quantum simulation with bose-einstein condensates · bose-einstein condensates jan arlt institut...

25/01 – 2013AARHUSUNIVERSITET

TATIONpRÆSEN

BOSE-EINSTEIN CONDENSATESJAN ARLTINSTITUT FOR FYSIK OG ASTRONOMI

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87Rb BEC

QUANTUM SIMULATION WITH

25/01 - 2013AARHUSUNIVERSITET JAN ARLT

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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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Classical: High velocities


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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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v

unprecedented accuracy

novel macroscopic quantum object


8

350

273250200

150

100

0

300

450

50

400

K


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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


Nobel Prize 2001


• Cooling schemes


Outline:



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Ioffe-Pritchard trap


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Necessary steps:

› Source of cold atoms

~RF WilliamPhillips

StevenChu

ClaudeCohen-

Tannoudji

Nobel Prize 1997


Nobel Prize 2001


• Cooling schemes


Outline:



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Evaporation

v

f(v)T, n

f(v)

v

T’<Tn’>n

Rethermalisation


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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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600 nK 400 nK <200 nK


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Necessary steps:

› Source of cold atoms

~RF WilliamPhillips

StevenChu

ClaudeCohen-

Tannoudji

Nobel Prize 1997


Nobel Prize 2001


• Cooling schemes


Outline:



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v

~RF


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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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~RF

v


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29

d


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1D Lattice 2D Lattice 3D Lattice


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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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EXPERIMENTS

Quantum mixture Experiment (K+Rb)

Lattice Experiment

http://phys.au.dk/forskning/uqgg/

quantum simulation with bose-einstein condensates · bose-einstein condensates jan arlt institut...

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