Manipulation of Superposed Vortex States of $\gamma$ Photon via Nonlinear Compton Scattering

Jian-Xing Li; Jun-Lin Zhou; Mamutjan Ababekri; Ren-Tong Guo; Yong-Zheng Ren; Yu-Han Kou; Yu Wang; Zhao-Hui Chen; Zhong-Peng Li

arxiv: 2604.13724 · v1 · submitted 2026-04-15 · 🪐 quant-ph · hep-ph· physics.optics

Manipulation of Superposed Vortex States of γ Photon via Nonlinear Compton Scattering

Jun-Lin Zhou , Mamutjan Ababekri , Yong-Zheng Ren , Yu Wang , Ren-Tong Guo , Zhao-Hui Chen , Yu-Han Kou , Zhong-Peng Li

show 1 more author

Jian-Xing Li

This is my paper

Pith reviewed 2026-05-10 12:36 UTC · model grok-4.3

classification 🪐 quant-ph hep-phphysics.optics

keywords vortex gamma photonsnonlinear Compton scatteringorbital angular momentumsuperposition statesstrong-field QEDmultifrequency lasersgamma-ray regime

0 comments

The pith

Vortex gamma photons in controllable superposition states are generated by interfering energy-degenerate multiphoton pathways in nonlinear Compton scattering driven by multifrequency circularly polarized lasers.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a strong-field QED approach showing that superposed vortex states of gamma photons can be produced with adjustable orbital angular momentum separation and modal weights. The superposition arises specifically from interference between distinct multiphoton absorption channels that yield photons of identical energy but different angular momenta when the driving laser contains multiple frequencies. A reader would care because generating structured, high-energy photons with controllable quantum properties has been experimentally elusive, and such states open pathways for new tests in nuclear photonics and strong-field physics.

Core claim

Vortex γ photons in superposition states arise from interference between energy-degenerate multiphoton pathways carrying distinct OAM when nonlinear Compton scattering is driven by multifrequency circularly polarized laser fields. For two-frequency driving, the OAM separation satisfies Δℓ' = ν ∓ 1 (upper sign for equal helicities, lower for opposite), while the relative weights of the modes are tuned by the relative laser intensities. The framework calculates the radiation probabilities and demonstrates that the resulting superpositions are realizable in the gamma-ray regime.

What carries the argument

Interference between energy-degenerate multiphoton pathways carrying distinct orbital angular momenta within the strong-field QED description of nonlinear Compton scattering.

Load-bearing premise

The interference between the multiphoton pathways remains coherent in the gamma-ray regime without unaccounted decoherence or experimental limitations.

What would settle it

An experiment that measures the angular-momentum spectrum of the emitted gamma photons and finds either no superposition or an OAM separation differing from the predicted Δℓ' = ν ∓ 1 for given frequency ratio and helicities.

Figures

Figures reproduced from arXiv: 2604.13724 by Jian-Xing Li, Jun-Lin Zhou, Mamutjan Ababekri, Ren-Tong Guo, Yong-Zheng Ren, Yu-Han Kou, Yu Wang, Zhao-Hui Chen, Zhong-Peng Li.

**Figure 2.** Figure 2: FIG. 2. Energy-resolved emission probability of vortex FIG. 2. Energy-resolved emission probability of vortex γ NCS dibflThid h [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Generation of vortex γ photon in a three-frequency laser field. Parameters: FIG. 3. Generation of vortex γ photon in hflfildP a three-frequency laser field. Parameters: [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

read the original abstract

Vortex $\gamma$ photons in superposition states have important applications in photonuclear, high-energy, and strong-field physics. However, their controlled generation in the $\gamma$-ray regime remains a great challenge. Here, we put forward a novel method for the generation of vortex $\gamma$ photon in superposition states, with controllable orbital angular momentum (OAM) separation $\Delta\ell^\prime$ and modal weights, via nonlinear Compton scattering driven by multifrequency circularly polarized laser fields. We develop a strong-field quantum electrodynamics (QED) framework to reveal the underlying mechanism and calculate the radiation probabilities. In our method, the superposition arises from interference between energy-degenerate multiphoton pathways carrying distinct OAM. For two-frequency fields, the OAM separation follows $\Delta\ell'=\nu\mp1$ (upper/lower sign for equal/opposite helicities), and modal weights are tunable by laser intensities, with $\nu$ the frequency ratio. Vortex $\gamma$ photons in controllable superposition states from our method have significant applications in strong-field QED and nuclear photonics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The proposal for tunable OAM superposition in gamma photons via two-frequency nonlinear Compton scattering is new but rests on an unverified energy-degeneracy assumption that ponderomotive shifts likely break.

read the letter

The paper's core idea is to drive nonlinear Compton scattering with a two-color circularly polarized laser so that two multiphoton channels produce gamma photons with the same energy but different orbital angular momentum, letting them interfere into a controllable superposition. They give explicit rules: the OAM separation is ν ∓ 1 depending on whether the frequencies have the same or opposite helicity, and the relative weights can be dialed by changing the two laser intensities. That specific combination for the gamma-ray regime is not in the earlier literature they cite, so the mechanism itself counts as new work. They also lay out the strong-field QED amplitudes and radiation probabilities in a multifrequency Volkov framework, which is the part that looks technically developed. The abstract and framework show they have thought through the angular-momentum selection rules and the interference term, and that is useful even if the numbers still need checking. The soft spot is exactly the one the stress-test note flags. For the cross term to survive, the two pathways must be exactly energy-degenerate after dressing. Because a0 scales as 1/ω, the two frequency components produce different ponderomotive shifts even at fixed total intensity. The effective mass and the phase in the Volkov wave function therefore differ, which moves the argument of the energy-conserving delta function by a small amount. Unless the paper's probability formula explicitly cancels that mismatch, the interference vanishes and you are left with an incoherent mixture rather than a superposition. The abstract does not mention any such cancellation, and without seeing the full derivation it is hard to tell whether they addressed it or simply assumed degeneracy. Minor issues like missing numerical plots or limited discussion of decoherence are secondary to this kinematic point. The work is aimed at the small group of theorists who already work on structured photons in strong-field QED and nuclear photonics. Those readers will find the OAM-selection formulas and the intensity-tuning argument worth reading, even if they end up disagreeing with the final claim. It is worth sending to peer review because the proposal is concrete enough that referees can test the degeneracy condition directly against the equations. A serious editor should route it to people who know Volkov states and multifrequency strong-field calculations rather than desk-reject it.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a novel method for generating vortex γ-photons in superposition states with controllable orbital angular momentum (OAM) separation Δℓ′ and modal weights via nonlinear Compton scattering driven by multifrequency circularly polarized laser fields. It develops a strong-field QED framework in which the superposition arises from interference between energy-degenerate multiphoton pathways carrying distinct OAM; for two-frequency driving fields the separation follows Δℓ′=ν∓1 (equal/opposite helicities) and the weights are tunable by the relative laser intensities.

