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TATIONpRÆSEN
BOSE-EINSTEIN CONDENSATESJAN ARLTINSTITUT FOR FYSIK OG ASTRONOMI
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87Rb BEC
QUANTUM SIMULATION WITH
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The dream quantum system :
A system in a well known potential
• in a prepared state, • isolated from the environment,• accessible to manipulation techniques.
Reality: T=300 K|v|=300 m/sv~300m/s
v
d
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Phase transition from an ideal gas toBose-Einstein-condensate (BEC):
A. Einstein
S. N. Bose
S. N. Bose, Z. Phys. 26, 178 (1924)A. Einstein, Sitzber. Kgl. Akad. Wiss. 3 (1924/25)
2.612 λn 3dB
1/2B
2dB Tmk2πλ )/(
thermal de Broglie wavelengthdensity
ultra low temperatures required:(solid)T = 1K n = 1023cm-3
T = 1K n = 1015cm-3
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K350
250200150100
500
300 10-3
10-4
10-5
10-6
10-7
10-8
10-2water freezes(273K = 0ºC)
Liquid nitrogen (77K)
Liquid helium (4K)
Bose-Einstein-condensate
(~ 10-7 K = 100nK)
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dB low temperatureswavepackets
T=TCBose-Einstein-condensation
v
d
high temperaturesclassical particles
T=0Pure BEC
“From a certain temperature on, the molecules condense without attractive forces, that is, they accumulate at zero velocity. The theory is pretty but is there also some truth to it?” - A. Einstein 1924
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~RF WilliamPhillips
StevenChu
ClaudeCohen-
Tannoudji
Nobel Prize 1997
E. Cornell W. Ketterle C. Wieman
Nobel Prize 2001
• Confining potential
• Cooling schemes
• Quantum simulation
Outline:
• Source of cold atoms
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Laser coolingK
350
250200150100
500
300 10-3
10-4
10-5
10-6
10-7
10-8
10-2
Laser Cooling(~ 10-5 K = 10K)
BEC
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Manipulation of atomic velocities with inner degrees of freedom:
Laser 0 < 0 vatom
F = = + p
t pAb s
t pspEm
tF
= 0
Cooling (leading to deceleration of atoms)
Limit of optical coolingsingle-photon processes ( T ~1µK at n < 1010 cm-3 )
v
|F| <v > ~ T2 n(v)
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Magneto-Optical Trap (MOT)
Typical values
Number N 109 atoms
density n 109 - 1011 cm-3
temperature T 10 - 100 K
size x 0.1…10 mm
Cooling and trapping in 3 dimensions
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~RF WilliamPhillips
StevenChu
ClaudeCohen-
Tannoudji
Nobel Prize 1997
E. Cornell W. Ketterle C. Wieman
Nobel Prize 2001
• Confining potential
• Cooling schemes
• Quantum simulation
Outline:
• Source of cold atoms
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Necessary steps:
› Source of cold atoms
~RF WilliamPhillips
StevenChu
ClaudeCohen-
Tannoudji
Nobel Prize 1997
E. Cornell W. Ketterle C. Wieman
Nobel Prize 2001
• Confining potential
• Cooling schemes
• Quantum simulation
Outline:
• Source of cold atoms
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W. Ketterle, D.S. Durfee, D.M. Stamper-Kurn, Making, probing and understanding Bose-Einstein condensatescond-mat/9904034 (1999)
Position x
E
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dispenser
MOT cell(10-9 mBar) science cell
(< 10-11 mBar)
Transport of a quantum degenerate heteronuclear Bose-Fermi mixture in a harmonic trapC. Klempt, T. Henninger, O. Topic, J. Will, St. Falke, W. Ertmer, and J. Arlt, Eur. Phys. J. D 48, 121-126 (2008)
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DETECTION
Absorption imaging
atoms lensresonant light camera
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Necessary steps:
› Source of cold atoms
~RF WilliamPhillips
StevenChu
ClaudeCohen-
Tannoudji
Nobel Prize 1997
E. Cornell W. Ketterle C. Wieman
Nobel Prize 2001
• Confining potential
• Cooling schemes
• Quantum simulation
Outline:
• Source of cold atoms
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600 nK 400 nK <200 nK
BEC
30 ms
120 ms
200 ms
300 ms
500 ms
We develop the building blocks for the Atom‐laser:
MirrorWaveguide:
Atom optics
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• Potential well: discrete energy levels
• Increase number: split levels
• Band structure
BAND STRUCTURE
http
://w
ww
.fkf.m
pg.d
e/kl
itzin
g
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“Currents“ in an optical lattice:
dEj1j
ti
j
j
e
J JdE
Drenkelforth, S., Büning, G. K., Will, J., Schulte, T., Murray, N., Ertmer, W., Santos, L., Arlt, J. J., 2008, Damped Bloch oscillations of Bose Einstein condensates in disordered potential gradients, New Journal of Physics, nr. 4, s. 045027
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MOTT INSULATOR TRANSITION
Ideal insulating state: Mott insulator
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Superfluid Mott insulator
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