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