TOPS, MIT, Cambridge, June 24th, 2009
Pairs and Loners in
Ultracold Fermi Gases
Martin Zwierlein
Massachusetts Institute of Technology
Center for Ultracold Atoms at MIT and Harvard
$$$: NSF, AFOSR- MURI, Sloan Foundation
Bosons vs Fermions
T
TC
T  TC
T 0
EF
e.g.: 1H, 23Na, 6Li2
e.g.: e-, 3He, 6Li, 40K
Degenerate gases
de Broglie wavelength ~ Interparticle spacing
n
dB  n
1/3
 n  10 cm
15
Want lifetime > 1s
TF 
2
kB m
n
2/3
 1 K
1/3
3
Ultradilute
Ultracold
Good news: Bosons condense at
TC  TF
How to measure temperature?
Gas
Effusive atomic beam
How to measure temperature?
Gas
Effusive atomic beam
Observation of the atom cloud
Trapped
Expanded
Atom cloud
Lens
CCD
Camera
Laser beam
Shadow image
of the cloud
1 mm
BEC @ MIT, 1995 (Sodium)
Superfluidity in Bosonic Gases
BEC @ JILA, Juni ‘95
(Rubidium)
• BEC 1995
All atoms occupy same
macroscopic wavefunction
MIT
• Phase coherence 1997
ENS
• Superfluidity 1999/2000
MIT
Frictionless flow,
BEC @ MIT, Sept. ‘95 (Sodium)
quantized vorticity
JILA
Fermions – The Building Blocks of Matter
Lithium-6
Harvard-Smithsonian Center for Astrophysics
Can we have superfluidity
in a Fermi gas?
1911: Discovery of Superconductors
Heike
Kamerlingh-Onnes
Nobel prize 1913
Resistance
• Discovery of Superconductivity in Metals
Temperature
Superfluids
Flow without friction
• No energy loss
• persistent flow
• Doesn’t want to rotate
Onnes 1908,
Kapitza, Allen & Misener 1938
Superconductors
Current without resistance
• No energy loss
• persistent currents
• expels magnetic fields
Onnes 1911
Müller & Bednorz 1987
What are superconductors?
• Apparently the electrical current flows without friction
• But: Carrier of electrical current are Electrons

Electrons are Fermions
What are superconductors?
• Apparently the electrical current flows without friction
• But: Carrier of electrical current are Electrons

Electrons are Fermions
L. Cooper (1956) (45 years after Onnes):

Pairing of electrons
Pairs are Bosons
Superconductivity: Condensation of Electron Pairs
J. Bardeen, L. Cooper, R. Schrieffer (BCS), 1957, Nobel prize 1972
Fermionic Superfluidity
Condensation of Fermion Pairs
Superconductors: Charged superfluids of electron pairs
Frictionless flow  Resistance-less current
John Bardeen
Leon N. Cooper
John R. Schrieffer
High-temperature Superconductors
J. Georg Bednorz
K. Alex Müller
Critical temperature:
35 K above Absolute Zero (-238 °C)
Nobel prize 1987
Record today:
138 K (-135 °C)
Room temperature superconductors?
Today:
• ~5-10% energy loss only
due to transport of energy
The hope:
• Superconducting cables
• No resistance
 No energy loss during transport
We need:
The
problem:
A model system
for superconductors
High-temperature
superconductivity
not really understood
Electrons interact
so strongly
it’s hard to model
Ultracold
atomicthat
gases
Can we do this with atoms?
YES! The ultracold Fermi gas at MIT:
• Lithium-6 (3p, 3n, 3e-) is a fermion
• The atoms form pairs like
electrons in a superconductor
• Size of pairs is
freely controllable
• The gas becomes superfluid
How can you distinguish a
superfluid from a normal one?
Rotating bucket
Normal
Fluid
Super
Fluid
Rotating superfluid
Superfluid does not want to rotate
Only possibility:
Vortices, “Mini-Tornados”, “Quantum whirlpools”
Superfluids are described by matter wave
The wave has to close in itself
(Example: Vibrating rubber band)
Only full wavelengths  are allowed
Circulation is only possible in certain
units (“Quanta”), carried by the Vortices
Look from top into the bucket
Look from top into the bucket
Aleksei A.
Abrikosov
Nobel prize
2003
Abrikosov lattice (honeycomb lattice)
Vortex lattices
in bosonic gases/fluids
Berkeley
(R.E. Packard, 1979)
Helium-4
ENS
(J. Dalibard, 2000)
Rubidium BEC
Rotation of a neutral Fluid
F  2mv 
Coriolis Force
Superconductor in a magnetic field
F  qv  B
Lorentz Force
U. Essmann and H. Träuble,
Physics Letters A, 24, 526 (1967)
Demonstration of superfluidity in a Fermi gas
Ultracold gas
Vortex lattices
• Demonstration of superfluidity in a gas of atom pairs
• A high-temperature superfluid
- 0.7
Pair size
B
Scaled to the density of electrons in a metal, the gas
M.W. Zwierlein, J.R. Abo-Shaeer, A. Schirotzek, C.H. Schunck, W. Ketterle,
would become superfluid far aboveNature
room435,
temperature
1047-1051 (2005)
Fermionic Superfluidity with
Imbalanced Spin Populations
What if there are too many singles?
Fermionic Superfluidity with Imbalanced Spin Populations
|1>
|2>
0%
6%
12%
22%
30%
56%
90%
94%
What is the Nature of the
Imbalanced State?
Direct observation of the density difference
Cooling Down
Normal
Superfluid
Y. Shin, M.W. Zwierlein, C.H. Schunck, A. Schirotzek, W. Ketterle,
PRL 97, 030401 (2006)
Reconstruction of 3D density profile
d = 0.6
Only assumption: cylindrical symmetry
Phase Separation !
Fermionic Superfluidity does not tolerate loners
Gallery of superfluid Gases
Atomic Bose-Einstein
Condensates (Sodium)
Molecular Bose-Einstein
Condensates (6Li2)
Pairs of fermionic atoms
(6Li)
Ultracold Atoms
As Model systems:
• How does matter work?
new quantum states, development of new materials
Quantum computer, Quantum simulators (Bose and Fermi gases)
As measuring device:
• Development of highly sensitive sensors
gravitational gradient sensors (important for mining, geophysics),
sensors for navigation
• New highly accurate atomic clocks as time
standard
basis of all GPS-systems, more accurate positioning, faster
telecommunication requires accurate clocks
The team
BEC 1:
Andre Schirotzek
Ariel Sommer
Fermi 1:
Cheng-Hsun Wu
Ibon Santiago
Dr. Peyman Ahmadi
Undergraduates:
Caroline Figgatt
Jacob Sharpe
Sara Campbell
Kevin Fischer
39K
40K
6Li