We present a non-perturbative framework for vibrational excitation in molecular systems driven by electric fields with arbitrary time-dependence. For harmonic potentials with linear dipole coupling, the dynamics is exactly described by a displaced coherent state [1] whose evolution is fully determined by a complex phase-space coordinate [2]. Closed-form expressions for this coordinate reveal clear distinction between resonant and off-resonant regimes. At resonance, and within the rotating wave approximation, the dynamics yields a time-dependent phase-space displacement, leading to a Poisson distribution of vibrational populations at all times. Off-resonant driving results in an exponentially suppressed displacement due to finite detuning between the driving and vibrational frequencies. The approach reduces to time-dependent perturbation theory in the weak-field limit but remains valid in the strong-field regime, where perturbative treatments fail. Our results provide a transparent phase-space picture of vibrational control and establish a non-perturbative route to tailored state preparation in ultrafast spectroscopy. 

[1] R. J. Glauber, Phys. Rev. 131, 2766 (1963). 

[2] D. Tannor, Introduction to Quantum Mechanics: A Time-Dependent Perspective,  (University Science Books, Sausalito, 2007).