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

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

I. Cold Fermions

Quantum Particles 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: 87 Rb, 23 Na, 7 Li, H, 39 K, 4 He*, 85 Rb, 133 Cs fermions: 40 K, 6 Li

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

Fermions half-integer spin Ψ 1,2 = - Ψ 2,1 (Pauli exclusion principle) T = 0 E F = k b T F spin spin Fermi sea of atoms 1999 other fermions: protons, electrons, neutrons

Quantum gases Bosons T C Fermions T F BEC phase transition Fermi sea of atoms gradually emerges for T<T F d λ debroglie d ultralow T

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

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

Cooling strategies for fermions Simultaneous cooling evaporate atoms in two spin-states magnetic trap 40 K optical trap 6 Li Sympathetic cooling evaporate bosonic atoms and cool fermionic atoms via thermal contact two isotopes 7 Li + 6 Li two species 87 Rb + 40 K 23 Na + 6 Li

40 K spin-states 4P 3/2 ~10 14 Hz 4S 1/2 hyperfine f=7/2 f=9/2 Zeeman ~10 9 m Hz ~10 6-10 7 f = 9/2 Hz m f = 7/2. m f =-9/2

More on spin-states spin spin Energy splitting is 10 s MHz. T = 1 μk corresponds to 20 khz. spin degree of freedom is frozen

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

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

Cooling a gas of 40 K atoms 1. Laser cooling and trapping 300 K to 1 mk, 10 9 atoms 2. Magnetic trapping & evaporative cooling 1 mk to 1 μk, 10 8 10 6 atoms spin 1 spin 2 3. Optical trapping & evaporative cooling 1 μk to 50 nk, 10 6 10 5 atoms can confine any spin-state can apply arbitrary B-field

Probing the ultracold gas Time-of-flight absorption imaging Probing the atoms

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

Quantum degenerate atomic Fermi gases 1999: 40 K JILA 6 Li - Rice, Duke, ENS, MIT, Innsbruck; 40 K - LENS, ETH Zurich E F = k B T F Fermi sea of atoms T ~ 0.05 T F low temperature, low density: T ~ 100 nk, n ~ 10 13 cm -3

Quantum degeneracy velocity distributions E F T/T F =0.77 n 0 = 0.28 T/T F =0.27 n 0 = 0.944 Fermi sea of atoms E F T/T F =0.11 n 0 = 0.99984

Quantum degeneracy 20 T/T Fermi = 0.05 N = 4 10 5, T = 16 nk T/T Fermi = 0.05 μ/k b T 10 0 0.01 0.1 1 T/T F

Fermi gas thermometry Determine temperature from (1) surface fit to expanded cloud (2) an embedded non-degenerate gas surface fit T / T Fermi 0.3 0.2 0.1 0.0 0.0 0.1 0.2 0.3 T impurity / T Fermi Impurity spin state Fermi gas

II. Feshbach resonance

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

Magnetic-field Feshbach resonance V(R) R repulsive R R R a>0, repulsive a<0, attractive > ΔB attractive molecules

Magnetic-field Feshbach resonance repulsive free atoms > ΔB attractive molecules

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

Experimental observation 2. Elastic collision rate (σ=4πa 2 ) 10-9 mf 10-10 = -9/2, -7/2 mixture σ (cm 2 ) 10-11 10-12 T. Loftus et al., PRL 88, 173202 (2002). 10-13 160 180 200 220 240 260 B (gauss)

More 40 K resonances σ (cm 2 ) 10-9 m f = -7/2 gas 10-10 10-11 10-12 a p-wave resonance! C. A. Regal et al., PRL 90, 053201 (2003) 10-13 180 200 220 B (gauss) 10-9 mf 10-10 =-7/2,-5/2 mixture σ (cm 2 ) 10-11 10-12 another s-wave resonance 10-13 150 160 170 180 190 B (gauss)

Experimental observation 3. Interaction energy 3000 (RF spectroscopy) scattering length (a o ) 2000 1000 0-1000 -2000-3000 repulsive attractive 215 220 225 230 Feshbach resonance between m f =-9/2,-5/2 Use Δν ~n 9 a 59 C. A. Regal and D. S. Jin, PRL, (2003) B (gauss)

