World of ultracold atoms
Daw-Wei Wang
National Tsing-Hua University
Early world
Cosmology
Our ordinary world
Small world
Particle phys.
Single (or few)
atoms:
AMO Phys.
Cold atoms
Many-particle (or atoms):
High T Plasma
Middle T Soft-matter
Low T Condensed
matter
Future world
Applied Physics
Large world
Astrophysics
Ultracold atoms as an emergent field….
Atomic, Molecular, and Optical Physics
Condensed matter Physics
Systems of ultracold atoms can be understood as a many-body
system of atoms, which are strongly affected by the fruitful
internal degrees of freedom of each single atom.
An Interdisciplinary field
Traditional
AMO
Precise
measurement
y
g
o
l rgy
o
m ne
s
Co igh e
H
&
Ultracold atoms Quantum Information
Nonlinear
Physics
Soft-matter/
chemistry
Condensed matter
How cold is an “ultracold system” ?
Thermal wavelength
 2π 
kBT ~
 
2m  λ 
2
2
Quantum degeneracy:
λ ~ L ~ 1 − 100µ m
T < 1µ K
Why low temperature ?
Ans: To see the quantum effects !
Uncertainty principle: ∆x∆p ≥ ∆p 2
~ k BT → ∆x ~
~
2m
∆p
≡ λT , Thermal wavelength
2mk BT
Therefore, if T ↓ ⇒ λT ↑
Quantum regime when λT ≥ d ~ n −1/ 3
λT
d
Why strong interaction ?
P. Anderson: “Many is not more”
Because interaction can make
“many” to be “different” !
Example: 1D interacting electrons
crystalization and no fermionic excitation
How to make interaction stronger ?
 p 2j
 1 N
+ V ( x j )  + ∑ U ( xi − x j )
H = ∑

 2 i≠ j
j =1  2m

N
1. U ( x) becomes stronger
2. Ek ~ k BT becomes smaller or m becomes smaller
3. V ( x) changes to make lower dimension
4. N becomes larger (for short interaction);
smaller for long range interaction
How to reach ultracold temperature ?
See also: Prof. Yu’s talk
1. Laser cooling !
(few K mK)
Use red detune laser
+ Doppler effect
1997 Nobel Price
Steven Chu
Claude Cohen-Tannoudji
Williams D. Phillips
How to reach ultracold temperature ?
1. Laser cooling !
(1997 Nobel Price)
Use red detune laser
+ Doppler effect
How to reach ultracold temperature ?
2. Evaporative cooling !
Reduce potential barrial
+thermal equilibrium
Typical experimental environment
MIT
How to do measurement ?
Trapping and cooling
Perturbing
Releasing and measuring
BEC
(2001 Nobel Price)
What is Bose-Einstein
condensation ?
Ψ ( x1 , x2 ) = ±Ψ ( x2 , x1 ), + for boson and - for fermion
Therefore, for fermion we have Ψ ( x, x) = 0,
i.e. fermions like to be far away,
but bosons do like to be close !
When T is small enough,
noninteracting bosons
like to stay in the lowest
energy state, i.e. BEC
How about fermions in T=0 ?
D(E)
Fermi sea
E
When T-> 0, noninteracting
fermions form a compact
distribution in energy level.
BEC and Superfluidity of bosons
(after Science, 293, 843 (’01))
BEC = superfluidity
v
Superfluid
condensate
repulsion
uncondensate
Normal fluid
Landau’s two-fluid model
Phonons and interference in BEC
Interference
Phonon=density fluctuation
v ph =
n0U
m
(after Science 275, 637 (’97))
Matter waves ?
Vortices in condensate
Vortex = topological disorder
E
0
(after Science 292, 476 (’01))
(after PRL 87, 190401 (’01))
1
2
3
L
En ,l = ω0 l + 3n + 2nl + 2n 2 − lωext
Vortices melting, quantum Hall regime ?
Spinor condensation in optical trap
Na F = 1, mF = ±1,0
E
F=2
F=1
F=I+J
B
(see for example, cond-mat/0005001)
2


g
g
+ ∇
H = ∫ d r  − ψˆ i
ψˆ i + 0 ψˆ i+ψˆ +j ψˆ jψˆ i + 2 (ψˆ i+ Fijψˆ j ) ⋅ (ψˆ k+ Fklψˆ l )
2m
2
2


Boson-fermion mixtures
Fermions are noninteracting !
phonon
fermion
phonon-mediated interaction
40
K −87Rb, 6Li − 7Li, or 6Li − 23Na
D(E)
rf-pulse
Interacting
fermi sea
E
Sympathetic cooling
Feshbach Resonance
(i) Typical scattering:

∆B 

a = a0 1 +
B − B0 

(ii) Resonant scattering:
a
B
Molecule state
Molecule and pair condensate
(MIT group, PRL
92, 120403 (’04))
6
Li
(JILA, after Nature 424, 47 (’03))
40
K
9 / 2,−5 / 2
9 / 2,−7 / 2
9 / 2,−9 / 2
9 / 2,−5 / 2
9 / 2,−9 / 2
(Innsbruck, after Science 305, 1128 (’04))
First evidence of superfluidity of fermion pairing
a
B
3D lattice
Optical lattice
1D lattice
2
V0 ∝ −
Entanglement control
ω
∆E
other lattice
Ω R (ω − ∆E )
(ω − ∆E )2 + Γ 2
Mott-Insulator transition
Bose-Hubbard model
H = −t ∑ ai+ a j + U ∑ ai+ ai ( ai+ ai − 1) − µ ∑ ai+ ai
<i , j >
i
i
µ
n=3
superfluid
n=2
n=1
t /U
(after Nature 415, 39 (’02))
Fermions in optical lattice
Fermi Hubbard model
H = −t ∑ ai+, s a j , s + U ∑ ni ,↑ ni ,↓
<i , j >
i
Superfluidity of fermion pairing in lattice is also realized.
Transport in 1D waveguide
wave guide
wire
Interference ?
Finite temperature
+ semiconductor technique
Cold dipolar atoms/molecules
(1) Heteronuclear molecules
(2) Atoms with large
magnetic moment
(a) Direct molecules
p~ 1-5 D
(b) But difficult to be cooled
Small moment µ ~ 6µ (for Cr)
B
(Doyle, Meijer, DeMille etc.)
But it is now ready to go !
(Stuhler etc.)
p ~ 1D, U dd ~ 10 µK, µ = 1µ B , U dd ~ 1nK
Condensate (superfluid)
µ = 6µB
Tc~700 nK
Artificial dipoles:
(1)Feshbach resonance
(KRb, JILA, ETH, etc.)
But not in ground state
weak dipole moment
short life time
(2) photo-association
(RbCs, Yale, etc.)
Now in ground state
But number of atoms
are still small
(J. Sage, et. al., PRL, 94, 203001 (’05))
Gallery of pictures
Bose-Einstein Condensation
Superfluid-Mott insulator transition
BEC-BCS crossover
Fermi surface in optical lattice