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?)

玻色－愛因斯坦凝聚現象之發現

Kapitza Cornell KetterleWieman

1938年,卡匹薩(Kapitza)與麥斯納(Misener)首度發現液態氦(4He)中形成超流體之現象,即由玻色－愛因坦凝聚所造成.

1995年,藉雷射冷卻及蒸發冷卻之助,康乃爾(Cornell),魏曼(Wieman),與凱特立(Ketterle)分別達成氣態銣原子與鈉原子之玻色－愛因斯坦凝聚.

d B

低 溫 時 d < d

“ 波 包 ” 行 為

低 溫 時 d < d

“ 波 包 ” 行 為

達 到 臨 界 溫 度 時 T = T c :“ 玻 色 – 愛 因 斯 坦 凝 聚 “

d ≧ d“ 物 質 波 重 疊 ”

達 到 臨 界 溫 度 時 T = T c :“ 玻 色 – 愛 因 斯 坦 凝 聚 “

d ≧ d“ 物 質 波 重 疊 ”

相 空 間 密 度n p 1 ! !

量 子 簡 併 態 ( q u a n t u m d e g e n e r a t e r e g i m e ) ! !量 子 簡 併 態 ( q u a n t u m d e g e n e r a t e r e g i m e ) ! !

高 溫 時熱 運 動 速 度 v

d < < d“ 彈 珠 ” 行 為

高 溫 時熱 運 動 速 度 v

d < < d“ 彈 珠 ” 行 為

d

v

Tph

d1

Goal to achieve?

Momentum space p: Cooling: lower T → larger d

Coordinate(Position) space r: Trapping: increase n → smaller d

spatial density

Phase Space!!

nphase 1 !!≧

氣態玻愛凝聚體之特色

• 達到較液態氦更低之溫度與密度1.原子之間作用力更小、更單純(甚至趨近於理想氣體),也更容易進行理論上之計算.

2.達成全然之物質波系統變為可能.

• 達到更長(數十秒以上)巨觀物質波之生命期

1. 更易於研究其中之物理2.未來之實際應用變為可能

Works on the Degenerate Bose Gas

Weakly Interacting Bose Gas

Feshbach Resonance ( a knob tuning the interactions!!)

Low Dimension

Strongly Correlated Boson Systems

Mott InsulatorQuantum Entanglement

Phase fluctuations Phase fluctuationsTonks Gas

SuperfluidityVortices

Excitation

SuperfluidityVortices

Excitation

CoherenceInterferenceAtom Laser

Cold Molecules

NonlinearityNonlinearity

Multi- Species

Cooling, Trapping, and Manipulating ToolsTools: 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 Trapsnot all the states are Trappable!!

Please see the other file!

Optical Dipole Trap

|E0(x)|2

x

F(x)

z

x

x

|E0(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!!

M e a n - F i e l d T h e o r y o f B o s e C o n d e n s a t e s

222

),(4

)(2

tNm

aV

m trap rr

a < 0 原 子 間 作 用 為 吸 引 力 凝 聚 體 呈 不 穩 定

a > 0 原 子 間 作 用 為 排 斥 力 凝 聚 體 呈 穩 定

a 主 宰 波 函 數 之 尺 度 , 形 狀 , 與 激 發 頻 率 . . 等

利 用 磁 場 與 光 場 , 有 可 能 調 變 a ! !

S - 波 散 射 長 度( s - w a v e s c a t t e r i n g l e n g t h )

凝 聚 體 平 均 場 理 論 之 H a m i l t o n i a n“internal energy”or “mean field energy”

Time-Evolution of a Wavefunction in Free Space

MIT, 1996

凝聚體於自由空間中隨時間膨脹

a → f (時間增加)

Thomas-Fermi Regime

• NBEC > 105 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 realizedexperimentally!!

Two-Component Condensates

JILA, 1997

Spinor Condensates

MIT, 1999

Coherence and Correlation

1st order correlation MIT, 1996

3rd order correlationJILA, 1997

interference betweentwo 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, 2002Dark solitons were also observed! (NIST, 1999)

Fechbach Resonaces- a tuning tool for atom-atom interaction

1 g+

3 u+

F = 2 & F = 2

F = 3 & F = 3

2S1/2 & 2S1/2

E

20 R (aB)400 60

–0.5 cm–1

0 cm–1

–1 cm–1

kdB

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)

x01 x0

2

xb2(t)

xa2(t)xb

1(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!!