Carrier-envelope phase control over pathway interference in strong-field dissociation of H$_2^+$ molecular ions*

The dissociation of an H$_2^+$ molecular-ion beam by linearly polarized, carrier-envelope-phase-tagged 5-fs laser pulses is studied experimentally and theoretically. A coincidence 3D momentum imaging technique is employed to fully characterize the dissociation kinematics. We observe carrier-envelope-phase-dependent asymmetries in the emission direction of H$^+$ fragments relative to the laser polarization for two kinetic energy release regions. These asymmetries are caused by the interference of odd and even photon number pathways [1-2]. In the low kinetic energy region (0.2-0.45 eV), the net-zero-photon and one-photon pathways interfere predominantly while net-two-photon and one-photon interference contributes at the higher kinetic energy region, 1.65-1.9 eV. These measurements are quantitatively compared to ab initio theoretical calculations [1-2] to further our understanding of strong-field coherent control via the carrier-envelope phase.\\[4pt] [1] Nora G. Kling et al. Phys. Rev. Lett. 111, 163004 (2013).\\[0pt] [2] V. Roudnev, B.D. Esry, and I. Ben-Itzhak, Phys. Rev. Lett. 93, 163601 (2004).