1. Experiments with ultracold atomic gases
Andrey Turlapov
Institute of Applied Physics, Russian Academy of Sciences
Nizhniy Novgorod

2. How ultracold Fermi atoms are related to nuclear physics ?
The atoms are fermions
With the atoms, one may see major Fermi phenomena (as in other Fermi systems):
Fermi statistics;
Cooper pairing and superfluidity
+ strong interactions, i.e. Uint ~ EF
One may see even more with the atoms (the phenomena unobserved in the other Fermi systems)
BEC-to-BCS crossover, i.e. crossover between a gas of Fermi atoms and a gas of diatomic Bose molecules;
stability of a resonantly interacting matter;
resonant superfluidity;
viscosity at the lowest quantum bound (???);
itinerant ferromagnetism (???).

3. Good about atoms: Bad about atoms: Fundamentally no impurities
Control over interactions:
tunable s-wave collisions
somewhat tunable p-wave collisions
dipole-dipole collisions (perspective)
Tunable spin composition, more than 2 spins
Tunable energy, temperature, density
Tunable dimensionality (2D – at Nizhniy Novgorod)
Direct imaging
Bad about atoms:
Small particle number (N = 102 – 106 << NAvogadro)
Non-uniform matter (in parabolic potential)
Coarse temperature tuning (dT > EF/20 as opposed to dT ~ EF/105 in solid-state-physics experiments)
No p-wave (and higher) collisions in thermal equilibrium

4. Ground state splitting in high B
Fermions: 6Li atoms
Ground state splitting in high B 2p
670 nm 2s
Electronic ground
state: 1s22s1
Nuclear spin: I=1

5. Optical dipole trap Laser: P = 100 W llaser=10.6 mm Trap: U ~ 0 – 1 mK
Trapping potential of a focused laser beam:
Laser: P = 100 W llaser=10.6 mm Trap: U ~ 0 – 1 mK
The dipole potential is nearly conservative: 1 photon absorbed per 30 min
b/c llaser=10.6 mm >> llithium=0.67 mm

6. w /2p =(wx wy wz)1/3 /2p ~few kHz
Fermi degeneracy
Fermi energy:
At T=0:
Optical dipole trap:
w /2p =(wx wy wz)1/3 /2p ~few kHz
Natoms=
EF ~ 100 nK - 10 mK
Focus of a CO2 laser:
700 x 50 x 50 mm3
Phase space density:
r = Natoms / Nstates = 1

7. 2-body strong interactions in a dilute gas (3D)
L = bohr
R=10 bohr ~ 0.5 nm
At low kinetic energy, only s-wave scattering (l=0).
For l=1, the centrifugal barrier ~ 1 mK >> typical energy ~ 1 mK
s-wave scattering length a is the only interaction parameter (for R<< a)
Physically, only a/L matters

8. Scattering in 1-channel model
V(r) r R r R
V(r)
a < ( | a| > >R )
Attractive mean field
a > (a > >R)
Repulsive mean field
The mean field (for weak interactions):

9. Fano – Feshbach resonance
Singlet 2-body potential:
electron spins ↑↓
Triplet 2-body potential:
electron spins ↓↓

10. Fano – Feshbach resonance: Zero-energy scattering length a vs magnetic field B
5000
834 gauss
2500
a, bohr
200
400
600
800
1000
1200
1400
1600
528 gauss
-2500
-5000
-7500
В, gauss

11. Instability of the a>0 region towards molecular formation
200
400
600
800
1000
1200
1400
1600
2500
5000
-5000
-2500
-7500
Singlet 2-body potential:
electron spins ↑↓
a, bohr
Triplet 2-body potential:
electron spins ↓↓
В, gauss

12. BCS-to-BEC crossover a, bohr BEC BCS of Li2 s/fluid
200
400
600
800
1000
1200
1400
1600
2500
5000
-5000
-2500
-7500
BEC
of Li2
BCS
s/fluid
Singlet 2-body potential:
electron spins ↑↓
a, bohr
Triplet 2-body potential:
electron spins ↓↓
В, gauss

13. Resonant s-wave interactions (a → ± ∞)
Is the mean field ? ?
Energy balance at a → - ∞:
Collapse
s-wave scattering amplitude:
In a Fermi gas k≠0. k~kF. Therefore, at a =∞,

14. Universality L R -V0 Compare with neutron matter: a = –18 fm, R = 2 fm
Strong interactions: |a|>L>>R
At a→∞, the system is universal, i.e.,
L is the only length scale:
- No dependence on microscopic details of binary interactions
- All local properties depend only on n and T
-V0 R
Experiment (sound propagation, Duke, 2007): b = (.015)
Theory: Carlson (2003) b = , Strinati (2004) b =
Compare with neutron matter: a = –18 fm, R = 2 fm

15. 2 stages of laser cooling
1. Cooling in a magneto-optical trap
Tfinal = 150 mK
Phase-space density ~ 10-6
2. Cooling in an optical dipole trap
Tfinal = 10 nK – 10 mK
Phase-space density ≈ 1

