Methods for molecular cooling

II.2.2.a. Sympathetic or 'buffer gas' cooling

Molecular cooling has been demonstrated via various experimental techniques. Some approaches involved cryogenic techniques and molecules have been loaded with this method into conservative traps were evaporating cooling can follow [Wein98]. In Fig. II.2.2.1 adapted from [Wein98], we see an schematic representation of a set up that permits this kind of cooling. In this method, the cooling in CaH2 molecules is achieved by collisions and thermalisation with cryogenically prepared cold helium atoms and the temperature of the molecular sample can reach as low as ~450µK. The CaH2 molecules are produced by laser ablation of a solid CaH2 sample. The ablated molecules are colliding with the cold helium atoms and are magnetically confined in the center of the chamber by the confining magnetic potential produced by the superconducting coils, where they are detected.

1 An additional proposed method considers enchantment of the spontaneous emission towards a particular ro-vibrational level with the use of external cavities. However, this and more proposals involving the use of cavities are not considered here, especially due to economy.

Fig. II.2.2.1: Experimental set up for the cryogenic cooling of CaH, taken from [Wein98].

II.2.2.b. Stark and Zeeman deceleration

Except for directly cooling molecules, there exist several techniques for the deceleration of molecules. One of the first demonstrated techniques for the deceleration of molecules in a molecular beam is the Stark deceleration technique, which manages to decelerate polar heteronuclear molecules, via the Stark interaction [Bert99]. In these experiments, electric fields are employed in order to interact with these molecule's permanent electric moment and the objective is to decelerate a supersonic beam of molecules either in their ground or in an excited 'Rydberg' level [Bert99, Pro03], while in other variations of the technique, the magnetic moment can provide the interaction with which molecules can be decelerated [Vanh07, Nar08]. Other techniques use electric fields combined to differential pumping, in order to select the slowest velocity groups in expanded molecular clouds [Rang03]. These methods have in common the electrostatic nature of the interaction, except for the case of the Zeeman decelerators, where the magnetic interactions substitute the electric ones.

InFig. II.2.2.2 we see the operating principle for the two most characteristic 'electrostatic methods', the Stark deceleration and the velocity selection. In part (a) we see the example of the Ammonia molecule as it is moving in the decelerating electrostatic potential. A low-field seeking molecule approaching the first pair of dipoles in the Stark decelerator will slow down a little as it experiences an increasing field. When it reaches a position close to the top of the energy hill (at (2), on the left) the fields are switched off in order to prevent it from running down the hill the other side (and hence accelerating). The voltages of the first and second pairs of electrodes are then swapped over so that the hill moves along suddenly, as shown in gray. The molecule thus instantaneously finds itself at the bottom of another hill and continues climbing, slowing down a little more. By repeating this sequence 100 times over with a carefully timed field it is possible to slow a subset of the molecules down to any arbitrary velocity. In part (b), we see the operating principle of the velocity selection technique. This technique uses the electrostatic field, shown up and to the left, to 'guide' the lowest velocity group of the expanded molecular cloud towards the detection chamber, or the conservative trap.

Fig. II.2.2.2: (a) operating principle of the Stark deceleration technique in the Ammonia molecule [Bert99].

(b) The velocity selection technique uses the electrostatic field shown up and to the left to 'guide' the lowest velocity group of the expanded molecular cloud towards the detection chamber, or the conservative trap [Rang03].

II.2.2.c. 'Mechanical' cooling

The techniques proposed or implemented for the cooling of molecules can be very diverse. I will try to group two interesting techniques in a family of 'mechanical' techniques, while there might exist more techniques that could be grouped in this 'family'. In these techniques the cooling mechanism does not come by electrostatic interactions or by cryogenic cooled atoms, but has more to do with simple classical dynamics of the moving molecules. In the technique reported in [Gup99]

and shown in Fig. II.2.2.3 (a), the flow velocity of gas emerging from a supersonic nozzle mounted on a high-speed rotor can be largely canceled by the rotor velocity, therefore producing an intense beam of molecules traveling in vacuum with translational speeds slowed to a few tens of m/sec.