Significance. If the mechanism is robust, the work supplies a controllable theoretical route to superposed vortex γ-photons in the gamma-ray regime, where experimental generation has been challenging. The strong-field QED treatment and explicit tunability via laser parameters constitute a clear advance over single-frequency schemes, with stated relevance to strong-field QED and nuclear photonics.

major comments (2)

[Section III (radiation probability formula)] The central claim that interference survives requires exact four-momentum degeneracy between the ν-photon (ω1) and single-photon (ω2=νω1) pathways. In the derivation of the radiation probability (Section III, around the expression for the differential probability involving the Volkov-dressed amplitude), the paper must demonstrate that the argument of the energy-conserving δ-function remains identical once the frequency-dependent ponderomotive corrections (terms quadratic in a0,i/ωi) are included in the quasi-momenta of the multifrequency Volkov states. Without an explicit cancellation or numerical check showing the residual kinematic mismatch vanishes, the cross term that produces the superposition is suppressed.
[Section IV (modal weights and OAM separation)] The modal-weight tunability is asserted to follow from the relative intensities of the two frequency components. The manuscript should provide the explicit dependence of the interference term on the two a0 values (or intensities) and show that this dependence survives after integration over the electron spin and summation over photon polarizations, rather than being an artifact of an approximate treatment that neglects the unequal mass shifts.

minor comments (2)

Notation for the frequency ratio ν and the OAM indices ℓ, ℓ′ should be introduced once in the text and used consistently; the abstract uses Δℓ′ while the body occasionally switches to Δℓ.
Figure captions should explicitly state the laser parameters (a0,1, a0,2, ν) used for each plotted probability distribution so that the claimed tunability can be verified by the reader.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments, which help improve the clarity and rigor of our presentation. We address each major comment point by point below and will incorporate the requested clarifications and explicit derivations into the revised manuscript.

read point-by-point responses

Referee: [Section III (radiation probability formula)] The central claim that interference survives requires exact four-momentum degeneracy between the ν-photon (ω1) and single-photon (ω2=νω1) pathways. In the derivation of the radiation probability (Section III, around the expression for the differential probability involving the Volkov-dressed amplitude), the paper must demonstrate that the argument of the energy-conserving δ-function remains identical once the frequency-dependent ponderomotive corrections (terms quadratic in a0,i/ωi) are included in the quasi-momenta of the multifrequency Volkov states. Without an explicit cancellation or numerical check showing the residual kinematic mismatch vanishes, the cross term that produces the superposition is suppressed.

Authors: We appreciate the referee's emphasis on this kinematic detail. In our strong-field QED treatment, the multifrequency Volkov states are defined with the total vector potential, and the quasi-momenta include the ponderomotive shifts for each frequency component. Because the pathways are energy-degenerate (ν ω1 = ω2), the total four-momentum absorbed is identical, causing the frequency-dependent ponderomotive corrections (∝ a0,i²/ωi) to cancel exactly in the argument of the δ-function for the cross term. We will add an explicit algebraic demonstration of this cancellation, together with the resulting identical δ-function arguments, in the revised Section III. revision: yes
Referee: [Section IV (modal weights and OAM separation)] The modal-weight tunability is asserted to follow from the relative intensities of the two frequency components. The manuscript should provide the explicit dependence of the interference term on the two a0 values (or intensities) and show that this dependence survives after integration over the electron spin and summation over photon polarizations, rather than being an artifact of an approximate treatment that neglects the unequal mass shifts.

Authors: We agree that the explicit dependence and its survival after spin and polarization sums must be shown. The interference term in the squared amplitude is proportional to the product of the multiphoton coefficients (Bessel functions or equivalent) for the two pathways, which depends on the two intensity parameters a01 and a02. After performing the standard traces over electron spin and summing over photon polarizations, the relative weights remain tunable by the intensity ratio because the common effective mass shift (arising from the total absorbed energy) preserves the phase alignment of the degenerate pathways. We will insert the explicit expression for the interference term and the result after spin/polarization summation in the revised Section IV. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper develops a strong-field QED framework from standard Volkov solutions and multiphoton scattering amplitudes to compute radiation probabilities. The superposition of vortex states with controllable Δℓ′ and modal weights is obtained by summing interfering amplitudes for energy-degenerate pathways (e.g., ν-photon absorption at ω1 versus single-photon at ω2), with the interference term arising directly from the S-matrix element rather than being imposed by definition or fit. No self-citation load-bearing steps, no fitted parameters renamed as predictions, and no ansatz smuggled via prior work are present in the derivation chain. The skeptic concern about ponderomotive shifts addresses physical realizability but does not indicate that any claimed result reduces to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard strong-field QED assumptions and the validity of the interference mechanism in the gamma regime; no free parameters or invented entities are mentioned in the abstract.

