Evaporative cooling to quantum degeneracy in magnetic and optical traps 

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6Li-40K dual-species MOT

This section deals with the technical implementation and performance of the 6Li-40K dualspecies MOT. A magneto-optical trap relies on the combination of a magnetic quadrupole field with three orthogonal pairs of counter-propagating red-detuned laser beams leading to cooling and magneto-optical confinement of atoms around the magnetic field zero [150]. For both 6Li and 40K, bichromatic MOT beams with a cooling and repumping frequency component are needed. The repumping component is in general required for all alkali atoms and ensures that the atoms are kept in the nearly cycling cooling transition. In particular 6Li atoms very likely leave the cooling transition due to the very narrow hyperfine structure of the excited-state. Thus the relatively large repumping component even contributes to the cooling of 6Li. For a dual-species MOT it is crucial to minimize light-induced interspecies collisions, since they lead to atom losses. We were able to limit these losses to less than 10%, by employing low magnetic field gradients and relatively low repumping light intensities for both atomic species, as detailed in [127].

CMOT and gray molasses cooling

The phase-space density of the 6Li-40K mixture is increased after the MOT-phase by applying a compressed MOT phase (CMOT) succeeded by an optical molasses phase. First, the CMOT phase compresses the atomic samples and enhances therefore their densities, then the D1 molasses phase cools them further down to deep sub-Doppler temperatures. In the following we describe the implementation of the 6Li-40K dual-species molasses beams in the setup of the main experimental table. The comprehensive characterization of this cooling technique is presented in Chapter 3.

Compressed MOT

In order to increase the density of the atomic clouds trapped in the MOT we apply a socalled compressed MOT phase. For this purpose, the magnetic field gradient is linearly ramped from 8G/cm to 45G/cm within 5ms. Simultaneously the MOT beam intensities are reduced, while the frequencies of both the cooling and repumping components are tuned closer to resonance. For 6Li this leads to a density increase from 2.6 × 1010 at./cm3 to 1.8 × 1011 at./cm3 and the temperature decreases from 1mK to 800 μK. For 40K the density increases from 7 × 1010 at./cm3 to 3.7 × 1011 at./cm3, while the temperature also increases from 240 μK to 2mK.

Implementation of the D1 molasses

The D1 molasses beams were implemented in the main experimental setup by superimposing the molasses beams with the 3D-MOT beams. The total power of the bichromatic fiber output is Pfiber,Li = 150mW for the 6Li molasses and Pfiber,K = 200mW for the 40K molasses. In Figure 2.12 we illustrate how the two molasses beams for 6Li and 40K, which are emitted from the optical fiber outputs labeled D1,Li and D1,K, are nearly superimposed with the 3D-MOT light via the D-shaped mirrors MD.
The lithium and potassium beams are subsequently combined at a dichroic mirror Mdichroic. This beam, that finally includes all MOT- and molasses frequency components, is expanded by a 1:10 lens telescope and distributed by means of polarization optics to the three pairs of σ+–σ− counter-propagating beams of the 3D-MOT and the D1 molasses. The 1/e2-diameter of the 3D-MOT beams is ∼ 22mm after expansion for both 6Li and 40K. The 1/e2-diameters of the molasses beams are ∼ 17.1mm and ∼ 17.8mm for 6Li and 40K, respectively.
The two beams in the horizontal plane are retro-reflected, whereas the vertical axis is driven by two independent beams. Two λ/2 plates, one of order four for lithium (λ/2 ∗ Li), and another one of order four for potassium (λ/2 ∗ K), allow to set the 6Li and 40K 3D-MOT power distribution independently. This is due to the fact that each of these wave plates can, to a very good approximation, turn the polarization axis for one wavelength without affecting the polarization axis of the other one since 4.5×671 ≈ 4×767 and 4.5×767 ≈ 5×671. Finally, the 3D-MOT beams are circularly polarized using first order λ/4 waveplates specified for the wavelength 40K 767 nm. However, these waveplates perform also sufficiently well for the 6Li wavelength 671 nm.

