冷冷冷冷冷冷冷冷冷冷 (I) 冷冷冷 冷冷冷冷冷冷冷冷冷 2003 冷 8 冷 5 冷 冷冷冷冷冷
Jan 09, 2016
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!!