Realization of adiabatic Aharonov-Bohm scattering with neutrons

The adiabatic Aharonov-Bohm (AB) effect is a manifestation of the Berry phase acquired when some slow variables take a planar spin around a loop. While the effect has been observed in molecular spectroscopy, direct measurement of the topological phase shift in a scattering experiment has been elusive in the past. Here, we demonstrate an adiabatic AB effect by explicit simulation of the dynamics of unpolarized very slow neutrons that scatter on a long straight current-carrying wire.

Figure 1

Scattered density of unpolarized neutrons moving with incoming velocity $0.02$ m/s perpendicular to a very long straight current-carrying wire. The left panel includes the adiabatic AB effect. The right panel neglects the adiabatic AB effect. The key difference is the AB-induced nodal line in the forward direction $(x>0,y=0)$ that is absent when neglecting the AB effect. The wire represented by the white region around the origin has radius ${10}^{-5}$ m and carries $10\mathrm{mA}$ electrical current.

Figure 2

Scattered density of unpolarized neutrons at incoming perpendicular incoming velocities $0.03$ m/s (left panel) and $0.04$ m/s (right panel) with the same wire radius and electrical current as in Fig. 1. The nodal line is clearly visible, demonstrating the nondispersive nature of the AB effect.

Figure 3

Local spin density of AB-scattered unpolarized neutrons. The incoming perpendicular velocity of the neutrons is $0.02$ m/s with the same wire radius and electrical current as in Fig 1. Due to the attractive (repulsive) scalar potential felt by the local spin down (up) state, the measurable AB effect is fully dominated by the spin down state.