Correlation-induced phase shifts and time delays in resonance enhanced high harmonic generation from Cr+

Abstract

We investigate resonance-enhanced high harmonic generation (rHHG) in Cr+ by comparing a 1D shape-resonant model, time-dependent density functional theory (TDDFT), and independent particle approximation (IPA) simulations. Previous studies linked rHHG to the 3p -> 3d giant resonance, suggesting a modified four-step model where recolliding electrons are first captured in the autoionizing state before recombining into the ground state, potentially leading to an emission delay associated with the resonance lifetime. While both the 1D-model and TDDFT reproduce experimental spectra, TDDFT reveals that rHHG counterintuitively originates from spin-down 3p states, while spin-up 3d electrons negligibly contribute. The IPA fails to reproduce rHHG, highlighting the significance of electron correlations. Furthermore, TDDFT revealed a correlation induced ~480 attosecond time delay, accompanied by a strong phase shift across the resonance, potentially explaining earlier RABBIT measurements. Our work sheds light on long-standing open questions in rHHG and should advance novel ultrafast spectroscopies of electron correlations and resonances.

Figures (4)

• Figure 1: rHHG from the 1D model. (a) Potential supporting a shape resonance (MS, black). The ground state (blue) and MS (green) densities are plotted in their respective eigen-energies. The vertical axis (energy) is normalized to the driving photon energy. (b) HHG spectra for different barrier widths/MS lifetimes. Curves are normalized to the 27th harmonic. The enhancement coefficient increases with the MS lifetime. (c) (Right) Gabor transform of HHG emission for an MS lifetime of 0.17T (T is the period of the driving laser). Red, purple, and black curves indicate the resonant harmonic energy, the semiclassical cutoff energy, and semiclassical emission times (trajectories), respectively. (Left) Corresponding spectrum. The enhancement of the resonant harmonic H29 is evident in both the spectrum and the Gabor transform. The harmonic emission times are in strong agreement with the semiclassical model.
• Figure 2: rHHG with TDDFT.(a) Energy level configuration in Cr$^{+}$. (b) (Right) Gabor transform of total calculated HHG emission. (Left) Corresponding HHG spectrum. Top and bottom red curves denote the emission time and energy according to the classical trajectories of the 3-step model (low energy curves associated to $3d$ electrons and high energy curves are associated to $3p$ electrons). White lines illustrate the driving field. (c) Same as (a) but for spin-up response, roughly following the semiclassical model for $3d$ electrons. (d) Same as (c) but for spin-down response, where $3p$ spin-down states dominate rHHG (see color scales in (c) and (d)), which is delayed by 250 as relative to spin-up response.
• Figure 3: rHHG within the IPA.(a-c) Same as (b-d) in Fig.\ref{['fig:TDFT_gabor']}. Note the spin-down response on resonance is in-phase with the maxima/minima of the driving field and strongly suppressed, unlike in Fig.\ref{['fig:TDFT_gabor']}.
• Figure 4: rHHG phase and RABBIT analysis.(a) Harmonic phase comparison with varying levels of theory. Yellow and orange curves denote the fully correlated and IPA simulations, respectively. The blue line denotes the group-delay-corrected 1D simulation. Gray dotted lines with dot markers indicate the vertically shifted IPA, while the gray dotted line with $\times$ markers corresponds to the unadjusted 1D result. (b) Observed and expected SB visibility (for SB28 and SB30) for various levels of theory and spin channels. (c) Normalized visibility for both sidebands and various levels of theory. The correlated theory shows strongly reduced normalized visibility, corresponding to the strong phase jump in (a).