Dispersive Gate Sensing the Quantum Capacitance of a Point Contact

The technique of dispersive gate sensing (DGS) uses a single electrode to readout a qubit by detecting the change in quantum capacitance due to single electron tunnelling. Here, we extend DGS from the detection of discrete tunnel events to the open regime, where many electrons are transported via partially- or fully-transmitting quantum modes. Comparing DGS with conventional transport shows that the technique can resolve the Van Hove singularities of a one-dimensional ballistic system, and also probe aspects of the potential landscape that are not easily accessed with dc transport. Beyond readout, these results suggest that gate-sensing can also be of use in tuning-up qubits or probing the charge configuration of open quantum devices in the regime where electrons are delocalized.