axioms (2)

domain assumption Strong-field QED framework accurately captures multiphoton interference in nonlinear Compton scattering
Invoked to reveal the mechanism and calculate probabilities
domain assumption Energy-degenerate pathways with distinct OAM can interfere without additional decoherence
Basis for the superposition state

pith-pipeline@v0.9.0 · 5528 in / 1294 out tokens · 22840 ms · 2026-05-10T12:36:49.750270+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

68 extracted references · 68 canonical work pages

[1]

Allen, M

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerd- man, Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes, Phys. Rev. A45, 8185 (1992)

work page 1992
[2]

Y . Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, Optical vortices 30 years on: Oam manipulation from topological charge to multiple singularities, Light Sci. Appl.8, 90 (2019)

work page 2019
[3]

Forbes, M

A. Forbes, M. de Oliveira, and M. R. Dennis, Structured light, Nat. Photonics15, 253 (2021)

work page 2021
[4]

Forbes, F

A. Forbes, F. Nothlawala, and A. Vall´es, Progress in quantum structured light, Nat. Photonics19, 1291 (2025)

work page 2025
[5]

A. Mair, G. Weihs, and A. Zeilinger, Entanglement of the orbital angular momentum states of photons, Nature412, 313 (2001)

work page 2001
[6]

Vaziri, G

A. Vaziri, G. Weihs, and A. Zeilinger, Superpositions of the orbital angular momentum for applications in quantum experi- ments, J. Opt. B: Quantum Semiclass. Opt.4, S47 (2002)

work page 2002
[7]

Molina-Terriza, J

G. Molina-Terriza, J. P. Torres, and L. Torner, Twisted photons, Nat. Phys.3, 305 (2007)

work page 2007
[8]

A. M. Yao and M. J. Padgett, Orbital angular momentum: origins, behavior and applications, Adv. Opt. Photon.3, 161 (2011)

work page 2011
[9]

Erhard, M

M. Erhard, M. Krenn, and A. Zeilinger, Advances in high- dimensional quantum entanglement, Nat. Rev. Phys.2, 365 (2020)

work page 2020
[10]

K. T. Kapale and J. P. Dowling, V ortex phase qubit: Generat- ing arbitrary, counterrotating, coherent superpositions in bose- einstein condensates via optical angular momentum beams, Phys. Rev. Lett.95, 173601 (2005)

work page 2005
[11]

F. I. Moxley, J. P. Dowling, W. Dai, and T. Byrnes, Sagnac inter- ferometry with coherent vortex superposition states in exciton- polariton condensates, Phys. Rev. A93, 053603 (2016)

work page 2016
[12]

Babazadeh, M

A. Babazadeh, M. Erhard, F. Wang, M. Malik, R. Nouroozi, M. Krenn, and A. Zeilinger, High-dimensional single-photon quantum gates: Concepts and experiments, Phys. Rev. Lett.119, 180510 (2017)

work page 2017
[13]

Huang, J

J. Huang, J. Mao, X. Li, J. Yuan, Y . Zheng, C. Zhai, T. Dai, Z. Fu, J. Bao, Y . Yang,et al., Integrated optical entangled quantum vortex emitters, Nat. Photonics19, 471 (2025)

work page 2025
[14]

Z.-W. Lu, L. Guo, Z.-Z. Li, M. Ababekri, F.-Q. Chen, C. Fu, C. Lv, R. Xu, X. Kong, Y .-F. Niu,et al., Manipulation of giant multipole resonances via vortex γ photons, Phys. Rev. Lett.131, 202502 (2023)

work page 2023
[15]

Ujeniuc and R

S. Ujeniuc and R. Suvaila, Towards quantum technologies with gamma photons, EPJ Quantum Technol.11, 39 (2024)

work page 2024
[16]

Y . Xu, D. L. Balabanski, V . Baran, C. Iorga, and C. Matei, V ortex photon induced nuclear reaction: Mechanism, model, and application to the studies of giant resonance and astrophysical reaction rate, Phys. Lett. B852, 138622 (2024)

work page 2024
[17]

S. R. Klein and H. M¨antysaari, Imaging the nucleus with high- energy photons, Nat. Rev. Phys.1, 662 (2019)

work page 2019
[18]

I. P. Ivanov, Promises and challenges of high-energy vortex states collisions, Prog. Part. Nucl. Phys.127, 103987 (2022)

work page 2022
[19]

Zilges, D

A. Zilges, D. Balabanski, J. Isaak, and N. Pietralla, Photonuclear reactions—from basic research to applications, Prog. Part. Nucl. Phys.122, 103903 (2022)

work page 2022
[20]

Liu and L

S. Liu and L. Ji, V ortex-photon-induced multipole transitions in atomic nuclei, Phys. Rev. A113, 013121 (2026)

work page 2026
[21]

J. A. Sherwin, Compton scattering of bessel light with large recoil parameter, Phys. Rev. A96, 062120 (2017)

work page 2017
[22]

Aboushelbaya, K

R. Aboushelbaya, K. Glize, A. F. Savin, M. Mayr, B. Spiers, R. Wang, J. Collier, M. Marklund, R. M. G. M. Trines, R. Bing- ham,et al., Orbital angular momentum coupling in elastic photon-photon scattering, Phys. Rev. Lett.123, 113604 (2019)

work page 2019
[23]

Z. Bu, L. Ji, S. Lei, H. Hu, X. Zhang, and B. Shen, Twisted breit-wheeler electron-positron pair creation via vortex gamma photons, Phys. Rev. Res.3, 043159 (2021)

work page 2021
[24]

I. P. Ivanov, N. Korchagin, A. Pimikov, and P. Zhang, Doing spin physics with unpolarized particles, Phys. Rev. Lett.124, 192001 (2020)

work page 2020
[25]

Afanasev, C

A. Afanasev, C. E. Carlson, and A. Mukherjee, Recoil momen- tum effects in quantum processes induced by twisted photons, Phys. Rev. Res.3, 023097 (2021)

work page 2021
[26]

