Spectral signature of back reaction in correlated electron dynamics in intense electromagnetic fields

Few-electron atoms interacting with electromagnetic fields provide for privileged scenarios for disentangling elemental correlation mechanisms. We demonstrate that high-order harmonic generation (HHG) from neutral helium presents a distinctive trace of correlation back reaction in the electron dynamics prior to ionization. We identify a mechanism in which the field interacts with one of the electrons, while the second is excited to a Rydberg level through the Coulomb interaction. As back response to this correlated excitation, the first electron is knocked down to a lower level, from which it ionizes to generate high-order harmonics. Unlike other multielectron phenomena, where the electron-field interaction is modified by cross correlations with the rest of the interacting electrons, back reaction is a mechanism of autocorrelation. Our numerical simulations reveal back reaction as a relevant aspect in HHG from correlated two-electron systems, and paves the way to disentangle valence electron-electron correlation dynamics using high-harmonic spectroscopy.

Figure 1

(a) High-order harmonic spectrum from He considering two active electrons (He TAE, solid black line), a single active electron (He SAE, solid yellow line), and the exact description of ${\mathrm{He}}^{+}$ (${\mathrm{He}}^{+}$, dash-dotted purple line). (b), (c) Time-frequency analysis of the HHG results from the TAE and SAE descriptions, respectively. The cutoff frequencies in the different cases are indicated with dotted lines. A high-energy secondary plateau emerges in the TAE calculations.

Figure 2

Fraction of the high-harmonic emission from the two active electron (TAE) He, shown in Fig. 1, corresponding to the neutral He (blue area) and ${\mathrm{He}}^{+}$ (yellow area) contributions. The total He TAE harmonic spectrum is shown for reference as a solid black line. Vertical dotted lines indicate the cutoff frequencies also shown in Fig. 1. The inset shows the regions of the two-electron coordinate space associated with the neutral atom (blue area) and the cation (yellow area).

Figure 3

High-order harmonic spectrum obtained from the idle electron model (He IDL, green area) compared to the exact two-electron description (He TAE, black solid line). The cutoff frequencies are indicated with vertical dotted lines.

Figure 4

(a) Relative strength of the atomic dipole excitations in the interaction with the laser pulse. (b) Energy levels of the neutral He and ${\mathrm{He}}^{+}$ cation. (c) Blue line: Energy of the ground electron as a function of the position of the Rydberg electron; green line: probability density profile of electron 2, assuming electron 1 located at $x_1=0, |{\varphi }_A(0,x_2){|}^2$. (d) Scheme of the correlated back-reaction mechanism previous to tunnel ionization: one electron is excited to a Rydberg level by correlation interaction (i), whereas the other is knocked down to a deeper level (ii). Finally this latter is ionized, leading to HHG (iii).

Figure 5

High-order harmonic spectrum from He considering two active electrons (He TAE, solid black line), a single active electron (He SAE, solid yellow line), the SAE description of ${\mathrm{He}}^{+}$ (${\mathrm{He}}^{+}$, dashed purple line), and the contribution from ${\mathrm{He}}^{+}$ calculated in the TAE model (dashed orange line). We choose a central wavelength of 515 nm and two different peak intensities: (a) $5.0\times {10}^{14}$ W/${\mathrm{cm}}^2$ and (b) $1.0\times {10}^{15}$ W/${\mathrm{cm}}^2$.

Figure 6

High-order harmonic spectrum from He, considering two active electrons (He TAE, solid black line), a single active electron (He SAE, solid yellow line), the SAE description of ${\mathrm{He}}^{+}$ (${\mathrm{He}}^{+}$, dashed purple line), and the contribution from ${\mathrm{He}}^{+}$ calculated in the TAE model (dashed orange line) at peak intensity $2.8\times {10}^{14}$ W/${\mathrm{cm}}^2$ and wavelengths (a) 1030 nm, (b) 800 nm, (c) 515 nm, and (d) 400 nm.

Figure 7

(a) High-order harmonic spectrum from He in a driving field with a ${\sin }^2$ envelope considering two active electrons (He TAE, solid black line), a single active electron (He SAE, solid yellow line), the SAE description of ${\mathrm{He}}^{+}$ (${\mathrm{He}}^{+}$, dashed purple line), and the contribution from ${\mathrm{He}}^{+}$ calculated in the TAE model (dashed orange line). Time-frequency analyses in TAE (b) and SAE (c) calculations are also shown.