Effect of interatomic repulsion on a Kitaev-transmon qubit based on double quantum dots

Abstract: We investigate the effect of interatomic Coulomb repulsion $V$ on the Kitaev-transmon system proposed by Pino \textit{et al.} \cite{pino} which consists of a Josephson junction between 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 can still be achieved in the presence of $V$ by appropriately tuning the system parameters. This adjustment allows the extension of previous results to the case of finite Coulomb repulsion $V \neq 0$. However, we observe modifications in the microwave spectrum, due to the presence of previously overlooked states. Additionally, we find that at the sweet spot of both DQDs, all eigenstates of the transmon system exhibit exact double degeneracy.