Revealing quantum path details in high-field physics

The fundamental mechanism underlying harmonic emission in the strong-field regime is governed by tunnel ionization of the atom, followed by the motion of the electron wave packet in the continuum, and finally by its recollision with the atomic core. Due to the quantum nature of the process, the properties of the electron wave packet strongly correlate with those of the emitted radiation. Here, by spatially resolving the interference pattern generated by overlapping the harmonic radiation emitted by different interfering electron quantum paths, we have succeeded in unravelling the intricacies associated with the recollision process. This has been achieved by mapping the spatial extreme-ultraviolet (EUV)-intensity distribution onto a spatial ion distribution, produced in the EUV focal area through the linear and nonlinear processes of atoms. By in situ manipulation of the intensity-dependent motion of the electron wave packets, we have been able to directly measure the difference between the harmonic emission times and electron path lengths resulting from different electron trajectories. Due to the high degree of accuracy that the present approach provides, we have been able to demonstrate the quantum nature of the recollision process. This is done by quantitatively correlating the photoemission time and the electron quantum path-length differences, taking into account the energy-momentum transfer from the driving laser field into the system. This information paves the way for electron-photon correlation studies at the attosecond time scale, while it puts the recollision process from the semiclassical prospective into a full quantum-mechanical context.

Figure 1

(a) Experimental setup used for imaging the EUV focus interference pattern. L: IR focusing lens. P-GJ: Harmonic production gas jet filled with xenon. A: Aperture. F: Thin metal filter. SM: Gold spherical mirror. T-GJ: Target gas jet filled with argon. I-ID: Ion imaging detector. (b) The dependence of the harmonic signal on $I_{\ell }$. The harmonic signal has been recorded up to $I_{\ell }$ values at which all the harmonics are in the plateau region. The vertical black lines depict the harmonic cutoff regions. (c) Typical harmonic spectrum recorded at $I_{\ell }$ ≈ 7 × 10${}^{13}$ W/${\mathrm{cm}}^2$. (d) Beam profile of the 11th harmonic on the surface of the gold spherical mirror determined by means of the knife-edge technique. The beam profile and the diameter of the 13th and 15th harmonics [for simplicity, not shown in (d)] are approximately the same with the 11th.

Figure 2

Spatial imaging the interference pattern created at the focus of the EUV beam. (a) Calculated profiles of the 11th, 13th, and 15th harmonics on the surface of the EUV focusing mirror, at $I_{\ell }$ = $I_{\max }$ = 10${}^{14}$ W/${\mathrm{cm}}^2$. (b), (c) Calculated images of the focused EUV beam for two different values of the drive laser intensity $I_{\ell }$, for both of which the harmonics are lying on the plateau spectral region having approximately equal relative amplitudes [see Fig. 1]. At these intensities the phase distribution of the EUV beam leads to on-axis $\left(z\right)$ (b) destructive and (c) constructive interference at the focus position with a double- and single-peak structure, respectively. (d), (e) EUV focus images produced by the single-photon ionization signal of argon at two different drive-laser intensities $I_{\ell }$. The relative amplitudes of the harmonics in the interaction region were approximately equal for both images [see Fig. 1]. The red lines are the 30-point running average of the raw data and the error bars represent one standard deviation of the mean. 600 shots were accumulated for each image.

Figure 3

Imaging the intensity-dependent spatial EUV interference pattern. (a) Contour plot showing the dependence of the interference pattern along the $z$ axis on $I_{\ell }$. The relative amplitudes of the 11th, 13th, and 15th harmonics in the interaction region are shown in Fig. 1. (b) Contour plot retrieved after normalization of the plot in (a) to equal ion-signal amplitudes. The black line depicts the mean value of the ion distribution. The error bars represent the standard deviation of the mean value resulting by taking into account the accuracy of the laser intensity measurement. (c) Calculated (and normalized) contour plot showing the dependence of the $z$-axis interference pattern on $I_{\ell }$. Although the “saw-type” structure and the position of the maxima on the $z$ axis are in fair agreement with the measured values, this calculation is based on rough assumptions (e.g., single-atom response, flat spatial harmonic phase distributions) and is only meant to provide a qualitative description of the data.

Figure 4

Measurement of harmonic emission time and electron path-length differences. (a) High-order-harmonic generation mechanism shown in the spirit of the “three-step model” [18, 20, 21]. The IR field suppresses the atomic potential and allows the valence electron to tunnel through. The electron moves almost freely in the driving field, gaining kinetic energy, which is converted to photons upon its recombination. Due to the different electron trajectories, the harmonic emission times are different. $t_e^S$ and $t_e^L$ correspond to the harmonic emission times resulting from the “short” and “long” trajectories, respectively. (b) Measured phase difference between the “short” and “long” trajectories as a function of $I_{\ell }$. (c) Difference between the emission times $\Delta t_e=t_e^S-t_e^L$. (d) Path-length difference $\Delta L_e$ normalized by the de Broglie electron wave λ${}_e$. For emission time differences $\Delta t_e^{}\approx n{T}_q/2$,the electron quantum path differences are changing by $\Delta L_e\approx n{\lambda }_e$. (e) Difference between the consecutive values of $f\left(I_{\ell }\right)$. In all graphs, the vertical black dotted lines depict the harmonic cutoff regions at which the 2-IR-photon absorption increases the electron momentum by $2\hslash k_{\ell }$ and the error bars represent one standard deviation of the mean value.