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We investigate the dynamics of diatomic molecules subjected to both a femtosecond midinfrared laser pulse and Gaussian white noise. The stochastic Schrödinger equation with a Morse potential is used to describe the molecular vibrations under noise and the laser pulse. For weak laser intensity, well below the dissociation threshold, it is shown that one can find an optimum amount of noise that leads to a dramatic enhancement of the dissociation probability. The enhancement landscape, which is shown as a function of both the noise and the laser strength, exhibits a global maximum. A frequency-resolved gain profile is recorded with a pump-probe setup which is experimentally realizable. With this profile we identify the linear and nonlinear multiphoton processes created by the interplay between laser and noise and assess their relative contribution to the dissociation enhancement.
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