Observation of the Phase Shift of a Neutron Due to Precession in a Magnetic Field

Abstract

We have directly observed the sign reversal of the wave function of a ferm. ion produced by its precession of 2& radians in a magnetic field using a neutron interferometer.

Neutron interferometry: a tale of three continents

“…But by the time I arrived to perform the experiment, in September 1975, I found to my consternation that the corresponding experiment had already been done -by the Rauch group (using an electromagnet inside a crystal interferometer), as well as by the Werner group (using a permanent magnet). eir results, verifying this strange property of fermions, were published simultaneously in Physics Letters [6] and Physical Review Letters [7], in October 1975. We lost the competition for priority, but we went ahead and did our version of the experiment anyway -because it used a significantly different method.…”

Topological phase for entangled two-qubit states and the representation of theSO(3) group

“…In order to make the π-phase appear, one of the two beams was subjected to the action of a tunable magnetic field, before recombining it with the other beam. Werner et al [10] used two detectors, D 1 and D 2 , in order to show the sinusoidal variation of the difference in neutron counts,…”

“…The density operator ρ that corresponds to the experimental arrangement of Werner et al [10] is build up as a statistical mixture of pure, antisymmetrized states of the form |ψ s = (|1 s , 0 − |0, 1 s )/ √ 2 , with s =↑, ↓ (spin up and down). It is thus given by ρ = 1 2 |ψ s ψ s |.…”

“…Depending on whether s =↑ or s =↓, we have △ϕ(s) = ±△ϕ, with △ϕ = 2πg n µ N M λBl/h 2 . We refer to [10] for the meaning of the parameters, noting only that B is the variable magnetic field and l the length over which it acts. With a ρ as given above we obtain…”

“…Around three decades ago a series of experiments in neutron interferometry were performed [10], whose aim was to bring into evidence the π-phase that arises when a spinor is subjected to a 2π rotation. Such a π-phase illustrates one of the most salient features characterizing the interplay between the groups SO(3) and SU (2).…”