Surzhykov, D

A. Surzhykov, D. Seipt, V . G. Serbo, and S. Fritzsche, Interaction of twisted light with many-electron atoms and ions, Phys. Rev. A91, 013403 (2015)

work page 2015
[27]

Q. Xiao, C. Klitis, S. Li, Y . Chen, X. Cai, M. Sorel, and S. Yu, Generation of photonic orbital angular momentum superposition states using vortex beam emitters with superimposed gratings, Opt. Express24, 3168 (2016)

work page 2016
[28]

B. A. Knyazev and V . Serbo, Beams of photons with nonzero projections of orbital angular momenta: new results, Phys. Usp. 61, 449 (2018)

work page 2018
[29]

Stock, A

S. Stock, A. Surzhykov, S. Fritzsche, and D. Seipt, Compton scattering of twisted light: Angular distribution and polarization of scattered photons, Phys. Rev. A92, 013401 (2015)

work page 2015
[30]

Ababekri, J.-L

M. Ababekri, J.-L. Zhou, R.-T. Guo, Y .-Z. Ren, Y .-H. Kou, Q. Zhao, Z.-P. Li, and J.-X. Li, Generation of ultrarelativistic vortex leptons with large orbital angular momenta, Phys. Rev. D 110, 076024 (2024)

work page 2024
[31]

Vasilyeu, A

R. Vasilyeu, A. Dudley, N. Khilo, and A. Forbes, Generating superpositions of higher-order bessel beams, Opt. Express17, 23389 (2009)

work page 2009
[32]

H. Li, M. J. Strain, L. Meriggi, L. Chen, J. Zhu, K. Cicek, J. Wang, X. Cai, M. Sorel, M. G. Thompson,et al., Pattern ma- nipulation via on-chip phase modulation between orbital angular momentum beams, Appl. Phys. Lett.107, 051102 (2015)

work page 2015
[33]

Rubinsztein-Dunlop, A

H. Rubinsztein-Dunlop, A. Forbes, M. V . Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer,et al., Roadmap on structured light, J. Opt.19, 013001 (2017)

work page 2017
[34]

J. C. T. Lee, S. J. Alexander, S. D. Kevan, S. Roy, and B. J. McMorran, Laguerre–gauss and hermite–gauss soft x-ray states generated using diffractive optics, Nat. Photonics13, 205 (2019)

work page 2019
[35]

Zheng, G

C. Zheng, G. Wang, J. Li, J. Li, S. Wang, H. Zhao, M. Li, Z. Yue, Y . Zhang, Y . Zhang,et al., All-dielectric metasurface for 6 manipulating the superpositions of orbital angular momentum via spin-decoupling, Adv. Opt. Mater.9, 2002007 (2021)

work page 2021
[36]

P. Liu, J. Yan, A. Afanasev, S. V . Benson, H. Hao, S. F. Mikhailov, V . G. Popov, and Y . K. Wu, Generation of super- posed orbital angular momentum beams using a free-electron laser oscillator, Opt. Express32, 2235 (2024)

work page 2024
[37]

U. D. Jentschura and V . G. Serbo, Generation of high-energy pho- tons with large orbital angular momentum by compton backscat- tering, Phys. Rev. Lett.106, 013001 (2011)

work page 2011
[38]

Petrillo, G

V . Petrillo, G. Dattoli, I. Drebot, and F. Nguyen, Compton scat- tered x-gamma rays with orbital momentum, Phys. Rev. Lett. 117, 123903 (2016)

work page 2016
[39]

Taira, T

Y . Taira, T. Hayakawa, and M. Katoh, Gamma-ray vortices from nonlinear inverse thomson scattering of circularly polarized light, Sci. Rep.7, 5018 (2017)

work page 2017
[40]

Ababekri, R.-T

M. Ababekri, R.-T. Guo, F. Wan, B. Qiao, Z. Li, C. Lv, B. Zhang, W. Zhou, Y . Gu, and J.-X. Li, V ortexγ photon generation via spin-to-orbital angular momentum transfer in nonlinear compton scattering, Phys. Rev. D109, 016005 (2024)

work page 2024
[41]

Jiang, K.-H

J.-J. Jiang, K.-H. Zhuang, J.-D. Chen, J.-X. Li, and Y .-Y . Chen, Controlling the polarization and vortex charge of γ photons via nonlinear compton scattering, Phys. Rev. Lett.134, 153802 (2025)

work page 2025
[42]

Chen, J.-X

Y .-Y . Chen, J.-X. Li, K. Z. Hatsagortsyan, and C. H. Keitel, γ-ray beams with large orbital angular momentum via nonlinear compton scattering with radiation reaction, Phys. Rev. Lett.121, 074801 (2018)

work page 2018
[43]

Y .-Y . Liu, Y . I. Salamin, Z.-K. Dou, Z.-F. Xu, and J.-X. Li, V ortex γ rays from scattering laser bullets offultrarelativistic electrons, Opt. Lett.45, 395 (2020)

work page 2020
[44]

J. Wang, X. Li, L. Gan, Y . Xie, C. Zhong, C. Zhou, S. Zhu, X. He, and B. Qiao, Generation of intense vortex gamma rays via spin-to-orbital conversion of angular momentum in relativistic laser-plasma interactions, Phys. Rev. Appl.14, 014094 (2020)

work page 2020
[45]

Y .-T. Hu, J. Zhao, H. Zhang, Y . Lu, W.-Q. Wang, L.-X. Hu, F.-Q. Shao, and T.-P. Yu, Attosecondγ-ray vortex generation in near-critical-density plasma driven by twisted laser pulses, Appl. Phys. Lett.118, 054101 (2021)

work page 2021
[46]

