AtomicAtomic OpticsOptics withwithBoseBose--EinsteinEinstein CondensationCondensation

Student: Xinglan LiuSupervisor: Maxim Mostovoy

History of Bose Einstein Condensation

S. N. Bose A. Einstein

Eric A. Cornell Wolfgang Ketterle Carl E. Wieman

Nobel Prize in 2001 was for ‘the achievement of Bose-Einstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of the condensates.’

Predicted in 1924 by:

Bose Einstein Condensation—a coherent matter wave

High Temperaturede Broglie wavelength λdB is small

Classical objects

T=0Pure CondensateGiant matter wave

T=Tcritical (~100nK)λdB ~d

Bose Einstein Condensation

Low TemperatureλdB ~T-1/2

Wave Packets

http://cua.mit.edu/ketterle_group/Nice_pics.htm

BEC in BEC in momentummomentum spacespace

• 99% atoms are in condensation• Number of atoms: ~106

• Density of atoms: 1013cm-3

(~0.00001 of air density)

http://www.physik.uni-mainz.de/quantum/bec/gallery/PhaseTrans.jpg

Atom optics using BECBose Einstein condensate (BEC) is a bunch of ultracold atoms that alloscillate in phase —a coherencematter wave formed by atoms

OUTLINEOUTLINE• BEC interference spectra—measure relative

PHASE• Justification of interference measurement —

the uncertainty relation between number and phase

Interference of laser—coherence light

1. Source

2. Double slits, grating, etc.

3. Interfere

4. Detection

InterferenceInterference of BECof BEC1. Source 2. ‘double slits’ 3. Interfere 4. Detection

Shin, Ketterle et. al. PRL 92 50405 (2004)

Time-of-flight (TOF) measurment

Probe laser

Potential well

BECAtom cloud

MdhtFringe =

TIME OF FLIGHT (TOF) TIME OF FLIGHT (TOF) measurementmeasurement

http://www.physik.uni-mainz.de/quantum/bec/gallery

Examples of BEC interference• Clear interference fringes demonstrate a well defined

relative phase between two BECs. • BEC can be modeled by a macroscopic wave function:

ϕieN=Ψ

Hadzibabic, Dalibard et. al. PRL 93 180403 (2004)

Greiner, Bloch et. al. Nature 415 39 (2002)

More examples of phase measurements

Fölling, Bloch, et. al. Nature 434 481 (2005)

Interference fringes disappear

Phase coherence is lost ?⇓

HeisenbergHeisenberg uncertaintyuncertainty principleprinciple

• State with well defined number:– Fock state

• States with well defined phase:– Macroscopic wave function

– Coherent state

The more precisely the number (intensity) is determined, the less precisely the phase is known in the same instant, and vice versa:

∑∝n

nn!1α

ϕieN=Ψ

21≥∆∆ ϕNW. Heisenberg(1901-1976) N

InterferenceInterference experimentexperiment——MeasureMeasure relativerelative phasephase• Interference of coherent states:

one measurement ‘create’ a relativephase.

– Two communicating, or independent BEC sources, perfect interference

– Many condensates with same chemicalpotential: high contrast interference

– Many condensates with different chemical potential: interferencecontrast smeared

• Many experimental realizations, created relative phase is random (in any case)

Loss of interference contrast

Fölling, Bloch, et. al. Nature 434 481 (2005)

• Many sources: 150000

• Independent sources: random relativephase

• Column absorption experiment: effectivelyaverage over many experiments:

No direct No direct relationrelation betweenbetween the the interferenceinterference contrast contrast and and sourcesource statestate

SUMMARYSUMMARYInterferenceInterference experimentsexperiments

Show evidence that Bose Einstein condensation is a coherent matter wave.

Interference experiment create a phase value.

BEC BEC cancan bebe usedused in:in:Atom interferometry (independent BEC interferes)

Nonlinear atom optics—natural nonlinear source.

AcknowledgementAcknowledgement

ThanksThanks toto Dr. M. Dr. M. MostovoyMostovoy forfor manymany helpshelps

M. Saba (MIT)

Anne, Auke, Bram, Michiel, Maxim, Ponky