Revealing the Sub-Barrier Phase using a Spatiotemporal Interferometer with Orthogonal Two-Color Laser Fields of Comparable Intensity

We measure photoelectron momentum distributions of Ar atoms in orthogonally polarized two-color laser fields with comparable intensities. The synthesized laser field is used to manipulate the oscillating tunneling barrier and the subsequent motion of electrons onto two spatial dimensions. The subcycle structures associated with the temporal double-slit interference are spatially separated and enhanced. We use such a spatiotemporal interferometer to reveal sub-barrier phase of strong-field tunneling ionization. This study shows that the tunneling process transfers the initial phase onto momentum distribution. Our work has the implication that the sub-barrier phase plays an indispensable role in photoelectron interference processes.

Figure 1

Experimental electron momentum distributions of Argon in an OTC field in the polarization plane for $\mathrm{\Delta }\phi =0$ (a), $0.25\pi$ (b), $0.5\pi$ (c), and $0.75\pi$ (d). The peak intensity of the fundamental light was $I_{800}=(0.72\pm 0.05)\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ and that of the second harmonic was $I_{400}=(0.87\pm 0.03)\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. The 800 and 400 nm fields are along the $x$ and $z$ axes, respectively. The data are integrated over an angular range $\theta =90°\pm 30°$ where $\theta =\mathrm{acos}(p_y/\sqrt{p_y^2+p_x^2+p_z^2})$ is the angle between the electron momentum vector and the normal to the ($p_x$, $p_z$) plane.

Figure 2

Simulated electron momentum distributions at $\mathrm{\Delta }\phi =0.5\pi$ are calculated by the CCSFA model without the sub-barrier phase (a), with the sub-barrier phase (b), the SFA model with numerical method (c), and the TDSE method (d). (e) The projection of the ionization probability along the dashed curves [$p_r=\sqrt{p_x^2+p_z^2}=(0.35\pm 0.01)\mathrm{a}.\mathrm{u}.$] with respect to the emission angle.

Figure 3

(a) The temporal sketch of the OTC field for $\mathrm{\Delta }\phi =0.5\pi$ with respect to one 800 nm cycle. The black line, red line, and blue line in (a) indicate the synthesized light electric field, negative vector potentials of 800 nm light and that of 400 nm light, respectively. (b) The spatial view of the OTC field and the emitting wave packets in the polarization plane (horizontal direction is the $x$ axis and vertical direction is the $z$ axis). In (b) the black line depicts the track of the end point of the synthesized electric-field vector in one 800 nm cycle (the radial coordinate represents the electric-field strength and the angular coordinate means its direction), and the yellow arrows on the black line mark the increase of time as the color gradually deepens. The four outer subplots in (b) depict the components of laser electric fields (the red arrow displays the 800 nm light and the blue solid arrow shows the 400 nm light) when the corresponding wave packet tunnels, and describe the wave-packet subsequent motions with green arrows schematically. (c) The subcycle interferogram calculated by the SFA model employing the saddle-point method without the plain sub-barrier phase. (d) The same calculation as (c) but with the plain sub-barrier phase.

Figure 4

The distribution of probability [(a) and (b)] and plain sub-barrier phase [(c) and (d)] of WP3 (left column) and WP4 (right column) in the final momentum plane. The ionization probability is normalized to the maximum, and the phase value is the real value in radian units.

Figure 5

Electron momentum distributions in the OTC field at $\mathrm{\Delta }\phi =0.25\pi$ calculated by the CCSFA model without the sub-barrier phase (a) and with the sub-barrier phase (b). The interference pattern between WP3 and WP4 is marked within the red rectangles.