Evaporative cooling to quantum degeneracy in magnetic and optical traps 

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Principle of a 2D-MOT

A 2D-MOT captures atoms from a background vapor, confines and cools them in the transversal directions, and out-couples a pre-cooled atomic beam in the axial direction passing through a differential pumping tube. At the same time this tube serves as a velocity filter, resulting in a transversally and longitudinally cold atomic beam arriving in the 3D-MOT chamber. Additional axial molasses cooling significantly increases the output flux 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 efficiently 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.

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.

Magnetic transport

The vacuum lifetime of the atomic samples prepared in the 3D-MOT chamber, as well as the optical access have to be increased for an efficient evaporation process and subsequent experiments. This is achieved by transferring the trapped atoms to the UHV science cell. We apply a magnetic transport technique [146] with a 90◦ elbow, featuring an additional optical access on the transport axis.
The magnetic transport consists of 14 coil pairs which are partly overlapping and one pushing coil. By continuously varying the currents over time, the magnetic trap center is moved over the total distance of 64 cm from the MOT chamber to the science cell.

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.


The magnetic quadrupole trap of the science cell is generated by a custom made coil pair manufactured by Oswald. It includes two pairs of coils, called the inner and the outer coil, see Figure 2.13. Both coil pairs are operated in anti-Helmholtz configuration during the magnetic transport sequence. As soon as the atoms have arrived in the center of the glass cell the current of the outer coil pair is slowly ramped to zero and only the inner coil pair generates the magnetic trapping potential. The entire coil consists of hollow 4mm thick copper wire with squared cross section impregnated in epoxy. The circular hole with 2.5mm diameter inside the wire permits permanent water cooling.
Each of the inner coils is composed of 4 layers with 12 turns per layer. The inner coil diameter is 40mm and the outer diameter is 72mm. Both coils are placed on the vertical axis of the science cell with a distance of 35mm, generating an axial magnetic field gradient of 2.5G/cmA.
The outer coils consist of 4 layers with 4 turns and have inner and outer coil diameter of 73mm and 90mm, respectively. In anti-Helmholtz configuration they generate an axial magnetic field gradient of 0.24G/cmA. Operation in Helmholtz configuration provides a magnetic bias field of 2.2G/A at the center of the science cell with a curvature of -0.027G/cm2 in the axial direction.
The coils are placed inside a stable mount consisting of a fiber-reinforced plastic material. It is attached to the transport coil assembly and provides high mechanical stability and electrical isolation, thus avoiding Eddy currents. Fast switching of the coil currents is ensured by the implementation of insulated-gate bipolar transistors (IGBTs) which are connected in series with the coils. Varistors in parallel to their source/drain junction protect them from induction currents. The high current circuits are galvanically isolated from the IGBT computer control channels by digital opto-couplers.

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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 incidenceon 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.
The two bichromatic imaging beams (X-Img, Y-Img), applied for absorption imaging of 6Li and 40K, are depicted in blue dotted lines, whereas the imaging beam in the vertical zdirection is not shown. We note that the magnetic trap center is shifted in y-direction with respect to the science cell center in order to improve the optical access in y-direction. In this direction, the trap center has a distance of 6.5mm from the glass windows. Due to this reason, also the laser beam foci are displaced with respect to the cell center. Since the height of the glass cell amounts to only 18mm, the z-direction has the best optical access. Therefore, we intend to install a future high resolution objective on this axis.

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 
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


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