D. Jin

JILA,NIST and

the University of Colorado

$ NIST, NSF

Using a Fermi gas to create Bose-Einstein condensates

Outline

I. Intro and motivationa) A little quantum physicsb) Basics of the experiment

II. Interactions - An amazing new knoba) Experimental demonstrationb) Implications (more motivation)

III. Condensates of correlated fermion pairs

Outline

I. Intro and motivationa) A little quantum physicsb) Basics of the experiment

II. Interactions - An amazing new knoba) Experimental demonstrationb) Implications (more motivation)

III. Condensates of correlated fermion pairs

Quantum Gases

d

high T low T

deBroglie d

classical behavior quantum behavior

matter waves

1 0

1 0

1 0 0

1 0

1

0 .1

0 .0 1

1 0

1 0

1 0

1 0

1 0

1 0

4

3

-3

-4

-5

-6

-7

-8

There are two types of quantum particles found in nature - bosons and fermions.

Bosons like to do the same thing.

Fermions are independent-minded.

Atoms, depending on their composition, can be either.

bosons: 87Rb, 23Na, 7Li, H, 39K, 4He*, 85Rb, 133Cs

fermions: 40K, 6Li

Quantum Particles

Bosons and Fermions half-integer spin

other fermions: protons, electrons, neutrons,

liquid 3He

integer spin

T = 0Atoms in a harmonic potential.

Bose-Einstein condensation

1995

other bosons: photons, liquid 4He

Fermi sea of atoms1999

EF= kbTF

(two spin states)

Ultracold atomic gases low density n ~ 1013 – 1014 cm-3

N~106

ultralow T ~ 100 nK

• amenable to theoretical analysis• unique experimental control• dramatic detection of condensation

Bose-Einstein condensationBEC shows up in condensed matter, nuclear physics, elementary particle physics, astrophysics, and atomic physics.

Excitons, biexcitonsin semiconductors

Cooper pairs of electrons in

superconductors

4He atoms in superfluid

liquid He

3He atom pairs in superfluid

3He-A,BNeutron pairs,

proton pairs in nuclei and neutron stars

Mesons in neutron star

matter

Alkali atomsin ultracold atom gases

Condensates with Fermions? Condensation requires bosons.

Material bosons are composite particles, made up of fermions.

Starting with a gas of bosonic atoms, you can only explore the behavior of bosons.

87Rb, 23Na, … By starting with a gas of fermionic atoms we can explore

the behavior of fermions AND BOSONS.

40K, 6Li, …

Cooling a gas of atoms1. Laser cooling and trapping

2. Magnetic trapping and evaporative cooling

300 K to 1 mK109 atoms

1 mK to 1 K108 → 106 atoms

spin 1spin 2

3. Optical trapping and evaporative cooling

4. Probing the atoms

Cooling a gas of atoms

1 K to 50 nK106 → 105 atoms

can confine any spin-state

can apply arbitrary B-field

Quantum degeneracy velocity distributions

T/TF=0.77

T/TF=0.27

T/TF=0.11

Fermi sea of atoms

EF

EF

n0= 0.28

n0= 0.944

n0= 0.99984

Outline

I. Intro and motivationa) A little quantum physicsb) Basics of the experiment

II. Interactions - An amazing new knoba) Experimental demonstrationb) Implications (more motivation)

III. Condensates of correlated fermion pairs

Interactions Interactions are characterized by the s-wave scattering length, a

In an ultracold atomic gas, we can control a!

a > 0 repulsive, a < 0 attractiveLarge |a| → strong interactions

0 scattering length

215 220 225 230-3000

-2000

-1000

0

1000

2000

3000

sc

atte

ring

leng

th (

a o)

B (gauss)

Magnetic-field Feshbach resonance

C. A. Regal and D. S. Jin, PRL 90, 230404 (2003)

repulsive

attractive

spectroscopic measurement of the mean-field energy shift

Magnetic-field Feshbach resonance

R

V(R)

RR R

a<0, attractivea>0, repulsive

215 220 225 230-3000

-2000

-1000

0

1000

2000

3000

scat

terin

g le

ngth

(a o)

B (gauss)

Magnetic-field Feshbach resonance

R

V(R)

RR R

a<0, attractivea>0, repulsive

molecules

→ ←B>

atoms

Turning atoms into molecules

Ramp across Feshbach resonance from high to low B

215 220 225 230-3000

-2000

-1000

0

1000

2000

0

5.0x105

1.0x106

1.5x106

scat

terin

g le

ngt

h (

ao)

B (G)

ato

m n

umbe

r

The atoms reappear if we sweep back to high B

ener

gy

B

→ ←

up to 90% conversion to molecules!

molecules are extremely weakly bound !

molecules can survive many collisions !

