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Physical Review Letters

Measurements of the Vertical Coherence Length in Neutron Interferometry

Dmitry A. Pushin, M. Arif, M. G. Huber, David G. Cory

Published Jun 26, 2008• 30 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.100.250404

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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.
Neutron interferometry has proved to be a very precise technique for measuring the quantum mechanical phase of a neutron caused by a potential energy difference between two spatially separated neutron paths inside interferometer. The path length inside the interferometer can be many centimeters (and many centimeters apart) making it very practical to study a variety of samples, fields, potentials, and other macroscopic medium and quantum effects. The precision of neutron interferometry comes at a cost; neutron interferometers are very susceptible to environmental noise that is typically mitigated with large, active isolated enclosures. With recent advances in quantum information processing especially quantum error correction (QEC) codes we were able to demonstrate a neutron interferometer that is insensitive to vibrational noise. A facility at NIST’s Center for Neutron Research (NCNR) has just been commissioned with higher neutron flux than the NCNR’s older interferometer setup. This new facility is based on QEC neutron interferometer, thus improving the accessibility of neutron interferometry to the greater scientific community and expanding its applications to quantum computing, gravity, and material research.
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 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 experiment described in this paper, a chopper serves as a source of neutron intensity pulses which pass through a perfect Si-crystal neutron interferometer (NI), where they are split coherently into two parts that recombine and interfere. As the occupation number of a single pulse is much smaller than unity, the results very clearly demonstrate the single-particle interference phenomena of neutron interferometry experiments. While traveling the pulses spread, with faster (slower) neutrons tending toward the leading (trailing) edge. The coherence length of the neutrons depends on the spectral width of their wavelength distribution. When a material with a neutron-nuclear optical potential is placed in one beam path in the NI, there is a loss of fringe visibility (contrast), which depends on the coherence length. By using time-of-flight techniques, we divide the pulse into time segments. Within a given time slice, the wavelength spectrum is narrower than in the pulse as a whole. As a result, contrast remains in the time slices even when it disappears in the overall pulse. We also observe an additional contrast modulation due to the overlap of neighboring pulses.