Spin to Orbital Angular Momentum Conversion in the Neutron Nucleus Weak Interaction

Technical Summary: Spin to Orbital Angular Momentum Conversion in the Neutron Nucleus Weak Interaction

Problem Statement
The neutron-nucleus weak interaction induces a small, parity-non-conserving (PNC) rotation of the neutron spin as it traverses matter. In specific systems, such as the $^{139}\text{La}$ nucleus at its 0.7 eV p-wave resonance, this parity-odd asymmetry is significantly amplified. While the conservation of total angular momentum dictates that any change in the neutron's spin angular momentum (SAM) must be compensated by a change in orbital angular momentum (OAM), the specific mechanism of OAM generation in this context had not been experimentally investigated. Existing theoretical formulations for paraxial rays in polarized neutron optics do not explicitly include terms for this OAM generation, raising the question of how total angular momentum is conserved during parity-violating spin rotation.

Methodology
The authors conducted an experiment at the IN3 triple-axis instrument at the Institut Laue-Langevin (ILL) to demonstrate that the weak interaction conserves total angular momentum by converting spin angular momentum into orbital angular momentum.

• Theoretical Framework: The study utilizes a non-relativistic effective Hamiltonian for P-odd interactions, $H_{\text{weak}} = \{F(r), \vec{\sigma} \cdot \vec{p}\}$. Theoretical analysis suggests that parity-odd spin rotations are accompanied by OAM generation. Specifically, if the spin is prepared perpendicular to the momentum (transverse spin rotation), the interaction generates transverse OAM.
• Experimental Setup: To observe this effect, the team simulated a neutron beam with a conical momentum distribution by creating a "conical spin distribution" using a magnetic quadrupole. This setup generates a spin-orbit entangled state where the spin is coupled to the azimuthal coordinate.
  • Beam Preparation: Thermal neutrons were monochromatized ($\approx 1.8$ Å) and polarized.
  • Spin-Orbit State Generation: A magnetic quadrupole (figure-eight coil) inside a zero-field chamber (PANDA) prepared the neutrons in a specific spin-orbit texture.
  • Interaction Region: The beam passed through a 5 cm long $^{139}\text{La}$ sample, known for its strong p-wave resonance amplification of the weak interaction. The entire interaction region was shielded to suppress residual magnetic fields to $\approx 100$ nT.
  • Detection: A position-sensitive detector (He-3 wire chamber) resolved the 2D polarization pattern of the beam. The experiment compared the spin-orbit pattern with and without the $^{139}\text{La}$ sample.

Key Contributions and Results

1. Experimental Demonstration of Angular Momentum Conservation: The authors experimentally demonstrated that the parity-odd spin rotation induced by the weak interaction in $^{139}\text{La}$ is consistent with the conservation of total angular momentum. By simulating the necessary conditions via a conical spin distribution, they showed that the interaction generates a mechanism where spin rotation is compensated by orbital angular momentum generation, a phenomenon not previously investigated in this system.
2. Measurement of Rotation: By performing azimuthal Fourier transforms on circular cuts of the polarization patterns, the team measured an image rotation phase. The raw measurement showed a rotation of $2.4 \pm 0.27 \cdot 10^{-3}$ radians. After correcting for a magnetic contribution (likely from ferromagnetic impurities in the sample) by rotating the sample 180°, the magnetic contribution was isolated at $1.1 \cdot 10^{-3}$ radians. The remaining rotation attributed to the weak interaction was found to be within the expected range for $^{139}\text{La}$, matching previous findings with cold neutrons.
3. Verification of Angular Momentum Conservation: The study calculated the expectation value for the orbital angular momentum operator ($-i \partial/\partial \phi$) and approximated the spin expectation value by the average magnitude of the measured 2D polarization vector. The results showed that the difference between the total angular momentum of the beam with and without the $^{139}\text{La}$ sample was zero to within statistical error ($\pm 4 \cdot 10^{-4}$). This confirms that the loss of spin angular momentum is compensated by the gain in orbital angular momentum within the limits of the experiment's precision.

Significance and Claims
The paper claims to provide the first experimental demonstration that parity violation in neutron-nucleus transmission generates a non-zero orbital angular momentum, thereby conserving total angular momentum in the weak interaction.

• Theoretical Implication: The authors state that a positive observation implies that the current theory of polarized neutron optics for paraxial rays requires revision, as existing formulations lack the specific terms describing this spin-to-OAM conversion.
• Entanglement: The phenomenon establishes that the weak interaction can induce spin-orbit entangled states. The authors note that this could enable the future generation of multiply-entangled single-particle neutron beams involving four quantum variables: spin, OAM, energy, and position.
• Scope: The work is modest in its immediate claims, focusing on the conservation of angular momentum and the measurement of the rotation angle. It does not claim to have created a fully entangled 4-degree-of-freedom state experimentally but suggests that adding OAM generators to existing interferometry or spin-echo techniques could make this achievable. The study also highlights that such beams could be sensitive to chiral structures and P-odd/T-odd interactions, though these are presented as potential future applications enabled by the demonstrated physics rather than results of this specific experiment.