Coherent control of vibrational state distribution in non-polar molecules*

A novel coherent control scheme for the vibrational state distribution in nonpolar molecules is proposed. We apply the scheme to H$_2^+$ and study it theoretically and numerically. Our results reveal a two-photon selective excitation, which is robust against dissociation, and a dynamical Stark shift, which depends linearly on the laser intensity. By using a controllable spectral-phase laser pulse (or a train of pulses) a complete coherent transfer can be achieved from one vibrational state to another.