Atomic Optics with Bose-Einstein Condensation€¦ · History of Bose Einstein Condensation S. N....
Transcript of Atomic Optics with Bose-Einstein Condensation€¦ · History of Bose Einstein Condensation S. N....
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