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Cold fermions, Feshbach resonance, and molecular condensates (II)

Cold fermions Feshbach resonance BCS-BEC crossover. Cold fermions, Feshbach resonance, and molecular condensates (II). D. Jin. JILA, NIST and the University of Colorado. (Experiments at JILA). $$ NSF, NIST, Hertz. I. Cold Fermions.

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Cold fermions, Feshbach resonance, and molecular condensates (II)

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  1. Cold fermions • Feshbach resonance • BCS-BEC crossover Cold fermions, Feshbach resonance, and molecular condensates (II) D. Jin JILA, NIST and the University of Colorado (Experiments at JILA) $$ NSF, NIST, Hertz

  2. I. Cold Fermions

  3. There are two types of quantum particles found in nature - • bosons and fermions. • Bosons like to do the same thing. • Fermions are independent-minded. • Atoms, depending on their composition, can be either.bosons: 87Rb, 23Na, 7Li, H, 39K, 4He*, 85Rb, 133Cs fermions: 40K, 6Li Quantum Particles

  4. Bosons • integer spin • Ψ1,2 = Ψ2,1 Atoms in a harmonic potential. Bose-Einstein condensation 1995 other bosons: photons, liquid 4He

  5. Fermions • half-integer spin • Ψ1,2 = - Ψ2,1 (Pauli exclusion principle) T = 0 EF= kbTF spin spin Fermi sea of atoms 1999 other fermions: protons, electrons, neutrons

  6. Quantum gases Bosons TC BEC phase transition Fermions TFFermi sea of atomsgradually emerges for T<TF ldeBroglied ultralow T

  7. Fermionic atoms 40KJin, JILA Inguscio, LENS others in progress… Future:Cr, Sr, Yb, radioactive isotopes Rb, metastable *He, *Ne … 6Li Hulet, Rice Salomon, ENS Thomas, Duke Ketterle, MIT Grimm, Innsbruck

  8. Evaporative cooling requires collisions, but at low T identical fermions stop colliding . Cooling fermions

  9. Cooling strategies for fermions Simultaneous cooling evaporate atoms in two spin-states Sympathetic cooling evaporate bosonic atoms and cool fermionic atoms via thermal contact • magnetic trap 40K • optical trap 6Li • two isotopes 7Li + 6Li • two species 87Rb + 40K23Na + 6Li

  10. 40K spin-states 4P3/2 4S1/2 ~1014 Hz hyperfine f=7/2 f=9/2 Zeeman mf= 9/2 mf= 7/2 . . . mf=-9/2 ~106-107 Hz ~109 Hz

  11. More on spin-states spin “” Energy splitting is 10’s MHz. T = 1 mK corresponds to 20 kHz. spin “” • spin degree of freedom is frozen

  12. Collision measurement 1. Add energy in one dimension of trap 2. Watch thermal relaxation before after relaxation

  13. Collisions and Fermions two spin-states elastic collision cross section one spin-state

  14. Laser cooling and trapping • Magnetic trapping & evaporative cooling • Optical trapping & evaporative cooling Cooling a gas of 40K atoms 300 K to 1 mK, 109 atoms spin 2 1 mK to 1 mK, 108→ 106 atoms spin 1 1 mK to 50 nK, 106→ 105 atoms • can confine any spin-state • can apply arbitrary B-field

  15. Time-of-flight absorption imaging • Probing the atoms Probing the ultracold gas

  16. Time-of-flight absorption imaging • Probing the atoms Stern-Gerlach imaging B gradient

  17. Quantum degenerate atomic Fermi gases 1999: 40K JILA 6Li - Rice, Duke, ENS, MIT, Innsbruck; 40K- LENS, ETH Zurich EF = kBTF Fermi sea of atoms T ~ 0.05 TF low temperature, low density: T ~ 100 nK, n ~ 1013 cm-3

  18. EF Quantum degeneracy velocity distributions EF T/TF=0.77 T/TF=0.27 T/TF=0.11 n0= 0.28 n0= 0.944 n0= 0.99984 Fermi sea of atoms

  19. Quantum degeneracy T/TFermi= 0.05 N = 4 ·105 ,T = 16 nK T/TFermi = 0.05

  20. Fermi gas thermometry Determine temperature from (1) surface fit to expanded cloud (2) an embedded non-degenerate gas Impurity spin state Fermi gas

  21. II. Feshbach resonance

  22. Interactions • Interactions are characterized by the • s-wave scattering length, a • In an ultracold atomic gas, we can control a! a > 0 repulsive, a < 0 attractive Large |a| → strong interactions  0 scattering length

  23. → ← repulsive DB > R R R attractive molecules R Magnetic-field Feshbach resonance V(R) repulsive a>0, repulsive a<0, attractive

  24. → ← Magnetic-field Feshbach resonance repulsive free atoms DB > attractive molecules

  25. Experimental observation 1. Trap Loss (3-body inelastic collisions) three 87Rb-40K Feshbach resonances: S. Inouye et al., cond-mat, 2004.

