Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Attosecond circular-dichroism chronoscopy of electron vortices

Abstract

Circular dichroism (CD) describes the different responses of a chiral object to circularly polarized light of opposite handedness and serves as the basis of most chirality-sensitive spectroscopy techniques. All previously observed CD effects originate from the chiral sensitivity of the amplitudes of transition-matrix elements. However, CD effects in the phase of such matrix elements have barely been studied, even theoretically. Here we present a combined experimental and theoretical investigation of amplitude- and phase-resolved CDs of continuum–continuum transitions for electron vortices. We employ a circularly polarized attosecond pulse train to prepare electron vortices in the continuum, and a circularly polarized near-infrared laser pulse to probe the chirality of the electron vortices. Our complete experimental reconstruction of the partial-wave amplitudes and phases demonstrates that the photoionization time delays of the continuum–continuum transitions depend not only on the angular-momentum quantum number l of the populated continuum state, but also on its magnetic quantum number m. Our work defines a general technique called attosecond circular-dichroism chronoscopy (ACDC), which can provide new insights into electron-vortex beams, chiral molecules and magnetic materials on the most fundamental timescales.

This is a preview of subscription content, access via your institution

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: Experimental results of the CD effects in continuum–continuum transitions of the electron vortex.
Fig. 2: TDSE simulations.
Fig. 3: Interference mechanism in co-rotating and counter-rotating geometries based on the p+ ground state.
Fig. 4: Amplitude and phase of the relevant partial waves at SB12.

Data availability

Data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.

References

  1. Uchida, M. & Tonomura, A. Generation of electron beams carrying orbital angular momentum. Nature 464, 737–739 (2010).

    Article  Google Scholar 

  2. Djiokap, J. N. et al. Electron vortices in photoionization by circularly polarized attosecond pulses. Phys. Rev. Lett. 115, 113004 (2015).

    Article  Google Scholar 

  3. Ngoko Djiokap, J. M. et al. Multistart spiral electron vortices in ionization by circularly polarized uv pulses. Phys. Rev. A 94, 013408 (2016).

    Article  Google Scholar 

  4. Pengel, D., Kerbstadt, S., Englert, L., Bayer, T. & Wollenhaupt, M. Control of three-dimensional electron vortices from femtosecond multiphoton ionization. Phys. Rev. A 96, 043426 (2017).

    Article  Google Scholar 

  5. Pengel, D. et al. Electron vortices in femtosecond multiphoton ionization. Phys. Rev. Lett. 118, 053003 (2017).

    Article  Google Scholar 

  6. Ngoko Djiokap, J. M. et al. Dynamical electron vortices in attosecond double photoionization of H2. Phys. Rev. A 98, 063407 (2018).

    Article  Google Scholar 

  7. Eckart, S. et al. Ultrafast preparation and detection of ring currents in single atoms. Nat. Phys. 14, 701–704 (2018).

    Article  Google Scholar 

  8. Han, M. et al. Probing photoionization dichroism of excited electron ring currents by chiral photoelectron spectroscopy. Phys. Rev. A 101, 043406 (2020).

    Article  Google Scholar 

  9. Herath, T., Yan, L., Lee, S. K. & Li, W. Strong-field ionization rate depends on the sign of the magnetic quantum number. Phys. Rev. Lett. 109, 043004 (2012).

    Article  Google Scholar 

  10. Tolstikhin, O. I. & Morishita, T. Strong-field ionization, rescattering and target structure imaging with vortex electrons. Phys. Rev. A 99, 063415 (2019).

    Article  Google Scholar 

  11. Verbeeck, J., Tian, H. & Schattschneider, P. Production and application of electron vortex beams. Nature 467, 301–304 (2010).

    Article  Google Scholar 

  12. Hartung, A. et al. Electron spin polarization in strong-field ionization of xenon atoms. Nat. Photon. 10, 526–528 (2016).

