Capacitance-based fermion parity readout and predicted Rabi oscillations in a Majorana nanowire

Recent experiments have measured flux-dependent capacitance at radio frequencies, leading to the potential for a fast parity read-out of a Majorana qubit. In this work, we argue that the quantum dot used in the capacitance measurement can be reasonably approximated by a noninteracting weakly coupled orbital. We then predict the measured flux and parity-dependent capacitance for several parameter regimes of the disordered Majorana nanowire model that are both topological and trivial. Following this, we study how such a fast capacitance readout can be used to characterize the quantum coherence of a Majorana nanowire-based qubit using Rabi oscillations. We additionally show that such measurements, if made possible by coherent interwire tunneling, would provide a valuable way of characterizing the low energy states in the frequency domain.