We investigate the effect of interatomic Coulomb repulsion V and particular states disregarded previously on the Kitaev-transmon system proposed by Pino et al. 43 which consists of a Josephson junction connecting two double quantum dots (DQDs) modeled by the spinless Kitaev Hamiltonian. For an isolated DQD, we demonstrate that a "sweet spot" hosting "poor man's Majorana" states persist in the presence of V , provided that system parameters are appropriately tuned. For the full system, we demonstrate that, at the sweet spots of both DQDs, all eigenstates are doubly degenerate. This degeneracy arises from the existence of an operator that maps between two decoupled Hilbert subspaces. Away from the sweet spots, the microwave spectrum becomes sensitive to the choice of initial state of the system. In our study, we consider transitions from the ground state (which depending on the flux alternates between the above mentioned subspaces) to all possible excited states. This scenario corresponds to a system initially in thermal equilibrium at low temperature.
Palacios et al. (2026) studied this question.