    Article  Google Scholar 

  13. Fleischer, A., Kfir, O., Diskin, T., Sidorenko, P. & Cohen, O. Spin angular momentum and tunable polarization in high-harmonic generation. Nat. Photon. 8, 543–549 (2014).

    Article  Google Scholar 

  14. Kfir, O. et al. Generation of bright phase-matched circularly-polarized extreme ultraviolet high harmonics. Nat. Photon. 9, 99–105 (2014).

    Article  Google Scholar 

  15. Hickstein, D. D. et al. Non-collinear generation of angularly isolated circularly polarized high harmonics. Nat. Photon. 9, 743–750 (2015).

    Article  Google Scholar 

  16. Huang, P.-C. et al. Polarization control of isolated high-harmonic pulses. Nat. Photon. 12, 349–354 (2018).

    Article  Google Scholar 

  17. Li, R., Sullivan, R., Al-Basheer, W., Pagni, R. & Compton, R. Linear and nonlinear circular dichroism of R-(+)-3-methylcyclopentanone. J. Chem. Phys. 125, 144304 (2006).

    Article  Google Scholar 

  18. Pitzer, M. et al. Direct determination of absolute molecular stereochemistry in gas phase by coulomb explosion imaging. Science 341, 1096–1100 (2013).

    Article  Google Scholar 

  19. Herwig, P. et al. Imaging the absolute configuration of a chiral epoxide in the gas phase. Science 342, 1084–1086 (2013).

    Article  Google Scholar 

  20. Böwering, N. et al. Asymmetry in photoelectron emission from chiral molecules induced by circularly polarized light. Phys. Rev. Lett. 86, 1187–1190 (2001).

    Article  Google Scholar 

  21. Garcia, G. A. et al. Circular dichroism in the photoelectron angular distribution from randomly oriented enantiomers of camphor. J. Chem. Phys. 119, 8781–8784 (2003).

    Article  Google Scholar 

  22. Baykusheva, D. & Wörner, H. J. Chiral discrimination through bielliptical high-harmonic spectroscopy. Phys. Rev. X 8, 031060 (2018).

    Google Scholar 

  23. Neufeld, O. et al. Ultrasensitive chiral spectroscopy by dynamical symmetry breaking in high harmonic generation. Phys. Rev. X 9, 031002 (2019).

    Google Scholar 

  24. Corkum, P. B. & Krausz, F. Attosecond science. Nat. Phys. 3, 381–387 (2007).

    Article  Google Scholar 

  25. Hentschel, M. et al. Attosecond metrology. Nature 414, 509–513 (2001).

    Article  Google Scholar 

  26. Itatani, J. et al. Attosecond streak camera. Phys. Rev. Lett. 88, 173903 (2002).

    Article  Google Scholar 

  27. Paul, P. M. et al. Observation of a train of attosecond pulses from high harmonic generation. Science 292, 1689–1692 (2001).

    Article  Google Scholar 

  28. Klünder, K. et al. Probing single-photon ionization on the attosecond time scale. Phys. Rev. Lett. 106, 143002 (2011).

    Article  Google Scholar 

  29. Huppert, M., Jordan, I., Baykusheva, D., von Conta, A. & Wörner, H. J. Attosecond delays in molecular photoionization. Phys. Rev. Lett. 117, 093001 (2016).

    Article  Google Scholar 

  30. Han, M. et al. Attosecond metrology in circular polarization. (2022). https://doi.org/10.48550/arXiv.2211.02769

  31. Ullrich, J. et al. Recoil-ion and electron momentum spectroscopy: reaction-microscopes. Rep. Prog. Phys. 66, 1463–1545 (2003).

    Article  Google Scholar 

  32. Dörner, R. et al. Cold Target Recoil Ion Momentum Spectroscopy: a ‘momentum microscope’ to view atomic collision dynamics. Phys. Rep. 330, 95–192 (2000).

