冷原子實驗之基本原理 (I) 韓殿君 國立中正大學物理系 2003 年 8 月 5 日 於理論中心

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

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

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

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

Cooling, Trapping, and Manipulating Tools Tools: Electric and magnetic fields (DC and AC ) EM waves – photons (visible, IR, microwave …) Systems: Atomic ensembles (atom number: 10 3 – 10 9 ) 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 |E 0 (x)| 2 x F(x) z x x |E 0 (x)| 2 F(x) z x “scattering force” “dipole force” near resonance light! far-detuned light light!

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 N BEC > 10 5 atoms  Thomas-Fermi regime kinetic energy << internal energy Cloud shape  inverted paraboloid neglected! Kanstanz, 1998

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

Remarks on the Current BEC Experiments and Future Directions

Collective Mode Excitations JILA, 1996

Sound Propagation MIT, 1997

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

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

Two-Component Condensates JILA, 1997

Spinor Condensates MIT, 1999

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

Superradiant Rayleigh Scattering MIT, 1999

Matter Wave Amplification NIST, 1999

Nonlinear Atom Optics - Four Wave Mixing NIST, 1999

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

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) (b) (a) x01x01 x02x02 xb2(t)xb2(t) xa2(t)xa2(t)xb1(t)xb1(t) xa1(t)xa1(t) 簡易之二位元量子邏輯閘 (two-qubit logic gate) Innsbruck, 1999 凝聚體原子於光晶格中進行 量子糾纏 (quantum entanglement)

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

Phase Fluctuations (1D trap) Orsay, 2003 Bragg spectroscopy in momentum space Hannover, 2001 stripes on1D traps (different aspect ratios)

Unexpected New Physics!!