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chapter 1 introduction
references
part ¢¡ toward strongly correlated systems

chapter 2 atomic structure
2.1 electronic levels of alkali-metal atoms
2.2 fine structure
2.3 hyperfinc structure
2.4 zeeman effect

chapter 3 atom-light interaction
3.1 atom-light interaction hamiltonian
3.2 spontaneous emission
3.3 stimulated absorption and emission
3.3.1 rabi oscillation
3.3.2 energy shifts
3.4 the optical bloch equations
3.4.1 density matrix
3.4.2 steady-state solutions
3.5 light forces on atoms
references

chapter 4 laser cooling and trapping
4.1 beam deceleration
4.2 doppler cooling
4.3 evaporative cooling
4.4 magnetic trapping
4.5 optical trapping
references

chapter 5 interaction between atoms
5.1 interaction potential between alkali-metal atoms
5.2 two-atom scattering in free space
5.3 effective interaction
5.3.1 bethe-peierls boundary condition
5.3.2 huang-yang pseudopotential
5.3.3 contact potential with renormalization
references

chapter 6 feshbach resonance
6.1 basic physics of feshbach resonance
6.2 magnetic feshbach resonance
6.3 optical feshbach resonance
references

part ¢¢ ultracold fermi gases

chapter 7 background and experimental achievements
7.1 brief introduction to experimental achievements
7.2 bcs-bec crossover
7.3 overview
references

chapter 8 bcs-bec crossover
8.1 cooper instability
8.2 bcs theory
8.3 description of bcs-bec crossover on the mean-field level
8.4 feshbach resonance and the two-channel model
8.5 narrow feshbach resonance
8.6 bcs-bec crossover in a harmonic trapping potential
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chapter 9 beyond-mean-field descriptions
chapter 10 polarized fermi gas
chapter 11 synthetic gange field
chapter 12 optical lattice and band structure
chapter 13 simulation of bose-hubberard model
chapter 14 dynamical process
chapter 15 disordered systems
chapter 16 simulation of spin systems