M ole cule cre atio n -5/2 1. 5-9/2 1. 0 0. 5 0. 02 02 24 26 28 B hold(g ) B(t ) -5/2-9/2 ato mnu mb er(1 06) Experimental observation 4. Molecule creation -5/2 Ramp across Feshbach resonance from high to low B -9/2 energy B -5/2-9/2 atom number (10 6 ) 1.5 1.0 0.5 0 215 220 225 230 B (gauss) C. A. Regal et al., Nature 424, 47 (2003). Motivation: E. A. Donley et al., Nature 417, 529 (2002)

Magnetic field sweep rate atom number (10 6 ) 1.5 1.0 0.5 Reversible energy B 0 0 20 40 60 80 inverse ramp speed (μs/g) Similar experiments: Bosons Innsbruck Garching JILA Fermions Rice ENS Innsbruck

Molecule detection Apply RF near the atomic m f =-5/2 to m f =-7/2 transition Σm f = -5/2 + -9/2 molecule -7/2 + -9/2-5/2-7/2-9/2 photodissociate the molecules -5/2-7/2-9/2

Molecule detection 1.0 transfer (arb) 0.8 0.6 0.4 0.2 molecules atoms kinetic energy (MHz) 0 0.4 0.3 0.2 0.1 dissociation threshold 0 49.8 50.1 50.4 50.7 rf frequency (MHz)

Molecule binding energy 0-100 Δν (khz) -200-300 -400-500 atoms molecules binding energy theory (Ticknor, Bohn) 220 221 222 223 224 B (gauss) extremely weakly bound! C. Regal et al. Nature 424, 47 (2003)

Molecule conversion efficiency depends strongly on energy of Fermi gas 1.0 molecule fraction 0.8 0.6 0.4 0.2 0.0 n pk ~10 13 cm -3 0.3 0.4 0.5 T Fermi (μk) up to 70% conversion N molecule > 250,000

Molecule decay rate N m /N m (ms -1 ) N a /N a (ms -1 ) 1 0.1 0.01 1E-3 1-3 -2-1 0 0.1 0.01 Theory prediction: D.S. Petrov, C. Salomon, G.V. Shlyapnikov, condmat/0309010 (2003) Expts: 1E-3 Rice, ENS, Innsbruck, JILA molecules atoms ΔB (gauss) -3-2 -1 0 ΔB (gauss) m f =-7/2, -9/2 m f =-5/2, -9/2 no molecules with molecules C. A. Regal, M. Greiner, and D. S. Jin, PRL 92, 083201 (2004) C. A. Regal, M. Greiner, and D. S. Jin, cond-mat/0308606 (2003)

III. BCS-BEC crossover

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

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

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

BCS-BEC landscape transition temperature T/T c F 10 0 10-2 10-4 10-6 M. Holland et al., PRL 87, 120406 (2001) BCS BEC alkali atom BEC superfluid 4 He high T c superconductors superfluid 3 He superconductors 10-5 10 5 10 10 2 Δ/ kt B energy to break fermion pair F

Pairing and Superfluidity Spin is additive: Fermions can pair up and form effective bosons: Ψ(1,,N) = Â [ φ(1,2) φ(3,4) φ(n-1,n) ] spin spin Molecules of fermionic atoms Generalized Cooper pairs of fermionic atoms Cooper pairs k F BEC of weakly bound molecules BCS - BEC crossover BCS superconductivity Cooper pairs: correlated momentum-space pairing BCS-BEC crossover for example: Eagles, Boulder Leggett, School Nozieres 2004 and Schmitt-Rink, Randeria, Strinati, Zwerger, Holland, Timmermans, Griffin, Levin

BCS-BEC crossover Predict a smooth connection between BCS and BEC 0.6 BEC BEC BCS 0.4 BCS T c / T F 0.2 A. Perali et al., cond-mat/0311309 0-2 -1 0 1 2 BCS 1/(k BEC (atoms) F a) (molecules) J. R. Engelbrecht et al., PRB 55, 15153 (1997) BCS BEC (atoms) (molecules) partial list: Eagles, Leggett, Nozieres and Schmitt-Rink, Randeria, Haussman, Strinati, Holland, Timmermans, Griffin, Levin,

Magnetic-field Feshbach resonance repulsive free atoms > ΔB attractive molecules

Changing the interaction strength in real time: FAST repulsive E F 2 μs/g > ΔB attractive molecules

Changing the interaction strength in real time: SLOW E F 40 μs/g > ΔB attractive molecules

