peter van der straten - universiteit utrecht
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An Intimate Gathering of Bosons
Peter van der Straten
Atom Optics (AOUD)
Topics in NanoScienceUtrecht
October 15, 2009
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Bose-Einstein condensation
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What is Bose-Einstein condensation (BEC)?
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Bose-Einstein condensation
ρ = nΛdeB3 = 2.612375349 . . .
with
ΛdeB =h√
2πmkBT
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Bosons and Fermions
Usual examples: electrons, protons, neutron (fermions), photon (boson)Example: 3He (I=1/2) and 4He (I=0), or 6Li (F=1/2,3/2) and 7Li (F=1,2)
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Pauli exclusion principle
The Pauli exclusion principle is a quantummechanical principle formulated by WolfgangPauli in 1925. It states that no two identicalfermions may occupy the same quantum statesimultaneously.
A more rigorous statement of this principle is that, for two identicalfermions, the total wave function is anti-symmetric. For electrons in asingle atom, it states that no two electrons can have the same fourquantum numbers, that is, if n, l, and ml are the same, ms must bedifferent such that the electrons have opposite spins.In relativistic quantum field theory, The Pauli principle follows fromapplying a rotation operator in imaginary time to particles of half-integerspin. It does not follow from any spin relation in nonrelativistic quantummechanics.
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Application of Pauli principle
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Population of states
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Outline
1 How to produce a Bose-Einstein condensateStep 1: Light pressureStep 2: Optical molassesStep 3: Magnetic trapping
2 Observation of BEC
3 What to do with a Bose-Einstein condensateSound propagationBosons versus FermionsAtom laser
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How to produce a Bose-Einstein condensate
Outline
1 How to produce a Bose-Einstein condensateStep 1: Light pressureStep 2: Optical molassesStep 3: Magnetic trapping
2 Observation of BEC
3 What to do with a Bose-Einstein condensateSound propagationBosons versus FermionsAtom laser
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How to produce a Bose-Einstein condensate Step 1: Light pressure
Light pressure
initial
mv0 h̄k
absorption
mv0 − h̄k
spontaneousemission
mv0 − h̄k + 〈h̄ki〉= mv0 − h̄k
recoil “kick”vr = ~k
m ≈ 3 cm/s (Na)thermal
v ≈ 1000 m/sNstop ≈ 33.000 fotons
lifetimeτ = 16 ns
Tstop ≈ 1 mseclstop ≈ 0.5 m
accelerationa ≈ 9× 105 m/s2
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How to produce a Bose-Einstein condensate Step 1: Light pressure
Zeeman technique
600 KNa oven solenoid
extractioncoils
pumpbeam
probebeam
coolingbeam
aom
Bz
1.25 m
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How to produce a Bose-Einstein condensate Step 1: Light pressure
Velocity distribution
200 400 600 800 1000 1200 1400 1600Velocity (m/s)
0
5
10
15
20
25At
om F
lux
(arb
. uni
ts)
A
B
B
Capture Velocity
180 200 220 240 260 2800
10
20
30
6.8 m/s
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How to produce a Bose-Einstein condensate Step 1: Light pressure
Funnel for atoms
-50 0 50 100Position (cm)
200
400
600
800
1000
1200Ve
loci
ty (m
/s)
-50 0 50 100Position (cm)
200
400
600
800
1000
1200
Velo
city
(m/s
)
�a�
�b�
Contour map of the velocity and position of atoms in the solenoid
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How to produce a Bose-Einstein condensate Step 2: Optical molasses
Laser cooling
mv -hk+hk
g
e
+kv
ωω0
δ
v
F
Cooling limit: Damping by Doppler tuning vs. heating by random recoil
kTD = ~Γ2 [Na : 240µK]
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How to produce a Bose-Einstein condensate Step 2: Optical molasses
Cold Atoms
D:/upload/Phys2000/bec/lascool4.html
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How to produce a Bose-Einstein condensate Step 3: Magnetic trapping
Magnetic Trap
Cloverleaf trap
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How to produce a Bose-Einstein condensate Step 3: Magnetic trapping
Evaporation
1 Cools a cup of coffee
2 Cools apples by overtree sprinkling
3 Is used in technical water coolers
4 Globular clusters do it by evaporation of stars
5 Compound nuclei do it by evaporating neutrons
6 Atom coolers love it.
Evaporative cooling of a trapped gas is based on the preferential removalof atoms with an energy higher than the average energy, followed bythermalization of the gas by elastic collisions.
