The Analysis of Neutron Wave Experiments.

Muhammad Arif

R. Clothier

Yuji Hasegawa, Rudolf Loidl, G. Badurek +2 more

We report an interferometric experiment with spin-1/2 neutrons to demonstrate the violation of a Bell-like inequality. The total wave function of neutrons is described by a tensor product Hilbert space. Appropriate combinations of the direction of the spin analysis and the position of the phase shifter allow to demonstrate the violation of the Bell-like inequality. The discussions are presented on the violation of the Bell-like inequality in terms of quantum contextuality and an entanglement-induced correlation in our experiment.

Daniel M. Greenberger

The neutron interferometer is a unique instrument that allows one to construct a neutron wave packet of macroscopic size, divide it into two components separated by centimeters, and then coherently recombine them. A number of experiments clearly showing the difference between quantum and classical theory have been performed with it, which are suitable for presentation in elementary quantum courses. This article presents a simple mathematical model of the interferometer, which can be used to illustrate clearly many of the surprising features of quantum systems. For example, one can describe an experiment to determine which component beam the neutron takes (an analog of the two-slit electron experiment). One can then trace in detail the loss of coherence of the wave function, rather than merely invoke the usual "handwaving" uncertainty arguments. The author discusses the effect of gravity on the neutron beam [the classic COW (Colella, Overhauser, and Werner) experiment], including a simple analysis in an accelerated reference frame, and its relation to the equivalence principle, the red shift, and the twin paradox. Also described are the effect of rotation of the neutron by 360\ifmmode^\circ\else\textdegree\fi{} to change its phase, the effect on the wave function of measuring the absence of the particle from a beam ("Dicke's paradox"), and a realizable version of Wheeler's "delayed-choice" experiments, as well as their relation to the problem of "Schr\"odinger's cat." The treatment is suitable for bright undergraduates and first-year graduate students.

Dietrick E. Thomsen

Salvatore Esposito, Ofelia Pisanti