High power 671 nm laser system

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Ultracold atoms – a highly controllable model system

The unprecedented degree of control over many system parameters makes ultracold Fermi gases an ideal model system to investigate quantum many body phenomena. Let us con-sider an experiment with a mixture of two components, 1 and 2. The components could be two di erent states of one atomic species or two di erent atomic species. The various parameters of the two components that can be controlled, range from the element and state of the component, the temperature, the populations of the components, the inter-atomic interaction strength, the mass ratio, over the con nement to the dimensionality of the system.
In an ultracold atom experiment, all these parameters can be varied from one experimen-tal cycle to another. The cycling time of an usual ultracold atom experiment is on the order of some tens of seconds. Therefore, it is possible to investigate full phase diagrams and examine phase transitions.
Another advantage of ultracold atom experiments is the variety of existing tools to probe the gas, such as radio-frequency (RF) spectroscopy [29], Ramsey interference [30], Bragg spectroscopy [31], quantum noise correlations [32{35], single side imaging in optical lat-tices [36{38], or time of ight (TOF) measurements [39], where the gas can freely expand after it has been released from the trap. Absorption images yield important information about each component, such as the atom number, and the atomic distribution in real-and momentum space. One experimental run consists of setting the parameters, probing the gas and analyzing the absorption images. Most of the data points presented in this thesis are obtained by a series of such runs.

Quantum degenerate Fermi gases

A Fermi gas is quantum degenerate when its temperature is lower than the Fermi tem-perature TF = EF/kB, where EF is the Fermi energy and kB the Boltzmann constant. The rst degenerate Fermi gas was realized with 40K [4], by adopting the cooling methods developed to reach BEC with bosonic atoms. At ultracold temperatures, the Fermi gas shows a strong deviation from the classical behaviour, unveiling the Fermi-Dirac distri-bution of the fermions over the trap states. To date, fermionic quantum degeneracy has also been reached for 6Li [40,41], metastable 3He∗ [42], the rare earth elements 173Yb [43], 161Dy [44] and recently 167Er [45], and the alkaline earth element 87Sr [46, 47]. Early ex-periments reached temperatures of about one quarter of the Fermi temperature. State-of-the-art experiments cool the atoms to below one tenth the Fermi temperature [48,49]. Reaching quantum degeneracy requires evaporative cooling, a method relying on the rethermalization of the gas by elastic collisions. Cooling Fermi gases is challenging, because ultracold gases only collide via s-wave collisions, and the Pauli exclusion principle prohibits these collisions for indistinguishable fermions. Therefore, the gas has to be either prepared in two di erent internal states or sympathetically cooled. Furthermore, the collision rate for fermions decreases for low temperatures, because scattering in low-lying momentum states requires these states to be empty, and becomes less likely [4, 50]. In addition, inelastic collisions diminish the cooling e ciency and can create hole excitations deep in the Fermi sea [51, 52].
To reach quantum degeneracy, several approaches are in use. The single-species evap-oration scheme with two di erent internal states has been used for 40K [4], 6Li [53, 54] and 173Yb [43]. Sympathetic cooling with bosons has been employed for 6Li-7Li [40, 41], 6 Li-23Na [48], 6Li-87Rb [55], 40K-87Rb [56{60], 3He∗-4He∗ [42], 6Li-40K-87Rb [61] and 6Li-40K-41K [62]. The Fermi-Fermi mixture 6Li-40K has been cooled with several methods. In Innsbruck, 6Li in two spin states is cooled in an optical trap, sympathetically cooling 40K along [63]. The Amsterdam group performed evaporation of a 40K spin-mixture in a magnetic trap, sympathetically cooling 6Li.
Early experiments investigated one-component, nearly ideal, non-interacting Fermi gases and their thermodynamics [4, 40, 64]. Interacting Fermi gases, composed of two com-ponents, became accessible by tuning the interactions between atoms using Feshbach resonances [65, 66]. These resonances, where two colliding atoms couple resonantly to a bound molecular state, were rst investigated in bosonic systems [24]. By applying a magnetic eld, one can change the relative energy of the colliding atoms and the bound state and hence tune the scattering length [67].
The research on strongly interacting Fermi gases began with the characterization of Feshbach resonances in fermionic systems, e.g. for 6Li [68{70] and 40K [71{73]. In con-trast to Bosons, fermionic atoms are quite stable in the vicinity of a Feshbach reso-nance, because the Pauli exclusion principle prohibits three-body relaxation [74]. There-fore, it was possible to create a Bose-Einstein condensate of weakly bound Feshbach molecules [75{77]. Subsequently, also the Bardeen-Cooper-Schriefer (BCS)-type super-uid was realized [78{80], where the pairing mechanism for weakly attractive interac-tions is not molecule formation but Cooper pairing. The stability of strongly interacting fermions enabled the investigation of the crossover from the BEC- to the BCS-type su-per uid [80{82]. The crossover smoothly connects the two super uid states across the strongly interacting regime.
Experiments with strongly interacting ultracold Fermi gases proved the super uid charac-ter by the creation of vortices [83], studied fermionic mixtures with population imbalance, leading to a phase separation between paired and unpaired fermions [84,85], measured the speed of sound in a Fermi gas [86] and the critical velocities [87]. Moreover, a fermionic Mott insulator was realized [88, 89] and the equation of state of a strongly interacting Fermi gas was directly measured [49, 90, 91]. The list could be continued, and is only a selection of examples, meant to illustrate the activity in this eld of research.
For a strongly interacting Fermi gas, the transition to a super uid of paired fermions occurs at a relatively high critical temperature relative to the Fermi temperature, TC ∼ 0.17 TF [92,93]. Therefore, strongly interacting Fermi gases might play an important role for understanding high-TC superconductivity, and future experiments could throw new light on the underlying physics of this phenomenon [94].

