Temperature scale Titan Superfluid He Ultracold atomic gases

Quantum mechanics in action 1) Particle-Wave duality de Broglie wave-length (de Broglie 1923) momentum Planck constant (1900) When confinement is present only certain modes are allowed, i.e., certain energies (levels).

2) Quantum Statistics: bosons and fermions “Bosons like staying together, i.e., in the same state” “Fermions dislike staying together, i.e., in the same state” Bose-Einstein statistics (1924) Fermi-Dirac statistics (1926) Dilute gases: 1995, JILA, MIT Dilute gases: 1999, JILA

New state of matter… W. Ketterle

One of the first BEC images (JILA 1995) Below a certain temperature a macroscopic atomic fraction occupies the lowest energy state

Temperature measured thruogh thermal component tails both thermal and BEC only thermal only BEC Temperature measured thruogh thermal component tails

Physics Nobel Prizes 2001 1997 "for the achievement of Bose-Einstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of the condensates" "for development of methods to cool and trap atoms with laser light"                   Eric A. Cornell Wolfgang Ketterle Carl E. Wieman                   Steven Chu Claude Cohen-Tannoudji William D. Phillips

Optical Lattices Periodic potential via the dipole force Laser standing wave 1D (optical) lattice 1D dynamics, (Fermi/Bose) Hubbard model description, Mott insulating phase…

Deeper (3D) optical lattices: quantum phase transition from superfluid to Mott insulator (I. Bloch et al., Nature 2002) Atoms move around, delocalized on many lattice site Incresing the lattice strength Atoms are localized on a single lattice site