Efimov trimers properties and domain

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Table of contents

Introduction
1 Ultracold Fermi gases: From few to many
1.1 Two-body problem
1.1.1 Universal dynamics and scaling
1.1.2 Scattering theory
1.1.3 Feshbach resonances
1.2 Three-body problem
1.2.1 Two-channels model for the three identical bosons
1.2.2 Efimov trimers properties and domain
1.2.3 Experimental evidence of Efimov physics
1.3 Ultra-cold Fermi gases
1.3.1 Non-interacting Fermi gas
1.3.2 Interacting Fermi gas and the BEC-BCS crossover
1.4 Impurity physics
1.4.1 Bose polaron
1.4.2 Fermi polaron
1.4.3 Impurity in a two-component Fermi gas
I The Lithium Experiment
2 A new generation Lithium machine
2.1 Overview of the setup
2.2 The 6Li atom
2.2.1 Level structure
2.2.2 Feshbach resonances of 6Li
2.3 Vacuum setup
2.4 671 nm Laser setup
2.5 Absorption imaging
2.6 Magneto-optical trap
2.6.1 Atomic beam
2.6.2 Zeeman Slower
2.6.3 Magneto-optical trap (MOT) and compressed MOT
2.7 Optical molasses
2.7.1 D2 molasses
2.7.2 D1 gray molasses and sub-Doppler cooling
2.8 Optical dipole traps
2.8.1 Optical transport
2.8.2 Cross dipole trap
2.9 Evaporative cooling
2.9.1 Working principle
2.9.2 State populations
2.9.3 Magnetic fields in the science cell
2.9.4 Cooling to degeneracy
3 From superfluidity to single atom imaging
3.1 Thermodynamics of ultracold Fermi gases
3.1.1 Equation of state
3.2 Quantitative analysis of density distributions
3.2.1 Non-interacting Fermi gas in a harmonic trap
3.2.2 Unitary Fermi gas
3.2.3 Implementation and results
3.3 Searching fermionic superfluidity
3.3.1 Spin imbalanced systems
3.4 Single-atom imaging of fermions
3.5 Prospects of the 6Li machine
II Impurity immersed in a two-component Fermi sea
4 Impurity in an interacting medium: a perturbative approach
4.1 Perturbative expansion of the impurity energy
4.1.1 Preliminary calculation
4.1.2 Asymptotic behavior
4.2 Green’s function for an interacting system
4.2.1 Green’s function: Definition
4.2.2 Time evolution operator
4.2.3 Adiabatic activation
4.2.4 Vacuum polarisation
4.3 Perturbative expansion using Green’s function formalism
4.3.1 The impurity’s Green function
4.3.2 Expectation value of the density-density correlation function .
4.3.3 Ladder approximation
5 Impurity immersed in a double non-interacting Fermi sea
5.1 Variational ansatz of the full problem
5.2 Polaron sector
5.3 Efimov sector
5.3.1 Trimer in vacuum
5.3.2 Cooper-like trimer
5.3.3 General case
5.4 Polaron-trimeron coupling
5.5 Dimer energy
Conclusion
A Calculation of the first contribution to the diagrammatic expansion
B Ladder diagram terms
C Derivation of polaron-trimeron coupled equations
D Numercial solution of Skornyakov-Ter-Martirosyan’s equation
E Cooper-like trimer for different values of kFRe
Acknowledgements