In order to force the cooling to proceed at a constant rate, the evaporationthreshold may be lowered as the gas cools (forced evaporation).D:/Upload/Phys2000/bec/xevap cool.html
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How to produce a Bose-Einstein condensate Step 3: Magnetic trapping
Experimental feasibility
Oven
Zeeman slower MOC MOT
Properties of the trapped atoms N n (atoms/cm3) T (µK )
MOT 1.2× 1010 3× 1011 320magnetic trap 8× 109 3× 1011 340evaporative cooling 1.5× 108 8× 1013 0.3
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Observation of BEC
Outline
1 How to produce a Bose-Einstein condensateStep 1: Light pressureStep 2: Optical molassesStep 3: Magnetic trapping
2 Observation of BEC
3 What to do with a Bose-Einstein condensateSound propagationBosons versus FermionsAtom laser
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Observation of BEC
Current setup
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Observation of BEC
Bose-Einstein condensation–The last stages
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Observation of BEC
Expansion of the cloud
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Observation of BEC
Phase contrast imaging–setup
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Observation of BEC
Phase contrast imaging–images
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Observation of BEC
Characteristic values
Dark magneto-optical trapTemperature 320 µKNumber of particles 1.2× 1010 atomsDensity 3× 1011 atoms/cm3
Magnetic trapTrap frequencies νr=96 Hz and νz=16→1.08 HzNumber of particles 8× 109 atomsElastic scattering rate 10 collisions/s
Bose-Einstein condensationEvaporation ramp 40 sNumber of particles 2.5× 108 atomsDensity 2.5× 1014 atoms/cm3
Chemical potential 3.5 kHzTemperature 300 nK
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What to do with a Bose-Einstein condensate
Outline
1 How to produce a Bose-Einstein condensateStep 1: Light pressureStep 2: Optical molassesStep 3: Magnetic trapping
2 Observation of BEC
3 What to do with a Bose-Einstein condensateSound propagationBosons versus FermionsAtom laser
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What to do with a Bose-Einstein condensate Sound propagation
Topic One
Sound propagation
“Observation of second sound”
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What to do with a Bose-Einstein condensate Sound propagation
Tisza-Landau two-fluid hydrodynamics (1938-1941)
Tisza
Superfluid: component of liquid which is associatedwith macroscopic occupation (BEC) of onesingle-particle state. Carries zero entropy, flowswithout dissipation with an irrotational velocity.
Landau
Normal fluid: comprised of incoherent thermalexcitations, behaves like any fluid at finitetemperatures in local thermodynamic equilibrium.This requires strong collisions.
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What to do with a Bose-Einstein condensate Sound propagation
First and second sound in liquid helium
First soundPressure waveIn-phase
Second soundTemperature waveOut-of-phase
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What to do with a Bose-Einstein condensate Sound propagation
Speed of sound
0.0 0.2 0.4 0.6 0.8 1.0 Temperature [μK]
0
5
10
15
20Sp
eed
of s
ound
[m
m/s
]
0.00 0.02 0.04 0.06 0.08 0.100
2
4
6
8
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What to do with a Bose-Einstein condensate Sound propagation
Density or temperature wave?
0.0 0.2 0.4 0.6 0.8 1.0 Temperature [μK]
-6
-4
-2
0
2(δ
T/T
) vs
. (δn
/n)
First sound
Second sound
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What to do with a Bose-Einstein condensate Sound propagation
In-phase or out-of-phase?
0.0 0.2 0.4 0.6 0.8 1.0 Temperature [μK]
1
10
100R
atio
First sound: δvn/δvs
Second sound: -δvs/δvn
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What to do with a Bose-Einstein condensate Sound propagation
Generating sound
t=0
t<0
t>0
Grow the condensate with blue detuned dipole beam in center
At t = 0 shut off dipole beam
Wait & see
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What to do with a Bose-Einstein condensate Sound propagation
Detecting sound
t=50ms
t=60ms
t=70ms
t=80ms
t=90ms
t=100ms
t=110ms
Density
difference
(arb.units)
z/Rtf
-0.9 -0.6 -0.3 0 +0.3 +0.6 +0.9
Sound propagation in a Bose-Einstein condensate at finite temperatures, R. Meppelink et al.,
Phys. Rev. A 80, . . . (2009), online 12 October 2009.
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What to do with a Bose-Einstein condensate Sound propagation
Comparison to theory
0.85
0.90
0.95
1.00
1.05
5 10 15 20 25 30
0.700.47 0.51 0.64 0.720.30 0.39 0.44 0.58
Norm
alized
speedofsound
T/Tc
b
Normalized to Landau & ZGN speed of sound
Thermal density (1018m−3)
Sound propagation in a Bose-Einstein condensate at finite temperatures, R. Meppelink et al.,
Phys. Rev. A 80, . . . (2009), online 12 October 2009.
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What to do with a Bose-Einstein condensate Bosons versus Fermions
Topic Two
Bosons versus Fermions“How quantum statistics changes everything”
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What to do with a Bose-Einstein condensate Bosons versus Fermions
“Fermi” pressure
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What to do with a Bose-Einstein condensate Bosons versus Fermions
Bunching or anti-bunching
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What to do with a Bose-Einstein condensate Bosons versus Fermions
Bunching or anti-bunching
Jeltes et al., Nature 2007
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What to do with a Bose-Einstein condensate Bosons versus Fermions
Bunching or anti-bunching
Jeltes et al., Nature 2007
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What to do with a Bose-Einstein condensate Atom laser
Topic Four
Atom laser“The creation of a continuous flow of Bose-condensed atoms”
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What to do with a Bose-Einstein condensate Atom laser
Atom lasers
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What to do with a Bose-Einstein condensate Atom laser
Evaporative cooling
Trap geometry vs. Beam geometry
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What to do with a Bose-Einstein condensate Atom laser
“The rollercoaster”
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What to do with a Bose-Einstein condensate Atom laser
Atom laser setup
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What to do with a Bose-Einstein condensate Atom laser
Shockwave
0 20 40 60 80 1000.0
0.2
0.4
0.6
0.8
Time �sec�
Opt
ical
dens
ity
shockwave
atmospheric compression
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