  We study spin-polarized quasiparticle transport in a mesoscopic
superconductor with a spin- splitting field in the presence of co-flowing
supercurrent. In such a system, the nonequilibrium state is characterized by
charge, spin, energy and spin energy modes. Here we show that in the presence
of both spin splitting and supercurrent, all these modes are mutually coupled.
As a result, the supercurrent can convert charge imbalance, that in the
presence of spin splitting decays on a relatively short scale, to a long-range
spin accumulation decaying only via inelastic scattering. This effect enables
coherent charge-spin conversion controllable by a magnetic flux, and it can be
detected by studying different symmetry components of the nonlocal conductance
signal.
