Cold fermions, Feshbach resonance, and molecular condensates (II)
D. Jin JILA, NIST and the University of Colorado
I. Cold fermions II. Feshbach resonance III. BCS-BEC crossover (Experiments at JILA)
$$ NSF, NIST, Hertz
Boulder School 2004 I. Cold Fermions
Boulder School 2004 Quantum Particles
¾ There are two types of quantum particles found in nature - bosons and fermions. Bosons like to do the same thing.
Fermions are independent-minded.
¾ Atoms, depending on their composition, can be either. bosons: 87Rb, 23Na, 7Li, H, 39K, 4He*, 85Rb, 133Cs fermions: 40K, 6Li
Boulder School 2004 Bosons
. integer spin
. Ψ1,2 = Ψ2,1
Atoms in a harmonic potential.
Bose-Einstein condensation 1995 other bosons: photons, liquid 4He
Boulder School 2004 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
Boulder School 2004 Quantum gases
Bosons
TC BEC phase transition Fermions
TF Fermi sea of atoms gradually emerges for T d λdeBroglie ∼ d ultralow T Boulder School 2004 Fermionic atoms 40 6 K Jin, JILA Li Hulet, Rice Inguscio, LENS Salomon, ENS Thomas, Duke Ketterle, MIT Grimm, Innsbruck others in progress… Future: Cr, Sr, Yb, radioactive isotopes Rb, metastable *He, *Ne … Boulder School 2004 Cooling fermions Evaporative cooling requires collisions, but at low T identical fermions stop colliding . Boulder School 2004 Cooling strategies for fermions Simultaneous cooling evaporate atoms in two spin-states magnetic trap 40K optical trap 6Li Sympathetic cooling evaporate bosonic atoms and cool fermionic atoms via thermal contact two isotopes 7Li + 6Li two species 87Rb + 40K 23Na + 6Li Boulder School 2004 40K spin-states 4P3/2 ~1014 Hz hyperfine f=7/2 Zeeman 9 m = 9/2 6 7 ~10 Hz f ~10 -10 Hz 4S1/2 mf= 7/2 . . f=9/2 mf=-9/2 Boulder School 2004 More on spin-states spin “↑” Energy splitting is 10’s MHz. T = 1 μK corresponds to 20 kHz. spin “↓” ¾ spin degree of freedom is frozen Boulder School 2004 Collision measurement 1. Add energy in one dimension of trap 2. Watch thermal relaxation before after relaxation Boulder School 2004 Collisions and Fermions two spin-states one spin-state cross section elastic collision Boulder School 2004 Cooling a gas of 40K atoms 1. Laser cooling and trapping 300 K to 1 mK, ∼109 atoms 2. Magnetic trapping & evaporative cooling 1 mK to 1 μK, ∼108 → 106 atoms spin 2 spin 1 3. Optical trapping & evaporative cooling 1 μK to 50 nK, 106 → 105 atoms ¾ can confine any spin-state ¾ can apply arbitrary B-field Boulder School 2004 Probing the ultracold gas Time-of-flight absorption imaging • Probing the atoms Boulder School 2004 Stern-Gerlach imaging Time-of-flight absorption imaging B gradient • Probing the atoms Boulder School 2004 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 Boulder School 2004 Quantum degeneracy velocity distributions EF EF T/TF=0.77 n0= 0.28 Fermi sea of atoms T/TF=0.27 n0= 0.944 T/TF=0.11 n0= 0.99984 Boulder School 2004 Quantum degeneracy T/TFermi = 0.05 N = 4 ·105 , T = 16 nK 20 T/TFermi = 0.05 T b k 10 / μ 0 0.01 0.1 1 T/T F Boulder School 2004 Fermi gas thermometry Determine temperature from 0.3 (1) surface fit to expanded cloud Fermi 0.2 0.1 surface fit T / T fit T surface 0.0 0.0 0.1 0.2 0.3 T / T impurity Fermi (2) an embedded non-degenerate gas Impurity spin state Fermi gas Boulder School 2004 II. Feshbach resonance Boulder School 2004 Interactions ¾ Interactions are characterized by the s-wave scattering length, a a > 0 repulsive, a < 0 attractive Large |a| → strong interactions ¾ In an ultracold atomic gas, we can control a! 0 scattering length Boulder School 2004 Magnetic-field Feshbach resonance V(R) R R R R repulsive a>0, repulsive a<0, attractive →← > ΔB attractive molecules Boulder School 2004 Magnetic-field Feshbach resonance repulsive free atoms →← > ΔB attractive molecules Boulder School 2004 Experimental observation 1. Trap Loss (3-body inelastic collisions) three 87Rb-40K Feshbach resonances: S. Inouye et al., cond-mat, 2004. Boulder School 2004 Experimental observation 2. Elastic collision rate (σ=4 πa2) 10-9 m = -9/2, -7/2 mixture f 10-10 ) 2 -11 10 (cm σ 10-12 T. Loftus et al., PRL 88, 173202 (2002). 