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Temperature scale Titan Superfluid He Ultracold atomic gases Quantum mechanics in action 1) Particle-Wave duality p mv momentum h p de Broglie wave-length (de Broglie 1923) h 6.6 10 27 cm 2 g sec 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 thermal only thermal both thermal and BEC only BEC Temperature measured thruogh thermal component tails Physics Nobel Prizes 2001 1997 "for development of methods to cool and trap atoms with laser light" Steven Chu Claude CohenTannoudji William D. Phillips "for the achievement of BoseEinstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of the condensates" Eric A. Cornell Wolfgang Ketterle Carl E. Wieman 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