Measurements of the Vertical Coherence Length in Neutron Interferometry

The study and use of macroscopic quantum coherence requires long coherence lengths. Here we describe an approach to measuring the vertical coherence length in neutron interferometry, along with improvements to the NIST interferometer that led to a measured coherence length of 790 Å. The measurement is based on introducing a path separation and measuring the loss in contrast as this separation is increased. The measured coherence length is consistent with the momentum distribution of the neutron beam. Finally, we demonstrate that the loss in contrast with beam displacement in one leg of the interferometer can be recovered by introducing a corresponding displacement in the second leg.

Figure 1

(a) A schematic diagram of the coherence length experiment. A neutron beam, entering left, is coherently divided via Bragg diffraction at the first blade of the neutron interferometer into two paths (paths I and II). The phases that the neutron accumulates over each path are experimentally controlled by rotating the phase flag. In each path we install two 45° prisms, which at 0 separation form a cube. By separating the prisms we shift the neutron beams in path I and II vertically with respect to each other. As expected we observe a loss in contrast with displacement, $\Delta z$. (b) A schematic diagram of the neutron paths through the prisms. For comparison here we show two beam paths. The upper path corresponds to the neutron passing through the separated prisms, and the lower path through the prisms in a cube. The neutron beam enters from the left and depending on the separation between the prisms is shifted vertically. The angles shown in the figure are described in the text.

Figure 2

A schematic diagram of the second monochromator. It consists of 9 PG blades and can focus the neutron beam to a smaller spot. By adjusting slit size after the second monochromator we can change the vertical momentum distribution.

Figure 3

(a) Vertical momentum distribution for the incoming neutron beam. The 9-blade distribution was measured and the 5 and 1 blades distributions are obtained by a simple model of a sum of displaced Gaussians. (b) Contrast plots for three different vertical beam divergences. In each subplot data are shown as closed circles. The lines are contrast curves derived as a sum of plane waves using the vertical momentum distribution ($k_z$) shown in (a). The data in (b) are very closely described by this approach.

Figure 4

Contrast plot for two cases: dark line is the contrast measured when the prism separation in path II is 0 mm, and the light line is the contrast measured when the prism separation in path I is set to 4 mm. We see that the two curves are the same (within experimental errors) simply shifted relative to each other by 4 mm. This shows that indeed the loss of the contrast can be recovered and is not due to decoherence inside the interferometer.