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Experiments with ultracold atomic gases

Experiments with ultracold atomic gases. Andrey Turlapov Institute of Applied Physics , Russian Academy of Sciences Nizhniy Novgorod. Ground state splitting in high B. Fermions: 6 Li atoms. 2p. 670 nm. 2s. Electronic ground state: 1s 2 2s 1. Nuclear spin: I=1.

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Experiments with ultracold atomic gases

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

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

  3. Laser:P = 100 Wllaser=10.6 mmTrap: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 Optical dipole trap Trapping potential of a focused laser beam:

  4. At low kinetic energy, only s-wave scattering (l=0). For l=1, the centrifugal barrier ~ 1 mK >> typical energy ~ 1 mK 2-body strong interactions in a dilute gas (3D) 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. 5000 2500 200 400 600 800 1000 1200 1400 1600 0 BEC of Li2 -2500 BCS s/fluid Triplet 2-body potential: electron spins↓↓ -5000 -7500 b/c s-wave scattering amplitude: Feshbach resonance. BCS-to-BEC crossover Singlet 2-body potential: electron spins↑↓ a, bohr В, gauss

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

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

  10. High-temperature superfluidity in theunitary 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 Image Trap ON Release Excitation & observation: Trap ON again, oscillation for variable 1 ms time 300 mm [Duke, PRL 2004, 2005]

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

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

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

  15. Damping rate 1/t vs temperaturefor strongly-interacting gas(B=840 G)

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

  17. Damping rate 1/t vs temperaturefor strongly-interacting gas(B=840 G)

  18. Black curve – modeling by kinetic equation

  19. Damping rate 1/t vs temperaturefor 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? Calculate viscosity from breathing mode Assumption: Universal isentropic hydrodynamics One eq.: normal & s/f component flow together Viscosity:

  22. Viscosity / Entropy densityfor a universal isentropic fluid

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

  24. 2D atT=0: Itinerant ferromagnetism in 2D Ferro- magnet Normal phase Ferromagnetism: An open problems Eferro < Enorm at g > 4p

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

  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 parameterizea universal Fermi gas ? Temperature: Temperature (T) or Total energy per particle (E) ?

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

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

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

  31. The apparatus

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

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

  34. 1st stage of cooling: Magneto-optical trap N ~ 109T≥ 150 mKn ~ 1011 cm-3phase space density ~ 10-6

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

  36. 2nd stage of cooling: Optical dipole trapEvaporative 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. Nfinal = 103 – 105 atoms, Tfinal = 0.05 EF, T = 10 nK – 1 mK, n = 1011 – 1014 cm-3

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

  38. 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>

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

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

  41. Temperature measurementfrom transverse density profile Linear density, mm-1 x, mm

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

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

  44. The apparatus (main vacuum chamber)

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

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