Gate-controlled charging effects in superconducting nanowires: low-energy spectrum and time scales for Majorana manipulation

In this talk, we investigate the gate-controlled crossover between different operating regimes of a superconducting nanowire segmented into two islands each Josephson-coupled to a bulk superconductor. This device may host two pairs of Majorana bound states and could be realized in the near future as a platform for testing Majorana fusion rules. We present a numerical study of the low-energy spectrum of this device covering both the charge-dominated regime utilizable for initialization and readout of the Majorana bound states as well as the Josephson-dominated transmon regime allowing for Majorana manipulations. Depending on the relative size of the energy scales associated with the Majorana coupling, the charging energy, and the transmon frequency, the „fine structure“ of the low-energy spectrum differs. We finally discuss the associated time scales for implementing a fusion-rule testing protocol discussed in the talks by J. Alicea and R. V. Mishmash.