Fermi-Fermi mixtures with two different atomic species

The study of mixtures of two di erent fermionic species is intriguing, because of the large number of controllable system parameters, such as the mass-imbalance and the dimen-sionality of the system. The di erent mass of the two species yields unmatched Fermi surfaces and symmetric BCS pairing cannot occur. New quantum phases with di erent pairing mechanisms are predicted [95]. For instance the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state [96{98] or the breached pair state [99, 100]. Other phenomena such as a crystalline phase transition [101] and the formation of long-lived trimers [102] might exist. One can study bosonic polar molecules with long-range dipole-dipole interactions [103, 104].

Fermi-Fermi mixtures with two different atomic species

Furthermore, species-selective potentials [105, 106] can be used to investigate systems in mixed dimensions, where species 1 particles evolve in three dimensions and species 2 evolve in two, one or zero dimensions [107]. The mixed dimensionality in uences the two-body interaction leading to con nement induced resonances [108{112]. The 3D-0D case corresponds to the Anderson impurity model and can lead to Kondo correlated states [113{115]. A dilute gas of trapped impurity scatterers also provides a novel system to study Anderson localization [116{118]. Few-body e ects such as p-wave resonances between species 1-2 dimers and species 1 atoms tunable by the lattice depth [102], and the E mov-e ect in mixed dimensions [119] can be studied. New many-body quantum phases, where species 1 mediates interactions between species 2 atoms in di erent layers might lead to interlayer super uidity [120].
The mixture 6Li-40K is a prime candidate for these studies. Lithium and potassium are widely used alkali atoms in a variety of applications ranging from Bose-Einstein condensation and fermionic pairing to atom interferometry and precision measurements. They possess easily accessible fermionic and bosonic isotopes and can be conveniently cooled and trapped by laser light. The bosonic isotopes can also be used to study Bose-Fermi mixtures in optical lattices [121, 122]. Moreover, 6Li and 40K are the only stable, fermionic alkali atoms.
To date, all research groups investigating Fermi-Fermi mixtures with two di erent atomic species chose the mixture 6Li-40K [62, 63, 123{125]. So far, three groups reported on quantum degeneracy of the mixture [61{63]. The interspecies Feshbach resonances are characterized [126{130] and weakly bound Feshbach molecules were studied [63,131]. Fur-thermore, the Innsbruck group studied the hydrodynamic expansion of 6Li and 40K in the strong interaction regime [132], measured the excitation spectrum of 40K impurities resonantly interacting with a Fermi sea of 6Li, where they observed repulsive polarons for strong interactions [133], and recently observed a strong atom-dimer attraction in a mass-imbalanced mixture [134].
To use an ultracold Fermi gas as a model for other physical systems, universality is a prerequisite. In the universal regime, the properties of the gas solely depend on the scattering length and the interparticle separation, and not on microscopic details of the interaction potential. To enter the universal regime a strong Feshbach resonance with a large width is required. To date, the universal regime can be only reached for the single species 6Li [135] and 40K [136]. However, it might be possible to reach the universal regime for the 6Li-40K-mixture, by using the 1.5 Gauss-wide Feshbach resonance at B0 .