  26. Experimental observation 2. Elastic collision rate (s=4pa2) T. Loftus et al., PRL 88, 173202 (2002).

  27. More 40K resonances a p-wave resonance! C. A. Regal et al., PRL 90, 053201 (2003) another s-wave resonance

  28. Experimental observation 3. Interaction energy (RF spectroscopy) Feshbach resonance between mf=-9/2,-5/2 Use Dn~ n9a59 repulsive attractive C. A. Regal and D. S. Jin, PRL, (2003)

  29. energy → ← B Experimental observation 4. Molecule creation Ramp across Feshbach resonance from high to low B C. A. Regal et al., Nature 424, 47 (2003). Motivation: E. A. Donley et al., Nature 417, 529(2002)

  30. → ← energy Magnetic field sweep rate Reversible B Similar experiments: Bosons Innsbruck Garching JILA Fermions Rice ENS Innsbruck

  31. → ← Σmf = -5/2 + -9/2 -7/2 + -9/2 molecule → ← Molecule detection • Apply RF near the atomic mf=-5/2 to mf=-7/2 transition photodissociate the molecules

  32. Molecule detection atoms molecules dissociation threshold

  33. Molecule binding energy C. Regal et al. Nature 424, 47 (2003) • extremely weakly bound !

  34. Molecule conversion efficiency • depends strongly on energy of Fermi gas npk ~ 1013 cm-3 • up to 70% conversion • Nmolecule > 250,000

  35. Molecule decay rate -3 -2 -1 0 DB (gauss) C. A. Regal, M. Greiner, and D. S. Jin, PRL 92, 083201 (2004) Theory prediction: D.S. Petrov, C. Salomon, G.V. Shlyapnikov, cond-mat/0309010 (2003) Expts: Rice, ENS, Innsbruck, JILA C. A. Regal, M. Greiner, and D. S. Jin, cond-mat/0308606 (2003)

  36. Cold fermions • Feshbach resonance • BCS-BEC crossover Cold fermions, Feshbach resonance, and molecular condensates (II) D. Jin JILA, NIST and the University of Colorado (Experiments at JILA) $$ NSF, NIST, Hertz

  37. III. BCS-BEC crossover

  38. Bose-Einstein condensation BEC shows up in condensed matter, nuclear physics, elementary particle physics, astrophysics, and atomic physics. Cooper pairs of electrons in superconductors 4He atoms in superfluid liquid He Excitons, biexcitons in semiconductors Alkali atoms in ultracold atom gases 3He atom pairs in superfluid 3He-A,B Neutron pairs, protron pairs in nuclei And neutron stars Mesons in neutron star matter

  39. For a gas of bosonic atoms, the underlying fermion degrees of freedom are not accessible. 87Rb, 23Na, … • By starting with a gas of fermionic atoms we can explore how bosonic degrees of freedom emerge.40K, 6Li, … Bosons and Fermions • Condensation requires bosons. • Material bosons are composite particles, made up of fermions.

  40. EF spin  spin  Making condensates with fermions • BEC of diatomic molecules • BCS superconductivity/superfluidity • Something in between? 1. Bind fermions together. 2. BEC Condensation of Cooper pairs of atoms (pairing in momentum space, near the Fermi surface) BCS-BEC crossover

  41. alkali atom BEC superfluid 4He high Tc superconductors superfluid 3He superconductors BCS-BEC landscape M. Holland et al., PRL 87, 120406 (2001) BEC transition temperature BCS energy to break fermion pair

  42.  Spin is additive: Fermions can pair up and form effective bosons: Y(1,…,N) = Â [ f(1,2) f(3,4) … f(N-1,N) ] Molecules of fermionic atoms Generalized Cooper pairs of fermionic atoms BCS - BEC crossover Cooper pairs kF spin  spin  BEC of weakly bound molecules BCS superconductivity Cooper pairs: correlated momentum-space pairing BCS-BEC crossover for example:Eagles, Leggett, Nozieres and Schmitt-Rink, Randeria, Strinati, Zwerger, Holland, Timmermans, Griffin, Levin … Pairing and Superfluidity

  43. BCS-BEC crossover Predict a smooth connection between BCS and BEC BEC BEC BCS BCS J. R. Engelbrecht et al., PRB 55, 15153 (1997) A. Perali et al., cond-mat/0311309  BCS BEC (atoms) (molecules)  BCS BEC (atoms) (molecules) partial list: Eagles, Leggett, Nozieres and Schmitt-Rink, Randeria, Haussman, Strinati, Holland, Timmermans, Griffin, Levin, …

  44. → ← Magnetic-field Feshbach resonance repulsive free atoms DB > attractive molecules

  45. EF Changing the interaction strength in real time : FAST repulsive 2 ms/G DB > attractive molecules

  46. EF Changing the interaction strength in real time: SLOW 40 ms/G DB > attractive molecules

  47. EF Changing the interaction strength in real time: SLOWER 4000 ms/G DB > attractive molecules Cubizolles et al., PRL 91, 240401 (2003); L. Carr et al., cond-mat/0308306

  48. Molecular Condensate initial T/TF: 0.19 0.06 Time of flightabsorption image M. Greiner, C.A. Regal, and D.S. Jin, Nature 426, 537 (2003).

  49. A BEC from a Fermi Sea!

  50. energy → ← EF B Timescales Creating moleculesCreating molecular BEC many-body 2-body • two orders of magnitude difference in timescales!

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