Quantum effect of laser-induced rescattering from the tunneling barrier

Rescattering mediated by intense laser fields is one of the dominant processes in strong-field physics. It was usually described classically or semiclassically. Recently, laser-induced recollisions with the tunneling barriers have attracted great theoretical interest. However, fully distinguishing the “quantum” effect of rescattering with the tunneling barrier on photoelectron energy and momentum distributions is very difficult if using the linearly polarized light field. Here we perform the measurement of photoelectron momentum distributions by strong-field ionization of Ar atoms in orthogonally polarized two-color laser fields with comparable intensities. We observe the strong ionization enhancement due to rescattering on two-dimensional momentum distribution, which is in striking disagreement with the predictions by the plain strong-field approximation and the classical-trajectory Monte Carlo simulation. With the help of the analysis on the electron complex trajectories in both sub-barrier and quasicontinuum regions, the enhancement is illustrated to originate from the quantum effect of forward scattering between the tunneling electron and its parent ion. The study shows that the electron probability will be significantly modified when the rescattered electrons excurse in the continuum and the “classical” rescattering process needs the quantum description.

Figure 1

(a) Experimental photoelectron momentum distribution of argon atoms in the OTC fields with $\mathrm{\Delta }\phi =0.5\pi$. The 800 and 400 nm laser fields are along the $x$ and $z$ axes, respectively. (b)–(f) The calculated photoelectron momentum distributions by the (b) zero-order SFA, (c) classical-trajectory Monte Carlo simulation, (d) solving time-dependent Schrödinger equation, (e) the first-order SFA, and (f) the coherent sum of SFA0 and SFA1, respectively. All the color bars are linearly scaled. The laser field is synthesized by an eight-cycle $\mathrm{si}{\mathrm{n}}^2$-envelope laser pulse at 800 nm, and the peaks of 800 and 400 nm electric fields are 0.045 and 0.05 a.u., respectively. The laser parameters are identical in all simulations.

Figure 2

(a) Four steps of the rescattering electron motion in the complex-time plane. (b) The laser electric fields with respect to the laser phase. The green shaded areas represent the ionization time windows for rescattering electrons. (c),(d) The two-dimensional trajectories of the electron with the final momentum of $\left(p_x,p_z\right)=\left(0.0,0.6\mathrm{a}.\mathrm{u}.\right)$ for the pathways of forward and backward rescattering, respectively.

Figure 3

The evolution of (a) imaginary position, (b) imaginary velocity, and (c) probability of the forward-rescattering electron [corresponding to Fig. 2]. In (a) and (b), the red solid and blue dash lines represent the components along the $x$ (800 nm) and $z$ (400 nm) direction, respectively. In (c), the curves with different colors were used to distinguish the four steps as shown in Fig. 2.

Figure 4

The angle-resolved distribution of the (a) scattering angle, (b) ionization instant, (c) rescattering instant, and (d) ionization probability for backward-scattering (black solid line) and forward-scattering [magenta (light gray) line] electrons with the final momentum $p=\sqrt{p_x^2+p_z^2}=0.6\mathrm{a}.\mathrm{u}.$. The emitting angle is defined by $arctan\left(p_z/p_x\right)$. The emitting angles of $\sim {90}^{\circ }$ and $\sim -{20}^{\circ }$ correspond to those two observed ionization-enhanced structures as shown in Fig. 1, respectively. In (d), the dashed lines represent the electron probabilities after tunneling, and the shaded areas represent the enhanced ionization probabilities because of rescattering.