Magnetic-Field Effect in High-Order Above-Threshold Ionization

We experimentally and theoretically investigate the influence of the magnetic component of an electromagnetic field on high-order above-threshold ionization of xenon atoms driven by ultrashort femtosecond laser pulses. The nondipole shift of the electron momentum distribution along the light-propagation direction for high energy electrons beyond the $2U_p$ classical cutoff is found to be vastly different from that below this cutoff, where $U_p$ is the ponderomotive potential of the driving laser field. A local minimum structure in the momentum dependence of the nondipole shift above the cutoff is identified for the first time. With the help of classical and quantum-orbit analysis, we show that large-angle rescattering of the electrons strongly alters the partitioning of the photon momentum between electron and ion. The sensitivity of the observed nondipole shift to the electronic structure of the target atom is confirmed by three-dimensional time-dependent Schrödinger equation simulations for different model potentials. Our work paves the way toward understanding the physics of extreme light-matter interactions at long wavelengths and high electron kinetic energies.

Figure 1

Schematic diagram of the experimental setup. Two counterpropagating femtosecond laser beams, termed as pathway $A$ and $B$, respectively, are focused onto the same spot of a supersonic gas jet inside the ultrahigh vacuum chamber of a COLTRIMS reaction microscope that allows for the measurement of electron and ion momenta in coincidence. By toggling between the two counterpropagating pathways of $A$ and $B$, the systematic error along the light-propagation direction can be minimized.

Figure 2

Nondipole effects in strong-field ionization of xenon atoms (linear polarization, $7\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$, 800 nm, 25 fs). (a) Experimentally measured two-dimensional momentum distribution in the plane formed by polarization axis ($z$ axis) and light-propagation direction ($x$ axis). (b) One-dimensional momentum distribution along the polarization axis, where a plateau structure is typical for high-order above-threshold ionization (HATI). (c) Peak electron momentum in the light-propagation direction $p_x$ as a function of the momentum along the polarization axis $p_z$. The error bars show statistical errors. The TDSE result calculated for the Tong-Lin potential [39, 40] is averaged over the carrier-envelope phase as well as the focal intensity distribution assuming a peak intensity of $7\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 3

Results of the classical and quantum-orbit analysis. (a) Momentum-shift estimate from the classical backreflection model and low-frequency approximation (LFA) for electrons scattered by 180°. (b) Probabilities of quantum orbits with final momentum $p_x=0$ in LFA. In (a) and (b), the results for the long and short trajectories are shown as solid and dashed lines for an intensity of $6\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$. (c) Focal-volume-averaged LFA result calculated with the differential cross section for the Tong-Lin potential including both long and short orbits (green line) and the experimental result (blue line).

Figure 4

Model potential dependence of the nondipole shift. Presented are TDSE calculations for three different single-active-electron potentials for xenon: Tong-Lin potential, see [39] (model potential 1); Green-Sellin-Zachor (GSZ) potential, see [39, 50] (model potential 2); and the effective potential $V(r)=-(Z+a_1{e}^{-a_{2}r})/r$, where $Z=1$, $a_1=1.985$, $a_2=0.5$ (model potential 3). Here, the results are averaged over the carrier-envelope phase, but only a single intensity of $6\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ is used.