  An Abrikosov vortex in a superconductor carries a flux quantum, Phi_0 =
hc/2e, localized at its center, but induces a global 2pi phase rotation in the
superconducting condensate. This long-range gauge field outside the area
pierced by a magnetic field is due to the Aharonov-Bohm effect, which is a
non-classical phenomenon that illustrates the significance of potentials rather
than forces in quantum mechanics. In the London gauge, the phase of the
condensate is given by the polar angle around the vortex. Here we raise the
question whether this phase shift could be detected by means of Cooper pair
interferometry using Josephson junctions as phase-sensitive detectors. We
introduce a single Abrikosov vortex into a superconducting lead with a detector
junction made at the edge of the lead. We observe that the vortex induces a
Josephson phase shift equal to the polar angle of the vortex within the
junction length. When the vortex is close to the junction it induces a pi-step
in the Josephson phase difference, leading to a controllable and reversible
switching of the junction into the 0 - pi state. This in turn results in an
unusual Phi_0/2 quantization of the flux in the junction. The vortex may hence
act as a tunable "phase battery" for quantum electronics.
