Methods for the preparation of cold molecules by association

Magneto-association

An alternative approach for the production of cold molecules is to create them from ultra cold atoms by the use of an associative technique. In the introduction of the first part of this thesis, the magneto-association technique or Feshbach resonance was discussed. We show how the variation of a bias magnetic field in the area of the Feshbach resonance can lead to the association of ultra cold atoms in long range molecules. In particular for the case of Cs, the magnetic resonances have been used not only for the creation of ultracold molecules, but also for the modification of the Cs collision properties towards condensation as discussed in [Web03b]. Apart from that, the Feshbach resonances find extensive applications in the area of cold and ultracold atoms, since they are related the study of BEC-BCS crossover, superfluidity and more [Kett07, Sal07]. The Innsbruck group, reported extensively in the first part of this thesis [Web03], is a pioneering group in the study of cold molecule formation via magneto-association, since directly after the preparation of a Cs BEC, a molecular BEC prepared via magneto-association was reported.

In Fig. II.2.3.1, we see the first observation of ultra-cold Cs2 molecules created by this method [Herb03]. The different magneto-dipole moment is used to separate the cold molecules by the atomic BEC. The molecules are either left to fall or they are levitated with respect to the Cs BEC.

Fig. II.2.3.1: Cold molecule formation by magneto-association. Figure adapted by [Herb03]. On the left we see a pure atomic Cs condensate. On the center, we see molecules created by magneto-association falling from the condensate, while in (c) they are levitated by means of external magnetic fields.

Photo-association

1. General description

Photoassociation is also a technique that permits the creation of cold molecules from an sample of cold atoms, usually performed in a MOT. Photoassociation is the process in which two atoms are colliding in the presence of a laser field. This laser can bring the atoms into resonance with a long range, but bound molecular state. Because the free-state thermal energy spread is negligibly small, this process leads to a well resolved free-bound absorption spectrum. This

"photoassociation spectroscopy" is proving to be a powerful tool for the analysis of atomic interactions at long range. Performing photoassociation in a MOT leads to loss in the number atoms magneto-optically trapped. The atoms which undergo photoassociation form loosely bound molecules, which are in their largest percentage dissociated to give hot free atom pairs. In any case, the photo-associated atoms exit the MOT, either because the MOT cannot support molecules, or because the atoms, that result from the dissociation of the molecules formed by photoassociation, are hot and escape the trapping. Thus, observing the losses in the MOT as a function of the photoassociation frequency, provides perhaps the easiest method for the realization of photoassociation spectroscopy. Another methods consist of detecting the molecules which are formed by photoassociation, usually by laser induced ionization. In Fig. II.2.3.2, we see photoassociation spectra acquired by both these methods. The red curves represent photoassociation spectra obtained by the 'trap-loss' method, while the black curves represent spectra of the ground singlet and triplet Cs2 states, acquired by pulsed laser 2 photon Resonance-Enhanced Multi-Photon Ionization (REMPI) [Comp99, Drag 00].

Fig. II.2.3.2: Photoassociation spectra acquired by two methods. The red curves represent photoassociation spectra obtained by the 'trap-loss' method, while the black curves represent spectra acquired by pulsed laser REMPI.

2. Stabilization of the produced molecules

The principle of photoassociation of cold atoms has been proposed in 1987 [Tho87] and was originally demonstrated six years later with sodium [Lett93] and rubidium atoms [Mill93], while potassium and lithium followed some years after [McAl95, Wang96]. Photoassociation was also performed in Cs and stabilization of the produced molecules has been demonstrated in [Fio98]. In our group, cold Cs molecules produced by photoassociation have been loaded to a magnetic [Vanh02] and a dipole trap [Zahz06], while their vibrational cooling was recently demonstrated with the use of shaped femtosecond pulses [Vit08].

Photoassociation can be represented as a light-assisted collision as in Eq. 1.13. Two colliding atoms absorb a photon resonant with an excited molecular level. This molecule is relaxing typically in some tens of nanoseconds.

CsCshvLCs2* (1.13)

Whether the relaxation is towards a bound molecular state, or towards two unbound hot atoms depends on the inter-nuclear distance in which the wavefunction of the excited molecule is centered. This is depended on the molecular potential via which photoassociation is realized. For the case of homonuclear atoms, the typical molecular potentials ('single well') leads to the production of molecules which are localized in large internuclear distances, and which relax principally to two unbound and hot atoms. In Fig. II.2.4.a.2, we see a schematic representation of photoassociation via a typical homonuclear molecular potential. Initially, the two free atoms collide with a photon resonant with an excited molecular level, with only their initial thermal energy kBT.

This photoassociation scheme created an excited molecule localized in large internuclear distances, a fact which principally results to the relaxation of the excited molecule to a pair of hot atoms, while relaxation towards a bound molecular state is strongly suppressed.

Fig. II.2.3.3: Schematic representation of photoassociation via a typical homonuclear molecular potential, which principally results to the relaxation of the excited molecule to a pair of hot atoms [Niko00].

However, relaxation towards a bound molecular state can be enhanced, if the potential via which the photoassociation is taking place is particular. In Fig. II.2.3.4 adapted by [Dion01], we see the two potential cases. In the upper part of the picture, photoassociation is taking place via a non particular molecular potential and relaxation towards unbound atoms is favorable. In the middle part, the photoassociation is taking place via a particular potential, which has an additional local minimum at an intermediate internuclear distance. The existence of this additional potential minimum leads to enhanced relaxation in short interatomic distances. In the lower part, coupling to an additional molecular potential perturbates the molecular wavefunction and leads to the stabilization of the produced molecules.

In the case of heteronuclear molecules, photoassociation can be different, since the excited (as well as the fundamental) potentials lead to the creation of molecular states in shorter internuclear distances. This has as an effect the reduction of the photoassociation efficiency, but on the other hand, leads to enhanced relaxation rates towards the ground molecular states. This characteristic of photoassociation in heteronuclear molecules is widely used for the preparation of molecule without vibration or rotation, in some of the techniques discussed in the next paragraph.

Fig. II.2.3.4: Figure adapted by [Niko00] showing (a) the photoassociation of molecules via a non particular molecular potential, (b) via a particular potential and (c) stabilization of the produced molecules in short internuclear distances, via coupling to another molecular potential.