Bose-Einstein Condensation Ultracold Quantum Coherent Gases.
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Bose-Einstein Condensation Ultracold Quantum Coherent Gases
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Transcript of Bose-Einstein Condensation Ultracold Quantum Coherent Gases.
Bose-Einstein CondensationUltracold Quantum Coherent Gases
What’s Ultra-Cold Matter ?What’s Ultra-Cold Matter ?
Very Cold Very Cold
Very Dense … in Phase SpaceVery Dense … in Phase Space
Typically nanoKelvin – microKelvin
Atoms/particles have velocity ~ mm/s – cm/s
x
p
x
p
x
p
Different temperaturesSame phase space density Higher
phase space density
mK
μK
nK
Ultra-cold Quantum MechanicsUltra-cold Quantum Mechanics
x
p
x
p
/2 px fundamental unit of phase space volume
Quantum mechanics requires
/2 px
Quantum physics is important when 1 ~ PSD
Equivalent:
deBroglie wavelength ~ inter-particle separation
1~deBroglien
Quantum régimeBoltzmann régime
Ei
Ni
1
EF
Quantum StatisticsQuantum Statistics
BosonsBosons FermionsFermions
symmetricsymmetric multi-particle wavefunction.
Integer spin: photons, 87Rb.
probability of occupying a state |i> with energy Ei.
1
1)( /)( kTEi ie
EP
anti-symmetricanti-symmetric multi-particle wavefunction.
½-integer spin: electrons, protons, neutrons, 40K.
probability of occupying a state |i> with energy Ei.
1
1)( /)( kTEi ie
EP
Ei
Ni
NBEC
Bose-Einstein Condensation of Bose-Einstein Condensation of 8787RbRb
1.095.3ln(N)
ln(PSD)
d
d
Evaporation Efficiency
BECthermalatoms
magnetictrapping
evap.coolingMOT
10-13 110-6 105
PSD
8787Rb BECRb [email protected] MHz:
N = 7.3x105, T>Tc
[email protected] MHz:
N = 6.4x105, T~Tc
[email protected] MHz:
N=1.4x105, T<Tc
8787Rb BECRb BEC
Surprise! Reach Tc with only a 30x loss in number.
(trap loaded with 2x107 atoms)
Experimental cycle = 5 - 15 seconds
[email protected] MHz:
N = 7.3x105, T>Tc
[email protected] MHz:
N = 6.4x105, T~Tc
[email protected] MHz:
N=1.4x105, T<Tc
Fermions: Sympathetic CoolingFermions: Sympathetic Cooling
Problem:
Cold identical fermions do not interact due to Pauli Exclusion Principle.
No rethermalization.
No evaporative cooling.
Problem:
Cold identical fermions do not interact due to Pauli Exclusion Principle.
No rethermalization.
No evaporative cooling.
Solution: add non-identical particles
Pauli exclusion principle does not apply.
Solution: add non-identical particles
Pauli exclusion principle does not apply.
We cool our fermionic 40K atoms sympathetically with an 87Rb BEC.We cool our fermionic 40K atoms sympathetically with an 87Rb BEC. Fermi
Sea
“Iceberg”BEC
The Problem with FermionsThe Problem with Fermions
At very low temperatures, 0 prl
If , then two atoms must scatter as an s-wave:0l
r
eaeerrr
rik
sikzikz
waves
2)( 21
s-wave is symmetric under exchange of particles: rr
Identical ultra-cold fermions do not interactIdentical ultra-cold fermions do not interact
as = 0 for fermions
Sympathetic CoolingSympathetic Cooling
8ln(N)
ln(PSD)
Cooling EfficiencyCooling Efficiency
108
106
104
102
100
102
104
105 106 107
108
106
104
102
100
102
104
105 106 107
108
106
104
102
100
102
104
105 106 107
Below TBelow TFF
0.9 TF0.9 TF0.35 TF0.35 TF
For Boltzmann statistics and a harmonic trap,
For ultra-cold fermions, even at T=0,
TvkTmv 212
21
m
EvEmv FFF 22
21
Fermi
Boltzmann
Gaussian Fit
Pauli PressurePauli Pressure
