Superelastic rescattering in single ionization of helium in strong laser fields

Rescattering is a central process in ultrafast physics, in which an electron, freed from an atom and accelerated by a laser field, loses its energy by producing high-order harmonics or multiple ionization. Here, taking helium as a prototypical atom, we demonstrate numerically superelastic rescattering in single ionization of an atom. In this scenario, the absorption of a high-energy extreme ultraviolet photon leads to emission of one electron and excitation of the second one into its first excited state, forming ${\mathrm{He}}^{+*}$. A time-delayed midinfrared laser pulse accelerates the freed electron, drives it back to the ${\mathrm{He}}^{+*}$, and induces the transition of the bound electron to the ground state of the ion. Identification of the superelastic rescattering process in the photoelectron momentum spectra provides a means to determine the photoelectron momentum at the time of rescattering without using any information of the time-delayed probe laser pulse.

Figure 1

Schematic energy-level diagram of the model He atom. The EUV pulse simultaneously ionizes one electron and excites the other one, producing ${\mathrm{He}}^{+}$ in the $n=2$ state. The time-delayed MIR pulse drives the free electron back to ${\mathrm{He}}^{+} \left(n=2\right)$ and extracts the energy stored in ${\mathrm{He}}^{+}(n=2)$ by deexciting the second electron to the ground state of the ion.

Figure 2

(a) The wave-function distribution in a logarithmic scale after the EUV pulse is terminated. (b) The photoelectron momentum spectrum associated with the single ionization of a helium atom. The inset in (a) is a zoom of the single-ionization region marked by the ellipse. The EUV intensity and frequency were ${10}^{16}$ W/${\mathrm{cm}}^2$ and ${\omega }_E=2.2$ a.u.

Figure 3

(a) The superimposed EUV and MIR fields (blue solid curve) and a typical electron trajectory (red dashed curve). $t_{r1}$ and $t_{r2}$ represent two rescattering instants obtained by solving the Newton equation without including the Coulomb potential. (b) The wave-function distribution at $t=110$ a.u. (half a MIR cycle). (c) The canonical momentum spectrum for the single ionization at $t=110$ a.u. The time delay between the EUV and MIR pulses is 220 a.u. (one full MIR cycle).

Figure 4

The rescattering momentum $p_k\left(t_{r1}\right)$ (upper row) and rescattering timing $t_{r1}$ (lower row) as a function of the time delay at ${\omega }_E=2.2$ a.u. (left column) and the EUV frequency at $\mathrm{\Delta }t=220$ a.u. (right column). The red dashed and black solid curves are obtained from classical calculations and the TDSE simulations, respectively.