10-13 160 180 200 220 240 260 B (gauss) Boulder School 2004 More 40K resonances -9 m = -7/2 gas 10 f 10-10 a p-wave resonance! ) 2 -11 C. A. Regal et al., PRL 90, 053201 (2003) 10 (cm σ 10-12 10-13 180 200 220 B (gauss) 10-9 m =-7/2,-5/2 mixture 10-10 f ) 2 -11 10 another s-wave resonance (cm σ 10-12 10-13 150 160 170 180 190 B (gauss) Boulder School 2004 Experimental observation 3. Interaction energy (RF spectroscopy) 3000 ) 2000 Feshbach o repulsive resonance between 1000 mf=-9/2,-5/2 0 Use Δν ~n9a59 -1000 attractive -2000 scatteringlength (a C. A. Regal and D. S. Jin, PRL, (2003) -3000 215 220 225 230 B (gauss) Boulder School 2004 Experimental observation 4. Molecule creation -5/2 -9/2 Ramp across Feshbach resonance from high to low B →← 1.5 ) 6 energy 1.0 M olecleu creaiot n -5/2 1.56) -9/2 1.0r( 10 be 0.5num at om 0.0220222224226228 B hold(G) B(t) -5/2 -9/2 B 0.5 -5/2 number (10 atom 0 215 220 225 230 -9/2 B (gauss) C. A. Regal et al., Nature 424, 47 (2003). Motivation: E. A. Donley et al., Nature 417, 529 (2002) Boulder School 2004 Magnetic field sweep rate 1.5 Reversible →← ) 6 1.0 energy 0.5 B atom number (10 0 0 20406080 Similar experiments: inverse ramp speed (μs/G) Bosons Fermions Innsbruck Rice Garching ENS JILA Innsbruck Boulder School 2004 Molecule detection Apply RF near the atomic mf=-5/2 to mf=-7/2 transition Σmf = -5/2 + -9/2 →← molecule -7/2 + -9/2 →← -5/2 -5/2 photodissociate -7/2 the molecules -7/2 -9/2 -9/2 Boulder School 2004 Molecule detection 1.0 0.8 atoms molecules 0.6 0.4 transfer (arb) transfer 0.2 0 0.4 0.3 dissociation 0.2 threshold 0.1 kinetic energy (MHz) energy kinetic 0 49.8 50.1 50.4 50.7 rf frequency (MHz) Boulder School 2004 Molecule binding energy 0 -100 -200 -300 (kHz) atoms Δν -400 molecules binding energy theory -500 (Ticknor, Bohn) 220 221 222 223 224 B (gauss) C. Regal et al. Nature 424, 47 (2003) ¾ extremely weakly bound ! Boulder School 2004 Molecule conversion efficiency ¾ depends strongly on energy of Fermi gas 1.0 0.8 13 -3 npk ~10 cm • up to 70% conversion 0.6 • N > 250,000 molecule 0.4 0.2 molecule fraction 0.0 0.3 0.4 0.5 T (μK) Fermi Boulder School 2004 Molecule decay rate 1 m =-7/2, -9/2 ) f -1 0.1 m =-5/2, -9/2 f (ms m /N 0.01 m molecules N 1E-3 1 -3 -2 -1 0 no molecules ) with molecules -1 atoms ΔB (gauss) 0.1 C. A. Regal, M. Greiner, and D. S. Jin, PRL 92, 083201 (2004) (ms a 0.01 /N Theorya prediction: D.S. Petrov, C. Salomon, G.V. Shlyapnikov, cond- mat/0309010N (2003) 1E-3 C. A. Regal, M. Greiner, and D. S. Expts: Rice, ENS, Innsbruck, JILA Jin, cond-mat/0308606 (2003) -3 -2 -1 0 Boulder School 2004 ΔB (gauss) Cold fermions, Feshbach resonance, and molecular condensates (II) D. Jin JILA, NIST and the University of Colorado I. Cold fermions II. Feshbach resonance III. BCS-BEC crossover (Experiments at JILA) $$ NSF, NIST, Hertz Boulder School 2004 III. BCS-BEC crossover Boulder School 2004 Bose-Einstein condensation BEC shows up in condensed matter, nuclear physics, elementary particle physics, astrophysics, and atomic physics. Cooper pairs of electrons in 4He atoms superconductors in superfluid liquid He Excitons, biexcitons Alkali atoms in semiconductors in ultracold 3He atom pairs atom gases in superfluid 3He-A,B Neutron pairs, protron pairs in nuclei Mesons in And neutron stars neutron star matter Boulder School 2004 Bosons and Fermions Condensation requires bosons. Material bosons are composite particles, made up of fermions. ¾ For a gas of bosonic atoms, the underlying fermion degrees of freedom are not accessible. 