments make use of superconducting islands and the reflectometry setup we developed for gate-based readout.
A practical quantum computer demands a physical quantum bit (qubit) that is scalable, has a well-defined initial state, and brings together coherence with reliable control and read-out. A compelling idea is to put together a locally protected Majorana qubit with a superconducting qubit. The superconducting qubit is used to read out the Majorana states while the Majorana qubit may act as a quantum memory. This thesis presents a series of studies on quantum transport in semiconducting nanowires coupled to superconductors to investigate various platforms for realizing Majorana. These studies are followed by microwave measurements on superconducting circuits compatible with semiconducting-superconducting heterostructures. We first evaluate the potential of Ge/Si core/shell nanowires by achieving induced superconductivity as well as estimating spin-orbit coupling. Next we explore the transport mediated by Andreev bound states formed in InSb nanowire quantum. A subgap negative differential conductance is investigated together with the coalescing Andreev resonances at zero bias relevant for the correct interpretation of Majorana experiments done on the same structures. We conclude our studies of semiconducting nanowires by exploring tunnel junctions in Sn-InSb nanowires that are prepared by in-situ shadowing using nearby nanowires and flakes. Tin shells are found to induce a hard superconducting gap persisting up to high magnetic fields. We observe the two-electron charging effect from a small superconducting island of Sn-InSb. This effect is attributed to charge parity stability, which makes this nanowire system an intriguing candidate for superconducting and topological quantum circuits. These Sn-InSb junctions are then used as the nonlinear element in a transmon qubit design where we observe a dispersive coupling between this nanowire Josephson junction and a superconducting resonator. We also present our progress towards building a magnetic field resilient superconducting circuit that allows integration with semiconducting and topological structures. In the last chapter, InSb semiconducting nanowires are utilized as shadow masks prior to superconductor deposition on an InAs quantum well. We study Josephson current properties in Josephson junctions made from these nanowire shadows. Our results point to highly transparent junctions that can be developed further for hybrid superconductor-semiconductor qubit systems.
One of the essential limitations for a physical realisation of topological-qubit based quantum computing is the problem of uncontrolled quasiparticle poisoning of the superconducting charge island. These quasiparticles have been previously reported as a known limiting factor in most of the superconducting architectures. To this end, we consider the importance of equilibrium quasiparticle poisoning in hybrid semiconducting-superconducting systems believed to be able to host Majoranas. We employed gate-based dispersive sensing by investigating a reflected radiofrequency (RF) signal from a resonator, which is capacitively coupled to one of the gate electrodes of the hybrid double dot realised in an InAs nanowire. This way, the quantum capacitance of the system can be probed, which in turn reveals charge tunnelling processes, and can be used as an indicator of single-electron tunnelling events. By operating the device in a so-called floating regime, where a double dot system is entirely decoupled from the leads, external non-equilibrium quasiparticle poisoning events can be exponentially suppressed. By appropriately tuning the chemical potentials on the quantum dot and the superconducting island, we attempt to scrutinise the dynamics of the quasiparticles innate to the superconductor. We investigated the dependence of quasiparticle tunnelling rates on the temperature of the system, as well as the applied RF power, as both are predicted to increase the average number of quasiparticles on the island. In both cases, we could find no observational proof of quasiparticle tunnelling events through the use of our measurement technique. We report an observation of a two-level resonator response, which we explain using a two-level fluctuator. Analysing telegraph measurements, we demonstrate the viability of the analysis tool, which allows us to determine the average occupation times of each state. In principle, for processes occurring at rates slower than the measurement frequency, this technique can be used to convert a\nrelatively faint difference between the “poisoned and unpoisoned state”, to the signal of the gate being on coulomb resonance versus on Coulomb blockade, which is a much clearer signal to distinguish. Both, the technique, as well as the expected rates of the physical processes within the island, are evaluated in the context of the experiment.