  We show that a single femtosecond optical frequency comb may be used to
induce two-photon transitions between molecular vibrational levels to form
ultracold molecules, e.g., KRb. The phase across an individual pulse in the
pulse train is sinusoidally modulated with a carefully chosen modulation
amplitude and frequency. Piecewise adiabatic population transfer is fulfilled
to the final state by each pulse in the applied pulse train providing a
controlled population accumulation in the final state. Detuning the pulse train
carrier and modulation frequency from one-photon resonances changes the time
scale of molecular dynamics but leads to the same complete population transfer
to the ultracold state. A standard optical frequency comb with no modulation is
shown to induce similar dynamics leading to rovibrational cooling.
