Hybrid semiconducting-superconducting mesoscopic circuits are the basis of topological and parity quantum bits or 'qubits'. Both qubits are expected to be intrinsically protected from decoherence, making them promising candidates for fault-tolerant quantum computation. As topological phases effectively manifest exotic nonabelian particles which might not exist in nature, these systems are also of fundamental interest. This thesis primarily employs radio-frequency (RF) reflectometry, an important measurement tool for qubit readout, in order to study localized states in hybrid circuits. Since the hybridization of localized quantum dot and Andreev bound states is foundational to the aforementioned qubit implementations, our focus is on using RF tools to characterize such hybridization. We therefore begin by outlining background theory of these states and of RF reflectometry accompanied by simulations. Subsequently, we describe the results of four distinct experiments.
First, in a system comprised of multiple quantum dots, we demonstrate a signal-to-noise ratio of 15 in 1 microsecond for resolving interdot electron tunneling with RF reflectometry of the dot gate electrodes, a proxy for the readout of numerous types of qubits including spin and topological qubits. Additionally, we show RF reflectometry of the device leads is mappable to DC conductance a priori, implying it can completely replace DC measurement techniques for the characterization of semiconducting quantum circuits.
In the next experiment, we probe a superconducting island surrounded on either side by a semiconducting quantum dot with RF gate reflectometry. Therein, we electrically isolate the system from its leads, fixing the system's total charge. Afterwards, we correlate electron tunneling events between dots using frequency multiplexing of different gate resonators, culminating in the controllable splitting of a single Cooper pair into its constituent electrons. We also demonstrate a form of parity sensing using a strongly coupled double quantum dot and gate reflectometry.
Continuing, we present a study of an irregularly shaped double quantum dot arranged in a loop and threaded by a magnetic flux. Employing gate reflectometry to measure the interdot hybridization, we observe that it oscillates as a function of flux with a period of one flux quantum but with unpredictably varying amplitude and contrast. This result is a prerequisite for the readout and manipulation of measurement-based topological qubits and hybrid parity qubits.
As a final experiment, we investigate markers of the hybridization between Andreev bound states in a multiterminal Josephson junction, itself a potential platform for simulating topological Weyl systems. There, we characterize the current-flux relation of a four-terminal junction using two coupled DC superconducting quantum interference loops, observing a 'nonlocal' Josephson effect tuned by the magnetic fluxes through both loops. With a minimal theoretical model, we show that this behavior can be fully described by an array of two-terminal Josephson junctions and is not a unique signature of the hybridization of Andreev bound states in the junction.
To conclude, we summarize our experimental results and discuss potential future work. Namely, we emphasize the importance of understanding quasiparticle poisoning for the performance of topological and parity qubits, and consider further applications of RF measurement tools in studying hybrid systems. The results of this dissertation establish RF sensing as a complete characterization tool for hybrid quantum circuits, display its utility in studying floating systems to probe the movement of single electrons and Cooper pairs, and demonstrate the flux-control of interdot tunnel couplings required for hybrid parity qubits. Lastly, we highlight the indistinguishability of hybridized Andreev states from trivial multiterminal Josephson effects in a multiterminal junction's current-phase relation.