Four-wave neutron-resonance spin echo

Abstract

We develop a technique of scattering from many-body systems. It is based on the principle of the neutron spin echo (SE), where a neutron wave in the magnetic field splits into two waves, which are separated in space or in time after propagation in this field. The neutron thus prepared as a probe passes through the sample to test its properties on a space R or time t scale. This separation in space or in time can be measured using coherence of these two waves as a phase shift between them. These two waves are collected or focused and compensated by the SE technique in order to compare their phases after interaction with the sample. In this way one studies interference between these waves and thus can directly measure the pair-correlation function in space or in time. Instead of two-wave SE we propose to realize the four-wave neutron-resonance spin-echo (NRSE). In our experiments, spin precession produced by a couple of the neutron-resonance coils in one arm is compensated by an identical couple of other NR coils in a second arm of a spin-echo machine. The neutron spin-flip probability in the resonance coils is a key parameter of the NRSE arm. The limiting cases, = 0 and = 1, provide, in quantum terms, a two-level-two-wave k splitting of the neutron and result in the separation of the split waves into two different lengths in space ͑R 1 , R 2 ͒ or in time ͑t 1 , t 2 ͒. These two cases correspond to Larmor precession with phase 1 in the static magnetic fields of the NR flippers or to NRSE precession with 2 , respectively. The intermediate case, 0 Ͻ Ͻ 1, provides a four-level-four-wave k splitting of the neutron with the corresponding separations in space ͑R 1 , R 2 , R 3 ͒ or in time ͑t 1 , t 2 , t 3 ͒. The interference of each pair of waves after compensation results in three different echos with phases 1 , 2 , and 3 = ͑ 1 + 2 ͒ / 2. Focusing or compensating all four waves into a single point of the phase-of-waves diagram produces quantum interference of all newly created waves. This task of focusing is experimentally performed. Different options for the compensation are discussed. The experiment opens the possibility to measure a composite correlation function, combined from several pair-correlation functions.

Magnetic Cluster Excitations

“…Adequate experimental techniques should be developed as well which provide a direct access to higher-order correlation functions. Indeed, novel neutron scattering techniques were suggested for this purpose which include neutron interferometry (Rauch and Suda, 1998) and spin-echo techniques (Grigoriev et al, 2004).…”

Development and perfomance of a miniaturised spin rotator suitable for neutron interferometer experiments

“…Thus, the phase relation to another arm of an interferometer strongly depends on the position in the beam cross-section and the contrast = -+ ( ) C I I I I , 2 max min max min of interferograms with maximum and minimum intensity, is consequently reduced. Another type of coils used in neutron optics are RF spin flippers [17][18][19][20][21]. They generate an oscillating field in beam direction with frequencies ∼50kHz with a solenoid around the axis of the beam.…”

Present status and prospects for Spin-Echo Small-Angle Neutron Scattering (SESANS) at PIK neutron source

“…We developed a software tool for a quantitative calculation of the precession. A rigorous treatment can for exam ple be found in [17,18]. Basically, this flipper is an RF coil inside a DC magnet with windings to super impose a DC field gradient.…”