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

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

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

4. 2-body strong interactions in a dilute gas (3D) At low kinetic energy, only s-wave scattering (l=0). For l=1, the centrifugal barrier ~ 1 mK >> typical energy ~ 1  K L = 10 000 bohr R=10 bohr ~ 0.5 nm s -wave scattering length a is the only interaction parameter (for R<< a ) Physically, only a/L matters

5. Feshbach resonance. BCS-to-BEC crossover 2004006008001000120014001600 0 2500 5000 -5000 -2500 -7500 В, gauss a, bohr Singlet 2-body potential: electron spins ↑↓ Triplet 2-body potential: electron spins ↓↓ BCS s/fluid BEC of Li 2 b/c s-wave scattering amplitude:

6. Superfluid and normal hydrodynamics of a strongly-interacting Fermi gas ( a → ∞) [Duke, Science (2002)] M. Gyulassy: “Elliptic flow is everywhere” Crab nebula Elliptic, accelerated expansion

7. Superfluid and normal hydrodynamics of a strongly-interacting Fermi gas ( a → ∞) [Duke, Science (2002)] T < 0.1 E F Superfluidity ?

8. 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

9. 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/E F = 0.21 – 0.27

10. 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 !!

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

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

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

14. TcTc Frequency  vs temperature for strongly-interacting gas (B=840 G) Hydrodynamic frequency, 1.84 at all T/E F !! Collisionless gas frequency, 2.11

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

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

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

18. Black curve – modeling by kinetic equation

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

20. Shear viscosity bound Kovtun, Son, Starinets (PRL, 2005): In a strongly-interacting quantum system s – entropy density Strongly-interacting atomic Fermi gas – fluid with min shear viscosity ?!!

21. Quantum Viscosity? Viscosity: Assumption: Universal isentropic hydrodynamics Calculate viscosity from breathing mode One eq.: normal & s/f component flow together

22. Viscosity / Entropy density for a universal isentropic fluid

23. Viscosity / Entropy density ? String theory limit 1/4  s/f transition 3 He & 4 He near -point Quark-gluon plasma, S. Bass, Duke, priv.

24. Ferromagnetism: An open problems Itinerant ferromagnetism in 2D Normal phase Ferro- magnet E ferro 4  2D at T=0:

25. where N = # of atoms 2D Fermi gas in a harmonic trap – condition of 2D in ideal gas at T=0

26. Open problems 2. Superfluidity in 2D Berezinskii – Kosterlitz – Thouless transition BKT transition not yet observed directly in Fermi systems. Indirect observations in s/c films questioned [Kogan, PRB (2007)] 3. 3-body bound states 2D and quasi-2D analogs of the 3D Efimov states ?

27. How to parameterize a universal Fermi gas ? Temperature (T) or Total energy per particle (E) ? Temperature:

28. Energy measured from the cloud size !! z U Trap potential Force Balance: pressure Local energy density (interaction + kinetic) In a universal Fermi system: [Ho, PRL (2004)] Virial Theorem: Thomas, PRL (2005)

29. 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~k F. Therefore, at a =∞, ?

30. 2 stages of laser cooling 1. Cooling in a magneto-optical trap T final = 150  K Phase-space density ~ 10 -6 2. Cooling in an optical dipole trap T final = 10 nK – 10  K Phase-space density ≈ 1

31. The apparatus

32. 1st stage of cooling: Magneto-optical trap

33. m j = –1m j = +1m j = 0 |g>

34. 1 st stage of cooling: Magneto-optical trap N ~ 10 9 T ≥ 150  K n ~ 10 11 cm -3 phase space density ~ 10 -6

35. 2 nd stage of cooling: Optical dipole trap Trapping potential of a focused laser beam: Laser: P = 100 W laser =10.6  m Trap: U ~ 250  K The dipole potential is nearly conservative: 1 photon absorbed per 30 min b/c laser =10.6  m >> lithium =0.67  m

36. 2 nd stage of cooling: Optical dipole trap Evaporative cooling 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. N final = 10 3 – 10 5 atoms, T final = 0.05 E F, T = 10 nK – 1  K, n = 10 11 – 10 14 cm -3

37. Absorption imaging CCD matrix Imaging over few microseconds Laser beam =10.6  m

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

39. Absorption imaging CCD matrix Imaging over few microseconds Laser beam =10.6  m Mirror

40. Photograph of 2D systems z,  m x,  m atoms/  m 2 Each cloud ≈ 700 atoms per spin state Period = 5.3  m T = 0.1 E F = 20 nK Each cloud is an isolated 2D system [N.Novgorod, PRL 2010]

41. Temperature measurement from transverse density profile Linear density,  m -1 x,  m

42. Temperature measurement from transverse density profile Linear density,  m -1 2D Thomas-Fermi profile: T=(0.10 ± 0.03) E F

43. Temperature measurement from transverse density profile Linear density,  m -1 Gaussian fit 2D Thomas-Fermi profile: T=(0.10 ± 0.03) E F =20 nK

44. The apparatus (main vacuum chamber)

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