Wigner function in neutron interferometry

Abstract

The quantum-mechanical superposition of the two coherent states behind the Laue neutron interferometer is described in terms of the Wigner function which depends on the action of a phaseshifter in one arm of the interferometer. The wavepacket formalism is used and the coherent superposition of simple Gaussian wavepackets is investigated in detail with regard to the components of the momentum vector parallel and normal to the reflecting planes of the crystal. The characteristic features of interference are already apparent without closer consideration of the dynamical theory of diffraction in single crystals. These entangled states of superposition exhibit characteristic squeezing phenomena if one applies the method of mean square deviation of momentum. On the other hand the method of Shannon entropy does not show squeezing. That is what is expected, because the Shannon entropy is an integral quantity which is not so sensitive to details of the momentum spectrum. The Q function is discussed briefly in an appendix.