Changing the interaction strength in real time: SLOWER E F 4000 μs/g > ΔB attractive molecules Cubizolles et al., PRL 91, 240401 (2003); L. Carr et al., cond-mat/0308306

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

A BEC from a Fermi Sea! 0.20 0.15 N 0 / N 0.10 0.05 0 0 0.1 0.2 0.3 0.4 initial T / T F

Timescales Creating molecules energy B Creating molecular BEC E F molecule number (10 3 ) 750 500 250 0 2-body 0 20 40 60 80 inverse ramp speed (μs/g) condensate fraction 0.15 0.10 0.05 many-body 0 0 2000 4000 6000 8000 inverse sweep speed (μs/g) two orders of magnitude difference in timescales!

Observing a Fermi condensate repulsive? E F 40 μs/g 4000 μs/g > ΔB? attractive

Condensates w/o a two-body bound state N molecules 3x10 5 2x10 5 1x10 5 0-0.5 0.0 0.5 ΔB (gauss) Dissociation of molecules at low density C. Regal, M. Greiner, and D. S. Jin, PRL 92, 040403 (2004) ΔB = 0.12 G ΔB = 0.25 G ΔB=0.55 G T/T F =0.08

Fermionic condensate N 0 / N 0.15 0.10 0.05 0-0.5 0 0.5 1.0 ΔB (G) T/T F =0.08 molecules atoms two-body molecules pairing due to many-body effects Clearly see condensation on the atom-side of the resonance!

Fermionic condensate 0.15 N 0 / N 0.10 0.05 T/T F =0.08 0-0.5 0 0.5 1.0 ΔB (gauss) Clearly see condensation on the atom-side of the resonance! Condensate lives much longer near resonance than in BEC limit.

Mapping out a phase diagram repulsive a E F 40 μs/g 4000 μs/g > ΔB attractive T/T F molecules

BCS-BEC Crossover T/T F 0.20 0.15 0.10 0.05 N 0 /N 0-0.020 0.010 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0-2 -1 0 1 1/(k F a) BCS (atoms) BEC (molecules) C. Regal, M. Greiner, and D. S. Jin, PRL 92, 040403 (2004)

BCS-BEC Crossover T/T F 0.20 0.15 0.10 0.05 0-2 -1 0 1 BCS 1/(k F a) Cooper pairs: collective, many-body effect weakly bound (pairing in momentum-space) pair size >> n -1/3 T c /T F << 1 T pairing = T c Fermion excitations N 0 /N 0-0.020 0.010 0.025 0.050 0.075 0.100 0.125 0.150 0.175 BEC diatomic molecules: two-body effect tightly bound (pairing in real space) pair size << n -1/3 T c /T F ~ 1 T pairing >> T c Boson excitations

Measuring the excitation spectrum Utilize tunable interaction to measure spectrum: dissociate pairs of atoms by modulating B-field a B B 0 B pert 1/ν pert t t pert E binding ΔB B(t)=B 0 +B pert sin(ωt) collective excitations: Grimm, Thomas rf measurement at crossover: Grimm

Excitation spectrum: BEC side 0.5 dissociation threshold: molecule binding energy E B /h Δ B=-801 m G 0.0 2 N tilde (khz ms mg -2 ) 0 5 0 5-491 m G -367 m G -119 m G single particle excitation spectrum: molecule dissociation 0 1 10 100 f (k H z)

Excitation spectrum: BCS side collective excitation pair dissociation ΔB=5 mg N tilde (khz ms mg -2 ) 5 0 1 0 1 253 mg 378 mg excitation spectrum shows pairing containing information about crossover regime, no theoretical model available yet 0 0.05 626 mg 0.00 1 10 100 f (khz)

Exctitation spectrum ν (khz) ν (khz) 100 80 60 40 20 0 20 15 10 5 0 ν max ν 0-800 -400 0 400 800 ΔB (mg) maximum position threshold position BEC side: dissociation threshold according to molecule binding energy BCS side: nonzero maximum pairing

Conclusion An atomic Fermi gas provides experimental access to the BCS-BEC crossover region. Fermi gas molecular BEC interconversion has been explored. Condensates of fermionic atom pairs have been achieved! Next Cooper pairs with strong interactions BEC with extremely weakly bound molecules Many opportunities for further experimental and theoretical work...

Current group members: M. Greiner J. Goldwin S. Inouye C. Regal J. Smith M. Olsen

The End.