Effect of interatomic repulsion and quasi-degenerate states on a Kitaev-transmon qubit based on double quantum dots

TL;DR

This paper explores how interatomic Coulomb repulsion and overlooked states influence a Kitaev-transmon qubit based on double quantum dots, revealing persistent Majorana-like states and eigenstate degeneracies at specific parameter points.

Contribution

It demonstrates the persistence of Majorana-like states at sweet spots despite Coulomb repulsion and analyzes eigenstate degeneracies and spectral sensitivities in the full system.

Findings

Sweet spots host Majorana-like states with Coulomb repulsion.

Eigenstates are doubly degenerate at sweet spots.

Microwave spectrum varies with initial state away from sweet spots.

Abstract

We investigate the effect of interatomic Coulomb repulsion $V$ and particular states disregarded previously 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 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. 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.