The geometric phase (GP) acquired by a neutron passing through a uniform magnetic field elucidates a subtle interplay between its spatial and spin degrees of freedom. In the standard setup using thermal neutrons, the kinetic energy is much larger than the typical Zeeman split. This causes the spin to undergo nearly perfect precession around the axis of the magnetic field and the GP becomes a function only of the corresponding cone angle. Here, we perform a plane wave analysis of the GP of very slow neutrons, for which the precession feature breaks down. Purely quantum-mechanical matter wave effects, such as resonance, reflection, and tunneling, become relevant for the behavior of the GP in this low energy scattering regime.The geometric phase (GP) acquired by a neutron passing through a uniform magnetic field elucidates a subtle interplay between its spatial and spin degrees of freedom. In the standard setup using thermal neutrons, the kinetic energy is much larger than the typical Zeeman split. This causes the spin to undergo nearly perfect precession around the axis of the magnetic field and the GP becomes a function only of the corresponding cone angle. Here, we perform a plane wave analysis of the GP of very slow neutrons, for which the precession feature breaks down. Purely quantum-mechanical matter wave effects, such as resonance, reflection, and tunneling, become relevant for the behavior of the GP in this low energy scattering regime.

arXiv:2003.13737Mar 30, 20200 citations

The Analysis of Neutron Wave Experiments.

R.L. Brehm

Jan 1, 19660 citations

Neutron optical tests of nonlinear wave mechanics

R. Gähler, A. G. Klein, Anton Zeilinger

We analyze the free-space propagation of matter waves with a view to placing an upper limit on the strength of possible nonlinear terms in the Schr\"odinger equation. Such additional terms of the form $\ensuremath{\psi}F({|\ensuremath{\psi}|}^{2})$ were introduced by Bialynicki-Birula and Mycielski in order to counteract the spreading of wave packets, thereby allowing solutions which behave macroscopically like classical particles. For the particularly interesting case of a logarithmic nonlinearity of the form $F=\ensuremath{-}\mathit{b}\mathrm{ln}{|\ensuremath{\psi}|}^{2}$, we find that the free-space propagation of slow neutrons places a very stringent upper limit on the magnitude of $\mathit{b}$ . Precise measurements of Fresnel diffraction with slow neutrons do not give any evidence for nonlinear effects and allow us to deduce an upper limit for $\mathit{b}<3.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ eV about 3 orders of magnitude smaller than the lower bound proposed by the above authors.We analyze the free-space propagation of matter waves with a view to placing an upper limit on the strength of possible nonlinear terms in the Schr\"odinger equation. Such additional terms of the form $\ensuremath{\psi}F({|\ensuremath{\psi}|}^{2})$ were introduced by Bialynicki-Birula and Mycielski in order to counteract the spreading of wave packets, thereby allowing solutions which behave macroscopically like classical particles. For the particularly interesting case of a logarithmic nonlinearity of the form $F=\ensuremath{-}\mathit{b}\mathrm{ln}{|\ensuremath{\psi}|}^{2}$, we find that the free-space propagation of slow neutrons places a very stringent upper limit on the magnitude of $\mathit{b}$. Precise measurements of Fresnel diffraction with slow neutrons do not give any evidence for nonlinear effects and allow us to deduce an upper limit for $\mathit{b}<3.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ eV about 3 orders of magnitude smaller than the lower bound proposed by the above authors.

Physical Review AApr 1, 1981116 citations

\mathit{b}

. Precise measurements of Fresnel diffraction with slow neutrons do not give any evidence for nonlinear effects and allow us to deduce an upper limit for $\mathit{b}<3.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ eV about 3 orders of magnitude smaller than the lower bound proposed by the above authors.