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Physical Review A

Measurement and characterization of the three-dimensional coherence function in neutron interferometry

H. Rauch, H. Wölwitsch, Helmut Kaiser, R. Clothier, S. Werner

Published Feb 1, 1996• 67 citations
Publisher

Abstract

The spatial coherence function in all three orthogonal directions has been measured by means of perfect crystal neutron interferometry. It has been demonstrated that the coherence function is given by the Fourier transform of the related momentum distribution, which in turn is determined by the collimation and monochromatization of the beam incident upon and traversing the interferometer. Thus, a measurement of the coherence function can replace a measurement of the momentum distribution in certain cases. Retrieval of the coherence can be accomplished by phase echo and/or postselection methods. A complete retrieval of the coherence is impossible in principle due to unavoidable loss factors.

DOI
10.1103/physreva.53.902

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The spatial coherence function in all three orthogonal directions has been measured by means of perfect crystal neutron interferometry. It has been demonstrated that the coherence function is given by the Fourier transform of the related momentum distribution, which in turn is determined by the collimation and monochromatization of the beam incident upon and traversing the interferometer. Thus, a measurement of the coherence function can replace a measurement of the momentum distribution in certain cases. Retrieval of the coherence can be accomplished by phase echo and/or postselection methods. A complete retrieval of the coherence is impossible in principle due to unavoidable loss factors.
Abstract Among the various areas of neutron optical research, neutron interferometry has provided some of the most challenging and spectacular developments. In most cases, separated coherent beams are used which are produced either by wavefront division (Young’s type) or by amplitude division (Mach− Zehnder type). These beams are subsequently coherently superposed after passing through regions of space where the neutron wavefunction is modified in phase and amplitude by various interactions: nuclear, magnetic, electromagnetic, gravitational, or by geometry and topology (as in Aharonov−Bohm-type experiments). Various types of neutron interferometers that have been tested are shown in Fig. 2.1. The first neutron interferometer was based upon wavefront division and biprism deflection, but it had several constraints for interferometric applications mainly due to the small beam separation (100 μm) (Maier-Leibnitz and Springer 1962). Nevertheless, this method gained further interest for diffraction experiments from macroscopic objects and for the detection of weak interaction effects where the long flight paths (10 m) enhance the sensitivity for the measurements of these effects (Gähler et al. 1980; Klein et al. 1981a). The perfect-crystal interferometer (Rauch et al. 1974) provides widely separated coherent beams and has become a standard method for advanced neutron optical investigations. The development of diffraction and phase grating interferometers extended the Mach-Zehnder interferometer method to very slow neutrons (loffe et al. 1985; Gruber et al. 1989). The superposition of spin-up and spin-down states in the longitudinal direction provides the basis for Larmor and Ramsey interferometry, where no lateral beam splitting is necessary. The well-known spin-echo systems (Mezei 1972) and zero-field spin-echo systems (Gähler and Golub 1987; Dubbers et al. 1989) are examples of such interferometers, which also play an important role in atom interferometry (Bord é 1989; Kasevich and Chu 1991; Riehle et al. 1991).
In the analysis of neutron scattering measurements of condensed matter structure, it normally suffices to treat the incident and scattered neutron beams as if composed of incoherent distributions of plane waves with wavevectors of different magnitudes and directions which are taken to define an instrumental resolution. However, despite the wide-ranging applicability of this conventional treatment, there are cases in which the wave function of an individual neutron in the beam must be described more accurately by a spatially localized packet, in particular with respect to its transverse extent normal to its mean direction of propagation. One such case involves the creation of orbital angular momentum (OAM) states in a neutron via interaction with a material device of a given size. It is shown in the work reported here that there exist two distinct measures of coherence of special significance and utility for describing neutron beams in scattering studies of materials in general. One measure corresponds to the coherent superposition of basis functions and their wavevectors which constitute each individual neutron packet state function whereas the other measure can be associated with an incoherent distribution of mean wavevectors of the individual neutron packets in a beam. Both the distribution of the mean wavevectors of individual packets in the beam as well as the wavevector components of the superposition of basis functions within an individual packet can contribute to the conventional notion of instrumental resolution. However, it is the transverse spatial extent of packet wavefronts alone that determines the area within which a coherent scattering process can occur in the first place. This picture is shown to be consistent with standard quantum theory. It is also demonstrated that these two measures of coherence can be distinguished from one another experimentally.
The coherence length of a neutron wave packet depends on the spectral width of the distribution of wave vectors that make up the packet. The coherent overlap of the wave packets traversing the two beam paths in a perfect-silicon-crystal neutron interferometer (NI) is altered by placing a material with a neutron-nuclear optical potential in one of the beam paths in the NI. If the optical potential is positive, it causes a delay of the wave packet and a loss of fringe visibility. By use of an analyzer crystal, we narrow the spectral distribution after the mixing and interference has occurred in the last crystal slab of the NI. This increases the coherence length and restores some of the fringe visibility.
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 A. 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.
Neutrons are proper tools for testing quantum mechanics because they are massive, they couple to electromagnetic fields due to their magnetic moment and they are subject to all basic interactions and they are sensitive to topological effects, as well. Related experiments will be discussed. Recent neutron interferometry experiments based on postselection methods renewed the discussion about quantum nonlocality and the quantum measuring process. It has been shown that interference phenomena can be revived even when the overall interference pattern has lost its contrast. This indicates a persisting coupling in phase space even in cases of spatially separated Schrödinger Cat-like situations. These states are extremely fragile and sensitive against any kind of fluctuations and other decoherence processes. More complete quantum experiments also show that a complete retrieval of quantum states behind an interaction volume becomes impossible in principle.
A two-loop perfect-crystal neutron interferometer was used for the quantitative determination of which-way (WW) information and the verification of the duality relation between predictability and visibility. Our interferometer has two remarkable features, it allows the absorption-free tuning of WW information and it enables the simultaneous measurement of the duality relation without changing the interferometer setup. In addition, the duality relation of three interfering beams is a good demonstration that WW information should not be misused as particle property because one interferometer beam remains in a coherent superposition of two path alternatives, which is not consistent with the particle picture. The coherent WW tuning was performed without changing the neutron's momentum and without dephasing.