molecules to the ultracold configuration and back using a single, phase-locked pulse train. Note, that qualitatively same result was obtained for the pule train repetition rate 500 MTz, ( T = 2 ns ), with the only difference in the dynamics duration, which was extended by an order of magnitude to 440 ns. 

Off-resonant Raman transitions are readily induced by a single, standard optical fre- quency comb, provided there are optical frequencies in the comb that satisfy the two-photon resonance condition and differ by exactly the Feshbach-to-ultracold state transitional fre- quency. In Fig.7 the case for the carrier frequency detuned off resonance with the ω 32 transitional frequency is presented for detuning δ = 3 / 2 ω 31 and two values of the Rabi frequency, the Ω$_{R}$ = 0 . 1 ω 31 = 12 . 55 THz and Ω$_{R}$ = 0 . 01 ω 31 = 1 . 26 THz related to the field intensity on the order of 10 14 and 10 12 W/cm 2 respectively. The chosen value of de- tuning δ is about ∼ 10 $^{14}$Hz . Bold black, bold red, and bold green lines show population dynamics in the Feshbach state, the excited electronic state and the final, ultracold state respectively, for the Rabi frequency Ω$_{R}$ = 1 . 26 THz , thin lines - same for the Rabi frequency Ω$_{R}$ = 12 . 55 THz . Since here we demonstrate the effects of the detuning, and the impact of different field intensity on the population dynamics to the deeply bound rovibrational state in the KRb molecule, the pulse train period is chosen to be short to accommodate the com- putational limitations, T = 6400 τ = 0 . 02 ns. (Same as for the resonance case, pulse train period in 2 ns elongates the duration of population accumulation.) Figure Fig.7 shows that almost complete population transfer, ( ∼ 98%), takes place when the carrier frequency is off-resonance with the one-photon transitions in the molecular system. It also demonstrates the field intensity dependence of the duration needed to accumulate population in the ul- tracold state. For the Ω$_{R}$=12.55 THz, ( 10 14 W/cm $^{2}$), the population transfer dynamics is accomplished five times faster than for the Ω$_{R}$=1.26 THz, ( 10 12 W/cm $^{2}$). 

In conclusion, we have demonstrated a possibility of molecular rovibrational cooling from the Freshbach states using a single femtosecond, optical frequency comb. We focused on the KRb molecule and modeled it by a three-level λ -system with the energy levels taken from [8] and [9]. Coherent accumulation of the population in the cold state is achieved by applying a standard optical frequency comb with zero offset frequency, and by an optical frequency comb generated by a pulse train with a phase modulation in the form of the sinusoidal function across an individual pulse. An optimal dynamics takes place when the carrier- envelope phase is equal to zero, ( f 0 = 0). The mechanism of the accumulative effect leading 

