Strong Field Electron Emission from Fixed in Space ${\mathrm{H}}_2^{+}$ Ions

We have studied electron emission from the ${\mathrm{H}}_2^{+}$ ion by a circularly polarized laser pulse (800 nm, $6\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$). The electron momentum distribution in the body fixed frame of the molecule is experimentally obtained by a coincident detection of electrons and protons. The data are compared to a solution of the time-dependent Schrödinger equation in two dimensions. We find radial and angular distributions which are at odds with the quasistatic enhanced ionization model. The unexpected momentum distribution is traced back to a complex laser-driven electron dynamics inside the molecule influencing the instant of ionization and the initial momentum of the electron.

Figure 1

Photoelectron momentum distribution from an atom (a)–(c) and a molecule (d)–(f) in a circularly polarized laser pulse at $6\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. (a) Expected ring distribution with the radius given by the maximum value of the vector potential $A_0$ for an atom (dashed line), (b) predictions of the quasistatic ionization theory [23], and (c) result of a TDSE simulation for a two-dimensional model of ${\mathrm{He}}^{+}$ atom. (d) Expected distribution for emission from ${\mathrm{H}}_2^{+}$, (e) experimental result for ${\mathrm{H}}_2^{+}$ integrated over the internuclear distance $R$ and $p_z$, and (f) result of a TDSE simulation for a two-dimensional model of ${\mathrm{H}}_2^{+}$ at $R=7\mathrm{a}.\mathrm{u}.$. Contributions I, II, and III (and I’, II’, III’) correspond to three different ionization events (see the text).

Figure 2

Dependence of the tilt angle (a) and the mean radial momentum (b) on $R$. Dashed lines, predictions of the simple quasistatic model; blue filled circles, experimental data; red open squares, results of TDSE calculations.

Figure 3

Angular distributions of the experimental data (black dots) and theoretical results (red solid line) for a clockwise circularly polarized laser pulse of intensity $6\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. The experimental data are integrated over $p_z$. The internuclear axis is set along the $x$ axis. The columns correspond to $R=5\mathrm{a}.\mathrm{u}.$, $R=7\mathrm{a}.\mathrm{u}.$, and $R=9\mathrm{a}.\mathrm{u}.$ from left to right, and the rows to different regions of electron radial momenta.

Figure 4

Snapshots of the calculated electron density in ${\mathrm{H}}_2^{+}$ under a circularly polarized laser pulse at $t=t_1=-1.3\times {10}^{-4}$ laser cycles (a), $t=t_2=0.13$ laser cycles (b), and $t=t_3=0.23$ laser cycles (c). Time zero is set at a maximum of the $x$ component of the electric field. The gray solid and dashed lines are the contour lines of the potential at the field free energies of the ground and first excited states, respectively. The $+$ signs mark the saddle points of the instantaneous potential. The bold white arrow with a black edge indicates the initial momentum ${\mathbf{p}}_i$ at the origin of the arrow, and the thin white arrow indicates $q_e\mathbf{A}(t)$. The two protons are placed at $(x,y)=(\pm 3.5\mathrm{a}.\mathrm{u}.,0)$.