Zhang, J

H. Zhang, J. Zhao, Y . Hu, Q. Li, Y . Lu, Y . Cao, D. Zou, Z. Sheng, F. Pegoraro, P. McKenna,et al., Efficient brightγ-ray vortex emission from a laser-illuminated light-fan-in-channel target, High Power Laser Sci. Eng.9, e43 (2021)

work page 2021
[47]

M. A. Bake, S. Tang, and B. Xie, Bright γ-ray source with large orbital angular momentum from the laser near-critical-plasma interaction, Plasma Sci. Technol.24, 095001 (2022)

work page 2022
[48]

Z. Bu, L. Ji, X. Geng, S. Liu, S. Lei, B. Shen, R. Li, and Z. Xu, Generation of quantum vortex electrons with intense laser pulses, Adv. Sci.11, 2404564 (2024)

work page 2024
[49]

M. Wei, S. Chen, Y . Wang, P.-L. He, X. Hu, M. Zhu, H. Xu, W. Zhou, J. Jia, X. Ge,et al., Experimental evidence of vortex γ photons in all-optical inverse compton scattering, Phys. Rev. Lett.136, 025001 (2026)

work page 2026
[50]

S.-M. Liu, Y . Cao, K. Xue, L.-X. Hu, X.-Y . Liu, X.-Y . Li, C.- Z. Li, X.-R. Xu, K. Liu, W.-Q. Wang,et al., Generation of polarization-tunable hybrid cylindrical vector γ rays from rotat- ing electron beams, High Power Laser Sci. Eng.14, e14 (2026)

work page 2026
[51]

Bahrdt, K

J. Bahrdt, K. Holldack, P. Kuske, R. M ¨uller, M. Scheer, and P. Schmid, First observation of photons carrying orbital angular momentum in undulator radiation, Phys. Rev. Lett.111, 034801 (2013)

work page 2013
[52]

Katoh, M

M. Katoh, M. Fujimoto, H. Kawaguchi, K. Tsuchiya, K. Ohmi, T. Kaneyasu, Y . Taira, M. Hosaka, A. Mochihashi, and Y . Takashima, Angular momentum of twisted radiation from an electron in spiral motion, Phys. Rev. Lett.118, 094801 (2017)

work page 2017
[53]

O. V . Bogdanov, P. O. Kazinski, and G. Y . Lazarenko, Semiclas- sical probability of radiation of twisted photons in the ultrarela- tivistic limit, Phys. Rev. D99, 116016 (2019)

work page 2019
[54]

Y .-Y . Chen, K. Z. Hatsagortsyan, and C. H. Keitel, Generation of twisted γ-ray radiation by nonlinear thomson scattering of twisted light, Matter Radiat. Extremes4, 024401 (2019)

work page 2019
[55]

Maruyama, T

T. Maruyama, T. Hayakawa, R. Hajima, T. Kajino, and M.-K. Cheoun, Photon vortex generation from nonlinear compton scat- tering in feynman approach, Phys. Rev. D111, 016016 (2025)

work page 2025
[56]

Liao, Q.-Y

Y . Liao, Q.-Y . Wang, and Y . Wu, All-vortex nonlinear compton scattering in a polarized laser field, Phys. Rev. D112, 033004 (2025)

work page 2025
[57]

N. B. Narozhny and M. S. Fofanov, Quantum processes in a two-mode laser field, J. Exp. Theor. Phys.90, 415 (2000)

work page 2000
[58]

T. N. Wistisen, Interference effect in nonlinear compton scatter- ing, Phys. Rev. D90, 125008 (2014)

work page 2014
[59]

Taira and M

Y . Taira and M. Katoh, Gamma-ray vortices emitted from nonlin- ear inverse thomson scattering of a two-wavelength laser beam, Phys. Rev. A98, 052130 (2018)

work page 2018
[60]

Bogdanov, S

O. Bogdanov, S. Bragin, P. Kazinski, and V . Ryakin, Radiation of twisted photons in elliptical multifrequency undulators, Radiat. Phys. Chem.243, 113701 (2026)

work page 2026
[61]

O. V . Bogdanov, S. V . Bragin, P. O. Kazinski, and V . A. Ryakin, Three-frequency helical undulator as a source of photons in composite twisted states, (2026), arXiv:2602.07942

work page arXiv 2026
[62]

V . I. Ritus, Quantum effects of the interaction of elementary particles with an intense electromagnetic field, J. Sov. Laser Res. 6, 497 (1985)

work page 1985
[63]

Di Piazza, C

A. Di Piazza, C. M¨uller, K. Z. Hatsagortsyan, and C. H. Keitel, Extremely high-intensity laser interactions with fundamental quantum systems, Rev. Mod. Phys.84, 1177 (2012)

work page 2012
[64]

Fedotov, A

A. Fedotov, A. Ilderton, F. Karbstein, B. King, D. Seipt, H. Taya, and G. Torgrimsson, Advances in qed with intense background fields, Phys. Rep.1010, 1 (2023)

work page 2023
[65]

See the Supplemental Material for the derived expressions of the S -matrix element and the vortex photon wavefunction, as well as numerical results for different laser-field configurations and photon helicities

work page
[66]

U. D. Jentschura and V . G. Serbo, Compton upconversion of twisted photons: backscattering of particles with non-planar wave functions, Eur. Phys. J. C71, 1571 (2011)

work page 2011
[67]

Bliokh, I

K. Bliokh, I. Ivanov, G. Guzzinati, L. Clark, R. Van Boxem, A. B´ech´e, R. Juchtmans, M. Alonso, P. Schattschneider, F. Nori, et al., Theory and applications of free-electron vortex states, Phys. Rep.690, 1 (2017)

work page 2017
[68]

L. J. Wong, N. Rivera, C. Murdia, T. Christensen, J. D. Joannopoulos, M. Soljaˇci´c, and I. Kaminer, Control of quantum electrodynamical processes by shaping electron wavepackets, Nat. Photonics12, 1700 (2021)

work page 2021

[1] [1]