    Article  Google Scholar 

  33. Heck, S. et al. Attosecond interferometry of shape resonances in the recoil frame of CF4. Sci. Adv. 7, eabj8121 (2021).

    Article  Google Scholar 

  34. Mazza, T. et al. Determining the polarization state of an extreme ultraviolet free-electron laser beam using atomic circular dichroism. Nat. Commun. 5, 3648 (2014).

    Article  Google Scholar 

  35. Mosert, V. & Bauer, D. Photoelectron spectra with Qprop and t-SURFF. Comput. Phys. Commun. 207, 452–463 (2016).

    Article  MathSciNet  Google Scholar 

  36. Fano, U. Propensity rules: an analytical approach. Phys. Rev. A Gen. Phys. 32, 617–618 (1985).

    Article  Google Scholar 

  37. Busto, D. et al. Fano’s propensity rule in angle-resolved attosecond pump-probe photoionization. Phys. Rev. Lett. 123, 133201 (2019).

    Article  Google Scholar 

  38. Kheifets, A. S. Symmetry analysis of the photoelectron continuum in two-photon XUV + IR ionization. Phys. Rev. A 105, 013114 (2022).

    Article  Google Scholar 

  39. Villeneuve, D., Hockett, P., Vrakking, M. & Niikura, H. Coherent imaging of an attosecond electron wave packet. Science 356, 1150–1153 (2017).

    Article  Google Scholar 

  40. Fuchs, J. et al. Time delays from one-photon transitions in the continuum. Optica 7, 154–161 (2020).

    Article  Google Scholar 

  41. Tokunaga, Y. et al. A new class of chiral materials hosting magnetic skyrmions beyond room temperature. Nat. Commun. 6, 7638 (2015).

    Article  Google Scholar 

  42. Rechtsman, M. C. et al. Photonic floquet topological insulators. Nature 496, 196–200 (2013).

    Article  Google Scholar 

  43. Beaulieu, S. et al. Attosecond-resolved photoionization of chiral molecules. Science 358, 1288–1294 (2017).

    Article  Google Scholar 

  44. Zipp, L. J., Natan, A. & Bucksbaum, P. H. Probing electron delays in above-threshold ionization. Optica 1, 361–364 (2014).

    Article  Google Scholar 

  45. Ji, J.-B., Heck, S., Han, M. & Wörner, H. J. Quantitative uncertainty determination of phase retrieval in RABBITT. Opt. Express 29, 27732 (2021).

    Article  Google Scholar 

  46. Meyer, M. et al. Two-color experiments in the gas phase at flash. J. Electron Spectrosc. Related Phenomena 181, 111–115 (2010).

    Article  Google Scholar 

Download references

Acknowledgements

M.H. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie grant agreement no. 801459 – FP-RESOMUS. This work was supported by ETH Zürich and the Swiss National Science Foundation through projects 200021_172946 and the NCCR-MUST. M.H. acknowledges fruitful discussions with Joss Wiese.

Author information

Authors and Affiliations

Authors

Contributions

M.H. performed the experiments with the support of J.-B.J. and T.B. M.H., K. U. and H.J.W. analysed and interpreted the data. Simulations were implemented by M.H. H.J.W. conceived the study and supervised its realization. All authors discussed the results and wrote the paper.

Corresponding author

Correspondence to Meng Han.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks Oleg Tolstikhin and Jean Marcel Ngoko Djiokap for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Experimental setup.

See Method section for the detailed description.

Extended Data Fig. 2 Angle-resolved photoelectron-energy spectra from the TDSE simulation in the XUV-only case from the p+, p and p0 orbitals.

(a-c), Results from the p+, p and p0 orbitals, respectively. The right panel shows the corresponding electronic transition and the finally populated state, which can explain the calculated photoelectron angular distributions. For example, from the p orbital the electron will undergo a transition to the d0 state which has three lobes, corresponding to the three maxima in the angular distribution. (d), Energy-integrated photoelectron angular distributions from these three orbitals. The ionization from the p+ orbital is dominant, occupying 70% of the total ionization probability.

