Photoassociation of heteronuclear 6Li40K molecules 

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Principle of a 2D-MOT

In a 2D-MOT, an atomic vapor is cooled and confined transversally and out-coupled longitudinally through an aperture tube. The role of the aperture tube is two-fold.
First, it isolates the 2D-MOT from the MOT chamber by differential pumping, and second, it acts as a geometric velocity filter, since only atoms with a small transverse velocity pass through. As the transverse cooling is more efficient for atoms which have a small longitudinal velocity—since those spend more time in the cooling region—most of the transversally cold atoms are also longitudinally cold. Thus, the filter indirectly filters atoms also according to their longitudinal velocity. A 2D-MOT thus produces an atomic beam which is transversally and longitudinally cold.
The flux of a 2D-MOT can be improved by adding a longitudinal molasses cooling to the 2D-MOT configuration [139]. Thus, the atoms spend more time in the transverse cooling region due to the additional longitudinal cooling. The longitudinal beam pair is referred to as the pushing and the retarding beam, where the pushing beam propagates in the direction of the atomic beam (see Fig. 2.9). We implemented such a configuration, making use of a 45◦-angled mirror inside the vacuum chamber. This mirror has a hole at its center which creates a cylindrical dark region in the reflected retarding beam. In this region, the atoms are accelerated along the longitudinal direction by the pushing beam only, which allows an efficient out-coupling of the atomic beam.

6Li-40K dual-species MOT

Previously, several groups have studied samples of two atomic species in a magnetooptical trap [144, 145, 146, 147, 89, 43, 44]. We describe here the implementation of our 6Li-40K dual-species MOT. Its characterization and a study of collisions between atoms of the different species is presented in chapter 3.

Principle of a MOT

In a magneto-optical trap six counter-propagating red-detuned overlapping laser beams cool and magneto-optically confine atoms in a magnetic quadrupole field around its zero [134]. MOTs for alkali atoms require laser light of two frequencies, namely the cooling and the repumping frequency. The latter ensures that the atoms stay in the (almost-) cycling transition used for cooling. Typically the repumping light has a much lower power than the cooling light as the atoms principally occupy the states belonging to the cooling transition. For 6Li, however, the power of the repumping light needs to be relatively high, since 6Li has a very small hyperfine structure in the excited-state manifold (of the order of the linewidth). When laser cooled, 6Li atoms thus very likely quit the cooling transition. Therefore, the repumping light needs to contribute to the cooling process. As a consequence it needs to be present in all six directions with the same polarization as the cooling light. Therefore, we use bichromatic MOT-beams containing both cooling and repumping frequencies. We adapt the same strategy also for 40K.

Transfer from the MOT to the magnetic quadrupole trap

As soon as the dual species MOT is loaded with a sufficiently large number of atoms, we transfer the atom cloud to the magnetic quadrupole trap, which is created by the coil pair which is also used for the MOT. For an efficient transfer the atom cloud first needs to be compressed and it needs to be polarized to magnetically trappable states.
This requires two stages termed the “compressed MOT”- and the “optical pumping”- stage, which are executed in immediate succession before the magnetic field of the trap is switched on.

Magnetic quadrupole trap of the final cell

The magnetic transport sequence ends when the atoms arrive in the magnetic quadrupole trap of the final cell. In this trap the atoms will be evaporatively cooled until they are sufficiently cold and compressed to be transferred into an optical dipole trap. The atom loss due to Majorana spin flips during the evaporative cooling will be avoided by the presence of an optical plug which repels the atoms from the region where the spin flips occur. We present here the specifications of the final quadrupole trap, the installation of the optical plug is described in the next section.
The coil pair for the magnetic trap in the science cell was wound by ourselves and it consists of 4 × 19 turns of 4mm thick copper wire of circular cross section which has a circular hole of 2.5mm diameter in its center to allow for efficient water cooling. The inner and outer coil diameters are 3.4 cm and 19.5 cm, respectively. The two coils are separated by 3.65 cm, leaving a distance of 3.3mm between the coils and the walls of the science cell. They create an axial magnetic field gradient of 3.75G/(cmA). We will soon replace this coil pair by a new one, which is manufactured by the company Oswald. The mount for this new coil pair will also support a coil pair which can create a strong bias field with a high precision which will allow tuning atomic interactions by means of Feshbach resonances in an optical trap.