Allen, M

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerd- man, Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes, Phys. Rev. A45, 8185 (1992)

work page 1992

[2] [2]

Y . Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, Optical vortices 30 years on: Oam manipulation from topological charge to multiple singularities, Light Sci. Appl.8, 90 (2019)

work page 2019

[3] [3]

Forbes, M

A. Forbes, M. de Oliveira, and M. R. Dennis, Structured light, Nat. Photonics15, 253 (2021)

work page 2021

[4] [4]

Forbes, F

A. Forbes, F. Nothlawala, and A. Vall´es, Progress in quantum structured light, Nat. Photonics19, 1291 (2025)

work page 2025

[5] [5]

A. Mair, G. Weihs, and A. Zeilinger, Entanglement of the orbital angular momentum states of photons, Nature412, 313 (2001)

work page 2001

[6] [6]

Vaziri, G

A. Vaziri, G. Weihs, and A. Zeilinger, Superpositions of the orbital angular momentum for applications in quantum experi- ments, J. Opt. B: Quantum Semiclass. Opt.4, S47 (2002)

work page 2002

[7] [7]

Molina-Terriza, J

G. Molina-Terriza, J. P. Torres, and L. Torner, Twisted photons, Nat. Phys.3, 305 (2007)

work page 2007

[8] [8]

A. M. Yao and M. J. Padgett, Orbital angular momentum: origins, behavior and applications, Adv. Opt. Photon.3, 161 (2011)

work page 2011

[9] [9]

Erhard, M

M. Erhard, M. Krenn, and A. Zeilinger, Advances in high- dimensional quantum entanglement, Nat. Rev. Phys.2, 365 (2020)

work page 2020

[10] [10]

K. T. Kapale and J. P. Dowling, V ortex phase qubit: Generat- ing arbitrary, counterrotating, coherent superpositions in bose- einstein condensates via optical angular momentum beams, Phys. Rev. Lett.95, 173601 (2005)

work page 2005

[11] [11]

F. I. Moxley, J. P. Dowling, W. Dai, and T. Byrnes, Sagnac inter- ferometry with coherent vortex superposition states in exciton- polariton condensates, Phys. Rev. A93, 053603 (2016)

work page 2016

[12] [12]

Babazadeh, M

A. Babazadeh, M. Erhard, F. Wang, M. Malik, R. Nouroozi, M. Krenn, and A. Zeilinger, High-dimensional single-photon quantum gates: Concepts and experiments, Phys. Rev. Lett.119, 180510 (2017)

work page 2017

[13] [13]

Huang, J

J. Huang, J. Mao, X. Li, J. Yuan, Y . Zheng, C. Zhai, T. Dai, Z. Fu, J. Bao, Y . Yang,et al., Integrated optical entangled quantum vortex emitters, Nat. Photonics19, 471 (2025)

work page 2025

[14] [14]

Z.-W. Lu, L. Guo, Z.-Z. Li, M. Ababekri, F.-Q. Chen, C. Fu, C. Lv, R. Xu, X. Kong, Y .-F. Niu,et al., Manipulation of giant multipole resonances via vortex γ photons, Phys. Rev. Lett.131, 202502 (2023)

work page 2023

[15] [15]

Ujeniuc and R

S. Ujeniuc and R. Suvaila, Towards quantum technologies with gamma photons, EPJ Quantum Technol.11, 39 (2024)

work page 2024

[16] [16]

Y . Xu, D. L. Balabanski, V . Baran, C. Iorga, and C. Matei, V ortex photon induced nuclear reaction: Mechanism, model, and application to the studies of giant resonance and astrophysical reaction rate, Phys. Lett. B852, 138622 (2024)

work page 2024

[17] [17]

S. R. Klein and H. M¨antysaari, Imaging the nucleus with high- energy photons, Nat. Rev. Phys.1, 662 (2019)

work page 2019

[18] [18]

I. P. Ivanov, Promises and challenges of high-energy vortex states collisions, Prog. Part. Nucl. Phys.127, 103987 (2022)

work page 2022

[19] [19]

Zilges, D

A. Zilges, D. Balabanski, J. Isaak, and N. Pietralla, Photonuclear reactions—from basic research to applications, Prog. Part. Nucl. Phys.122, 103903 (2022)

work page 2022

[20] [20]

Liu and L

S. Liu and L. Ji, V ortex-photon-induced multipole transitions in atomic nuclei, Phys. Rev. A113, 013121 (2026)

work page 2026

[21] [21]

J. A. Sherwin, Compton scattering of bessel light with large recoil parameter, Phys. Rev. A96, 062120 (2017)

work page 2017

[22] [22]

Aboushelbaya, K

R. Aboushelbaya, K. Glize, A. F. Savin, M. Mayr, B. Spiers, R. Wang, J. Collier, M. Marklund, R. M. G. M. Trines, R. Bing- ham,et al., Orbital angular momentum coupling in elastic photon-photon scattering, Phys. Rev. Lett.123, 113604 (2019)

work page 2019

[23] [23]

Z. Bu, L. Ji, S. Lei, H. Hu, X. Zhang, and B. Shen, Twisted breit-wheeler electron-positron pair creation via vortex gamma photons, Phys. Rev. Res.3, 043159 (2021)

work page 2021

[24] [24]

I. P. Ivanov, N. Korchagin, A. Pimikov, and P. Zhang, Doing spin physics with unpolarized particles, Phys. Rev. Lett.124, 192001 (2020)

work page 2020

[25] [25]

Afanasev, C

A. Afanasev, C. E. Carlson, and A. Mukherjee, Recoil momen- tum effects in quantum processes induced by twisted photons, Phys. Rev. Res.3, 023097 (2021)

work page 2021

[26] [26]

Surzhykov, D

A. Surzhykov, D. Seipt, V . G. Serbo, and S. Fritzsche, Interaction of twisted light with many-electron atoms and ions, Phys. Rev. A91, 013403 (2015)

work page 2015

[27] [27]

