Evaporative cooling to quantum degeneracy in magnetic and optical traps 

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General design approach

Quantum degeneracy is reached as soon as the thermal deBroglie wavelength of the atomic wavepackages is on the same order of magnitude as the inter-particle distances. An equivalent criterion states that the phase space density (PSD) has to reach the order of unity. This means that the atoms need to be cooled down as low as possible while remaining conned in a trap that should be as tight as possible. In order to meet these goals we follow the common pathway to quantum degeneracy, which consists in a rst laser cooling stage followed by a further stage of forced evaporative cooling.
The laser cooling stage is provided by two techniques, a magneto-optical trap (MOT), see Section 2.6, and a gray optical molasses, presented in Chapter 3. The MOT is simultaneously loaded with both atomic species via two distinct and continuous beams of pre-slowed atoms. This loading method is advantageous for several reasons. Firstly, in contrast to loading from a background vapor, the MOT can be operated in an ultra-high vacuum (UHV) environment, see Section 2.2. Secondly, the atomic beam ux and consequently the MOT loading rate are larger than for pulsed loading schemes using alkali getter dispensers [143] or employing ultraviolet light-induced absorption [144, 145]. Finally, we are able to utilize distinct sources for both species employing even dierent pre-cooling techniques, namely a Zeeman slower for 6Li, presented in Section 2.4, and a 2D-MOT for 40K, see Section 2.5. Subsequent to the MOT loading phase, a three dimensional gray optical molasses is performed cooling the atoms of both species down to sub-Doppler temperatures.

D1 laser system

Figure 2.5 presents the level schemes corresponding to the D1 line transitions of 6Li and 40K, together with the molasses beams driving these transitions. The AOMs of the D2 systems cannot be employed for shifting to the D1 wavelengths, since they operate only in the range of hundreds of MHz, see Figure 2.4. However, the frequencies of the D1 and D2 lines for 6Li and 40K, are separated by 10 GHz and 11 THz, respectively, see Figure 2.2 and 2.3.
Therefore two additional laser systems were required for the implementation of the D1 sub- Doppler cooling scheme in our experimental setup.
The D1 laser systems for 6Li and 40K are presented in Figure 2.6. For both setups the frequency-lock point can be shifted by tuning the double-pass AOM in the path of the saturated absorption spectroscopy. For the 40K D1 system, the repumping frequency is generated by an electro-optic modulator (EOM). In general, a EOM creates two sidebands separated from the original carrier frequency by the modulation frequency of the EOM. In our case the sideband with the lower frequency constitutes the repumping component. The power loss due to the unused second sideband can be neglected, since only low modulation amplitudes are required for the D1 cooling scheme operating with relatively low repumping power. Furthermore, this second sideband does not address the atoms by exciting unwanted transitions.

40K 2D-MOT

A two-dimensional magneto-optical trap (2D-MOT) serves as atom source for our 40K 3DMOT. A 2D-MOT is a high ux cold atom source, that was realized for rubidium[151{ 153], potassium[154], cesium[155] and lithium[156]. Even though the atom uxes generated by Zeeman slowers are generally higher, they are also sources of magnetic elds and hot atom jets in the MOT region. In comparison, 2D-MOTs have a more compact design and can be operated at lower temperatures, being thus more economic with regard to sample consumption. This is an important point for fermionic potassium, since the 4% enriched 40K samples that we use are quite expensive. In addition, the 2D-MOT separates the 40K isotope from the more abundant 39K, since only the 40K atoms are cooled and form the atomic beam, thus reducing the thermal background considerably.

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Principle of a 2D-MOT

A 2D-MOT captures atoms from a background vapor, connes and cools them in the transversal directions, and out-couples a pre-cooled atomic beam in the axial direction passing through a dierential pumping tube. At the same time this tube serves as a velocity lter, resulting in a transversally and longitudinally cold atomic beam arriving in the 3D-MOT chamber. Additional axial molasses cooling signicantly increases the output ux of a 2D-MOT[151], since the atoms are hold in the transverse cooling region for a longer time. In our old setup we employed two independent, counter propagating, axial molasses beams, labelled axial+ and axial- in Figure 2.8, injected by means of a 45-angled mirror inside the vacuum chamber. For the upgraded setup we added an independent pushing beam, out-coupling the atomic beam more eciently through the small hole in the center of the 45-angled mirror.

