World of zero World of zero temperature temperature
--- introduction to systems of ultr--- introduction to systems of ultracold atomsacold atoms
National Tsing-Hua University
Daw-Wei Wang
Temperature ?
What we mean by “ultracold” ?
610 K !T
Why low temperature ?Why low temperature ?
x p
Therefore, if TT
2
~ ~ ~ , Thermal wavelength2 2
B T
B
pk T x
m p mk T
Ans: To see the quantum effects !
Uncertainty principle:
1/3Quantum regime when ~T d n
dT
(after Nature, 416, 225 (’02))
How to reach ultracold temperatuHow to reach ultracold temperature ?re ?
Normal pressure: He 4 4.2 K
We need very low densityto avoid strong binding,i.e. we need low “kinetic energy”,not low “potential energy” !
How to reach ultracold temperature ?How to reach ultracold temperature ?1. Laser cooling !(1997 Nobel Price)
Use red detune laser+ Doppler effect
How to reach ultracold temperature ?How to reach ultracold temperature ?2. Evaporative cooling !
Reduce potential barrial+thermal equilibrium
Typical experimental environmentTypical experimental environment
MIT
How to do measurement ?How to do measurement ?Trapping and cooling
Perturbing
Releasing and measuring BEC
(2001 Nobel Price)
What is Bose-Einstein What is Bose-Einstein condensation ?condensation ?
Therefore, for fermion we have ( , ) 0,
i.e. fermions like to be far away,
but bosons do like to be close !
x x
1 2 2 1( , ) ( , ), + for boson and - for fermionx x x x
Therefore, when T-> 0,noninteracting bosonslike to stay in the lowestenergy state, i.e. BEC
How about fermions in How about fermions in T=0 ?T=0 ?
Therefore, when T-> 0,noninteracting fermionsform a compact distributionin energy level.
E
D(E)
Fermi sea
BEC and Superfluidity of bosonsBEC and Superfluidity of bosons
Superfluid
Normal fluid
v repulsion
Landau’s two-fluid model
BEC = superfluidity
uncondensate
condensate(after Science, 293, 843 (’01))
Phonons and interference in BECPhonons and interference in BEC
m
Unvph
0
Phonon=density fluctuation Interference
Matter waves ?
(after Science 275, 637 (’97))
Vortices in condensateVortices in condensate
extln lnnlnlE 20, 223
Vortex = topological disorder
E
L1 320
Vortices melting, quantum Hall regime ?
(after Science 292, 476 (’01))
(after PRL 87, 190401 (’01))
Spinor condensation in optical trapSpinor condensation in optical trap0,1,1 FmF
JIF
Na
B
EF=2
F=1
lklkjijiijjiii
gg
mdH ˆˆˆˆ
2ˆˆˆˆ
2ˆ
2ˆ 20
2
FFr
(see for example, cond-mat/0005001)
Boson-fermion mixturesBoson-fermion mixturesSympathetic cooling
collapse
E
D(E)
Interacting fermi sea
Fermions are noninteracting !
rf-pulse
phonon-mediated interaction
fermion
phonon
(after Science 291, 2570 (’01))
(after Nature 412, 295 (’01))
NaLiLiLiRbK 236768740 or , ,
Feshbach ResonanceFeshbach Resonance(i) Typical scattering:
(ii) Resonant scattering:
0
0 1BB
Baa
B
a
Molecule and pair condensateMolecule and pair condensate
(JILA, after Nature 424, 47 (’03))
K40
(MIT group, PRL 92, 120403 (’04))
Li6
(Innsbruck, after Science 305, 1128 (’04))
2/9,2/9
2/5,2/9
2/5,2/9
2/9,2/9 2/7,2/9
Optical latticeOptical lattice3D lattice 1D lattice
Entanglement control 22
2
0
)(
E
EV R
other lattice
E
Mott-Insulator transitionMott-Insulator transition
i
iii
iiiiji
ji aaaaaaUaatH )1(,
(after Nature 415, 39 (’02))
Ut /
n=1
n=2
n=3 superfluid
Atom laserAtom laser
Bragg scattering
Continuous source for coherent atoms
Transport in 1D waveguideTransport in 1D waveguide
Interference ?
Finite temperature+ semiconductor technique
wave guide
wire
Interdisciplinary fieldInterdisciplinary field
Ultracold atoms
TraditionalAMO Quantum Information
NonlinearPhysics
Precise measurement
Condensed matter