Bosonic molecules

220 221 222 223 224

-500

-400

-300

-200

-100

0

atoms molecules binding energy theory

(Ticknor, Bohn)

(

kHz)

B (gauss)

Interestingregime

Theory: D.S. Petrov et al., cond-mat/0309010, Expts: Rice, ENS, Innsbruck, JILA

rf photodissociation

C. Regal et al. Nature 424, 47 (2003)

BEC of diatomic molecules

BCS superconductivity/superfluidity

Something in between?

Making condensates with fermions

1. Bind fermions together.

2. BEC

Condensation of Cooper pairs of atoms

(pairing in momentum space,

near the Fermi surface)

EF

spin spin

BCS-BEC crossover (“generalized Cooper pairs”)

1 05

1 0- 5

1 010

1 00

1 0- 2

1 0- 4

1 0- 6

2 / k TB F

T/T

c F

BCS-BEC landscape

energy to break fermion pair

tra

nsiti

on

tem

per

atu

re

BEC

BCSsuperfluid 4He

alkali atom BEC

high Tc superconductors

superfluid 3He

superconductors

M. Holland et al.,PRL 87, 120406 (2001)

interactions

Outline

I. Intro and motivationa) A little quantum physicsb) Basics of the experiment

II. Interactions - An amazing new knoba) Experimental demonstrationb) Implications (more motivation)

III. Condensates of correlated fermion pairs

Magnetic-field Feshbach resonance

molecules

→ ←

attractive

repulsive

B>

free atoms

repulsive

Changing the interaction strength in real time

molecules

attractive

B>

EF

2 s/G

: FAST

Changing the interaction strength in real time: SLOW

molecules

attractive

B>

EF

40 s/G

Changing the interaction strength in real time: SLOWER

molecules

attractive

B>

EF

4000 s/G

Cubizolles et al., PRL 91, 240401 (2003); L. Carr et al., cond-mat/0308306

Molecular Condensate

M. Greiner, C.A. Regal, and D.S. Jin, Nature 426, 537 (2003).

Time of flightabsorption image

initial T/TF: 0.19 0.06

repulsive

40 s/G

Observing a Fermi condensate

attractive

B>

EF?4000 s/G

?

-0.5 0.0 0.5

0

1x105

2x105

3x105

N m

olec

ules

Condensates w/o a two-body bound state

C. Regal, M. Greiner, and D. S. Jin, PRL 92, 040403 (2004)

Dissociation of moleculesat low density

B = 0.12 G B = 0.25 G B=0.55 G

T/TF=0.08

B (gauss)

Fermionic condensate

-0.5 0 0.5 1.00

0.05

0.10

0.15

N0/

N

B (G)

Clearly see condensation on the “atom-side” of the resonance!

T/TF=0.08

molecules atoms -0.5 0 0.5 1.0

0

0.05

0.10

0.15

N0/

N

B (G)

two-bodymoleculespairing dueto many-bodyeffects

-2 -1 0 10

0.05

0.10

0.15

0.20

1/(kFa)

T/T

F

-0.0200.0100.0250.0500.0750.1000.1250.1500.175

-2 -1 0 10

0.05

0.10

0.15

0.20

1/(kFa)

T/T

F

-0.0200.0100.0250.0500.0750.1000.1250.1500.175

BCS-BEC Crossover

BCS (atoms) BEC (molecules)

N0/N0

C. Regal, M. Greiner, and D. S. Jin, PRL 92, 040403 (2004)

Conclusion An atomic Fermi gas provides experimental access to the BCS-BEC crossover region.

Fermi gas ↔ molecular BEC interconversion has been explored.

Condensates of correlated fermionic atom pairs have been achieved !

• generalized “Cooper pairs” with strong interactions

Many opportunities for further experimental and theoretical work ...

Next…

Current group members:

M. GreinerJ. GoldwinS. InouyeC. RegalJ. SmithM. Olsen