Subcycle interference upon tunnel ionization by counter-rotating two-color fields

We report on three-dimensional (3D) electron momentum distributions from single ionization of helium by a laser pulse consisting of two counter-rotating circularly polarized fields (390 and 780 nm). A pronounced 3D low-energy structure and subcycle interferences are observed experimentally and reproduced numerically using a trajectory-based semiclassical simulation. The orientation of the low-energy structure in the polarization plane is verified by numerical simulations solving the time-dependent Schrödinger equation.

Figure 1

Three-dimensional electron momentum distributions from ionization of helium by counter-rotating two-color fields are shown. The 3D momentum distributions are visualized by combining five semitransparent isosurfaces encoding the intensity of the 3D histogram by color. The $p_y{p}_z$ plane is the polarization plane. The 2D histograms show projections. (a) The field ratio of the two colors and their combined intensity are $E_{390}/E_{780}=0.84$ and $I=8.14\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. Note the pronounced (red) inner low-energy structure in the 3D distribution which is almost invisible in projection I. (b) shows the same as (a) but for $E_{390}/E_{780}=1.20$ and $I=6.75\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 2

The momentum distribution in the light propagation direction is investigated for various selected momenta in the plane of polarization. (a) shows projection II from Fig. 1. The dots in the polarization plane in (a) indicate the used condition for panels (b)–(d) that show the momentum ($p_x$) in the light propagation direction. (b) shows a Gaussian-like distribution (as for circularly polarized light), (c) shows subcycle interference (fringes), and (d) shows the cusplike initial momentum distribution (as for linear light). The side peaks of the subcycle interference in (c) correspond to an electron energy of 2.3 eV. The fringe visibility is indicated by contour lines in (a). The gray contour lines indicate 50% fringe visibility compared to the black contour line.

Figure 3

(a) Comparison of the experiment, (b) a solution of the TDSE, and (c) the SCTS result for low momenta in the light propagation direction of $|p_x|<0.02\mathrm{a}.\mathrm{u}.$ shows very good agreement. The temporal evolution of the laser field magnitude used in the SCTS model is shown in (d). (e) shows the electron momentum distribution from the SCTS immediately after the end of the laser pulse (without interferences and only electrons with positive total energy are shown). In (f) the same electrons are presented for asymptotically long times. It can be graphically seen that the Coulomb potential slows down the electrons after the laser pulse is over. This is the reason for the pronounced low-energy structure in the CRTC fields. (g) is the same as (f) but includes interferences. The red circle in (f) guides the eye to the overlapping region of two neighboring lobes. The momentum component which is not shown ($p_x$) is projected out in (e)–(g).

Figure 4

The origin of the subcycle interferences is investigated using the semiclassical SCTS simulation. Only electrons with energies of $2.3\pm 0.1\mathrm{eV}$ are selected. The resulting subset is presented as 2D momentum distributions in (a) and (c) for ionization within one lobe of the combined electric field [indicated as the gray shaded phases of the electric field and the vector potential in (e)] and a full single cycle of the combined electric field, respectively. Panels (b) and (d) show subsets from (a) and (b) selecting the angle in the polarization plane to be $-6\pm 6^{\circ }$. Manifestly panel (d) shows modulations which panel (b) does not show. This indicates that the observed modulations are indeed subcycle interferences. Tracing back all electrons by showing their negative vector potential [panel (e)] reveals their corresponding birth times. Those times (phases) are seen as dots on the vector potential in panel (e). Panel (f) shows the sum of the negative vector potential at the instant of ionization and the initial momentum of the electrons just after tunneling. Panel (g) shows the final momentum. The data shown in (e)–(g) have been convoluted with a Gaussian distribution to facilitate visibility. The arrows in (e) indicate the time evolution of the electric field and the negative vector potential.