Molecular cooling by optical pumping with shaped femtosecond pulses

Vibrational cooling of translationally cold Cs$_{2}$ molecules into a selected vibrational level v = 0,1,2 or v=7 of the singlet X$^{1}\Sigma _{g}^{+}$ ground electronic state has been realized. Our method is based on repeated optical pumping by laser light with a spectrum broad enough to excite all populated vibrational levels but frequency-shaped in such a way to eliminate transitions from the chosen v level, in which molecules accumulate. Using ultrashort pulse shaping techniques based on Liquid Crystal spatial light modulator a large fraction of the initial molecules is transfered into a single selected vibrational level such as v = 0,1, 2 and 7. Limitations of the method as well as the possible extension to rotational and translational cooling will also be discussed.