Ground-state phase diagram and parity-flipping microwave transitions in a gate-tunable Josephson junction

We probed a gate-tunable InAs nanowire Josephson weak link by coupling it to\na microwave resonator. Tracking the resonator frequency shift when the weak\nlink is close to pinch-off, we observe that the ground state of the latter\nalternates between a singlet and a doublet when varying either the gate voltage\nor the superconducting phase difference across it. The corresponding microwave\nabsorption spectra display lines that approach zero energy close to the\nsinglet-doublet boundaries, suggesting parity flipping transitions, which are\nin principle forbidden in microwave spectroscopy and expected to arise only in\ntunnel spectroscopy. We tentatively interpret them by means of an ancillary\nstate isolated in the junction acting as a reservoir for individual electrons.\n