1. Collective Modes and Sound Velocity in a Strongly Interacting Fermi Gas
John E. Thomas
Students: Joe Kinast, Bason Clancy,
Le Luo, James Joseph
Post Doc: Andrey Turlapov
Theory: Jelena Stajic, Qijin Chen, Kathy Levin
Supported by: DOE, NSF, ARO, NASA

2. Strongly- Interacting Fermi Gases as a Paradigm
Duke, Science 2002
– Quark-gluon plasma of Big Bang
Fermions are the building blocks of matter
Strongly-interacting Fermi gases are stable
Link to other interacting Fermi systems:
High-TC superconductors – Neutron stars
– Effective Field Theory, Lattice Field Theory
- Elliptic flow
– String theory!
- Quantum Viscosity
MIT
JILA
Innsbruck
Rice
ENS
Duke

3. Degeneracy in Fermi Gases
Our atom: Fermionic
Trap Fermi Temperature Scale: =
Harmonic Potential:
Optical Trap Parameters:
Zero Temperature
TF = 2.4 mK

4. Tunable Interactions: Feshbach Resonance
*generated using formula published in Bartenstein, et al, PRL (2005)
Scattering length
@ 528 G
840 G

5. Universal Strong Interactions at T = 0
George Bertsch’s problem: (Unitary gas)
Baker, Heiselberg
Ground State:
Effective mass:
Trap Fermi Temperature: L
Cloud size:

6. Outline All-optical trapping and evaporative cooling Experiments
Virial Theorem (universal energy measurement)
Thermodynamics: Heat capacity (transition energy)
Oscillations and Damping (superfluid hydrodynamics)
Quantum Viscosity
Sound Waves in Bose and Fermi Superfluids

7. Preparation of Degenerate 6Li gas
Atoms precooled
in a magneto-optical trap
to 150 mK
2 MW/cm2
U0=0.7 mK

8. Forced Evaporation in an Optical Trap

9. High-Field Imaging

10. Experimental Apparatus

11. Experimental Apparatus

12. Tools for Thermodynamic Measurements
Energy input R I
Temperature

13. Temperature from Thomas-Fermi fit
Shape Parameter: (T/TF)fit
Zero Temp
T-F
Maxwell-
Boltzmann
(T/TF)fit
Integrate x
Fermi Radius: sF
From Thomas – Fit:
“true” temperature for
non-interacting gas
empirical temperature for
strongly-interacting gas

14. Calibrating the Empirical temperature
Conjecture:
Calibration using
theoretical density
profiles:
Stajic, Chen, Levin
PRL (2005)
S/F transition
predicted

15. Precision energy input
Initial energy E0
Trap ON again,
gas rethermalises
time
Trap ON
Expansion factor:
Final Energy E(theat)

16. Virial Theorem (Strongly-interacting Fermi gas obeys the
Virial theorem for an Ideal gas!)

17. Virial Theorem in a Unitary Gas
Local energy density
(interaction and kinetic)
Ho, PRL (2004)
Pressure: x U
Trap potential
Force Balance:
Virial Theorem:
Test!

18. Verification of the Virial Theorem
Fermi Gas at 840 G
Linear Scaling Confirms
Virial Theorem
Consistent with hydrodynamic
expansion over wide range of T!
Fixed
expansion
time
E(theat) calculated assuming hydrodynamic expansion

19. Heat Capacity Energy versus empirical temperature
(Superfluid transition)

20. Input Energy vs Measured Temperature
Noninteracting Gas (B=528 G)
Ideal Fermi Gas Theory

21. Input Energy vs Measured Temperature
Strongly-Interacting Gas at 840 G
Ideal Fermi Gas Theory
with scaled Fermi temperature

22. Low temperature region
Strongly-Interacting Gas (B=840 G)
Ideal Fermi gas theory
with scaled temperature
Power law fit

23. Energy vs on log-log scale
Blue – strongly-int. gas
Green – non-int. gas
Fit
Ideal Fermi
gas theory
Transition!

24. Energy vs
Theory for Strongly-
interacting gas
(Chicago, 2005)

25. Oscillation of a trapped Fermi gas
Study same system (strongly-interacting Fermi gas)
by different method

26. Breathing mode in a trapped Fermi gas
Image
Excitation &
observation:
Trap ON
Trap ON again,
oscillation for variable
1 ms
Release
time

