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Quantum degenerate Fermi gases
Quantum degeneracy of a Fermi gas is reached as soon as its temperature becomes lower than the Fermi temperature TF = EF/kB, where EF is the Fermi energy and kB the Boltzmann constant. The rst degenerate Fermi gas of atoms was realized in 1999 with 40K [8], by adapt-ing the cooling methods developed to reach BEC with bosonic atoms to a two-component fermionic system. At ultracold temperatures, it was possible to observe signi cant deviations of the Fermi gas from the classical behaviour, thus substantiating the Fermi-Dirac distribu-tion of the fermions over the low-lying trap states. Fermionic quantum degeneracy has, as of this writing, also been reached for 6Li [44, 45], metastable 3He∗ [46], the alkaline earth ele-ment 87Sr [47,48], the rare earth elements 173Yb [49], 161Dy [50] and recently 167Er [51]. Early experiments cooled the atoms to temperatures of about T = 0.2−0.3 T /TF. Current state-of-the-art experiments reach even temperatures below one tenth the Fermi temperature [52,53]. Reaching quantum degeneracy requires in general an evaporative process as last cooling stage. The evaporative cooling techniques rely fundamentally on the fast rethermalization of the gas by elastic collisions. The cooling of Fermi gases is challenging in this context, since in the ultracold temperature limit gases can only collide via s-wave collisions, whereas the Pauli exclusion principle forbids these collisions for indistinguishable fermions. A gas of single-state fermionic particles thus becomes collisionless at low temperatures. Therefore, the gas has either to be cooled sympathetically or prepared in two di erent internal states. Furthermore, the collision rate of fermions decreases in the degenerate regime due to Pauli blocking, meaning that it becomes less likely that scattering into empty low-lying momentum states can occur [8, 54]. Moreover, inelastic collisions can additionally reduce the cooling e ciency and create hole excitations located deep inside the Fermi sea [55, 56].
Several experimental approaches have been applied in order to attain the quantum degenerate regime. The single-species evaporation scheme using two di erent internal states has been employed for 40K [8], 6Li [57, 58] and 173Yb [49]. Sympathetic cooling with bosonic isotopes has been applied for 6Li-7Li [44, 45], 6Li-23Na [52], 6Li-87Rb [59], 6Li-40K-87Rb [60], 6Li-40K-41K [61], 3He∗-4He∗ [46] and 40K-87Rb [62{66]. Also for the Fermi-Fermi mixture 6Li-40K several approaches have been validated. In Amsterdam, a 40K spin-mixture was evaporated in a magnetic trap, sympathetically cooling 6Li [67]. The Innsbruck group prepared 6Li in two spin states, evaporatively cooled it in an optical trap, while sympathetically cooling 40K [68]. Historically, the rst experiments investigated nearly ideal, non-interacting, one-component Fermi gases and their related thermodynamics [8, 44, 69]. Interacting Fermi gases could be realized by tuning the interactions between atoms belonging to di erent internal states by means of Feshbach resonances. The rst investigations on strongly interacting Fermi gases dealt with the characterization of Feshbach resonances in fermionic systems, for instance for 40K [70{72] and 6Li [73{75]. Contrary to bosonic atoms, fermions are surprisingly stable in the vicinity of a Feshbach resonance, which is due to the fact that the Pauli exclusion principle prohibits three-body relaxation [76] thus increasing the lifetime of the fermion dimers considerably. It was therefore possible to observe Bose-Einstein condensates of weakly bound Feshbach molecules [77{79]. Shortly afterwards also the Bardeen-Cooper-Schriefer (BCS)-regime could be probed and the corresponding super uid was realized [80{82], proving that in the case of weakly attractive interactions the pairing mechanism is based on Cooper pairing and not on formation of molecules. Moreover, the crossover from the BEC- to the BCS-regime could be investigated [82{84], this crossover smoothly connecting the two limiting cases of super uid states across the strongly interacting regime.
The super uid character of strongly interacting Fermi gases was demonstrated by the creation of vortices [85], the phase separation between paired and unpaired fermions in fermionic mixtures with population imbalance [86,87], the determination of the speed of sound [88] and the critical velocities [89] related to a fermionic super uid. Moreover, a Mott insulator state was realized with fermions [90,91] and the equation of state of a strongly interacting Fermi gas could be measured directly [53, 92, 93]. Interestingly, the transition to a super uid of paired fermions occurs at a relatively high critical temperature for a strongly interacting Fermi gas, namely at TC ‘ 0.17 TF [94,95]. In this context, future experiments with strongly interacting Fermi gases might play an important role for the understanding of high-TC superconductivity and give new insights into the underlying physics [96].
