Download 冷原子實驗之基本原理(I)

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
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?)
玻色－愛因斯坦凝聚現象之發現
Kapitza
Cornell
Wieman
Ketterle
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.
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
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
Superfluidity
Vortices
Excitation
Mott Insulator
Quantum Entanglement
Feshbach Resonance
( a knob tuning the interactions!!)
Coherence
Interference
Atom Laser
Weakly Interacting
Bose Gas
Strongly Correlated
Boson Systems
Cold Molecules
Low Dimension
Multi- Species
Nonlinearity
Phase fluctuations
Tonks Gas
Cooling, Trapping, and Manipulating Tools
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”
|E0(x)|2
x
F(x)
z
x
far-detuned light light!
|E0(x)|2
F(x)
“dipole force”
x
z
BEC Behavior
Starting from the
Gross-Pitaevskii equation!!
Mean-Field Theory of Bose Condensates
“internal energy”
凝聚體平均場理論之 Hamiltonian or “mean field
energy”
2
4 2 a
2

  Vtrap (r ) 
 N   (r, t )
2m
m
S-波散射長度
a < 0 原子間作用為吸引力  凝聚體呈不穩定
a>0
(s-wave scattering length)
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 !!
Time-Evolution of a Wavefunction in Free Space
MIT, 1996
a →f
(時間增加)
凝聚體於自由空間中隨時間膨脹
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
1st order correlation
MIT, 1996
3rd 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
kdB
1
2
S1/2 & 2S1/2
+
g
3 +
u
0 cm–1
F=3&F=3
F=2 &F=2
–0.5 cm–1

E
–1 cm–1
0
20
40
60
R (aB)
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)
x01
x02
(b)
xb1(t)
xa1(t)
xb2(t)
xa2(t)
簡易之二位元量子邏輯閘
(two-qubit logic gate)
Innsbruck, 1999
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)
stripes on1D traps
(different aspect ratios)
Hannover, 2001
Bragg spectroscopy
in momentum space
Orsay, 2003
Unexpected New Physics!!