Aharonov-Bohm effect without closing a loop

We discuss the consequences of the Aharonov-Bohm (AB) effect in setups involving several charged particles, wherein none of the charged particles encloses a closed loop around the magnetic flux. We show that in such setups, the AB phase is encoded either in the relative phase of a bipartite or multipartite entangled photons states, or alternatively, gives rise to an overall AB phase that can be measured relative to another reference system. These setups involve processes of annihilation or creation of electron-hole pairs. We discuss the relevance of such effects in “vacuum birefringence" in QED, and comment on their connection to other known effects.

Figure 1

The electron and the hole each completes half a loop and annihilate to a photon. The photon can be absorbed by either the left or the right atom. The bipartite entangled atom’s final state depends on the AB phase.

Figure 2

The two electrons and the two holes each complete quarter of a loop and together collect the topological phase which is encoded in the phase of the emitted photons. The final state has either two photons in arms 1 and 3, or in arms 2 and 4.

Figure 3

The photon creates an electron and a hole and collects the topological phase on recombination. The process takes place in one of the arms of a Mach-Zender interferometer.