Revealing the Microscopic Real-Space Excursion of a Laser-Driven Electron

High-order harmonic spectroscopy allows one to extract information on fundamental quantum processes, such as the exit time in the tunneling of an electron through a barrier with attosecond time resolution and molecular structure with angstrom spatial resolution. Here, we study the spatial motion of the electron during high-order harmonic generation in an in situ pump-probe measurement using high-density liquid water droplets as a target. We show that molecules adjacent to the emitting electron-ion pair can disrupt the electron’s trajectory when positioned within the range of the maximum electronic excursion distance. This allows us to use the parent ion and the neighboring molecules as boundaries for the electronic motion to measure the maximum electronic excursion distance during the high-order harmonic generation process. Our analysis of the process is relevant for optimizing high-harmonic yields in dense media.

Popular Summary

Coherent radiation in the extreme ultraviolet spectral domain can be applied to reveal phenomena with attosecond-level temporal resolution and angstrom-level spatial resolution. This type of radiation is therefore an excellent tool for studying not only fundamental physical processes but also chemical and biological processes with unprecedented precision. Here, we study the underlying mechanics that result in attosecond pulses: high-order harmonic generation.

High-order harmonic generation can be described by a semiclassical three-step model. First, an intense laser field tunnel ionizes a molecule, releasing an electron into the continuum. Second, the electron is accelerated by the electric field, making an excursion that can be described by a classical trajectory. Finally, the electron recombines with its parent ion by emitting a high-energy photon. While the first and the last steps are objects of recent pioneering investigations in high-order harmonic spectroscopy and attosecond science, the electronic excursion in real space has not thus far been investigated in detail. In this study, we inject a 15-$\mu m$-diameter liquid water droplet into a vacuum; this droplet is used as a target for high-order harmonic generation in an in situ pump-probe setup that allows us to modulate the density of the target by over 6 orders of magnitude. Increasing the density (and therefore reducing the mean interparticle distance in the target) can cause a collision of the free electron with an adjacent molecule and accordingly a decrement in the extreme-ultraviolet emission. We focus on determining the relative proximity of an ion and a molecule to induce a perturbation in the electron’s trajectory. This process allows us to use the parent ion and the neighboring molecules as boundaries for the electronic motion, thereby using the high-order harmonic generating medium itself to measure the maximum electronic excursion distance in situ.

We expect that our findings will pave the way for additional experimental studies of the attosecond dynamics of atoms and molecules.

Figure 1

Determination of the maximum tolerable target density for HHG. (a) Calculated electron trajectories during HHG. Depending on the time of ionization by the electric field (solid red line), different quantum paths contribute to the HHG process, such as the short (dotted blue line), the cutoff (solid blue line), and the long trajectory (dashed red line). Different trajectories may result in the same photon energy, but can be distinguished by the time spent within the continuum and by the maximum displacement of the electron $x_{\max }$. (b) Calculated range of maximum electron displacement as a function of harmonic order. The blue solid line indicates the displacement along the cutoff trajectory. As the driving intensity increases, the maximum excursion of the electron contributing to a fixed harmonic order decreases (color scale) since the harmonic shifts from the cutoff into the plateau region, and the process occurs via the short quantum path. (c) Mean interparticle distance versus target density (solid red line). Comparing (b) and (c) allows us to determine the maximum tolerable density of the target, upon which a perturbation of electronic trajectories sets in and the HHG process is suppressed. Depending on the trajectory, two values are obtained: ${\rho }_c$ (dashed black arrow exemplarily for the 21st order) for the cutoff, and a lower, intensity-dependent value for the short trajectory ${\rho }_s$ (dashed red arrow).

Figure 2

Schematic illustration of the experimental setup. Two intense, time-delayed laser pulses interact with a liquid droplet in the vacuum. While the first pulse (pump) makes the droplet expand via laser-induced optical breakdown, the second pulse (probe) generates harmonic radiation. Depending on the time delay between the pulses, different densities of the target are accessible for HHG. (a) Different intensities lead to different electronic excursions, such that the electron can be perturbed by surrounding molecules. (b),(c) For a fixed intensity of the probe pulse, this gives access to probe the electronic excursion by increasing the target’s density and detecting the harmonic yield. At high densities, the mean interparticle distance of the target’s components matches the electronic excursion during HHG, which allows us to induce a perturbation to the quantum paths and (d) results in a decreasing harmonic signal as a function of the density.

Figure 3

Observing the perturbation of electronic trajectories. (a) Spectra of the harmonic radiation for different densities of the target. (b)–(d) Density-mapped harmonic radiation of the 19th, 21st, and 27th order, respectively (blue dots). The signal increases for low densities. A loss in the signal of the harmonic radiation is observed for increasing density due to a higher probability of a perturbation of the electronic trajectory by an adjacent molecule. The measured data are compared with a calculation of the harmonic signal as a function of the density for two cases: including (blue line) and excluding (gray line) a perturbation of electronic trajectories. All trajectories are perturbed for densities ${\rho }_s$ corresponding to the excursion distance of the short trajectory, and no harmonic radiation is emitted (red area). Since $x_{\max }$ increases as a function of the harmonic order, ${\rho }_s$ shifts towards lower values with increasing harmonic order.

Figure 4

Controlling the electronic excursion with the driving intensity. (a) Spectra of harmonic radiation as a function of the intensity of the probe pulse for a fixed density of the target. No harmonic radiation is observed within the red area, where the electronic displacement is larger than the mean interparticle distance. The displacement is reduced with increasing intensity, and the emission process turns from incoherent to coherent. (b) Signal of the 29th harmonic order as a function of the target density and the intensity of the driving pulse. A perturbation of the trajectories becomes more probable for densities higher than the position of the maximum in intensity. Again, no harmonic radiation is detected for densities and intensities where the electronic excursion matches the mean interparticle distance assigned to the short trajectory ($\rho >{\rho }_s$, dashed red line).