Sub-Doppler laser cooling

The road towards quantum degeneracy in atomic gases usually starts by a laser cooling and trapping phase that should provide a large initial phase space density of the atomic ensemble. This favors a high collision rate for initiating e cient evaporative cooling to quantum degeneracy. Sub-Doppler cooling has proven to be a powerful technique to increase the phase-space density of the atomic sample [137]. However, cooling lithium and potassium using optical transitions is di cult compared to the other alkali-metal atoms. The small separation of the excited-state structure of the D2 transition, compromises the e ciency of standard sub-Doppler cooling techniques such as polarization gradient cooling [137{139].
The central scienti c result of my thesis is the simultaneous sub-Doppler cooling of 6Li and 40K using a bichromatic cooling scheme on the D1 transitions [140, 141]. The D1 molasses phase not only cools the atoms to deep sub-Doppler temperatures, 44 µK for 6 Li and 11 µK for 40K, but preserves the large atom numbers of the magneto optical trap (MOT). In combination with a preceding compressed MOT phase, the atomic density is increased by a factor of ve, yielding a phase space density of ∼10−4 for both species. The combined temperature and density improvement after the D1 molasses is at least a thirty-fold increase in phase space density compared to our MOT. The D1 cooling scheme is applicable to other alkali atoms [141{145], and enables fast evaporation to quantum degeneracy in optical or magnetic traps. Furthermore, it can be used to directly load atoms in a far detuned optical trap with high e ciency [144, 145], o ering a promising route for the all-optical production of alkali degenerate gases.
Another possibility to pre-cool 6Li and 40K is to operate the MOT on a transition with smaller linewidth to reduce the Doppler-temperature. Such transitions exist for 6Li and 40K in the near-UV and blue regions of the spectrum respectively, leading to temperatures near 60 µK [146, 147]. Yet, special optics and a coherent source at 323 nm (405 nm) for 6 Li (40K) are needed for this approach. Additionally, at these wavelengthes the available power is still a limiting factor.

