In strong laser fields, sub-femtosecond control of chemical reactions with the carrier-envelope phase (CEP) becomes feasible. We have studied the control of reaction dynamics of acetylene and allene in intense few-cycle laser pulses at 750 nm, where ionic fragments are recorded with a reaction microscope. We find that by varying the CEP and intensity of the laser pulses it is possible to steer the motion of protons in the molecular dications, enabling control over deprotonation and isomerization reactions. The experimental results are compared to predictions from a quantum dynamical model, where the control is based on the manipulation of the phases of a vibrational wave packet by the laser waveform. The measured intensity dependence in the CEP-controlled deprotonation of acetylene is well captured by the model. In the case of the isomerization of acetylene, however, we find differences in the intensity dependence between experiment and theory. For the isomerization of allene, an inversion of the CEP-dependent asymmetry is observed when the intensity is varied, which we discuss in light of the quantum dynamical model. The inversion of the asymmetry is found to be consistent with a transition from non-sequential to sequential double ionization.
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