27. Breathing Mode Frequency and Damping
Noninteracting Gas
840 G Strongly- Interacting Gas
w = frequency
t = damping time

28. Radial Breathing Mode: Frequency vs Magnetic Field
Hu et al.

29. Radial Breathing Mode: Damping Rate vs Magnetic Field
Pair
Breaking

30. Frequency w versus temperature for strongly-interacting gas (B=840 G)
Hydrodynamic
frequency, 1.84
Collisionless gas
frequency, 2.10

31. Damping 1/t versus temperature for strongly-interacting gas (B=840 G)
Transition in damping:
Transition!
Transition in heat capacity:
Superfluid behavior:
Hydrodynamic damping
0 as T 0
S/F transition (theory):
Levin:
Strinati:
Bruun:

32. Quantum Viscosity? Viscosity: Shuryak (2005) Radial mode: Axial mode:
Innsbruck Axial: a = 0.4
Duke Radial: a = 0.2

33. Wires!

34. Sound Wave Propagation in Bose and Fermi Superfluids

35. Magnetic tuning between Bose and Fermi Superfluids=
Singlet Diatomic Potential:
Electron Spins Anti-parallel
B = 900G
Cooper Pairs
B = 834 G
Resonance
Stable molecules
B = 710 G B
Triplet Diatomic Potential: Electron Spins Parallel

36. Molecular BECs are cold
“Hot” BEC, 710 G
(after free expansion)
“Cold” BEC, 710 G
(after free expansion,
from the same trap)

37. Sound: Excitation by a pulse of repulsive potential
Slice of green
light (pulsed)
Trapped atoms
Sound excitation:
Observation:
hold, release & image
thold= 0

38. Sound propagation on resonance (834 G)

39. Sound propagation at 834 G
Forward Moving Notch
Backward Moving Notch

40. Speed of Sound, u1 in the BEC-BCS Crossover

41. Sound Velocity in a BEC of Molecules
Mean field:
Dalfovo et al,
Rev Mod Phys
1999
Harmonic Trap:
Local Sound Speed c:
Full trap average:
For
(Petrov, Salomon, Shlyapnikov)
vF0= Fermi velocity, trap center, noninteracting gas

42. Speed of Sound, u1 for a BEC of Molecules

43. Sound Velocity at Resonance
Pressure:
Local Sound Speed c:
Harmonic Trap:
vF0 = Fermi velocity, trap center, noninteracting gas

44. b from the sound velocity at resonance
Full trap average:
Experiment:
(Feshbach resonance
at 834 G)
Rice, cloud size 06
Duke, cloud size 05
Duke, sound velocity 06
Carlson (2003) b =
Strinati (2004) b =
Theory:

45. Transverse Average—I lied!
More rigorous theory with correct c(0)
agrees with trap average to 0.2 %
(Capuzzi, 2006):

46. Speed of sound, u1 in the BEC-BCS crossover
Monte-Carlo Theory
Theory: Grigory Astrakharchik (Trento)

47. Speed of sound, u1 in the BEC-BCS crossover
Monte-Carlo Theory
Theory: Grigory Astrakharchik (Trento)

48. Speed of sound, u1 in the BEC-BCS crossover
Monte-Carlo Theory
Leggett Ground
State Theory
Theory: Grigory Astrakharchik (Trento)
Theory: Yan He & Kathy Levin (Chicago)

49. Summary Strongly-interacting Fermi gases:
- Nuclear Matter – High Tc Superconductors
2 Experiments reveal high Tc transitions in behavior:
- Heat capacity
- Breathing mode
Sound-wave measurements:
- First Sound from BEC to BCS regime
- Very good agreement with QMC calculations

50. The Team (2005)
Left to Right: Eric Tong, Bason Clancy, Ingrid Kaldre, Andrey Turlapov, John Thomas, Joe Kinast, Le Luo, James Joseph