Relative phase control over tunneling ionization of H-2(+) with a synthesized omega-2 omega laser pulse

We demonstrate an efficient scheme for controlling the tunneling ionization of a 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