Coherent control at its most fundamental: carrier-envelope-phase-dependent electron localization in photodissociation of a H2(+) molecular ion beam target.

Measurements and calculations of the absolute carrier-envelope-phase (CEP) effects in the photodissociation of the simplest molecule, H2(+), with a 4.5-fs Ti:sapphire laser pulse at intensities up to (4±2)×10(14)  W/cm2 are presented. Localization of the electron with respect to the two nuclei (during the dissociation process) is controlled via the CEP of the ultrashort laser pulses. In contrast to previous CEP-dependent experiments with neutral molecules, the dissociation of the molecular ions is not preceded by a photoionization process, which strongly influences the CEP dependence. Kinematically complete data are obtained by time- and position-resolved coincidence detection. The phase dependence is determined by a single-shot phase measurement correlated to the detection of the dissociation fragments. The experimental results show quantitative agreement with ab initio 3D time-dependent Schrödinger equation calculations that include nuclear vibration and rotation.