1. Creating new states of matter:
Experiments with ultra-cold Fermi gases
Selim Jochim
MPI für Kernphysik and
Universität Heidelberg
Henning Moritz
ETH Zürich

2. Today The molecular BEC – what can we do with it?
Crossover to a gas of (weakly bound) Cooper pairs Fundamental excitations, gap
Fermi Superfluidity
With tunable interactions: Model system for High-TC superconductors, Neutron stars, Quark-Gluon Plasma and more ….

3. The molecular condensate:
What makes it special?
Why does it work?
What can we do with it?
How cold is it?

4. Change the magnetic field!
molecular
BEC
na3 = 0.04

5. exploring the crossover
na3 = 0.28
molecular
BEC
na3 = 0.04

6. exploring the crossover
Bosons
Fermions
na3,kF|a| = 
na3 = 0.28
molecular
BEC
na3 = 0.04

7. exploring the crossover
Bosons
Fermions
na3,kF|a| = 
na3 = 0.28
kF|a| = 6
molecular
BEC
na3 = 0.04

8. exploring the crossover
Bosons
Fermions
na3,kF|a| = 
na3 = 0.28
kF|a| = 6
molecular
BEC
degenerate
Fermi gas
na3 = 0.04
kF|a| = 1
Bartenstein et al, PRL 92, (2004)

9. crossover reversible and lossless !
reversibility
BEC 1s Fermi gas 1s BEC
BEC after 2s
crossover reversible and lossless !
T/TF  0.03 in Fermi gas limit Carr et al.,PRL 92, (2004)
for 90% condensate fraction in BEC limit

10. BEC – BCS crossover 1980 crossover molecules Cooper pairs
strong coupling
Cooper pairs
weak coupling
crossover
1980

11. A tunable BEC-BCS gas! 6Li2 BEC critical temperature
We can freely change the interaction without increasing the entropy
B-field
kBTF: Fermi energy
Epair : pairing energy
M. Holland et al., PRL (2001)

12. What determines the shape of a BEC?
Noninteracting atoms: ground state of the trap

13. Shape of a BEC Interacting atoms: mean fieldV
n = N/V N ri r
Valid for na3<<1 !!!

14. Gross-Pitaevskii equation
Describe system as single particle wave function
external potential
interaction
chemical potential
kinetic term
Ignore kinetic term:
Thomas-Fermi approx.

15. Size of a Fermi gas Ignoring interactions:
With interactions: no analytic expression, even difficult to calculate numerically RF
Fermi
energy
EF=kBTF

16. Interacting Fermi gas
Description difficult: kinetic energy is dominant (Fermi momentum), or of similar magnitude as interaction, simple mean field interaction only works for a<< 1/kF
More general: scattering cross section is limited:

17. Unitary interaction
For unitary interaction (k>>1/a), the mean field energy scales just as the kinetic energy:
This results in a rescaling of the Fermi energy by a constant factor (1+b)
EF,unitary=(1+b)EF,ideal

18. Universal behavior on resonance!
EF,unitary=(1+b)EF,ideal
is supposed to be a universal parameter independent of the physical system:
In neutron stars, nuclei, quark-gluon plasma
Hard to determine quantitatively
Now measured experimentally
Also quantum Monte Carlo and other methods are now in good agreement, best precision caclulation so far:
b=-0.58(1)
Astrakharchik et al.
PRL (2004)

19. How to measure b ? Simply measure cloud size!
shape should be the same as for noninteracting gas …
Unfortunately: Precision very poor!

20. More precise measurements
Which quantities can be measured with the highest accuracy?

21. collective modes cigar-shaped trap nr = 755(10) Hz, nz  22 Hz axial
radial

22. collective modes two kinds of radial modes: „breathing“ compression
„quadrupole“
surface mode

23. axial coll. excitation on resonance: frequency (normalized to sloshing
mode)
600
800
1000
1200
magnetic field (G)
on resonance:

24. axial coll. excitation
frequency
(normalized
to sloshing
mode)

25. axial coll. excitation frequency (normalized to sloshing mode) 600 800
1000
1200

26. radial coll. excitation

27. What kind of mode was excited?
surface mode? compression mode?
need to have a closer look!
Lee, Huang, Yang prediction

28. More frequency measurements …
Radio frequency spectroscopy rf
~80MHz
breaking molecules
costs energy →
molecular signal
up-shifted
breaking pairs
costs energy →
pair signal
up-shifted
mI= -1
|3>
|2> 1
|1>
high B-field

29. rf spectra in BEC limit atoms only atom-molecule mixture
no evaporation
T >> Tc
atoms only
atom-molecule mixture
evaporation to
T  Tc
P = 300 mW
molecular signal:
two-body physics !!
evaporation to
T < 0.4 Tc
P = 35 mW
pure molecular sample
(BEC)
rf offset (kHz)
100kHz  4.8mK  0.4neV

30. rf spectra in BEC limit T ≈ 0.2 TF double-peak structure:
very large pos. sc. length
T ≈ 0.2 TF
double-peak structure:
atoms and pairs
T = 0.0? TF
pairs only !
pair signal shifts with EF !
many-body physics
rf offset

31. rf spectra in crossover regime
very large neg.
scatt. length
rf offset (kHz)

32. rf spectra in crossover regime
large neg. sc. length
rf offset (kHz)
100kHz  4.8mK  0.4neV
1kHz  48nK  4peV!

33. gap vs. interaction strength
Fermi energy
at two different levels of trap power
1.1µK (23 35mW
3.3µK (68 1 W

34. gap vs. interaction strength
comparison with radial trap frequency

35. universal lineshape data taken on resonance,
frequency scale normalized to Fermi energy
0.16 EF

36. Where’s superfluidity?
We’ve seen the gap: But is there superfluidity?? Is there a “condensate”???
Yes, there it is!!
Condensate above resonance, 900G
Zwierlein et al., MIT
First observation: JILA
Observe bimodal distributions, with both condensed pairs and thermal cloud

37. Condensate Fraction Data: MIT (2004)
Temperature measurement difficult:
Alternative: measure condensate fraction

38. Superfluidity???
Bimodal distributions are a strong indication for a phase transition, but is there a superfluid phase?
To date best method: Rotating superfluid needs to develop a vortex lattice
Challenge: The visibility of the vortices might be very small: condensate fraction is rather tiny in BCS regime

39. Observation of vortices!
MIT experiment (2005)
Vortices on BEC side of resonance!

40. Vortices in the cross over
792G
740G
766G
812G
833G
843G
853G
863G
Now a tool to check superfluidity!!!

41. Polarized gases
What happens if you change the balance between the two different spin states in the experiment?
What would that correspond to in a superconductor?
…..

42. Many different answers ….

43. Superfluidity in an imbalanced gas
MIT

44. Condensate fraction ….
MIT

45. Polarization detection scheme
MIT experiment

46. Phase separation
MIT experiment

47. Condensate fraction vs. P
MIT experiment

48. Phase separation (elongated trap)
Rice University

49. A matter of temperature??
This trap is very elongated!!

50. tomorrow Condensed Matter Physics with atoms?
Periodic potentials, bosonic Case: Mott isolator
Fermions: The Fermi Surface
Interactions of Fermions in optical lattices
Low dimensional systems
Future directions with optical lattices
Final discussion
Slides available at