  We study combined interference effects due to the Aharonov-Bohm (AB) and
Aharonov-Casher (AC) phases in a Josephson supercurrent of local and nonlocal
(split) Cooper pairs. We analyze a junction between two superconductors
interconnected through a normal-state nanostructure with either (i) a ring,
where single-electron interference is possible, or (ii) two parallel nanowires,
where the single-electron interference can be absent, but the cross Andreeev
reflection can occur. In the low-transmission regime in both geometries the AB
and AC effects can be related to only local or nonlocal Cooper pair transport,
respectively.
