Experimental Limit on Neutron Orbital Angular Momentum Detection Using Polarized 3He

Abstract

A recent proposal suggested that neutron orbital angular momentum (OAM) states could be detected via spin-polarized absorption in polarized 3He, with predicted cross-section variations linked to the neutron's OAM. We experimentally tested this hypothesis using spin-polarized neutron beams with OAM =-2 to 2, generated by fork-dislocation phase-gratings, and transmitted through a polarized 3He cell. Within statistical precision, no OAM-dependent change in the absorption cross section was observed. This null result places stringent constraints on polarized 3He-based OAM detection schemes. The absence of an effect in the given regime is traced to the proposal's disregard of the spatial character of neutron OAM: unlike spin, OAM arises from the transverse phase structure of the wavefunction and couples only through spatial gradients and overlap. The transverse extent of neutron OAM modes expands rapidly, producing a doughnut-shaped intensity profile with negligible overlap with on-axis 3He nuclei, while off-axis capture samples only a locally uniform phase and reduces the interaction to the known spin dependence. These results clarify the limits of absorptive nuclear methods for probing neutron OAM and emphasize the necessity of spatially resolved interactions in any viable detection scheme.

Figures (4)

• Figure 1: A schematic of the experimental setup. (i) The incident neutron beam is spin-polarized perpendicular to the beam propagation direction ($\pm y$) using a supermirror. Neutrons pass through the first collimating slit $A_1$ and then through the Drabkin spin flipper (ii). Next, stray magnetic fields are used to rotate the spin parallel to the propagation direction ($z$). After passing through the second slit $A_2$, the beam illuminates a silicon-wafer phase grating (iii) with a fork-dislocation phase profile, inducing OAM in the nonzero diffraction orders. The direct beam (blue) and diffracted orders (red/pink) then pass through the $q=0$ silicon-wafer phase-grating (iv), oriented perpendicular to the $q\neq0$ grating. The green/cyan beams indicate the $\pm1$ orders from the $q=0$ grating. The neutron beams then pass through a spin-polarized $^3\text{He}$ cell (v) polarized along the beam axis, which serves as the spin analyzer. Neutrons propagate $z=10$ m to the position sensitive neutron detector. Shown in (vi) is the experimental intensity map (log-scale) for the multi-day measurement of $q=0$, $q=2$, integrated from $9.0$ Å to $14.0$ Å. The inset demonstrates the characteristic neutron OAM doughnut intensity profile for the $m=+2$ diffraction order from the $q=2$ grating. To resolve the OAM profile we limit the wavelength range to $12.0$ Å to $13.0$ Å and decrease the slit sizes to reduce the beam divergence.
• Figure 2: The measured polarization, as defined by Eq. \ref{['eqn:pol']}, across the wavelength range $9.0\text{--}14.0$ Å for both the $\ell = 0$ & $1$ and $\ell = 0$ & $2$ experimental configurations. As described in Section \ref{['meth']}, the data are corrected for the depolarization of the $^3$He cell, accounting for the efficiency of the supermirror and spin flipper (see Appendix). Error bars are determined from neutron counting statistics, assuming a Poisson distribution. A potential source of systematic error arises from treating the polarization of the $^3\text{He}$ cell as constant during an individual 30 minute measurement.
• Figure 3: The normalized absorption cross section differences, as defined by Eq. \ref{['eqn:cross_diff']}, across the wavelength range $9.0\text{--}14.0$ Å for both the $\ell = 0$ & $1$ and $\ell = 0$ & $2$ experimental configurations shown in Fig. \ref{['fig:pdata']}. The results indicate no statistically significant dependence of the neutron absorption cross section on the OAM state of the neutron, for both individual 1Å wavelength bins and the entire wavelength range. Error bars are determined from neutron counting statistics, assuming a Poisson distribution.
• Figure 4: Efficiency of the supermirror and Drabkin spin flipper at ZOOM for polarizing the neutron beam and selecting the $\uparrow$, $\downarrow$ spin states.