16. The apparatus

17. 1st stage of cooling: Magneto-optical trap

18. 1st stage of cooling: Magneto-optical trap
mj = –1
mj = +1
mj = 0
|g>

19. 1st stage of cooling: Magneto-optical trap
N ~ T ≥ 150 mK n ~ 1011 cm-3 phase space density ~ 10-6

20. 2nd stage of cooling: Optical dipole trap
Trapping potential of a focused laser beam:
Laser: P = 100 W llaser=10.6 mm Trap: U ~ 250 mK
The dipole potential is nearly conservative: 1 photon absorbed per 30 min
b/c llaser=10.6 mm >> llithium=0.67 mm

21. 2nd stage of cooling: Optical dipole trap Evaporative cooling
- Turn on collisions by tuning to the Feshbach resonance
- Evaporate
The Fermi degeneracy is achieved at the cost of loosing 2/3 of atoms.
Nfinal = 103 – 105 atoms, Tfinal = 0.05 EF, T = 10 nK – 1 mK,
n = 1011 – 1014 cm-3

22. Imaging over few microseconds
Absorption imaging
Laser beam
l=10.6 mm
CCD matrix
Imaging over few microseconds

23. Trapping atoms in anti-nodes of a standing optical wave
Laser beam
l=10.6 mm
Mirror
V(z) z
Fermions: Atoms of lithium-6 in spin-states |1> and |2>

24. Imaging over few microseconds
Absorption imaging
Laser beam
l=10.6 mm
Mirror
CCD matrix
Imaging over few microseconds

25. Photograph of 2D systems
Each cloud is
an isolated 2D system
Each cloud ≈ 700 atoms
per spin state
Period = 5.3 mm
x, mm
atoms/mm2
T = 0.1 EF = 20 nK
z, mm
[N.Novgorod, PRL 2010]

26. Temperature measurement from transverse density profile
Linear density, mm-1
x, mm

27. Temperature measurement from transverse density profile
T=(0.10 ± 0.03) EF
Linear density, mm-1
2D Thomas-Fermi profile:

28. Temperature measurement from transverse density profile
Gaussian fit
T=(0.10 ± 0.03) EF =20 nK
Linear density, mm-1
2D Thomas-Fermi profile:

29. The apparatus (main vacuum chamber)

30. Superfluid and normal hydrodynamics of a strongly-interacting Fermi gas
T < 0.1 EF
Superfluidity ?
Duke,
Science (2002)

31. Superfluidity 1. Bardeen – Cooper – Schreifer hamiltonian
on the far Fermi side of the Feshbach resonance
2. Bogolyubov hamiltonian
on the far Bose side of the Feshbach resonance

32. High-temperature superfluidity in the unitary limit (a → ∞)
Bardeen – Cooper – Schrieffer:
Theories appropriate for strong interactions
Levin et al. (Chicago):
Burovsky, Prokofiev, Svistunov, Troyer
(Amherst, Moscow, Zurich):
The Duke group has observed signatures of phase transition in different
experiments at T/EF = 0.21 – 0.27

33. High-temperature superfluidity in the unitary limit (a → ∞)
Group of John Thomas
[Duke, Science 2002]
Superfluidity ?
vortices
Group of Wolfgang Ketterle
[MIT, Nature 2005]
Superfluidity !!

34. Breathing mode in a trapped Fermi gas
Image
Excitation &
observation:
Trap ON
Trap ON again,
oscillation for variable
1 ms
Release
time
300 mm
[Duke, PRL 2004, 2005]

35. Breathing Mode in a Trapped Fermi Gas
840 G Strongly-interacting Gas ( kF a = -30 )
w = frequency
t = damping time
Fit:

36. Breathing mode frequency w
Transverse frequencies of the trap:
Trap
Prediction of universal isentropic hydrodynamics
(either s/fluid or normal gas with many collisions):
at any T
Prediction for normal collisionless gas:

37. Frequency w vs temperature for strongly-interacting gas (B=840 G)
Collisionless gas
frequency, 2.11 Tc
Hydrodynamic
frequency, 1.84
at all T/EF !!

38. Damping rate 1/t vs temperature for strongly-interacting gas (B=840 G)

39. Hydrodynamic oscillations. Damping vs T/EF
Superfluid
hydrodynamics
Collisional hydrodynamics
of Fermi gas
In general,
more collisions longer damping.
Bigger superfluid
fraction.
Collisions are Pauli blocked b/c
final states are occupied.
Slower damping
Oscillations damp faster !!

40. Damping rate 1/t vs temperature for strongly-interacting gas (B=840 G)

41. Black curve – modeling by kinetic equation

42. Damping rate 1/t vs temperature for strongly-interacting gas (B=840 G)
Phase
transition
Phase transition

43. Maksim Kuplyanin, A.T., Tatyana Barmashova, Kirill Martiyanov, Vasiliy Makhalov