The BEC-BCS crossover

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Table of contents

Introduction
􀍙 Bose-Einstein condensates and Fermi superfluids
1.1 Ideal Quantum Gases
1.2 The Local Density Approximation
1.3 S-wave Interactions and Feshbach Resonances
1.3.1 S-wave interactions
1.3.2 Feshbach resonances
1.3.3 Feshbach resonances in lithium
1.3.4 6Li-7Li interactions and Feshbach resonances
1.4 Interacting Bose-Einstein Condensates
1.4.1 Weakly interacting Bose-Einstein condensates
1.4.2 Approaching the unitary Bose gas
1.5 Fermi Superfluids in the BEC-BCS crossover
1.5.1 Stability of Fermi gases on Feshbach resonances
1.5.2 The BEC-BCS crossover
1.5.3 The equation of state
1.6 Superfluidity of Bose and Fermi gases
1.6.1 Landau’s criterion for superfluidity
1.6.2 Landau’s criterion for a mixture of Bose and Fermi superfluids
1.6.3 Beyond Landau’s criterion
1.6.4 Some experiments on a critical velocity in superfluid dilute gases
1.6.5 Other hallmarks of superfluidity
􀍚 Experimental set-up
2.1 Lithium isotopes, atomic structure
2.2 Laser cooling
2.2.1 Laser system
2.2.2 The lithium source
2.2.3 Double Magneto-Optical trap
2.2.4 Optical pumping
2.3 Magnetic trapping and radio-frequency evaporation
2.3.1 Quadrupole trap, magnetic transport and transfer to the Ioffe- Pritchard Trap
2.3.2 Doppler cooling of 7Li
2.3.3 Radio-frequency evaporative cooling of 7Li
2.4 The hybrid optical dipole – magnetic trap (ODT)
2.5 Preparation of strongly interacting degenerate gases
2.5.1 Preparing a resonantly interacting Bose gas
2.5.2 Preparing a mixture of Bose and Fermi superfluids
2.6 Imaging
2.7 Calibrations
2.7.1 Imaging Calibration
2.7.2 Frequencies measurement
2.7.3 Magnetic field calibration
􀍛 D􀍙 sub-Doppler cooling of 7Li
3.1 Grey molasses cooling in a nutshell
3.2 Implementation on 7Li
3.3 The Λ model.
3.4 The perturbative approach
3.5 The continued fractions approach
􀍜 Three-body losses in strongly interacting Bose gases
4.1 Three-body losses
4.2 A glance at Efimov Physics
4.3 Results on the stability of a unitary Bose gas
4.4 Conclusion: stability domain of the strongly interacting Bose gas
􀍝 Mixtures of Bose and Fermi superfluids
5.1 Two-body interactions in the |1f⟩ , |2f⟩ , |2b⟩ mixture
5.2 Mean-field interactions and phase separation
5.3 Evidences for superfluidity
5.3.1 Thermometry of the mixture
5.3.2 Degeneracy points
5.3.3 Superfluidity of 7Li
5.3.4 Superfluidity of 6Li
5.3.5 Frictionless counter-flow
5.4 Coupled dipole modes, theory
5.4.1 Simple model for the BEC dipole frequency shift
5.4.2 Sum rules and coupled 6Li-7Li dipole oscillations
5.5 Coupled dipole modes, experiments
5.5.1 Dipole modes excitation
5.5.2 Uncoupled oscillations
5.5.3 Coupled oscillations
5.5.4 Discussion of the model
5.6 Damping of the dipole modes and critical velocity
5.6.1 Damping at unitarity
5.6.2 Damping in the BEC-BCS crossover
5.6.3 Friction at finite temperature
5.7 Concluding remarks and prospects with Bose-Fermi superfluid mixtures
Conclusion
Appendix
References