Quantum-Path-Resolved Attosecond High-Harmonic Spectroscopy

Strong-field ionization of molecules releases electrons which can be accelerated and driven back to recombine with their parent ion, emitting high-order harmonics. This ionization also initiates attosecond electronic and vibrational dynamics in the ion, evolving during the electron travel in the continuum. Revealing this subcycle dynamics from the emitted radiation usually requires advanced theoretical modeling. We show that this can be avoided by resolving the emission from two families of electronic quantum paths in the generation process. The corresponding electrons have the same kinetic energy, and thus the same structural sensitivity, but differ by the travel time between ionization and recombination—the pump-probe delay in this attosecond self-probing scheme. We measure the harmonic amplitude and phase in aligned ${\mathrm{CO}}_2$ and ${\mathrm{N}}_2$ molecules and observe a strong influence of laser-induced dynamics on two characteristic spectroscopic features: a shape resonance and multichannel interference. This quantum-path-resolved spectroscopy thus opens wide prospects for the investigation of ultrafast ionic dynamics, such as charge migration.

Figure 1

(a) Spatially resolved harmonic spectrum produced by two sources in ${\mathrm{N}}_2$ at $\sim 1.5\times {10}^{14}\mathrm{W}{\mathrm{cm}}^{-2}$. One XUV source is generated in unaligned ${\mathrm{N}}_2$ while the other is produced from ${\mathrm{N}}_2$ molecules aligned at 54° from the probe polarization. The gray and red lines mark out the short and long QP contributions. (b) Calculated ionization (solid) and recombination (dashed) times for short (gray, circles) and long (red) QPs within the strong field approximation. The schematic drawing illustrates the resolution of attosecond dynamics by different QPs. An electron tunnels out from an orbital, triggering ultrafast hole dynamics in the ion. The ion has not evolved much during the short travel time of the short QP and the electron recombines to the same orbital. For the long QP, the ionic state has changed and the electron recombines to a different orbital.

Figure 2

Intensity (a), (b) and phase (c), (d) of the short (a), (c) and long (b), (d) QP contributions to high-harmonic generation in aligned ${\mathrm{N}}_2$. (e) Calculated modulus square and (f) phase of the molecular-frame scattering-wave recombination dipole matrix element to the $X$ channel.

Figure 3

Quantum-path-resolved high-harmonic spectroscopy in ${\mathrm{CO}}_2$. Amplitude for short (a) and long (b) QPs and phase evolution for short (c) and long (d) QPs.