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Measurements and calculations of the absolute carrier-envelope phase (CEP)effects in the photodissociation of the simplest molecule, H2+, with a 4.5-fsTi:Sapphire laser pulse at intensities up to (4 +- 2)x10^14 Watt/cm^2 arepresented. Localization of the electron with respect to the two nuclei (duringthe dissociation process) is controlled via the CEP of the ultra-short laserpulses. In contrast to previous CEP-dependent experiments with neutralmolecules, the dissociation of the molecular ions is not preceded by aphotoionization process, which strongly influences the CEP dependence.Kinematically complete data is obtained by time- and position-resolvedcoincidence detection. The phase dependence is determined by a single-shotphase measurement correlated to the detection of the dissoziation fragments.The experimental results show quantitative agreement with ab inito 3D-TDSEcalculations that include nuclear vibration and rotation.

Coherent control at its most fundamental: CEP-dependent electron localization in photodissoziation of a H2+ molecular ion beam target