Outline Introduction Works on the Degenerate Bose Gas

Outline • Introduction • Works on the Degenerate Bose Gas • Cooling, Trapping, and Manipulating Tools • BEC Behavior • Remarks on the Current BEC Experiments and Future Directions

Introduction • Brief History of Bose-Einstein condensation (BEC) • Special Features of Dilute Bose condensates (Why dilute is important? )

nphase≧ 1 !! Goal to achieve? Phase Space!! Momentum space p: Cooling: lower T → larger d Coordinate(Position) space r: Trapping: increase n → smaller d spatial density

Works on the Degenerate Bose Gas Superfluidity Vortices Excitation Coherence Interference Atom Laser Mott Insulator Quantum Entanglement Feshbach Resonance ( a knob tuning the interactions!!) Weakly Interacting Bose Gas Strongly Correlated Boson Systems Cold Molecules Low Dimension Multi- Species Nonlinearity Phase fluctuations Tonks Gas

Cooling, Trapping, and Manipulating Tools: Electric and magnetic fields (DC and AC ) EM waves – photons (visible, IR, microwave …) Systems: Atomic ensembles (atom number: 103 – 109) Macroscopic size: 5 – 500 m Ultrahigh vacuum environment (very little impurities) Ultralow temperatures ( 1 K) • No physical wall • Quiet and almost no defect potentials (as in the texbooks) are possible

Magnetic Traps not all the states are Trappable!! Please see the other file!

Optical Dipole Trap x near resonance light! “scattering force” |E 0(x)|2 x F(x) z x far-detuned light! |E 0(x)|2 “dipole force” F(x) x z

BEC Behavior Starting from the Gross-Pitaevskii equation!!

“internal energy” or “mean field energy”

Time-Evolution of a Wavefunction in Free Space

Thomas-Fermi Regime • NBEC > 105 atoms Thomas-Fermi regime kinetic energy << internal energy neglected! • Cloud shape inverted paraboloid Kanstanz, 1998

Phase transition (Lambda Point) energy per particle (Bose gas) condensate fraction JILA, 1996

Remarks on the Current BEC Experiments and Future Directions

Collective Mode Excitations JILA, 1996

Sound Propagation MIT, 1997

Superfluidity and Vortices laser beam condensate Votex lattice (a line-like excitation) MIT, 2002 critical velocity in a superfluid MIT, 2000

Skyrmions in a Multicomponent BEC - point-like excitation NOT YET realized experimentally!! Utrecht, 2001

Two-Component Condensates JILA, 1997

Spinor Condensates MIT, 1999

Coherence and Correlation interference between two condensates three-body recombination rate 1 st order correlation MIT, 1996 3 rd order correlation JILA, 1997

Superradiant Rayleigh Scattering MIT, 1999

Matter Wave Amplification NIST, 1999

Nonlinear Atom Optics - Four Wave Mixing NIST, 1999

Bright Solitons Dark solitons were also observed! (NIST, 1999) Rice, 2002

Fechbach Resonaces - a tuning tool for atom-atom interaction MIT, 1998

Optical Lattices

Quantum Phase Transition 超流態轉變為非超流態(Mott 絕緣態)之量子相變 Max-Planck Institute, 2002

Quantum Entanglement (proposed idea) 凝聚體原子於光晶格中進行 量子糾纏(quantum entanglement) (a) x 01 x 02 (b) xb 1(t) xa 1(t) xb 2(t) xa 2(t) 簡易之二位元量子邏輯閘 (two-qubit logic gate) Innsbruck, 1999

Low Dimension Atom Traps 1 D traps: large aspect ratio in one direction with the other two optical dipole trap and magnetic Ioffe traps are available 2 D (surface) Traps: optical dipole trap and magnetic traps are available too

Phase Fluctuations (1 D trap) stripes on 1 D traps (different aspect ratios) Hannover, 2001 Bragg spectroscopy in momentum space Orsay, 2003

Unexpected New Physics!!