Attosecond Real-Time Observation of Recolliding Electron Trajectories in Helium at Low Laser Intensities

Laser-driven recollision physics is typically accessible only at field intensities high enough for tunnel ionization. Using an extreme ultraviolet pulse for ionization and a near-infrared (NIR) pulse for driving of the electron wave packet lifts this limitation. This allows us to study recollisions for a broad range of NIR intensities with transient absorption spectroscopy, making use of the reconstruction of the time-dependent dipole moment. Comparing recollision dynamics with linear vs circular NIR polarization, we find a parameter space, where the latter favors recollisions, providing evidence for the so far only theoretically predicted recolliding periodic orbits.

Figure 1

Schematic of the measurement principle. (a) Illustration of the mechanism. The spatial representation of an electronic ground-state wave function (blue) is depicted in a Coulomb potential together with the XUV-produced excited wave packet (green) illustrated at two moments in time. The intensity of the green color scale along the NIR-driven trajectory illustrates the absolute dipole moment to the ground state. (b) Experimentally, an XUV (purple) and an NIR (red) pulse are focused into a helium gas target. The NIR pulse can be tuned in delay ($\tau$) and intensity ($I$) with linear (LP) or circular polarization. The initial XUV field together with the dipole response of the system are analyzed in a grating spectrometer. The green shading illustrates the amplitude of the dipole response (not to scale). (c) The measured spectrum at the ionization edge is depicted in purple. The dashed curve is the spectrum without NIR interaction. By restricting to the relevant energy window (shown in pink), the amplitude modulation of the dipole moment shown in (d) is retrieved by a Fourier transform [Eq. (2)]. The dipole without NIR interaction is subtracted for better visibility.

Figure 2

1D TDSE simulation results showing recollison features. (a) The time evolution of the NIR-introduced changes $\mathrm{\Delta }|\psi |$ of a wave function triggered by an XUV pulse. The 5 fs FWHM NIR pulse with an intensity of $4.3\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ is delayed by 2 fs with respect to the XUV. The left panel shows the time-dependent dipole response difference between the NIR-driven and XUV-only case filtered by the window function. The white dashed line corresponds to a classical trajectory with 0.4 eV initial energy. It agrees with the local maxima of the electron probability distribution (dark red regions). (b) Absorbance spectra in the continuum calculated out of the dipole moment with and without the subsequent NIR pulse. The purple shaded area indicates the spectrum of the initial XUV pulse, which is identical with the window used for the dipole reconstruction. (c) The reconstructed absolute dipole moment calculated from the absorption spectrum according to Eq. (2). The times of local maxima $t_i$ are marked with dotted black lines. They are also illustrated in panel (a), partly replaced by a cross at the origin for better visibility.

Figure 3

(a) Difference between CP and LP of the time-dependent absolute dipole moment as a function of intensity from experiments. The first two experimental data points are grayed to account for the reconstruction error due to the finite XUV pulse duration. (b) Difference between CP and LP recollision probabilities as a function of recollision time and NIR intensity from CTMC simulations. The probabilities are weighted by the recollision angle ${\cos }^2\alpha$, which takes into account that experimentally only the recollisions that happen in the same direction as the XUV polarization are observed. The time delay is $\tau =7\mathrm{fs}$. Note the prominent red feature in both panels that is caused by enhanced recollisions for CP light. Between the gray dotted lines recolliding periodic orbits are predicted by theory for all considered recollision energies.

Figure 4

Exemplary recolliding trajectories in the rotating frame for intensity $I={10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ and time delay $\tau =7\mathrm{fs}$. Solid and dashed curves correspond to the trajectory before and after recollision, respectively. The red curves are RPOs associated with the respective recollision energy. The time of recollision $t_c$ is indicated.