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
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