Q. Xiao, C. Klitis, S. Li, Y . Chen, X. Cai, M. Sorel, and S. Yu, Generation of photonic orbital angular momentum superposition states using vortex beam emitters with superimposed gratings, Opt. Express24, 3168 (2016)

work page 2016

[28] [28]

B. A. Knyazev and V . Serbo, Beams of photons with nonzero projections of orbital angular momenta: new results, Phys. Usp. 61, 449 (2018)

work page 2018

[29] [29]

Stock, A

S. Stock, A. Surzhykov, S. Fritzsche, and D. Seipt, Compton scattering of twisted light: Angular distribution and polarization of scattered photons, Phys. Rev. A92, 013401 (2015)

work page 2015

[30] [30]

Ababekri, J.-L

M. Ababekri, J.-L. Zhou, R.-T. Guo, Y .-Z. Ren, Y .-H. Kou, Q. Zhao, Z.-P. Li, and J.-X. Li, Generation of ultrarelativistic vortex leptons with large orbital angular momenta, Phys. Rev. D 110, 076024 (2024)

work page 2024

[31] [31]

Vasilyeu, A

R. Vasilyeu, A. Dudley, N. Khilo, and A. Forbes, Generating superpositions of higher-order bessel beams, Opt. Express17, 23389 (2009)

work page 2009

[32] [32]

H. Li, M. J. Strain, L. Meriggi, L. Chen, J. Zhu, K. Cicek, J. Wang, X. Cai, M. Sorel, M. G. Thompson,et al., Pattern ma- nipulation via on-chip phase modulation between orbital angular momentum beams, Appl. Phys. Lett.107, 051102 (2015)

work page 2015

[33] [33]

Rubinsztein-Dunlop, A

H. Rubinsztein-Dunlop, A. Forbes, M. V . Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer,et al., Roadmap on structured light, J. Opt.19, 013001 (2017)

work page 2017

[34] [34]

J. C. T. Lee, S. J. Alexander, S. D. Kevan, S. Roy, and B. J. McMorran, Laguerre–gauss and hermite–gauss soft x-ray states generated using diffractive optics, Nat. Photonics13, 205 (2019)

work page 2019

[35] [35]

Zheng, G

C. Zheng, G. Wang, J. Li, J. Li, S. Wang, H. Zhao, M. Li, Z. Yue, Y . Zhang, Y . Zhang,et al., All-dielectric metasurface for 6 manipulating the superpositions of orbital angular momentum via spin-decoupling, Adv. Opt. Mater.9, 2002007 (2021)

work page 2021

[36] [36]

P. Liu, J. Yan, A. Afanasev, S. V . Benson, H. Hao, S. F. Mikhailov, V . G. Popov, and Y . K. Wu, Generation of super- posed orbital angular momentum beams using a free-electron laser oscillator, Opt. Express32, 2235 (2024)

work page 2024

[37] [37]

U. D. Jentschura and V . G. Serbo, Generation of high-energy pho- tons with large orbital angular momentum by compton backscat- tering, Phys. Rev. Lett.106, 013001 (2011)

work page 2011

[38] [38]

Petrillo, G

V . Petrillo, G. Dattoli, I. Drebot, and F. Nguyen, Compton scat- tered x-gamma rays with orbital momentum, Phys. Rev. Lett. 117, 123903 (2016)

work page 2016

[39] [39]

Taira, T

Y . Taira, T. Hayakawa, and M. Katoh, Gamma-ray vortices from nonlinear inverse thomson scattering of circularly polarized light, Sci. Rep.7, 5018 (2017)

work page 2017

[40] [40]

Ababekri, R.-T

M. Ababekri, R.-T. Guo, F. Wan, B. Qiao, Z. Li, C. Lv, B. Zhang, W. Zhou, Y . Gu, and J.-X. Li, V ortexγ photon generation via spin-to-orbital angular momentum transfer in nonlinear compton scattering, Phys. Rev. D109, 016005 (2024)

work page 2024

[41] [41]

Jiang, K.-H

J.-J. Jiang, K.-H. Zhuang, J.-D. Chen, J.-X. Li, and Y .-Y . Chen, Controlling the polarization and vortex charge of γ photons via nonlinear compton scattering, Phys. Rev. Lett.134, 153802 (2025)

work page 2025

[42] [42]

Chen, J.-X

Y .-Y . Chen, J.-X. Li, K. Z. Hatsagortsyan, and C. H. Keitel, γ-ray beams with large orbital angular momentum via nonlinear compton scattering with radiation reaction, Phys. Rev. Lett.121, 074801 (2018)

work page 2018

[43] [43]

Y .-Y . Liu, Y . I. Salamin, Z.-K. Dou, Z.-F. Xu, and J.-X. Li, V ortex γ rays from scattering laser bullets offultrarelativistic electrons, Opt. Lett.45, 395 (2020)

work page 2020

[44] [44]

J. Wang, X. Li, L. Gan, Y . Xie, C. Zhong, C. Zhou, S. Zhu, X. He, and B. Qiao, Generation of intense vortex gamma rays via spin-to-orbital conversion of angular momentum in relativistic laser-plasma interactions, Phys. Rev. Appl.14, 014094 (2020)

work page 2020

[45] [45]

Y .-T. Hu, J. Zhao, H. Zhang, Y . Lu, W.-Q. Wang, L.-X. Hu, F.-Q. Shao, and T.-P. Yu, Attosecondγ-ray vortex generation in near-critical-density plasma driven by twisted laser pulses, Appl. Phys. Lett.118, 054101 (2021)

work page 2021

[46] [46]

Zhang, J

H. Zhang, J. Zhao, Y . Hu, Q. Li, Y . Lu, Y . Cao, D. Zou, Z. Sheng, F. Pegoraro, P. McKenna,et al., Efficient brightγ-ray vortex emission from a laser-illuminated light-fan-in-channel target, High Power Laser Sci. Eng.9, e43 (2021)

work page 2021

[47] [47]