These features are demonstrated by model calculations and experimental results for beams of Xe, O² and CH³F seeded in Xe. In part (b) we see the operating principle of a technique that manages to produce NO molecules in low temperatures by collisions between two jets, an atomic and a molecular one in particular angles [Eli03]. The technique, relies on a kinematic collapse of the velocity distributions of the molecular beams for the scattering events in particular angles, which produceNO molecules in sub-Kelvin temperatures.

Fig. II.2.2.3: Operating principle of the 'mechanical' techniques: (a) a supersonic nozzle mounted on a high-speed rotor. The flow velocity of the emerging gas can be largely canceled by the rotor velocity, thereby producing an intense beam of molecules traveling in vacuum with translational speeds slowed to a few tens of m/sec [Gup99]. (b) Operating principle of the technique reported in [Nar08], which manages to prepare NO molecules in low temperatures by collisions between two jets, an atomic and a molecular one, in particular angles [Nar08].

NO beam Ar beam

Extractor +500

Repeller +750

Ionization

laser beam

II.2.2.d. Theoretical proposal for the molecular cooling via dynamically trapped states

Finally, there exist a variety of theoretical proposals for the achievement of laser cooling.

Some of these proposals involve femtosecond lasers, shaped or not [Tann99], others the use of frequency combs [Pe'Er07, Saph07], while others the use of coherent population transfer via STIRAP [Ooi03]. Another group of proposals are the ones that involve high quality cavities, which can be used to favor spontaneous emission to a particular level, and thus create a closed transition with which the molecules can be laser cooled [Mor07]. In [Vul00] we see an alternative approach, where cooling is achieved inside a cavity, since preferential scattering due to the molecule-cavity interaction can lead to cooling. However, to our knowledge, no direct laser cooling of molecules is demonstrated for the time being.

However, one theoretical proposal is chosen to be described here, due to the close relation to the vibrational cooling technique reported in [Vit08] and discussed throughout this part of my thesis. This is the “vibrationally selective coherent population transfer” technique described in [Tann99, Bart00]. It is addressing the issue of vibrational cooling in molecules as a problem of population transfer to the ground vibrational state. Having as background, coherent population transfer between atomic states with STIRAP [Berg98], and S-STIRAP (extension of the previous) the authors propose a technique for the laser cooling of the internal degrees of freedom (vibration) in molecules. The preparation of an internal, dynamical dark state, in corespondent to the dark states in the atom field 'dressed' states picture considered in STIRAP, can be achieved via Optimal Control Theory. The condition for the creation of the dark state, and thus population trapping is achieved by the instantaneous phase-locking of the laser to the transition dipole moment of the 'target' state v = 0. Thus, molecules that are transferred to the desired state by spontaneous emission, are 'dynamically' trapped and finally accumulated in it. The pulse that can create such a dynamical trapping is calculated with the use of Optimal Control Theory. In Fig. II.2.3.3, the basic elements of the proposed experiment are schematically displayed.

Fig. II.2.2.4: The “vibrationally selective coherent population transfer” technique; A pulse optimized with means of OCT excites a group of molecular transitions. The pulse is such that the molecule's ground state is a 'dark' state of the system and all molecular population is transferred there by spontaneous emission. Figure adapted from [Kim01].

In summary, this proposal aims in the molecular population transfer to the ground (or a nearby) ro-vibrational level via spontaneous emission. This is accomplished by exciting the system in such a way, that the state in which we need to transfer the molecular population is a 'dark state' of the system, which means that it does not interact with the driving pulse. This is accomplished with the use of sophisticated pulse as described earlier. However, if we leave aside the mechanism with which the 'dark state' is obtained, we find great similarities between this proposal and the vibrational cooling method described in this part of my thesis. These similarities will become evident in the beginning of the following chapter, where the operating principle of the vibrational cooling technique is going to be discussed.

II.2.3. Methods for the preparation of cold molecules by