We present an analytical and numerical analysis of neutron multilevel interference phenomena generated when a neutron passes through a series of $N$ resonant coils operated at the successive conditions $\ensuremath{\hbar}({\ensuremath{\omega}}_{0}+n\ensuremath{\Delta}\ensuremath{\omega})=2{\ensuremath{\mu}}_{n}({B}_{0}+n\ensuremath{\Delta}B)$ with $n=0,1,\dots{},N\ensuremath{-}1$. Each coil produces spin flip with probability $\ensuremath{\rho}$ between 0 and 1; thus the number of waves for the neutron is doubled after each coil, finally giving ${2}^{N}$ interfering neutron waves. The phase difference between any pair is a multiple of a time dependent ``phase quantum'' $\ensuremath{\Delta}\ensuremath{\Phi}(t)$. The analysis predicts for each number $N$ a highly regular pattern for the quantum mechanical probability to find the neutron spin in one specific state as a function of $\ensuremath{\rho}$ and $\ensuremath{\Delta}\ensuremath{\Phi}$. These patterns evolve in time and show revivals after a time $T$ determined by the step $\ensuremath{\Delta}\ensuremath{\omega}$ according to $T=2\ensuremath{\pi}∕\ensuremath{\Delta}\ensuremath{\omega}$. For some adjustments of the system an analytical solution is obtained. Application of multilevel interference in high-resolution neutron modulated-intensity-by-zero-effort--type spectrometers is discussed.We present an analytical and numerical analysis of neutron multilevel interference phenomena generated when a neutron passes through a series of $N$ resonant coils operated at the successive conditions $\ensuremath{\hbar}({\ensuremath{\omega}}_{0}+n\ensuremath{\Delta}\ensuremath{\omega})=2{\ensuremath{\mu}}_{n}({B}_{0}+n\ensuremath{\Delta}B)$ with $n=0,1,\dots{},N\ensuremath{-}1$. Each coil produces spin flip with probability $\ensuremath{\rho}$ between 0 and 1; thus the number of waves for the neutron is doubled after each coil, finally giving ${2}^{N}$ interfering neutron waves. The phase difference between any pair is a multiple of a time dependent ``phase quantum'' $\ensuremath{\Delta}\ensuremath{\Phi}(t)$. The analysis predicts for each number $N$ a highly regular pattern for the quantum mechanical probability to find the neutron spin in one specific state as a function of $\ensuremath{\rho}$ and $\ensuremath{\Delta}\ensuremath{\Phi}$. These patterns evolve in time and show revivals after a time $T$ determined by the step $\ensuremath{\Delta}\ensuremath{\omega}$ according to $T=2\ensuremath{\pi}∕\ensuremath{\Delta}\ensuremath{\omega}$. For some adjustments of the system an analytical solution is obtained. Application of multilevel interference in high-resolution neutron modulated-intensity-by-zero-effort--type spectrometers is discussed.

Physical Review AOct 6, 20062 citations

Information in neutron interference experiments

Willem M. de Muynck

Physics Letters ANov 1, 19937 citations

Neutron optics

Bertram T. M. Willis, Colin J. Carlile

Abstract Neutron optics refers to phenomena which arise from the interference between the incident and the scattered neutron waves. This is in contrast to the topics in earlier chapters of this book, where we have been concerned with interference between the scattered waves alone. The wave Halban and Preiswerk (1936) and by Mitchell and Powers (1936) using ‘white’ neutrons from a radium–beryllium source, and more convincingly by Zeilinger et al. (1988) using monochromatic neutrons from a reactor source. The subject of neutron optics itself began with the work of Fermi and Zinn (1946), who demonstrated the mirror reflection of a collimated beam of thermal neutrons. Since then nearly all the classical optical phenomena of reflection, refraction and interference have been shown to occur with neutrons.Abstract Neutron optics refers to phenomena which arise from the interference between the incident and the scattered neutron waves. This is in contrast to the topics in earlier chapters of this book, where we have been concerned with interference between the scattered waves alone. The wave Halban and Preiswerk (1936) and by Mitchell and Powers (1936) using ‘white’ neutrons from a radium–beryllium source, and more convincingly by Zeilinger et al. (1988) using monochromatic neutrons from a reactor source. The subject of neutron optics itself began with the work of Fermi and Zinn (1946), who demonstrated the mirror reflection of a collimated beam of thermal neutrons. Since then nearly all the classical optical phenomena of reflection, refraction and interference have been shown to occur with neutrons.

Mar 19, 20090 citations

We present an analytical and numerical analysis of neutron multilevel interference phenomena generated when a neutron passes through a series of

N

resonant coils operated at the successive conditions $\ensuremath{\hbar}({\ensuremath{\omega}}_{0}+n\ensuremath{\Delta}\ensuremath{\omega})=2{\ensuremath{\mu}}_{n}({B}_{0}+n\ensuremath{\Delta}B)$ with $n=0,1,\dots{},N\ensuremath{-}1$. Each coil produces spin flip with probability $\ensuremath{\rho}$ between 0 and 1; thus the number of waves for the neutron is doubled after each coil, finally giving

{2}^{N}

interfering neutron waves. The phase difference between any pair is a multiple of a time dependent ``phase quantum'' $\ensuremath{\Delta}\ensuremath{\Phi}(t)$. The analysis predicts for each number

N

a highly regular pattern for the quantum mechanical probability to find the neutron spin in one specific state as a function of $\ensuremath{\rho}$ and $\ensuremath{\Delta}\ensuremath{\Phi}$. These patterns evolve in time and show revivals after a time

T

determined by the step $\ensuremath{\Delta}\ensuremath{\omega}$ according to $T=2\ensuremath{\pi}∕\ensuremath{\Delta}\ensuremath{\omega}$. For some adjustments of the system an analytical solution is obtained. Application of multilevel interference in high-resolution neutron modulated-intensity-by-zero-effort--type spectrometers is discussed.