Topological shaping of vortex neutron beams using forked phase gratings

TL;DR

This work demonstrates the generation of neutron orbital angular momentum beams using forked phase gratings and validates the OAM content with spin-echo small-angle neutron scattering (SESANS), a phase-sensitive interferometric technique. The authors develop a phase-object approximation (POA) framework to model neutron diffraction through FDGs and derive an analytical plane-wave solution showing Bragg donuts carry $\ell=\pm m$ and that donut radii scale linearly with $|nm|$. They show that diffraction modifies the spatial profile while preserving the OAM, and SESANS polarization provides a direct real-space probe of the topological structure. Experimentally, SESANS measurements on FDGs with charges $m=1,2,3$ yield charge-specific polarization fingerprints that agree with POA simulations, and stacking gratings enhances contrast without requiring registry. The results establish SESANS as a powerful tool for probing topological neutron states and magnetically textured materials, with open questions about whether the observed OAM is a single-neutron property or a beam attribute requiring refined coherence characterisation.

Abstract

Beams of light or matter that carry well-defined states of orbital angular momentum (OAM) are promising probes of topological and textured condensed matter systems such as magnetic skyrmions. Using spin-echo small-angle neutron scattering (SESANS), we demonstrate the production of vortex neutron beams from forked phase gratings of various topological charges. In contrast to some previous techniques used to verify OAM production, SESANS is a more precise measurement of the neutron's OAM as it is a phase-sensitive, interferometric technique that directly measures the phase between the scattered neutron spin states.

Figures (8)

• Figure 1: (a) Examples of binary forked phase grating profiles with topological charges $m =1,2,3$. (b) Plane wave simulation of the diffraction pattern produced from an $m=1$, period $p = 2µ m$ forked phase grating vs. transverse momentum transfer $\bm q = (q_x,q_y)$. Notice that at the usual Bragg peak locations at $\bm q = (\pm 2 \pi n/p,0)$ for $n \neq 0$ we instead observe annular "Bragg donuts," one of the characteristic indications of an OAM state.
• Figure 2: Experimental setup of the SESANS measurement. Collimation was performed by two square apertures placed before the polarizer (Aperture 1) of size $14 \times 14m m^2$ and before the FDG (Aperture 2) of size $6 \times 6m m^2$. The distances between the two apertures and the FDG and Aperture 2 are $L_1 = 4.82m$ and $L_2 = 0.09m$, respectively. The green components label "P" and "A" are the neutron spin polarizer and analyzer, respectively. The two $\pi/2$-flippers start and stop the neutron precession while the central $\pi$-flipper corrects for the magnetic inhomogeneities in the rf flippers. Additional weak guide fields are not shown. The wavepacket size and separation are exaggerated for clarity.
• Figure 3: Simulated SESANS polarization for a plaquette with charge (a) $m=1$ and (b) $m=2$, with the insets being the original FDG profile. For visual clarity, we used a constant $\lambda=0.4n m$ incident neutron spectrum and a $10\times10$ µ m^2 plaquette size with $d = 38µ m$ (such that $\Phi = -\pi \chi$) and $p = 2µ m$. Notice that the polarization is periodic in both $\xi_x$ and $\xi_y$ with plaquette size. These plots demonstrate that SESANS can serve as a direct probe of the sample's topological structure as the polarization signal for each $m$ is markedly distinct. (c) Slices through the origin along $\xi_y=0$ of the simulated SESANS polarizations for plaquettes of various charges. These particular $\xi = \xi_x$ slices of the 2D polarizations correspond to the case where the grooves in the $\hat{y}$ direction are perpendicular to the encoding direction $\hat{x}$. An arbitrary slice through $(\xi_x,\xi_y)$ can be chosen by changing the angle between the sample and encoding direction.
• Figure 4: Measured SESANS polarization data of two charge $m=1$ gratings in the (a) perpendicular and (b) parallel orientation. Measured polarizations of two charge (c) $m=2$ and (d) $m=3$ gratings in the perpendicular orientation. In all parts, the dashed black trace corresponds to a SESANS POA simulation convolved with the instrument resolution function discussed in the supplemental material Supp. The two solid traces and data points in each part correspond to the measured polarizations from a particular FDG.
• Figure 5: Comparison of the measured SESANS polarization data of a single grating (blue), and two (orange) and three (green) stacked charge $m=1$ gratings. The red dashed trace is the simulation result for a single charge $m=1$ grating of depth $d=5.5µ m$ reproduced from Fig. \ref{['fig:Exp data']}(a), and the black and purple dashed traces the result of a simulation with a single FDG of depth $d\sqrt{2}$ and $d \sqrt{3.5}$, respectively. For the three-grating simulation, we attribute the deviation from the expected apparent depth of $d\sqrt{3}$ to the fact that the third grating was produced by a slightly different process that most likely resulted in slightly deeper grooves Supp.