Source data

Extended Data Fig. 3 Angle-resolved RABBIT traces and the extracted RABBIT phases of SB12 from the TDSE simulation based on the p and p0 ground-state orbitals.

(a-c), Results from the p orbital. In this case the m of the main peaks created by the XUV photoionization is zero and thus the continuum electron wave packet has no chirality. Therefore, both the sideband yield and phase don’t depend on the helicity of the probe IR. (d-f), Results from the p0 orbital. In this case the m of the main peaks created by the XUV photoionization is 1, and thus the degree of chirality is less than that from the p+ ground-state orbital. Therefore, the CD effects on the sideband yield and phase are decreased compared to those from the p+ orbital shown in Fig. 2g-i, but the basic structures are not changed.

Source data

Extended Data Fig. 4 TDSE simulations on helium atoms.

To illustrate the discrepancy with the previous study [33] on helium atoms, here we performed the TDSE simulations of helium atoms based on the roughly equal parameters. In their study, they used a circularly polarized XUV femtosecond pulse at around 48.4 eV to ionize helium atoms and a circularly polarized IR at 800 nm to probe the electron vortices in the continuum, and they observed the sideband yield in the counter-rotating geometry to be dominant with a CD effect of -6%. To calculate the dichroic RABBIT phase, here we have to use two harmonic orders [H31 (48.05 eV) and H33 (51.15 eV)]. In this single-electron-approximation TDSE simulation, we used the effective potential of helium according to the reference [47]. The electric-field amplitudes of the two harmonics are both equal to 0.0119 a.u., corresponding to an intensity of 1013 W/cm2, and the electric-field amplitude of the IR field is 0.001 a.u.. The spatial step size is reduced to 0.025 a.u. and the temporal step size is reduced to 0.01 a.u.. Other parameters are the same as those described in Methods section. (a, b), Calculated angle-resolved photoelectron energy spectra in co-rotating and counter-rotating geometries, respectively, where the XUV-IR phase delay and the ϕ angle are both integrated over 2π. (c), θ-integrated energy spectra and the corresponding CD spectrum. Note the energy spectra are in the logarithmic scale in order to show the high-order sidebands created by absorbing or releasing two IR photons. The absolute value of our calculated CD of one-IR-photon sidebands is about +7%. Because the electron kinetic energy is much higher than that in our experiments on Argon, the magnitude of the yield CD is decreased. (d, e), Delay- and θ-resolved photoelectron distributions of SB32 in the two geometries. (f), Extracted θ-resolved RABBIT phases from d and e using Fourier transformation. To conclude, the amplitude and phase CDs observed in this study should be qualitatively similar to those of helium atoms.

Source data

Extended Data Fig. 5 Retrieval of partial-wave amplitudes and phases from the measured photoelectron interferogram using global fitting.

(a, b), Measured time-resolved photoelectron angular distributions of SB12 in co-rotating and counter-rotating geometries, which are the enlarged plots of Fig. 1f,g, respectively. (c, d), Reconstructed photoelectron interferograms in the two geometries using global fitting of the three-wave interference model based on the p+ ground state.

Source data

Source Data Fig. 1

Source data for Fig. 1e and Fig. 1h.

Source Data Fig. 2

Source data for Fig. 2c, f and i.

Source Data Fig. 4

Source data for Fig. 4.

Source Data Extended Data Fig. 2

Source data for Extended Data Fig. 2d.

Source Data Extended Data Fig. 3

Source data for Extended Data Fig. 3c and f.

Source Data Extended Data Fig. 4

Source Data for the Extended Data Fig. 4c and f.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Han, M., Ji, JB., Balčiūnas, T. et al. Attosecond circular-dichroism chronoscopy of electron vortices. Nat. Phys. (2022). https://doi.org/10.1038/s41567-022-01832-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1038/s41567-022-01832-4

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing