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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. How ultracold Fermi atoms are related to nuclear physics ?. The atoms are fermions

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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. 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: 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 2p 670 nm 2s Electronic ground state: 1s22s1 Nuclear spin: I=1

  5. 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:

  6. Fermi degeneracy Optical dipole trap: w /2p=(wx wy wz)1/3 /2p~few kHz Natoms=200000 EF ~ 100 nK - 10mK Focus of aCO2 laser: 700x50x50 mm3 Fermi energy: AtT=0: Phase space density: r =Natoms/ Nstates = 1

  7. 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

  8. V(r) r V(r) R r a <0 ( |a| >>R ) Attractive mean field R Scattering in 1-channel model a >0 (a >>R) Repulsive mean field The mean field (for weak interactions):

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

  10. 834gauss 528gauss Fano – Feshbach resonance: Zero-energy scattering lengtha vs magnetic field B 5000 2500 a, bohr 200 400 600 800 1000 1200 1400 1600 0 -2500 -5000 -7500 В, gauss

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

  12. 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 BCS-to-BEC crossover Singlet 2-body potential: electron spins↑↓ a, bohr В, gauss

  13. ? 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 ?

  14. R -V0 Universality L 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 nandT Experiment (sound propagation, Duke, 2007): b = - 0.565(.015) Theory: Carlson (2003)b = - 0.560, Strinati (2004)b = - 0.545 Compare with neutron matter: a = –18 fm, R = 2 fm

  15. 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

  16. The apparatus

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

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

  19. 1st stage of cooling: Magneto-optical trap N ~ 109T≥ 150 mKn ~ 1011 cm-3phase space density ~ 10-6

  20. 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:

  21. 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

  22. CCD matrix Absorption imaging Laser beam l=10.6 mm 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. CCD matrix Absorption imaging Laser beam l=10.6 mm Mirror 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 atoms/mm2 x, mm T = 0.1 EF = 20 nK z, mm [N.Novgorod, PRL 2010]

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

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

  28. Temperature measurementfrom 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 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

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

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

  36. 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

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

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

  39. 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 !!

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

  41. Black curve – modeling by kinetic equation

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

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

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