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Using quantum-mechanical, one-dimensional, non-Born-Oppenheimer simulations we study the control over the strong-field dynamics of the helium hydride molecular ion HeH + due to interaction driven by short and strong two-color laser pulses. We calculate yields of two competing fragmentation channels: electron removal and dissociation. We find that by changing the relative phase of the two colors, we can select the dominating channel. Nuclear motion is decisive for explaining ionization in thisdoi:10.1088/1361-6455/ab9a93 fatcat:asj5n4gxijgzhogwwfwevicc3q