Adaptive control of CO$_2$ bending vibration: deciphering field-system dynamics

We combined adaptive closed-loop optimization, phase-shaping with a restricted search space and imaging to control dynamics and decipher the optimal pulse. The approach was applied to controlling the amplitude of CO$_2$ bending vibration during strong-field Coulomb explosion. The search space was constrained by expressing the spectral phase as a Taylor series, which generated pulses with characteristics commensurate with the natural physical features of this problem. Optimal pulses were obtained that enhanced bending by up to 56% relative to what is observed with comparably intense, transform limited pulses. We show that (1) this judicious choice of a reduced parameter set made unwrapping the dynamics more transparent and (2) the enhancement is consistent with field-induced structural changes to a bent excited state of CO$_2^{2+}$, which theoretical simulations have identified as the state from which the explosion originates.