冷原子實驗之基本原理 (I)
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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
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• Introduction
• Works on the Degenerate Bose Gas
• Cooling, Trapping, and Manipulating Tools
• BEC Behavior
• Remarks on the Current BEC Experiments and Future Directions
Outline
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Introduction
• Brief History of Bose-Einstein condensation (BEC)
• Special Features of Dilute Bose condensates (Why dilute is important?)
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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.
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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
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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 !!≧
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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
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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
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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
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Magnetic Trapsnot all the states are Trappable!!
Please see the other file!
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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!
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BEC Behavior
Starting from the
Gross-Pitaevskii equation!!
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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”
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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)
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Thomas-Fermi Regime
• NBEC > 105 atoms Thomas-Fermi regime
kinetic energy << internal energy
• Cloud shape inverted paraboloid
neglected!
Kanstanz,1998
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Phase transition (Lambda Point)
JILA, 1996
condensate fraction
energy per particle (Bose gas)
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Remarks on the
Current BEC Experiments
and Future Directions
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Collective Mode Excitations
JILA, 1996
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Sound Propagation
MIT, 1997
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Superfluidity and Vortices
MIT, 2000
critical velocity in a superfluid
MIT, 2002
Votex lattice
condensate
laser beam
(a line-like excitation)
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Skyrmions in a Multicomponent BEC - point-like excitation
Utrecht, 2001
NOT YET realizedexperimentally!!
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Two-Component Condensates
JILA, 1997
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Spinor Condensates
MIT, 1999
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Coherence and Correlation
1st order correlation MIT, 1996
3rd order correlationJILA, 1997
interference betweentwo condensates
three-body recombination rate
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Superradiant Rayleigh Scattering
MIT, 1999
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Matter Wave Amplification
NIST, 1999
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Nonlinear Atom Optics - Four Wave Mixing
NIST, 1999
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Bright Solitons
Rice, 2002Dark solitons were also observed! (NIST, 1999)
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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
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Optical Lattices
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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
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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)
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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
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Phase Fluctuations (1D trap)
Orsay, 2003
Bragg spectroscopy in momentum space
Hannover, 2001
stripes on1D traps (different aspect ratios)
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Unexpected New Physics!!