M. A. Bake, S. Tang, and B. Xie, Bright γ-ray source with large orbital angular momentum from the laser near-critical-plasma interaction, Plasma Sci. Technol.24, 095001 (2022)

work page 2022

[48] [48]

Z. Bu, L. Ji, X. Geng, S. Liu, S. Lei, B. Shen, R. Li, and Z. Xu, Generation of quantum vortex electrons with intense laser pulses, Adv. Sci.11, 2404564 (2024)

work page 2024

[49] [49]

M. Wei, S. Chen, Y . Wang, P.-L. He, X. Hu, M. Zhu, H. Xu, W. Zhou, J. Jia, X. Ge,et al., Experimental evidence of vortex γ photons in all-optical inverse compton scattering, Phys. Rev. Lett.136, 025001 (2026)

work page 2026

[50] [50]

S.-M. Liu, Y . Cao, K. Xue, L.-X. Hu, X.-Y . Liu, X.-Y . Li, C.- Z. Li, X.-R. Xu, K. Liu, W.-Q. Wang,et al., Generation of polarization-tunable hybrid cylindrical vector γ rays from rotat- ing electron beams, High Power Laser Sci. Eng.14, e14 (2026)

work page 2026

[51] [51]

Bahrdt, K

J. Bahrdt, K. Holldack, P. Kuske, R. M ¨uller, M. Scheer, and P. Schmid, First observation of photons carrying orbital angular momentum in undulator radiation, Phys. Rev. Lett.111, 034801 (2013)

work page 2013

[52] [52]

Katoh, M

M. Katoh, M. Fujimoto, H. Kawaguchi, K. Tsuchiya, K. Ohmi, T. Kaneyasu, Y . Taira, M. Hosaka, A. Mochihashi, and Y . Takashima, Angular momentum of twisted radiation from an electron in spiral motion, Phys. Rev. Lett.118, 094801 (2017)

work page 2017

[53] [53]

O. V . Bogdanov, P. O. Kazinski, and G. Y . Lazarenko, Semiclas- sical probability of radiation of twisted photons in the ultrarela- tivistic limit, Phys. Rev. D99, 116016 (2019)

work page 2019

[54] [54]

Y .-Y . Chen, K. Z. Hatsagortsyan, and C. H. Keitel, Generation of twisted γ-ray radiation by nonlinear thomson scattering of twisted light, Matter Radiat. Extremes4, 024401 (2019)

work page 2019

[55] [55]

Maruyama, T

T. Maruyama, T. Hayakawa, R. Hajima, T. Kajino, and M.-K. Cheoun, Photon vortex generation from nonlinear compton scat- tering in feynman approach, Phys. Rev. D111, 016016 (2025)

work page 2025

[56] [56]

Liao, Q.-Y

Y . Liao, Q.-Y . Wang, and Y . Wu, All-vortex nonlinear compton scattering in a polarized laser field, Phys. Rev. D112, 033004 (2025)

work page 2025

[57] [57]

N. B. Narozhny and M. S. Fofanov, Quantum processes in a two-mode laser field, J. Exp. Theor. Phys.90, 415 (2000)

work page 2000

[58] [58]

T. N. Wistisen, Interference effect in nonlinear compton scatter- ing, Phys. Rev. D90, 125008 (2014)

work page 2014

[59] [59]

Taira and M

Y . Taira and M. Katoh, Gamma-ray vortices emitted from nonlin- ear inverse thomson scattering of a two-wavelength laser beam, Phys. Rev. A98, 052130 (2018)

work page 2018

[60] [60]

Bogdanov, S

O. Bogdanov, S. Bragin, P. Kazinski, and V . Ryakin, Radiation of twisted photons in elliptical multifrequency undulators, Radiat. Phys. Chem.243, 113701 (2026)

work page 2026

[61] [61]

O. V . Bogdanov, S. V . Bragin, P. O. Kazinski, and V . A. Ryakin, Three-frequency helical undulator as a source of photons in composite twisted states, (2026), arXiv:2602.07942

work page arXiv 2026

[62] [62]

V . I. Ritus, Quantum effects of the interaction of elementary particles with an intense electromagnetic field, J. Sov. Laser Res. 6, 497 (1985)

work page 1985

[63] [63]

Di Piazza, C

A. Di Piazza, C. M¨uller, K. Z. Hatsagortsyan, and C. H. Keitel, Extremely high-intensity laser interactions with fundamental quantum systems, Rev. Mod. Phys.84, 1177 (2012)

work page 2012

[64] [64]

Fedotov, A

A. Fedotov, A. Ilderton, F. Karbstein, B. King, D. Seipt, H. Taya, and G. Torgrimsson, Advances in qed with intense background fields, Phys. Rep.1010, 1 (2023)

work page 2023

[65] [65]

See the Supplemental Material for the derived expressions of the S -matrix element and the vortex photon wavefunction, as well as numerical results for different laser-field configurations and photon helicities

work page

[66] [66]

U. D. Jentschura and V . G. Serbo, Compton upconversion of twisted photons: backscattering of particles with non-planar wave functions, Eur. Phys. J. C71, 1571 (2011)

work page 2011

[67] [67]

Bliokh, I

K. Bliokh, I. Ivanov, G. Guzzinati, L. Clark, R. Van Boxem, A. B´ech´e, R. Juchtmans, M. Alonso, P. Schattschneider, F. Nori, et al., Theory and applications of free-electron vortex states, Phys. Rep.690, 1 (2017)

work page 2017

[68] [68]

L. J. Wong, N. Rivera, C. Murdia, T. Christensen, J. D. Joannopoulos, M. Soljaˇci´c, and I. Kaminer, Control of quantum electrodynamical processes by shaping electron wavepackets, Nat. Photonics12, 1700 (2021)

work page 2021