c. Cooling the molecular vibration with the use of shaped broadband lasers

The next challenge was to prepare these molecules in a well-defined vibrational level. This was accomplished by the realization of a novel optical pumping scheme which operating principle is displayed in Fig. II.3.1.a.1. The effect of the broadband radiation is such, that all vibrational levels of the X state can be simultaneously excited towards the B state, with the exception of the fundamental vX = 0 vibrational state. The frequency components of the femtosecond pulse that lied above ~13030 cm^-1 (energy of the vX → vB transition) have been removed. Thus the vX = 0 vibrational state cannot be excited and is a dark state of the system. Since all other vibrational levels are repeatedly pumped to the B state and relax to various vibrational levels of the X state, it is expected that a large part of the molecular population will end up been accumulated to the vX = 0 vibrational state, since once relaxed in this state, it is not excited anymore.

Ending up in the vX = 0 vibrational ground state is not the only possibility. It is possible that a series of excitation-relaxation circles transfers the molecules to high vibrational levels that lie outside of the femtosecond spectral range. In this case, the molecules are trapped in those high lying vibrational states and the process leads to heating instead to vibrational cooling of the molecules.

Fig. II.3.1.b.3: Cs²+ion count (left vertical axis) resulting from a narrow-band REMPI detection (frequency 627 nm). The PA laser energy is fixed at 11730.1245 cm^-1 corresponding to the position of the most intense line marked with a circled cross in Fig. II.3.1.b.2. Transition labels vC–vX are extracted from computed Franck–Condon factors (right vertical axis) between vibrational levels of the spectroscopically known C and X states. Figure adapted from [Vit09b].

Weather the molecular population will end up to higher or lower lying vibrational levels depends on the relative value of the Franck-Condon coefficients, as long as the dipole transition moment can be considered constant. The Franck-Condon coefficients for the Cs2 X-B optical pumping transition considered in the initial experiment, were calculated by O.Dulieu and N.Bouloufa, members of the theoretical group of 'Cold Molecules'. This information, gives the possibility to simulate the evolution of the system under the influence of the femtosecond pulse. The result of this simulation is shown in Fig. II.3.1.c.1 along with a plot of the Franck-Condon coefficients in gray scale. The femtosecond laser spectra shown in the inlet up and to the right does not excite the transitions corresponding to the hatched area. The example of the excitation of the vX=5 state is shown with the red arrow. The most possible final state after the broadband excitation (corresponding to larger Franck-Condon factor) is to the vB = 1 state an for the relaxation step, the most possible state is the fundamental vX = 0. Relaxation to a higher lying vibrational level is possible, but the corresponding probability is smaller.

The result is shown in the part (b) where the evolution of the system is plotted as a function of the number of pulses. The evolution of the molecular population is calculated as follows. The original population is extracted by the analysis of the spectrum in Fig. II.3.1.b.3, and can be used as an initial situation for this study. However, it is not necessary since to know the precise distribution of the molecular population initially, since the large number of excitation-relaxation circles redistributes molecular population in such a way, that the final distribution does not depend on the initial one, as long as all the initially populated states lye within the range of the femtosecond laser.

This is the case here since Cs2 molecules are populating levels with vx = 1-10. The number corresponding to the initial population of one vibrational level is multiplied to the laser power and the Franck-Condon coefficient which corresponds to transitions towards all exited states. The process is repeated for all initial states and this way the population distribution in the exited state is obtained. Then, the population after relaxation is calculated with the same way, only that here the laser power does not get inserted to the calculation. As we see, a large part of the total molecular Fig. II.3.1.c.1: Simulation of the optical pumping process (b) with the use of the the Franck-Condon coefficients shown in (a). The red arrows indicate the most probable evolution of the molecular population initially lying in a given vibrational level, for example the vX = 4. The relative probability of excitation or relaxation to a particular vibrational level is given by the Frank-Condon factors shown in gray scale. Figure adapted from [Vit08c].

population which corresponds to ~69% is pumped to the the ground vibrational level.

The experimental demonstration of vibrational cooling consists in the comparison of REMPI spectra of molecules that have been radiated with the femtosecond laser and of molecules that have not. This is shown in Fig. II.3.1.c.2 while the scan is now focused to an area from ~15900 to 16050 cm^-1 to detect transitions from the vX=0 state. We see that the femtosecond laser modifies dramatically the molecular population distribution as displayed by the two REMPI spectra. The resonance lines corresponding to the transition vX = 0 → vB = 0–3, mostly absent in the initial spectrum, are now very strong. Their broadening corresponds to the saturation of the resonance in the REMPI process. The intensity of the lines indicates a very efficient transfer of the molecules in the lowest vibrational level, meaning a vibrational laser-cooling of the molecules. Taking into account the efficiency of the detection (<10%), the detected ion signal corresponds to about one thousand molecules in the vX = 0 level, corresponding to a flux of vX = 0 molecules of a few 10⁵ per second. Fig. II.3.1.c.3 shows the time evolution of the population in the different vibrational levels.

We see that for a power of ~100 mW the transfer of population in the vX = 0 level is almost saturated after the application of 10000 pulses, which requires one hundred microseconds.

Fig. II.3.1.c.2: Original data set for the demonstration of vibrational cooling. The presence of the shaped femtosecond radiation results to the observation of strong lines corresponding to transitions from the ground vibrational level (b-purple line) which were absent in the spectrum acquired without its presence (a-blue line). The colored numbered lines indicate the position of transitions corresponding to excitation from different initial vibrational levels. Figure adapted from [Vit08c].

0 - 0 0 - 1 0 - 2 0 - 3

Fig. II.3.1.c.3: Temporal evolution of the population transfer. (a) Compilation of experimental spectrum for different durations of the femtosecond laser (number of pulses). (b) Simulation of the vibrational laser cooling. Figure adapted from [Vit08c].