We theoretically analyze the Andreev bound states and their coupling to external radiation in superconductor-nanowire-superconductor Josephson junctions. We provide an effective Hamiltonian for the junction projected onto the Andreev level subspace and incorporating the effects of nanowire multichannel structure, Rashba spin-orbit coupling, and Zeeman field. Based on this effective model, we investigate the dependence of the Andreev levels and the matrix elements of the current operator on system parameters such as chemical potential, nanowire dimensions, and normal transmission. We show that the combined effect of the multichannel structure and the spin-orbit coupling gives rise to finite current matrix elements between odd states having different spin polarizations. Moreover, our analytical results allow to determine the appropriate parameters range for the detection of transitions between even as well as odd states in circuit QED like experiments, which may provide a way for the Andreev spin qubit manipulation.
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