Direct measurement of Coulomb-laser coupling

Abstract

The Coulomb interaction between a photoelectron and its parent ion plays an important role in a large range of light-matter interactions. In this paper we obtain a direct insight into the Coulomb interaction and resolve, for the first time, the phase accumulated by the laser-driven electron as it interacts with the Coulomb potential. Applying extreme-ultraviolet interferometry enables us to resolve this phase with attosecond precision over a large energy range. Our findings identify a strong laser-Coulomb coupling, going beyond the standard recollision picture within the strong-field framework. Transformation of the results to the time domain reveals Coulomb-induced delays of the electrons along their trajectories, which vary by tens of attoseconds with the laser field intensity.

Figure 1

Differential phase measurement using XUV-XUV interferometry. (a) Experimental scheme. A delay controlled APT (black) and its generating annular IR pulse (red) are focused into a gas target, where a second phase-locked and independent APT (purple) is generated by the same IR pulse. The interference signal between the two APTs as a function of delay is spectrally resolved and recorded in the far-field for a range of IR intensities, controlled by a motorized iris. (b) Fourier amplitudes of an interference signal extracted from a delay scan where argon is used in both sources. Harmonics 11 to 23 oscillate at their fundamental frequency. (c) Schematic description of the phase accumulated during the HHG process. The phase of the emitted XUV photon encodes all the steps of the HHG interaction: strong-field tunneling and acceleration ${\varphi }^{\mathrm{SF}}$ and the dipole transition phase ${\varphi }^{\mathrm{D}}$ at recollision. In addition, the electron accumulates phase ${\varphi }^{\mathrm{C}}$ as it interacts with the ionic Coulomb potential. Changing the IR intensity leads to a variation of the electron trajectory, as indicated by the red and blue lines for higher and lower intensity, respectively. As a result, both ${\varphi }^{\mathrm{SF}}$ and ${\varphi }^{\mathrm{C}}$ are modified, while ${\varphi }^{\mathrm{D}}$ remains unchanged.

Figure 2

Differential phase measurements of the XUV phase. (a,b) Measured (circles) and calculated (lines) $\mathrm{\Delta }\varphi (\mathrm{\Omega },\mathrm{\Delta }I)$ for argon (a) and nitrogen (b) at harmonics 11–23. For both targets, the reference intensity $I_0$ is $1.46\times {10}^{14}{\mathrm{W}\mathrm{cm}}^{-2}$. The dashed lines represent the uncertainty in the IR intensity.

Figure 3

Differential phase measurements of the Coulomb phase. (a,b) Measured (black symbols) and calculated (red lines) Coulomb phase as a function of intensity variation in argon (a) and nitrogen (b). In both the measurements and the calculations, we subtract the strong-field phase from the phases presented in Fig. 2a,b.

Figure 4

Coulomb time delays. Measured (circles) and calculated (lines) Coulomb induced delays as a function of intensity variation, extracted for electrons with a final kinetic energy of approximately 3 eV, in argon (black) and nitrogen (blue).

Figure 5

Schematic description of the XUV–XUV interferometer. For a detailed description see the text.

Figure 6

Measurement of the Gouy phase variation. (a) Experimental scheme. By turning off the reference HHG source and removing the Al filter, we induce an interference between the inner and outer parts of the IR beam. Scanning the relative delay leads to oscillations of the HHG signal at the target gas nozzle with the IR frequency ${\omega }_{\mathrm{IR}}$. Varying the iris affects only the outer part of the IR beam, which enables us to determine the Gouy phase shift as a function of iris size from the Fourier analysis of the HHG signal oscillations. (b) Experimental Gouy phase variation as a function of the intensity variation $\mathrm{\Delta }I$. The black line represents a linear fit to the experimental data (red points).