Magneto-Optical trap

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Table of contents

Introduction
1 From few to many
1.1 Two-body problem
1.1.1 Interacting potential
1.1.2 Scattering theory
1.1.3 Pseudo-potential
1.1.4 Feshbach resonance
1.2 Three-body problem
1.2.1 Setting up the framework
1.2.2 Zero-range model
1.2.3 Efimov’s ansatz
1.2.4 Hyperangular problem
1.2.5 Hyperradial problem
1.2.6 Finite scattering length
1.2.7 Adding more bodies
1.3 Universal thermodynamics of the many-body problem
1.3.1 Ideal gases
1.3.2 Interacting bosons
1.3.3 Interacting fermions: The BEC-BCS crossover
2 Producing a dual Bose-Fermi superfluid
2.1 General description
2.2 The lithium atom
2.2.1 Atomic structure
2.2.2 Feshbach resonances
2.3 Laser system
2.4 Loading the dual magneto-optical trap
2.4.1 The atomic beam source
2.4.2 The Zeeman slower
2.4.3 Magneto-Optical trap
2.5 Magnetic trapping
2.5.1 Optical pumping
2.5.2 Lower magnetic trap and transfer to the appendage
2.5.3 Doppler Cooling
2.5.4 RF evaporation
2.6 Hybrid magnetic-optical trap
2.6.1 Trap description
2.6.2 Trap loading
2.6.3 Mixture preparation
2.6.4 Evaporation at 835 G
2.7 Imaging
2.7.1 Absorption imaging
2.7.2 Imaging directions
2.7.3 Imaging transitions
2.7.4 Double and triple imaging sequences at high field
2.8 Evidence for superfluidity
2.8.1 Bose gas
2.8.2 Fermi gas
2.9 Final trap calibrations
2.9.1 Magnetic field calibration
2.9.2 Trap frequency calibration
2.9.3 Number calibration
2.10 Conclusion
3 Counterflowing mixture of Bose and Fermi superfluids
3.1 Creating a counterflow of Bose and Fermi superfluids
3.2 Low amplitude oscillations: Coherent energy exchange
3.2.1 Frequency shift
3.2.2 Amplitude modulation
3.2.3 Sum-rule approach
3.2.4 Frequency shift in the crossover
3.3 Large amplitude oscillations: Friction and critical velocity
3.3.1 Simple and generalized Landau criterion for superfluidity
3.3.2 Critical velocity in the BEC-BCS crossover
3.4 Conclusion
4 Numerical simulation of counterflowing superfluids
4.1 Mathematical and numerical settings
4.1.1 Gross-Pitaevskii equations
4.1.2 Dimensionless equations
4.1.3 Numerical methods
4.1.4 Simulation parameters
4.2 Low amplitude oscillations
4.3 Large amplitude oscillations
4.3.1 First observations: The center of mass evolution
4.3.2 Fluctuation analysis using a principal analysis component
4.3.3 PCA’s modes versus collective excitations of the superfluids
4.3.4 Linearly forced modes
4.3.5 Parametric modes
4.4 Conclusion
5 Contact relations
5.1 General framework
5.2 The two and three-body contact
5.3 Relation to the tail of the momentum distribution
5.4 Relations to the pair and triplet distributions at short distances
5.4.1 Pair distribution
5.4.2 Triplet distribution
5.5 Relation to the energy
5.6 Extension to statistical mixtures
5.7 Conclusion
6 Universal inelastic losses in cold gases
6.1 Three-body recombination
6.2 General principles
6.2.1 A general statement
6.2.2 A justification using a microscopic model
6.2.3 Application to some generic cases
6.2.4 Inelasticity parameter
6.3 Scalings for the Bose gas
6.4 Conclusion
7 Inelastic losses in a strongly interacting Bose gas
7.1 Universal loss dynamics
7.1.1 The model
7.1.2 Analysis of the experimental data
7.1.3 Conclusion
7.2 Momentum distribution of a dilute unitary Bose gas with three-body losses
7.2.1 The model
7.2.2 Comment on the depletion time scale
7.2.3 First virial correction
7.2.4 Comparison to the JILA experiment
7.2.5 Conclusion
8 Inelastic losses of a weakly coupled impurity immersed in a resonant Fermi gas
8.1 Bose-Fermi losses scalings in the BEC-BCS crossover
8.2 Experiments on the BEC side
8.2.1 Nature of the losses
8.2.2 Loss coefficient measurement on the BEC side
8.2.3 Molecule fraction
8.2.4 Bose-fermi losses versus molecular fraction and magnetic field
8.3 Experiment at unitarity
8.3.1 Loss coefficient measurement
8.3.2 Density dependence of the loss rate
8.4 Concluding remarks and perspectives
Conclusion
A Derivation of the coupled oscillator model using the sum-rule approach
B Instability domains of modified 2D Mathieu’s equations
C Numerical simulation of counterflowing superfluids: supplemental data
D Momentum distribution of a dilute unitary Bose gas: Supplemental material
D.1 Derivation of the loss equations
D.2 Decomposition of the solution over the Laguerre Polynomial basis
D.3 Calculation of C
D.4 Momentum distribution in a harmonic trap
E Analysis of impurity losses of the Innsbruck experiment.
Remerciements