Section 5.3.7.3. Neutron interferometry

Because diffraction by perfect crystals provides a well defined distribution of the intensity and phase of the beam, interferometry with X-rays or neutrons is possible using ingeniously designed and carefully manufactured monolithic devices carved out of single crystals of silicon. The technical and scientific features of this family of techniques are well summarized by Bonse (1979, 1988), as well as other papers in the same volumes, and by Shull (1986).

X-ray interferometry started with the Bonse–Hart interferometer (Bonse & Hart, 1965). A typical device is the LLL skew-symmetric interferometer, where the L's stand for Laue, indicating transmission geometry in all crystal slabs. In these slabs, which can be called the splitter, the mirrors and the recombiner, the same pair of opposite reflections, in symmetrical Laue geometry, is used three times. In the first slab, the incident beam is coherently split into a transmitted and a diffracted beam. Each of these is then diffracted in the two mirrors, and the resulting beams interfere in the recombiner, again yielding a forward-diffracted and a diffracted beam, the intensities of both of which are measured. This version, the analogue of the Mach–Zehnder interferometer in optics, offers a sizeable space (several cm of path length) where two coherent parallel beams can be submitted to various external actions. Shifting the relative phase of these beams (e.g. by π, introducing an optical path-length difference of ) results in the intensities of the outgoing beams changing from a maximum to a minimum.

Applications of neutron interferometry range from the very useful to the very exotic. The most useful one is probably the measurement of coherent neutron scattering lengths. Unlike the Pendellösung method described in Section 5.3.7.2, this method does not require the measured samples to be perfect single crystals, nor indeed crystals. Placing a slab of material across one of the beams and rotating it will induce an optical path-length difference of if t is the effective thickness along the beam, hence a phase shift of . With the expression of the refractive index n as given in Section 5.3.2.2, it is clear that for an isotopically pure material the scattering length can be deduced from the measurement of intensity versus the rotation angle of the phase shifter. This is a very versatile and much used method. The decrease in oscillation contrast can be used to obtain information of relevance to materials science, such as statistical properties of magnetic domain distributions (Korpiun, 1966) or precipitates (Rauch & Seidl, 1987); Rauch (1995) analyses the effect in terms of the neutron coherence function.

Many elegant experiments have been performed with neutron interferometers in efforts to set an upper limit to effects than can be considered as nonexistent, or to test expectations of basic quantum physics. Many papers are found in the same volumes as Bonse (1979) and Bonse (1988); excellent reviews have been given by Klein & Werner (1983), Klein (1988), and Werner (1995). Among the topics investigated are the effect of gravity (Colella et al., 1975), the Sagnac effect, i.e. the influence of the Earth's rotation (Werner et al., 1979), the Fizeau effect, i.e. the effect of the movement of the material through which the neutrons are transmitted (Arif et al., 1988) and the Aharonov–Casher effect, i.e. the dual of the Aharonov–Bohm effect for neutral particles having a magnetic moment (Cimmino et al., 1989).