Relative phase control over tunneling ionization of ${{\mathrm{H}}_2}^{+}$ with a synthesized ω-2ω laser pulse

We demonstrate an efficient scheme for controlling the tunneling ionization of a ${{\mathrm{H}}_2}^{+}$ molecular ion. Our scheme is based on the idea that the tunneling ionization rate is highly dependent on the instantaneous magnitude of the electric field. By manipulating the relative phase of the synthesized 5-fs, 790–395-nm laser field, the fragments yielded by the tunneling ionization show a large asymmetry relative to the laser polarization. We find that the time-dependent ionization rate is sharply peaked near the antinodes of the synthesized field. Most importantly, the critical internuclear distances at which the tunneling ionization rate is enhanced depend on the field strength of the antinodes. It is well explained by tracing the laser-driven motion of the electron in the field-dressed double well potential.

Figure 1

(a) Ionization spectrum of ${{\mathrm{H}}_2}^{+}$ for the 5 fs, 790–395-nm laser field at each intensity of $6\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$, the KER averaged over the interval $0\le \varphi \le 2\pi$. (b) The corresponding asymmetry plot showing the dependence of $A(\mathrm{KER},\varphi )$ on the KER and RP. (c) The asymmetry parameter $A$ as a function of the RP, integrated over the high-KER region (>8 eV).

Figure 2

Time evolution of the electronic probability densities (a–c) and the corresponding positive-negative ionization rates (d–f) for the 790–395-nm laser field. The RPs are 0.2π (left column), 0.6π (middle column), and 1.2π (right column). The white lines (a–c) depict the profiles of the time-dependent electric fields. The black and red (gray) lines (d–f) correspond to the ionization rates in the positive and negative directions, respectively.

Figure 3

The subcycle wave forms (a–c) and the space-dependent ionization rates (d–f) for the 790–395-nm laser field when RPs $\varphi =0.2\pi ,0.6\pi ,\mathrm{and}1.2\pi$. The letters indicate the short instants where the tunneling ionization occurs. The black and red (gray) lines correspond to the ionization rates in the positive and negative directions, respectively.

Figure 4

The field-dressed double well potentials $V_{en}-Ez$ for the electron of ${{\mathrm{H}}_2}^{+}$ along the $z$ axis. The left and right columns correspond to the $R=2.2\mathrm{and}3.2\mathrm{a}.\mathrm{u}.$ The dashed and red (gray) lines depict the energy levels and wave packets of the dressed $1s\sigma$ electronic state, respectively.