Quantum gases
In this chapter, we discuss the three paradigmatic accomplishment of the field of cold atoms: Bose-Einstein condensation, the superfluid to Mott insulator transition, and superfluid Fermi gases., These are three current frontiers of research, all made possible by the combination of laser cooling and evaporative cooling. In the first section of this chapter, we present evaporative cooling and magnetic trapping, the two key techniques to achieve the nanokelvin temperature range (although more recently, evaporative cooling in optical traps has been used).
We hope that in the near future, we can add another section to this chapter, the study of magnetism in spin systems, realized with ultracold bosons and fermions. This goal is currently pursued in several labs.
- Ultracold Bosons
- Ideal Bose Gas
- Weakly Interacting Homogeneous Bose Gas
- Inhomogeneous Bose Gas
- Superfluid Hydrodynamics
- Superfluid to Mott Insulator Transition
- Superfluid to Mott insulator transition: Original paper on analytic decoupling solution File:PRA Stoof MI e053601.pdf
- Further reading: Bose-Einstein Condensation in Dilute Gases, C.J. Pethick and H. Smith, selected pages
- On Bogoliubov transformation and collective excitation: handout pp. 205-214 (link broken)
- On nonlinear Schrödinger equation: handout pp. 146-156 (link broken)
- On hydrodynamics: handout pp. 165-179 (link broken)
- 2009 Class Notes File:AMO class BEC 09-05-04 short.pdf
- Ultracold Fermi gases
- Ideal Fermi Gas
- Attractively Interacting Fermi gases - Pairing Instability
- BEC-BCS Crossover
- Repulsively Interacting Fermi gases - Stoner Instability
- Further reading: Varenna summer school notes: File:Kett08 Varenna notes Fermi Gases.pdf
- 2009 Class notes File:AMO Fermions 2009.pdf
