Observation of the Goos-Hänchen Shift with Neutrons

The Goos-Hänchen effect is a spatial shift along an interface resulting from an interference effect that occurs for total internal reflection. This phenomenon was suggested by Sir Isaac Newton, but it was not until 1947 that the effect was experimentally observed by Goos and Hänchen. We provide the first direct, absolute, experimental determination of the Goos-Hänchen shift for a particle experiencing a potential well as required by quantum mechanics: namely, wave-particle duality. Here, the particle is a spin-polarized neutron reflecting from a film of magnetized material. We detect the effect through a subtle change in polarization of the neutron. Here, we demonstrate, through experiment and theory, that neutrons do exhibit the Goos-Hänchen effect and postulate that the associated time shift should also be observable.

Figure 1

Reflection of a plane wave with incident angle $\theta$ on a substrate boundary at $y=0$ indicating the Goos-Hänchen shift, $\zeta$. Inset: nuclear $V_n$ and magnetic $\pm V_m$, scattering potential and kinetic energy $E_k$ associated with neutron velocity component perpendicular to the surface.

Figure 2

Goos-Hänchen shift, $\zeta$ along the interface for an incident angle of 2 mrad as function of the wave vector component perpendicular to the surface, $k_y$ for up (full line) and down (dashed line) spin state for fully magnetized iron. Inset: Splitting, $s$ of the neutron wave function at the interface.

Figure 3

Measured normalized polarization, $P/P_0$ as function of perpendicular wave vector, $k_y$ representing the Larmor pseudo precession due to the Goos-Hänchen shift along the interface for a single (top) and double (bottom) reflection from a Permalloy thin film. The black lines represent the theoretical predictions. The (red) dashed line in the lower graph represents a simulation (see text).