Experiments with ultracold atomic gases

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