Utilizing dispersive gate sensing (DGS), we investigate the spin-orbit field (BSO) orientation in a many-electron double quantum dot (DQD) defined in an InSb nanowire. While characterizing the interdot tunnel couplings, we find the measured dispersive signal depends on the electron-charge occupancy, as well as on the amplitude and orientation of the external magnetic field. The dispersive signal is mostly insensitive to the external field orientation when a DQD is occupied by a total odd number of electrons. For a DQD occupied by a total even number of electrons, the dispersive signal is reduced when the finite external magnetic field aligns with the effective BSO orientation. This fact enables the identification of BSO orientations for different DQD electron occupancies. The BSO orientation varies drastically between charge transitions, and is generally neither perpendicular to the nanowire nor in the chip plane. Moreover, BSO is similar for pairs of transitions involving the same valence orbital, and varies between such pairs. Our work demonstrates the practicality of DGS in characterizing spin-orbit interactions in quantum dot systems, without requiring any current flow through the device.

Cooper pair splitters hold utility as a platform for investigating the entanglement of electrons in Cooper pairs, but probing splitters with voltage-biased Ohmic contacts prevents the retention of electrons from split pairs since they can escape to the drain reservoirs. We report the ability to controllably split and retain single Cooper pairs in a multi-quantum-dot device isolated from lead reservoirs, and separately demonstrate a technique for detecting the electrons emerging from a split pair. First, we identify a coherent Cooper pair splitting charge transition using dispersive gate sensing at GHz frequencies. Second, we utilize a double quantum dot as an electron parity sensor to detect parity changes resulting from electrons emerging from a superconducting island.

We demonstrate the use of radio-frequency (rf) resonators to measure the capacitance of nanoscale semiconducting devices in field-effect transistor configurations. The rf resonator is attached to the gate or the lead of the device. Consequently, tuning the carrier density in the conducting channel of the device affects the resonance frequency, quantitatively reflecting its capacitance. We test the measurement method on InSb and InAs nanowires at dilution-refrigerator temperatures. The measured capacitances are consistent with those inferred from the periodicity of the Coulomb blockade of quantum dots realized in the same devices. In an implementation of the resonator using an off-chip superconducting spiral inductor we find the measurement sensitivity values reaching down to 75zF/Hz at 1 kHz measurement bandwidth, and noise down to 0.45 aF at 1 Hz bandwidth. We estimate the sensitivity of the method for a number of other implementations. In particular, we predict a typical sensitivity of about 40zF/Hz at room temperature with a resonator composed of off-the-shelf components. Of several proposed applications, we demonstrate two: the capacitance measurement of several identical 80-nm-wide gates with a single resonator, and the field-effect mobility measurement of an individual nanowire with the gate capacitance measured in situ.

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.