  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.
