High-Harmonic Generation Enhanced by Dynamical Electron Correlation

We theoretically study multielectron effects in high-harmonic generation (HHG), using all-electron first-principles simulations for a one-dimensional model atom. In addition to the usual plateau and cutoff (from a cation in the present case, since the neutral is immediately ionized), we find a prominent resonance peak far above the plateau and a second plateau extended beyond the first cutoff. These features originate from the dication response enhanced by orders of magnitude due to the action of the Coulomb force from the rescattering electron, and, hence, are a clear manifestation of electron correlation. Although the present simulations are done in 1D, the physical mechanism underlying the dramatic enhancement is expected to hold also for three-dimensional real systems. This will provide new possibilities to explore dynamical electron correlation in intense laser fields using HHG, which is usually considered to be of single-electron nature in most cases.

Figure 1

Pictorial explanation of orbital subspace decompositions for Be used in this study. (a) MCTDHF (0, 0, 10) with ten active orbitals, considered to be the most accurate, (b) CASSCF (0, 1, 9) with one DC and nine active orbitals, and (c) CASSCF (1, 0, 9) with one FC and nine active orbitals.

Figure 2

High-harmonic spectra from a 1D Be model atom calculated with three different subspace decompositions depicted in Fig. 1.

Figure 3

Charge-state-resolved harmonic spectra extracted from the simulation starting from neutral Be and calculated as the squared magnitude of the Fourier transform of Eq. (4). The total HHG spectrum (the same as the red curve in Fig. 2) is also shown.

Figure 4

(a) High-harmonic spectra from 1D Be (thick solid red), ${\mathrm{Be}}^{+}$ (thick dotted black), and ${\mathrm{Be}}^{2+}$ (dotted blue), respectively, calculated with the MCTDHF methods with ten orbitals. The spectrum from ${\mathrm{Be}}^{2+}$ in the field of the rescattering electron Eq. (5) is also shown (thin dashed green). Note that simulations have been started with Be, ${\mathrm{Be}}^{+}$, and ${\mathrm{Be}}^{2+}$, respectively, as an initial state. The thick solid red curve (Be) is the same as that in Fig. 2 and the thick solid black curve in Fig. 3. (b) Excitation spectra of 1D Be, ${\mathrm{Be}}^{+}$, and ${\mathrm{Be}}^{2+}$, respectively, calculated through excitation by a quasi-delta-function pulse. The highest peak is located at 30.6 eV and corresponds to the first excited state of 1D ${\mathrm{Be}}^{2+}$. The gray vertical dashed line indicates the position of 30.6 eV.

Figure 5

Time-frequency analysis, or Gabor transform with a temporal window size of 0.095 cycle, of HHG from ${\mathrm{Be}}^{+}$ by a $5.2\times 10^{14}\mathrm{W}/{\mathrm{cm}}^2$ flattop pulse with a half-cycle ramp-on. Horizontal dash-dotted line: position of 30.6 eV. Dotted (dashed) curves: classically calculated kinetic energies of the returning electrons plus 1.32 times the ionization energy of ${\mathrm{Be}}^{+}$ (${\mathrm{Be}}^{2+}$). Note that we use factor 1.32 to take account of the upward shift due to finite distance between the origin and tunnel exit [35, 36].