Quantum interference and multielectron effects in high-harmonic spectra of polar molecules

We experimentally and theoretically analyze the manifestations of quantum interference and multiple ionization channels (multiple orbitals) in high-harmonic spectra of aligned N${}_2$O molecules. Increasing the probe wavelength from 1.17 to 1.46 $\mu$m, we demonstrate the gradual disappearance of multielectron effects and quantitatively explain the observation through calculations. We thus identify a minimum in the high-harmonic spectrum of N${}_2$O caused only by its structure. By comparing its position with that measured in the isoelectronic CO${}_2$ molecule for similar axis distributions, we find a difference of 10 eV, confirmed by ab initio quantum scattering calculations. Quantum interference in photorecombination is thus shown to be sensitive to subtle differences in the valence orbital structure of molecules with nearly identical lengths. This property may find applications in time-resolved studies.

Figure 1

High-harmonic spectra generated in transiently aligned N${}_2$O molecules with 40–50 fs laser pulses of central wavelengths 1.17 $\mu$m (a), 1.36 $\mu$m (b), and 1.46 $\mu$m (c) and a range of intensities indicated in the legends. The spectra recorded at the lowest intensity in each panel are indicated by a thin dark green (gray) line, and the highest by a thick dark blue (gray) line. The arrows indicate the positions of the observed minima.

Figure 2

(a) HOMO and HOMO-1 orbitals of N${}_2$O from a HF calculation using a cc-pVTZ basis set. (b) Angular variation of the strong-field ionization rates of the HOMO (solid line) and HOMO-1 (dashed line) orbitals calculated for an intensity of $1.0\times {10}^{14}$ W/cm${}^2$. (c) Photoionization cross sections of HOMO (top panel) and HOMO-1 (bottom panel) as a function of the emitted photon energy and the electron emission angle $\alpha$ in the molecular frame. (d), (e) Calculated squared amplitude (solid line) and phase (dashed line) of the induced dipole moment for recombination from a single side of the molecule, using a typical axis distribution characterized by $\langle {\cos }^2\theta \rangle =0.60$.

Figure 3

Calculated high-harmonic spectra including the HOMO and HOMO-1 channels using the quantities shown in Fig. 2 and calculated photoelectron wave packets. Wavelengths, intensities, and pulse durations are chosen according to the experimental conditions of Fig. 1. The spectra recorded at the lowest intensity in each panel are indicated by a thin dark green (gray) line, and the highest by a thick dark blue (gray) line. The degree of axis alignment ($\langle {\cos }^2\theta \rangle$) has been slightly adjusted to reproduce the experimental spectra and is indicated in each panel.

Figure 4

(a) Experimental high-harmonic spectra recorded under identical conditions with a driving wavelength of 1.46 $\mu$m. The positions of the minima are highlighted using a smoothed replica of the spectra. (b) Calculated maximal degrees of axis alignment for N${}_2$O [thick blue (gray) line] and CO${}_2$ [thin green (gray) line] for $T_{\mathrm{rot}}=40$ K impulsively aligned by a 120-fs pulse. (c) Calculated spectra with adjusted degrees of axis alignment given in the legend. (d) Calculated spectra using the same axis distribution for both molecules. (e) HOMOs of N${}_2$O and CO${}_2$. (f) Spectral envelope of the high-harmonic emission from the HOMO channel only of N${}_2$O (solid line) and CO${}_2$ (dashed line), assuming an energy-independent photoelectron wave-packet amplitude [$a_{ewp}\left(\Omega \right)=1$].