Except for a MOT, efficient loading of the traps introduced in the previous sec-tion can only be accomplished if the particles entering the trapping region have translational temperatures below 1 K. They first have to be brought into the gas phase, however, which often leads to initial ensemble temperatures beyond 1000 K. Various approaches are available to dissipate the excess kinetic energy in such samples:
Radiation pressure cooling
Light forces can be employed in many ways to slow down particles. With counter-propagating laser beams on three perpendicular axes, for instance, laser cooling can be efficiently used to severely restrict their motion in all three dimensions. At low enough velocities, the slowing force has a viscous damping character, giving this setup the name optical molasses.
As previously discussed, however, configurations relying on momentum transfer from resonant absorption and spontaneous emission of photons are only applicable to very few molecular systems.
In contrast, optical cooling by coherent scattering inside an optical res-onator does not depend on the particles’ internal structure and is applica-ble to polarizaapplica-ble atoms as well as molecules [37]. Translational energies corresponding to K temperatures can be achieved here in all three di-mensions by coupling the particles to a far-detuned light field inside a single standing-wave optical resonator [38].
Sympathetic cooling
The term sympathetic cooling refers to situations where one particular species is cooled through thermal contact with a second, directly cooled species in the gas phase. Since it relies on elastic collisional energy trans-fer, a prerequisite is the effective absence of state changing inelastic col-lisions between the involved particles which would otherwise lead to an unacceptable loss rate in the trap. Sympathetic cooling then offers a good
8 INTRODUCTION alternative for species not amenable to laser cooling techniques. It was first demonstrated for ions in 1986 [39], but since has also been used to cool ensembles of neutral particles into the BEC regime [40].
Buffer-gas loading
Closely related to sympathetic cooling is buffer-gas loading [41], in which the species of interest is injected into a vapor of cryogenically cooled he-lium atoms for thermalization via elastic collisions. The use of the inert noble gas in conjunction with cryogenic techniques offers several advan-tages. Inelastic collisions and chemical reactions with the buffer-gas are strongly suppressed, so that buffer-gas loading should be applicable to a great variety of different particles, including rather large molecules. By slightly changing the temperature of the buffer-gas, the helium vapor pressure — and thus the collision rate — can be adjusted over several orders of magnitude. Unlike sympathetic cooling, this also allows to more or less completely remove the buffer-gas from the trapping region once the sample has been cooled sufficiently for confinement in a suitable trap.
Since the volume covered by the buffer-gas is relatively large, high initial particle numbers and densities in the trap are possible.
Cryogenic surface thermalization
For completeness it should be mentioned that atomic hydrogen can be loaded into a magnetic trap by thermalization with a superfluid helium surface. It presently still constitutes the most efficient loading scheme in terms of the initial number of particles transferred into the trap. While this technique was crucial for the realization of a hydrogen BEC in 1998 [42], the unique binding properties of hydrogen to liquid helium limit its use to this particular species.
Instead of starting with a hot vapor, one can also take advantage of the already high phase space densities found in ensembles generated by a pulsed supersonic expansion from a nozzle. Here, the spread of velocities already corresponds to a temperature suitable for trapping. It is therefore sufficient to reduce the high forward velocity of the sample in the laboratory frame as a whole. This may be accomplished with one of the following techniques:
Stark deceleration
Bunches of polar molecules can be efficiently slowed down with time-varying electric fields in a Stark decelerator [43]. It is based on the same principle that is also utilized in electrostatic traps. Molecules possessing an electric dipole moment will exchange kinetic energy for Stark energy upon entering an electric field, if they are in an appropriate quantum state. When the electric field is quickly switched off before the molecules are gone, they will not regain the lost kinetic energy. Multiple pulsed
COOLING AND TRAPPING TECHNIQUES 9 electric field stages can thus be used successively to bring the molecules to a virtual standstill.
Optical dipole force slowing
Although not yet demonstrated, it is conceivable to scoop particles ex-iting a nozzle at right angles with a nonresonant laser beam steered by a scanner. They can then be decelerated on a circular path by gradually reducing the beam’s angular speed [44]. Such a “laser scoop” resembles a moving optical dipole trap and therefore works both for atoms and molecules.
Alternatively, polarizable particles in a pulsed supersonic jet might also be decelerated by using optical dipole forces in a travelling far-off-resonant optical lattice [45]. According to theoretical predictions, the moving lattice potential can be tailored such that it reflects particles in the jet to zero velocity in the laboratory frame while keeping the initial phase space density.
Mechanical slowing
The rapid forward flow of gas emerging from a nozzle can be largely cancelled if the nozzle is moved in a direction opposing the particle flow.
By mounting it on a high-speed rotor, sample temperatures around 10 K have been obtained in the laboratory frame [46]. It is believed that these can be reduced to below 1 K in an optimized apparatus.
An entirely different approach for the preparation of cold molecules is to form them directly in the trap from their atomic constituents:
Conversion processes
Here, all required precursor substances are loaded into the trap first, so that the trapping mechanism needs to be able to accommodate those as well as the target molecules. All issues concerning the cooling of more complex particles are thereby completely avoided, as long as the produc-tion process does not involve an accompanying momentum transfer.
In recent research, a very successful method of inducing the chemical con-version has been photoassociation [47, 48], where laser light excites two adjacent atoms into a vibrationally excited state of a bound molecule.
Bringing these molecules to the vibrational ground state is not straight-forward, though, which significantly reduces their lifetime and so far pre-vented further progress in this field towards large numbers of trapped, stable molecules.
The use of so-calledFeshbach resonancesin swept magnetic fields has now opened up a new possibility to reversibly create more stable molecules consisting of local pairs from an ultracold atomic quantum gas. Although
10 INTRODUCTION this process still leads to relatively high vibrational quantum numbers, it has lately permitted the first realization of a molecular BEC in thermal equilibrium with Li2 [49, 50].