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Table of contents :

1 Introduction 
1.1 Quantum degenerate Fermi gases
1.2 Mixtures of Fermi gases
1.3 Heteronuclear Fermi-Fermi molecules
1.4 Outline of this thesis
2 Construction of the experimental apparatus 
2.1 Design considerations
2.2 Vacuum manifold
2.2.1 Setup
2.2.2 Assembly, pump down and bake out
2.3 Laser systems
2.3.1 Optics
2.3.2 Diode lasers
2.3.3 Saturated absorption spectroscopy
2.3.4 Tapered amplifiers
2.4 6Li Zeeman slower
2.4.1 Principle of Zeeman-tuned slowing
2.4.2 Oven
2.4.3 Coil assembly
2.4.4 Optics
2.5 40K 2D-MOT
2.5.1 Principle of a 2D-MOT
2.5.2 Experimental setup
2.6 6Li-40K dual-species MOT
2.6.1 Principle of a MOT
2.6.2 Experimental setup
2.7 Magnetic trapping
2.7.1 Principle of magnetic trapping
2.7.2 Transfer from the MOT to the magnetic quadrupole trap
2.7.3 Magnetic transport
2.7.4 Magnetic quadrupole trap of the final cell
2.7.5 Optical plug
2.7.6 Evaporative cooling
2.8 Diagnostic tools
2.8.1 Principle of absorption imaging
2.8.2 Evaluation of absorption images
2.8.3 Optical setup
2.8.4 Practical aspects
2.8.5 Auxiliary detection systems
2.8.6 Experiment control and data acquisition
2.9 Conclusion and outlook
3 Characterization of the experimental apparatus 
3.1 6Li Zeeman slower
3.2 40K 2D-MOT
3.3 6Li-40K dual-species MOT
3.3.1 Single-species MOTs
3.3.2 Heteronuclear Collisions in the dual-species MOT
3.4 Transfer of the atoms into the magnetic trap
3.5 Magnetic quadrupole trap
3.6 Magnetic transport
3.7 Conclusion
4 Photoassociation of heteronuclear 6Li40K molecules 
4.1 Introduction
4.1.1 Principle of photoassociation
4.1.2 Applications of ultracold photoassociation
4.1.3 Photoassociation of LiK∗ compared to other dimers
4.1.4 Detection techniques for photoassociation
4.1.5 Molecular potentials
4.1.6 Selection rules
4.1.7 Rotational barriers for ultracold ground-state collisions
4.1.8 The LeRoy-Bernstein formula
4.1.9 Previous work on LiK
4.2 Experimental results
4.2.1 Experimental setup
4.2.2 Optimization of the photoassociation signal
4.2.3 Photoassociation spectroscopy of 40K∗2 molecules
4.2.4 Photoassociation spectroscopy of 6Li40K∗ molecules
4.3 Conclusion
5 Particle motion in rapidly oscillating potentials 
5.1 Introduction
5.2 Classical motion in a rapidly oscillating potential
5.2.1 Time-independent description
5.2.2 Coupling between the mean motion and the potential’s phase .
5.2.3 The effect of a phase hop
5.3 Quantum motion in a rapidly oscillating potential
5.3.1 Time-independent description
5.3.2 The effect of a phase hop
5.3.3 Numerical simulations
5.4 Consistency between classical and quantum mechanical results
5.4.1 Coherent states
5.4.2 Effect of phase hop on a coherent mean-motion state
5.5 Conclusion
6 Conclusion 
A Determination of vapor pressure by light absorption 
B Saturation spectroscopy of the violet 4S1/2 → 5P3/2 transition of K 
C Engineering drawings 
C.1 Octagonal cell
C.2 Science cell
C.3 Tapered amplifier support for potassium
C.4 Tapered amplifier support for lithium
C.5 2D-MOT vacuum parts
D Publications 


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