The preceding list is only a selection of examples and far from exhaustive, but illustrates the research activity in the eld of quantum degenerate Fermi gases.
Fermi-Fermi mixtures
The investigation of mixtures of di erent fermionic species promises interesting prospects for the future, since these systems o er a large number of controllable parameters, such as the dimensionality of the system and the mass-imbalance of its components.
Systems in mixed dimensions, where the particles of one species evolve in three dimensions whereas the second species evolves in two, one or zero dimensions [97], can be created by the application of species-selective potentials [98, 99]. The two-body interaction being altered by the mixed dimensionality, this can result in con nement induced resonances [100{104]. Few-body e ects, for instance the E mov-e ect in mixed dimensions [105] or p-wave resonances between interspecies dimers and single atoms [106] that are tuned by the lattice depth, can be investigated. The particularly appealing case of 3D-0D con nement is equivalent to the Anderson impurity model and allows the study of Kondo correlated states [107{109]. in addition, Anderson localization can be observed in such a dilute gas of trapped impurity scatterers [110{112]. Moreover, new many-body quantum phases are predicted for the case in which one freely evolving species mediates interactions between a second atomic species con ned in di erent layers, which might lead to interlayer super uidity [113].
Thesis outline
Furthermore, the mass imbalance of the two fermionic species results in unmatched Fermi surfaces, which means that symmetric BCS pairing is not possible any more. Di erent pairing mechanisms leading to new quantum phases are predicted for this case [114]. Examples of these exotic phases are the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state [115{117] and the breached pair state [118,119]. The formation of long-lived trimers [106] and a crystalline phase transition [120] are also in the scope of new phenomena that might arise. Another important motivation for the use of di erent fermionic species is certainly the possibility to form bosonic polar molecules providing long-range, anisotropic dipole-dipole interaction [121, 122], which may lead to qualitatively new quantum regimes.
The 6Li-40K mixture is an evident candidate for realizing these studies, since lithium and potassium are widely used and experimentally well mastered atoms possessing the only stable, fermionic isotopes among the alkali metals. Both elements have been used in a large spectrum of applications ranging from Bose-Einstein condensation and atom interferometry to fermionic pairing. They possess fermionic and bosonic isotopes which can be conveniently trapped and cooled with laser light delivered by a ordable laser sources. Furthermore, the bosonic and fermionic isotopes can also be mixed in order to study Bose-Fermi mixtures, for example in optical lattices [123,124] or in order to study the dynamics of two interacting super uids [125]. As of this writing, all research groups intending to study Fermi-Fermi mixtures with di erent atomic species have employed the 6Li-40K mixture [61,67,68,126,127]. To date, three groups in Munich, Innsbruck and at MIT have reported on double quantum degeneracy of this mixture [60, 61, 68]. Characterizations of the interspecies Feshbach resonances have been performed [128{132] and weakly bound Feshbach molecules could be observed [68, 133]. In particular, the Innsbruck group investigated the hydrodynamic expansion of 6Li and 40K in the strong interaction regime [134], measured the excitation spectrum of 40K impurities interacting with a Fermi sea of 6Li[135] and observed a strong attraction between atoms and dimers in the mass-imbalanced two-component fermionic gas [136]. By now, the unitary regime has only been reached for the single species 6Li [137] and 40K [138]. However, it might be possible to attain this regime also for the 6Li-40K-mixture, by using the 1.5 Gauss-wide Feshbach resonance at B0 ∼ 115 G [130].
This thesis reports on novel techniques for the experimental investigation of ultracold fermionic quantum gas mixtures of lithium and potassium, the further design, construction and charac-terization of our 6Li- 40K experimental setup and the development of powerful laser sources for laser cooling of lithium.
At the beginning of my thesis, a partially functional experiment including an operational dual-species MOT had already been constructed. It could produce large atomic gas samples of 6Li and 40K, with atom numbers on the order of 109 for both species, and temperatures of several hundreds of microkelvins. Furthermore, we were able to perform the rst magnetic transport sequences in order to transfer the atomic samples to a high vacuum region.
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. 6 Li-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
