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arXiv:2604.16544

Comment on "Angular momentum dynamics of vortex particles in accelerators''

S. S. Baturin

physics.acc-phhep-phphysics.opticsquant-phSubmitted Apr 17, 2026• Announced Apr 20, 2026
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Abstract

We comment on Ref.[D. Karlovets, D. Grosman, and I. Pavlov, Phys. Rev. Lett. 136, 085002 (2026)], which proposes a BMT-like equation for the mean kinetic orbital angular momentum (OAM) of vortex particles in accelerator fields and draws spin-like conclusions about depolarization, resonances, and control. We show that the proposed closure is not generally valid even at the mean-value level. In the authors' own homogeneous-field model, Eq.(8) already makes $\langle L_z\rangle$ depend on the packet second moment $\langle ρ^2\rangle(τ)$; for an exact family of breathing Landau/LG packets this yields an explicit oscillation incompatible with Eq.(9) except in the nongeneric matched case. Moreover, the Appendix A assumption that mixed correlators are negligible suppresses the transverse kinetic-OAM components themselves, since those correlators are precisely the building blocks of $L_x$ and $L_y$. We also stress that, even if a closed equation for $\langle \hat{\mathbf L}\rangle$ were available, it would still not constitute a transport equation for a vortex quantum state. Mean-OAM transport does not determine OAM spectra, inter-mode coherences, or fidelity. State-level claims therefore require a mode-resolved density-matrix treatment rather than an Ehrenfest equation for a low-order moment.

Comments
4 pages. This is the comment on the paper D. Karlovets, D. Grosman, and I. Pavlov, Phys. Rev. Lett. 136, 085002 (2026) DOI https://doi.org/10.1103/gsrz-cscl. ArXiv ID arXiv:2507.08763

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We comment on Ref.[D. Karlovets, D. Grosman, and I. Pavlov, Phys. Rev. Lett. 136, 085002 (2026)], which proposes a BMT-like equation for the mean kinetic orbital angular momentum (OAM) of vortex particles in accelerator fields and draws spin-like conclusions about depolarization, resonances, and control. We show that the proposed closure is not generally valid even at the mean-value level. In the authors' own homogeneous-field model, Eq.(8) already makes ⟨Lz⟩\langle L_z\rangle⟨Lz​⟩ depend on the packet second moment ⟨ρ2⟩(τ)\langle ρ^2\rangle(τ)⟨ρ2⟩(τ); for an exact family of breathing Landau/LG packets this yields an explicit oscillation incompatible with Eq.(9) except in the nongeneric matched case. Moreover, the Appendix A assumption that mixed correlators are negligible suppresses the transverse kinetic-OAM components themselves, since those correlators are precisely the building blocks of LxL_xLx​ and LyL_yLy​. We also stress that, even if a closed equation for ⟨L^⟩\langle \hat{\mathbf L}\rangle⟨L^⟩ were available, it would still not constitute a transport equation for a vortex quantum state. Mean-OAM transport does not determine OAM spectra, inter-mode coherences, or fidelity. State-level claims therefore require a mode-resolved density-matrix treatment rather than an Ehrenfest equation for a low-order moment.
We show that the covariance matrix of any cylindrically symmetric coherent orbital angular momentum (OAM) eigenmode with quantum number ℓ\ellℓ takes a universal form depending only on ⟨r2⟩\langle r^2\rangle⟨r2⟩, ⟨kr2⟩\langle k_r^2\rangle⟨kr2​⟩, and ℓ\ellℓ, independently of the radial profile, and that this form is identical to the covariance matrix of a twisted Gaussian Schell-model (TGSM) beam.} More specifically, both matrices share the same pattern of zero and nonzero entries, with the off-diagonal blocks proportional to ℓ\ellℓ and the TGSM twist parameter uuu, respectively. This result holds for an arbitrary radial profile and provides direct term-by-term identification of parameters between the two sets of beams. We work out the correspondence in detail for three important families: Laguerre--Gaussian (LG), Bessel--Gaussian, and perfect vortex beams (PVBs), and derive the conditions under which each coherent OAM mode maps onto a physically realizable TGSM beam. {Because the covariance matrix governs second-moment evolution under arbitrary ABCD (symplectic) transformations, any two beams sharing the same covariance matrix are second-order indistinguishable at every propagation plane. In particular, the matched TGSM and coherent OAM beams share identical beam-width evolution, far-field divergence, and M2M^2M2 beam-quality factor.} In particular, the well-developed TGSM propagation toolbox applies directly to the second-order moment evolution of the three coherent families. We further show that within each beam family the covariance matrix uniquely determines the beam parameters, with exact uniqueness established for LG modes. Additional results include cross-family second-moment equivalence conditions and a proof that PVB modes form a complete orthonormal basis in the limit w→0w\to 0w→0.
We study the material requirements for transferring the total-angular-momentum (TAM) projection of a twisted photon to the orbital angular momentum (OAM) of a photoelectron emitted from an nnn-type semiconductor surface. Within a single-valley effective-mass model of surface photoemission, we calculate OAM-resolved spectra for GaAs, InSb, InAs0.34Sb0.66\mathrm{InAs}_{0.34}\mathrm{Sb}_{0.66}InAs0.34​Sb0.66​, and Hg0.76Cd0.24Te\mathrm{Hg}_{0.76}\mathrm{Cd}_{0.24}\mathrm{Te}Hg0.76​Cd0.24​Te irradiated by twisted photons with Laguerre--Gaussian--like momentum profile. The OAM transfer is characterized by the mean electron OAM, its root-mean-squared width, and the fraction of electrons with OAM-projection equal to the photon TAM-projection. Efficient transfer requires the transverse momentum of the conduction electron to be much smaller than the transverse momentum width of the photon, which favors low temperatures, small conduction-band effective masses, and shallow donor levels. GaAs is less favorable within the present model because of its larger effective mass and deeper donor levels. We also discuss the demanding photon-wave packet parameters, possible extensions to Dirac and Weyl semimetals, and post-emission OAM selection. Although the generation of vortex electrons with a vanishing OAM uncertainty via photoemission seems challenging, we argue that it is still possible to generate single-electron vortex states with a finite OAM dispersion.
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