Characterization of the 2D-MOT upgrade

The performance of the 2D-MOT can be characterised by measuring the loading rate of the 40K-MOT as a function of the 2D-MOT parameters that are at our disposal. The impact of several parameters, as for example the light intensity ratios, frequency detunings and the vapor pressure in the 2D-MOT cell, have already been studied in [141]. In the following we concentrate on the improvements that have been made on the 2D-MOT setup, namely the new approach to control the pressure in the 2D-MOT glass cell and the implementation of an additional pushing beam whose intensity can be controlled independently.

Table of contents :

1. Introduction 
1.1. Ultracold quantum gases
1.2. Quantum degenerate Fermi gases
1.3. Fermi-Fermi mixtures
1.4. Thesis outline
I. 6Li-40K Experiment 
2. Experimental setup 
2.1. General design approach
2.2. Vacuum chamber
2.3. Laser systems
2.3.1. D2 laser system
2.3.2. D1 laser system
2.4. 6Li Zeeman slower
2.5. 40K 2D-MOT
2.5.1. Principle of a 2D-MOT
2.5.2. Experimental setup
2.5.3. Characterization of the 2D-MOT upgrade
2.6. 6Li-40K dual-species MOT
2.6.1. Experimental setup
2.7. CMOT and gray molasses cooling
2.7.1. Compressed MOT
2.7.2. Implementation of the D1 molasses
2.8. Magnetic trapping
2.9. Magnetic transport
2.10. Optically plugged magnetic quadrupole trap
2.10.1. Coils
2.10.2. Optical plug
2.11. RF evaporative cooling
2.12. RF system
2.13. Optical dipole trap
2.13.1. Power stabilization
2.13.2. ODT2
2.14. Optical setup of Science cell
2.15. Computer control system
2.16. Imaging and data acquisition
2.16.1. Absorption imaging
2.16.2. Auxiliary uorescence monitoring
2.17. Conclusion
3. Sub-Doppler laser cooling of alkalines on the D1-transition 
Appendix 3.A Publications
4. Evaporative cooling to quantum degeneracy in magnetic and optical traps 
4.1. Introduction
4.2. Principle of evaporative cooling
4.3. Experimental approach and results
4.3.1. RF evaporation
4.3.2. Optical dipole trap
II. Multi-watt level 671-nm laser source 
Introduction
5. Fundamental laser source at 1342 nm 
5.1. Nd:YVO4 as laser gain medium
5.1.1. Crystal structure
5.1.2. Emission
5.1.3. Absorption
5.2. Laser cavity design: Theory and realization
5.2.1. Hermite-Gaussian beam modes and resonators
5.2.2. Thermal eects and power scaling
5.2.3. Characteristic curve and output power
5.2.4. Laser cavity design
5.3. Single-mode operation and frequency tuning
5.3.1. Unidirectional operation via Faraday rotator
5.3.2. Frequency-selective ltering via Etalons
5.3.3. Etalon parameters
5.3.4. Etalon temperature tuning
5.4. Characterization of performance
5.4.1. Output power
5.4.2. Output spectrum
5.4.3. Spatial mode
5.5. Conclusion
6. Second harmonic generation 
6.1. Theory of second-harmonic generation
6.1.1. Nonlinear conversion
6.1.2. Quasi-phase matching
6.1.3. Physical properties of the selected nonlinear media
6.2. Enhancement cavity
6.2.1. Mode matching and intra-cavity loss
6.2.2. Impedance matching
6.2.3. Locking scheme
6.2.4. Cavity characterization and SH output power
6.3. Intracavity frequency-doubling
6.3.1. The fundamental laser
6.3.2. Ecient intracavity second-harmonic generation
6.3.3. Tuning behavior and nonlinear-Kerr-lens mode locking
6.3.4. Conclusion
6.4. Waveguide
6.4.1. Setup and characterization
6.4.2. Theoretical model
6.5. Conclusion
Appendix 6.A Publications
General conclusion and outlook
A. Publications
Bibliography 

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