Extended Data Fig. 4: TDSE simulations on helium atoms.
From: Attosecond circular-dichroism chronoscopy of electron vortices
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.