Optically plugged magnetic quadrupole trap

After arrival in the science cell, the atomic samples undergo an evaporative cooling step driven by RF transitions in an optically plugged magnetic quadrupole trap. The optical plug repels the atoms from the trap center, where the magnetic field cancels, avoiding thus atom losses due to Majorana spin-flips. The quadrupole trap provides a steep, linear confinement, yielding high elastic collision rates, and allows therefore for efficient evaporation dynamics.

RF evaporative cooling

Compared to bosons, the evaporative cooling of fermions is much more problematic, since swave collisions between identical fermions are forbidden and thermalization can thus not take place. Due to the angular momentum barrier, p-wave collisions are furthermore suppressed in the limit of low temperatures, typically below T ∼ 6mK for 6Li and T ∼ 50 μK for 40K[10, 157]. At low temperatures, only two different species or two different internal states can therefore provide high elastic collision rates and are able to thermalize.
Collisions between 6Li and 40K have several drawbacks concerning their thermalization efficiency. Firstly, their mass difference increases the thermalization time by a factor of two [67] and secondly, their collision cross section is rather modest. Collisions occur in the triplet channel and have a s-wave scattering length of a = 64.41 a0 [129], resulting in a collision cross section of σLiK = 1.5 × 10−10m2.
Exclusively the stretched state of 6Li is stable inside a magnetic trap, since spin relaxation takes place between different trappable spin states [158]. In the case of 40K, however, spin relaxation is suppressed because of the inverted hyperfine structure [8]. The s-wave scattering length between the magnetically trappable spin states |F,mFi =  9/2, 9/2  and  9/2, 7/2  of 40K is a ∼ 170 a0 [159]. The resulting collision cross section σKK = 1 × 10−9m2 is thus an order of magnitude larger than σLiK.
In consequence, we apply the approach presented in [67] for the evaporation of a 6Li-40K mixture inside a magnetic trap. It consists in evaporating a spin mixture of 40K, while sympathetically cooling a small cloud of 6Li [158]. In the following we present the technical tools, applied in our experiment in order to perform RF evaporation in the plugged magnetic quadrupole trap.

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Optical setup of Science cell

In this section we present the optical setup implemented around the science cell. It is mounted on an U-shaped optical table elevated to the height of the lower transport plate, see Figure 2.15. The two thick red paths, whose starting points are designated ODT1 and ODT2 corresponding to our 1064 nm laser source setup, indicate the beampaths of the crossed dipole trap. Since both beams originate from the same laser source we have to take precautions in order to avoid interference effects and modulation of the crossed trap potential. First of all, the polarisation axis of ODT2 is turned orthogonal to the polarization of ODT1 by a λ/2 plate. Secondly, both beams are shifted in frequency, since for ODT1 we utilize the -1st diffraction order of the first AOM, and the +1st diffraction order of the second AOM is used for ODT2, yielding a frequency difference of 160MHz. For the purpose of power regulation, see Figure 2.14, reflections or leaking light of both trapping beams are detected on photodiodes (D1 and D2) whose current output is converted logarithmically. An additional third photodiode (D4) in linear operation is employed to monitor ODT1. The off-resonant blue-detuned plug beam is superimposed with the ODT2 beam via the dichroic mirror Mdich,3 (DMLP567, Thorlabs). The position of the plug beam focus is monitored by means of a four-quadrant photodiode (4Q-D5) connected to the control computer and is regulated by a piezo-driven mirror (M4).
This feedback loop is required as the plug beam focus has to precisely cover the magnetic field zero of the magnetic quadrupole trap. In future, the same technique will be employed in order to regulate the position of the lattice laser which we plan to superimpose with ODT1 via Mdich,5 (BSR-15-1025, CVI Melles Griot). For this purpose, a back reflection on the glass cell will be utilized. It is important to note that all beams have a non zero angle of incidence on the glass cell in order to avoid interference effects by back reflections. These beam angles are not illustrated in Figure 2.15 for reasons of clarity.

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 fluorescence 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 effects 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 filtering 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. Efficient 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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