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Thesis outlin

This thesis presents novel techniques for experimental studies of ultracold quantum gas mixtures of fermionic lithium and potassium and the further construction of our 6Li- 40K experimental apparatus. Our machine is designed to produce a degenerate Fermi-Fermi mixture with large atom number. Large atom numbers bring several advantages, such as a high Fermi temperature and a large signal-to-noise ratio.
At the beginning of my thesis, a fully functional dual-species MOT existed and produced large samples of 6Li and 40K, with atom numbers on the order of 109 for both species, and temperatures of ∼1 mK and ∼240 µK, respectively. All subsequent steps to reach quantum degeneracy, such as D1 cooling, magnetic transport, vacuum improvements, and the setup to perform evaporative cooling in a plugged optical quadrupole magnetic trap and a crossed optical dipole trap, had to be developed and have been implemented during my thesis work.
This manuscript is structured such as it follows an atomic gas from its creation to its evaporation to quantum degeneracy. In Chapter 2, we present the experimental setup. Chapter 3 describes home-made, high power all solid state laser sources at 671 nm for laser cooling of lithium. In Chapter 4, we introduce the simultaneous D1 sub-Doppler laser cooling of 6Li and 40K. Finally, Chapter 5 presents thermalization experiments in the magnetic trap, the magnetic transport from the MOT- to the science chamber, and evaporative cooling to quantum degeneracy.
We present the complete experimental apparatus, focusing on the updates and new parts of the setup. These comprise a new part of the vacuum assembly, including the transport region and the ultra-high vacuum chamber, with a pressure lower than 10−11 mbar in the science cell, the laser systems and the optical setup for the D1 sub-Doppler cooling, the modi ed 2D-Mot for 40K, a new magnetic trap, the optimized magnetic transport, the parts necessary to perform evaporation in an optically plugged magnetic quadrupole trap and in a crossed optical dipole trap as well as a new experimental control.
We describe the development of our home-made all solid-state laser sources for laser cool-ing of lithium atoms. The lasers are based on a diode-end-pumped neodymium-doped yttrium orthovanadate (Nd:YVO4) gain medium, lasing at the fundamental wavelength of 1342 nm. Second harmonic generation is then established using periodically-poled potassium titanyl phosphate (ppKTP) as the nonlinear medium. We present three de-velopment stages. The rst laser generation already existed when I started my thesis, and emitted up to 670 mW at 671 nm. With the second laser version, we investigated intracavity-frequency doubling and achieved output powers of up to 2.1 W at 671 nm.
The third and latest version comprises a new built up cavity for second harmonic gen-eration and emits up to 5 W at 671 nm. We used this laser for the D1 sub-Doppler laser cooling of 6Li.
This chapter presents a new, three-dimensional optical molasses scheme for simultaneous sub-Doppler cooling of fermionic 6Li and 40K. The cooling scheme is suitable for all alkali atoms, operates on the D1 line and is based on gray optical molasses. We obtain phase-space densities on the order of 10−4 for both 6Li and 40K. After recalling the principles of cooling schemes that are useful to understand the mechanism behind the D1 molasses, we start with a description of the D1 cooling mechanism, followed by the experimental results for 40K and 6Li in single species and dual-species operation. Moreover, we compare experimental results with semiclassical simulations of the D1 cooling mechanism. Thereby we investigate the cooling e ciency as a function of the repumping-detuning from the Raman-resonance-condition.
We start this chapter by recalling the principles of magnetic trapping, before describ-ing thermalization experiments, that unveil the non-ergodicity of a quadrupole magnetic trap. Furthermore, we characterize the magnetic transport from the MOT- to the sci-ence chamber and explain how the D1 molasses phase helped to increase the transport e ciency to 80%. Finally, we present our current evaporative cooling sequence, which we are still optimizing. To achieve high nal atom numbers, we rst evaporatively cool the atoms in a plugged magnetic quadrupole trap. After this intermediate stage, we load an optical dipole trap, where we continue the evaporation. To date, we are able to create a degenerate spin mixture of 40K in the spin-states F = 9/2, mF = 9/2 and F = 9/2, mF = 7/2 , with atom numbers of ∼1.2 × 106 and ∼7.1 × 105, temperatures of 260 nK and 270 nK, and T /TF ∼ 0.27 and T /TF ∼ 0.34, respectively.
In this chapter we describe the di erent parts of the Fermix machine, focusing on the upgrades and further developments of the experimental setup described in [125,148,149]. Our goal is to produce degenerate mixtures of ultracold fermions of two di erent atomic species with large atom numbers and high repetition rates of experimental cycles. A dual-species experiment is more complex, than just joining two single-species setups. The requisite of combining certain techniques for the two species and constraints imposed by the dual-species operation, demand for sophisticated strategies to accomplish a high performing system. Our approach yields large atom numbers for both atomic species while minimizing the complexity of the experimental setup.

