  In a Josephson junction, the transfer of Cooper pairs from one superconductor
to the other one can be associated with the formation of Andreev bound states.
In a Josephson junction made with a semiconducting nanowire, the spin
degeneracy of these Andreev states can be broken thanks to the presence of
spin-orbit coupling and a finite phase difference between the two
superconducting electrodes. The lifting of the spin degeneracy opened the way
to the realization of Andreev spin qubits that do not require the application
of a large magnetic field. So far the operation of these qubits relied on a
Raman process involving two microwave tones and a third Andreev state [M. Hays
et al., Science 373, 430 (2021)]. Still, time-reversal preserving impurities in
the nanowire allow for spin-flip scattering processes. Here, using the
formalism of scattering matrices, we show that these processes generically
couple Andreev states with opposite spins. In particular, the non-vanishing
current matrix element between them allows for the direct manipulation of
phase-driven Andreev spin qubits, thereby circumventing the use of the
above-mentioned Raman process.
