A Review of Bose-Einstein Condensates MATTHEW BOHMAN UNIVERSITY OF WASHINGTON MARCH 7,

Overview Development and history Experimental Setups Novel Physics and Applications o Isolated Quantum Systems o Superfluidity and Superconductivity 2

Development and History 3

Early Quantum Mechanics 4

Planck’s Law and the Hypothesis of Light Quanta 5

Bose-Einstein Statistics Einstein realizes Bose’s derivation describe novel physics Postulates the existence of states in which most particles are in a common ground state 1939 Markus Fierz and Paul Dirac formulate spin- statistics theorem Spin-1 particles, bosons, allowed to occupy same state Spin-1/2 particles, fermions, obey Fermi exclusion principle 6

Fermi-Dirac and Bose-Einstein Gases 7

Bose-Einstein Condensation 8

Fermi Gases and Bose Einstein Gases Population of states in Fermi Gases and Bose-Einstein Gases 9

Short Animations 10 [delete for ]

Experimental Confirmation Velocity distribution plot showing the population of states just before and after condensation 11 Eric Cornell and Carl Wieman at NIST and Boulder receive Nobel prize in 1995 along with Wolfgang Kettrle Required bosons high densities, and very cold atoms Achieved through magneto-optical trap (MOT), and evaporative, and Sisyphus cooling 16,000 rubidium-85 atoms at 3 nK

Experimental Setups 12

Magneto-Optical Traps (MOTs) 13

Cooling Techniques 14 Sisyphus Cooling Recognized in 1997 Nobel Prize given to Claude Cohen-Tannoudji, Steven Chu, and William Daniel Phillips Partcles lose kinetic energy travelling ”up” the wave of the electric field At the “peak” optical pumping takes over Recoil limited

Cooling Techniques 15

Experiments and Applications 16

Superfluidity and Superconductivity Nobel Prize awarded (in part) for low temperature superfluidity discovery, again in 1996 Bose-Einstein statistics allow for superfluidity of bosons at high tempertures Connects Bose-Einstein statistics to degenerate fermi gases and Cooper pairs Superfluid He-4 “opposes” gravity and will escape its container Phase diagram for He-4 (boson) and He-3 (fermion)

Feschbach Resonance Physically realizable BECs motivate investigation “Tuneable” cross sections through magnetic hyperfine splitting 18

Quantum Interference 19 Quantum mechanical wave effects arising from large collections of atoms

Interferometry 20

Conclusion and Future Research Bosonic systems and bosonization have direct technology applications Technology applications still many decades away Condensates and traps allow fundamental research on idealized quantum systems Exotic atomic systems e.g. phonons in BECs, exiton formation Coherent atoms 21