Design

To reach quantum degeneracy, the thermal deBroglie wavelength of the atoms must be on the same order of magnitude as the inter-particle distance. Therefore the atoms need to be cooled and tightly con ned in a trap. We follow the standard pathway to quantum degeneracy: laser pre-cooling followed by forced evaporative cooling.
A magneto-optical trap (MOT) (Section 2.6) and a gray optical molasses (Chapter 4) serve as pre-cooling stages. To load the MOT we use continuous beams of slow atoms for both atomic species. This has several advantages: First, the MOT can operate in an ultra-high vacuum environment (Section 2.2), in contrast to a MOT loaded from a back-ground vapor. Second, the ux of the atomic beam and hence the MOT loading rate is large compared to pulsed loading with an alkali getter dispenser [150] or ultraviolet light-induced absorption [151, 152]. Furthermore, we use a separate source for each species, namely a Zeeman slower for 6Li (Section 2.4) and a 2D-MOT for 40K (Section 2.5).
After the MOT phase, a three dimensional gray optical molasses phase cools the atoms to sub-Doppler temperatures.
The evaporative cooling e ciency improves with the vacuum quality, because of the longer lifetime of the trapped atoms. Therefore the cloud is magnetically transported [153] to a ultra-high vacuum (UHV) glass cell (Section 5.3). We perform radio-frequency (RF) evaporative cooling in an optically plugged magnetic quadrupole trap. A magnetic quadrupole trap is advantageous because of the large optical access compared to other magnetic traps. Its large trapping volume and steep con nement yield an e cient cooling procedure. We evaporate 40K in two di erent spin states while sympathetically cooling 6 Li.
The pre-cooled atoms are loaded into an optical dipole trap, where we continue to cool the atoms by means of optical evaporation (Section 5.4).

Table of contents :

1 Introduction 
1.1 Quantum gases
1.2 Ultracold atoms { a highly controllable model system
1.3 Quantum degenerate Fermi gases
1.4 Fermi-Fermi mixtures with two different atomic species
1.5 Sub-Doppler laser cooling
1.6 Thesis outline
2 Experimental setup 
2.1 Design
2.2 Vacuum system
2.3 D2 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 Optical molasses { D1 sub-Doppler cooling
2.7.1 Compressed MOT
2.7.2 D1 laser system
2.7.3 Implementation of the D1 molasses
2.8 Magnetic trapping
2.8.1 Transfer to the magnetic quadrupole trap
2.9 Magnetic transport
2.10 Optically plugged magnetic quadrupole trap
2.10.1 Coils
2.10.2 Optical plug
2.10.3 RF evaporative cooling
2.11 Optical dipole trap
2.11.1 Power stabilization
2.11.2 ODT2
2.12 Optical setup { Science Cell
2.13 Diagnostic tools
2.13.1 Fluorescence monitoring
2.13.2 Absorption imaging
2.13.3 Experiment control and data acquisition
2.14 Conclusion
3 High power 671 nm laser system 
3.1 Introduction
3.2 First generation
3.2.1 The Nd:YVO4 gain medium
3.2.2 Crystal structure
3.2.3 Absorption
3.2.4 Thermal effects in solid-state lasers
3.2.5 Performance
3.3 Second generation: Intracavity-frequency-doubling
3.3.1 The fundamental laser
3.3.2 Encient intracavity second-harmonic generation
3.3.3 Tuning behavior and nonlinear-Kerr-lens mode locking
3.3.4 Conclusion
3.4 Third generation: Power scaling
3.4.1 Scheme
3.4.2 Infrared laser
3.4.3 Doubling cavity
3.4.4 Locking scheme
3.4.5 Experimental results
3.5 Conclusion
4 Simultaneous sub-Doppler laser cooling of fermionic 6Li and 40K 
4.1 Prelude: Laser cooling
4.1.1 Doppler cooling
4.1.2 Bright optical molasses
4.1.3 Sub-recoil laser cooling
4.1.4 Velocity selective coherent population trapping (VSCPT)
4.1.5 Gray optical molasses
4.2 D1 sub-Doppler laser cooling
4.2.1 40K D1 molasses
4.2.2 6Li D1 molasses
4.2.3 Raman-detuning dependance
4.2.4 Simultaneous D1 cooling of 6Li and 40K
4.3 Conclusion
5 Magnetic trapping, transport and evaporation 
5.1 Magnetic trapping
5.1.1 Principles of magnetic trapping
5.1.2 Transfer from the D1 molasses to the magnetic quadrupole trap
5.2 Thermalization and non-ergodicity
5.2.1 Thermalization experiment
5.2.2 Non-ergodicity
5.3 Magnetic transport
5.3.1 Algorithm { Keynote
5.3.2 Algorithm { Calculating the time-dependent transport currents
5.3.3 Experimental results
5.4 Evaporative cooling
5.4.1 Principle of evaporative cooling
5.4.2 Cooling approach
5.5 Conclusion
6 Conclusion

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