Probing Single-Particle Spatial Extent With Helical Neutron Wavefronts

Abstract: Distinguishing transverse coherence length from single-particle wavepacket extent is fundamentally challenging, as both manifest through spatial broadening of observed intensity profiles in conventional experiments. Here we introduce a method based on helical neutron wavefronts that enables this separation. Helical neutron states produce annular intensity profiles whose peak radius depends on the transverse wavepacket extent, while coherence length only contributes to profile broadening. In our experimental geometry we measure a beam divergence of ~1.1 mrad, corresponding to a transverse coherence length of ~180 nm. In contrast, the same measurement places a lower bound of >= 2 um on the spatial extent of the individual neutron wavepackets, more than an order of magnitude larger than the coherence length. These results provide direct experimental evidence that transverse coherence length and single-particle wavepacket extent are distinct physical quantities, resolving a longstanding source of confusion in the neutron literature.

• The paper demonstrates that helical neutron wavefronts decouple single-neutron spatial extent from transverse coherence, resolving a longstanding ambiguity in neutron beam physics.
• The experiments employ OAM-encoded diffraction and Laguerre-Gaussian mode analysis, revealing a wavepacket extent exceeding the coherence length by over an order of magnitude.
• The methodology, validated through SANS experiments and simulations, sets new benchmarks for neutron beam manipulation and quantum state engineering.

Formal Summary of "Probing Single-Particle Spatial Extent With Helical Neutron Wavefronts" (2606.22292)

Introduction and Motivation

The paper addresses a persistent conceptual ambiguity in neutron beam physics—the distinction between transverse coherence length and single-particle wavepacket extent. Previous conventional experiments have been unable to clearly separate these two quantities because both manifest as spatial broadening in measured intensity profiles. Misinterpretations in the literature have led to conflation of coherence length with the spatial extent of individual neutrons, causing erroneous theoretical predictions, such as OAM-dependent cross sections, that contradict empirical results. The authors propose and demonstrate a method based on helical neutron wavefronts, leveraging OAM states to access wavepacket extent directly and resolve this longstanding ambiguity.

Theoretical Framework

The spatial coherence properties of neutron beams are treated classically via the Van Cittert-Zernike (VCZ) theorem, establishing that the mutual coherence function in the detection plane is governed by the angular divergence of the source. This framework contrasts with the outdated small-wavepacket picture that equates coherence length with single-neutron spatial extent.

Using Glauber's formalism for partially coherent fields, the paper frames neutron beams as ensembles of extended wavepackets with distributed mean propagation directions. Angular divergence determines ensemble-level coherence length, whereas the spatial extent of each wavepacket, $w$, is governed by the envelope of the single-neutron wavefunction. Conventional measurements, via diffraction, interferometry, or resolution characterization, are primarily sensitive to ensemble coherence, not individual-particle spatial extent.

Helical Neutron States and Spatial Probing

Helical neutron states (with quantized OAM, $l$) generate annular intensity profiles whose peak radius depends on the transverse extent $w$ of the wavepacket. Crucially, the coherence length only affects profile broadening, not the radius position, decoupling these two effects experimentally. The first diffraction order behind a fork-dislocation phase grating produces a wavefunction well described as a superposition of Laguerre-Gaussian (LG) modes. The annular peak's position, parameterized as $r_{\text{peak}} \sim 0.34(l+1.1) w_g$ for grating width $w_g$, yields direct sensitivity to $w$.

Experimental Methods

Small-angle neutron scattering experiments were performed at the SANS2D instrument, ISIS Neutron and Muon Source. The setup included multiple phase gratings for generating OAM states ($l = 0,3,5,7$) in first-order diffraction. The beam geometry produced an angular divergence of $1.1$ mrad. Azimuthally integrated intensity profiles were collected across the relevant OAM states and compared to simulations varying both angular divergence and wavepacket envelope width.

Results

The data analysis yielded robust numerical separation:

• Measured divergence (angular): $\theta \approx 1.1$ mrad
• Transverse coherence length: $\sigma \approx 180$ nm (for $l$0 Å)
• Single-neutron wavepacket extent lower bound: $l$1 $l$2m

The wavepacket extent was found to exceed the coherence length by over an order of magnitude. This establishes unequivocally that the spatial extent of individual neutron wavepackets and the transverse coherence length of the beam are distinct physical quantities. Further, manipulations such as collimation and post-selection affect ensemble coherence but leave the intrinsic wavepacket extent unchanged, a critical point for interpretation of neutron scattering data.

Implications and Future Directions

The findings have immediate implications for both fundamental neutron optics and the interpretation of neutron scattering experiments. The OAM-enabled spatial probing technique for neutron beams can be leveraged for characterizing advanced sources and for experimental configurations where spatial correlations are paramount. The distinction between ensemble coherence and single-particle spatial extent informs design criteria for collimation, focusing, and structured neutron beams.

Theory-wise, the results support continued application of Glauber-style partially coherent field frameworks and highlight the inapplicability of simple wavepacket pictures to ensemble behavior. The approach's generality suggests applicability to non-Gaussian structured states (e.g., Airy beams) and opens prospects for exploring longitudinal coherence and wavepacket structure. Extension to probe longitudinal spatial extent remains an open technical objective.

Technologically, advances in structured neutron optics—phase gratings, vortex generation, and multimode beams—can support precision measurement, quantum state engineering, and device development for quantum information interfaces with neutron beams.

Conclusion

The paper rigorously demonstrates, via OAM-resolved measurements, that transverse coherence length and single-particle spatial extent are fundamentally distinct and measurable quantities in neutron beams. The spatial probing method using helical neutron wavefronts achieves separation of these parameters for the first time, resolving conceptual ambiguities and setting a methodological foundation for future work in neutron quantum optics, structured beam engineering, and theory-driven scattering analysis. The results validate the theoretical expectations from VCZ and Glauber-type frameworks and establish new practical standards for neutron beam manipulation and characterization.