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Attosecond circular-dichroism chronoscopy of electron vortices


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.

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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.

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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.


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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.

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Authors and Affiliations



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.

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The authors declare no competing interests.

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

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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.

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Han, M., Ji, JB., Balčiūnas, T. et al. Attosecond circular-dichroism chronoscopy of electron vortices. Nat. Phys. 19, 230–236 (2023).

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