87Rb, 23Na, … ¾ By starting with a gas of fermionic atoms we can explore how bosonic degrees of freedom emerge. 40K, 6Li, … Boulder School 2004 Making condensates with fermions spin ↑ ¾ BEC of diatomic molecules spin ↓ 1. Bind fermions together. 2. BEC ¾ BCS superconductivity/superfluidity Condensation of Cooper pairs of atoms (pairing in momentum space, EF near the Fermi surface) ¾ Something in between? BCS-BEC crossover Boulder School 2004 BCS-BEC landscape M. Holland et al., PRL 87, 120406 (2001) 0 BEC 10 alkali atom BEC -2 10 superfluid 4He c F T/T BCS high Tc superconductors -4 10 superfluid 3He transition temperature superconductors 10-6 10-5 105 1010 2/Δ kTBF energy to break fermion pair Boulder School 2004 Pairing and Superfluidity Æ 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 Generalized Cooper Cooper pairs fermionic atoms pairs of fermionic atoms kF BEC of weakly BCS - BEC BCS superconductivity bound molecules crossover Cooper pairs: correlated momentum-space pairing BCS-BEC crossover for example: Eagles,Boulder Leggett, School Nozieres 2004and 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 F / T c T 0.2 J. R. Engelbrecht et al., A. Perali et al., PRB 55, 15153 (1997) cond-mat/0311309 0 -2 -1 0 1 2 ← BCS 1/(k a) BEC → ← BCS BEC → (atoms) F (molecules) (atoms) (molecules) partial list: Eagles, Leggett, Nozieres and Schmitt-Rink, Randeria, Haussman, Strinati, Holland, Timmermans, Griffin, Levin, … Boulder School 2004 Magnetic-field Feshbach resonance repulsive free atoms →← > ΔB attractive molecules Boulder School 2004 Changing the interaction strength in real time: FAST repulsive EF 2 μs/G > ΔB attractive molecules Boulder School 2004 Changing the interaction strength in real time: SLOW EF 40 μs/G > ΔB attractive molecules Boulder School 2004 Changing the interaction strength in real time: SLOWER EF 4000 μs/G > ΔB attractive molecules Cubizolles et al., PRL 91, 240401 (2003); L. Carr et al., cond-mat/0308306 Boulder School 2004 Molecular Condensate initial T/TF: 0.19 0.06 Time of flight absorption image M. Greiner, C.A. Regal, and D.S. Jin, Nature 426, 537 (2003). Boulder School 2004 A BEC from a Fermi Sea! 0.20 0.15 / N 0.10 0 N 0.05 0 0 0.1 0.2 0.3 0.4 initial T / T F Boulder School 2004 Timescales Creating molecules Creating molecular BEC → EF ← energy B ) 3 750 0.15 500 0.10 250 many-body 2-body 0.05 0 molecule number (10 molecule number condensate fraction 0 0 20406080 0 2000 4000 6000 8000 inverse ramp speed (μs/G) inverse sweep speed (μs/G) ¾ two orders of magnitude difference in timescales! Boulder School 2004 Observing a Fermi condensate repulsive E ? F 40 μs/G 4000 μs/G > ΔB attractive ? Boulder School 2004 Condensates w/o a two-body bound state 3x105 2x105 Dissociation of molecules at low density 1x105 molecules C. Regal, M. Greiner, N 0 and D. S. Jin, PRL 92, 040403 (2004) -0.5 0.0 0.5 ΔB (gauss) ΔB = 0.12 G ΔB = 0.25 G ΔB=0.55 G T/TF=0.08 Boulder School 2004 Fermionic condensate 0.15 T/TF=0.08 two-body 0.10 / N / N molecules 0 0 N N pairing due 0.05 to many-body effects 0 -0.5 0 0.5 1.0 ← molecules atoms → ΔB (G) ¾ Clearly see condensation on the “atom-side” of the resonance! Boulder School 2004 Fermionic condensate 0.15 T/T =0.08 0.10 F / N / N 0 0 N N 0.05 0 -0.5 0 0.5 1.0 ΔB (gauss) ¾ Clearly see condensation on the “atom-side” of the resonance! ¾ Condensate lives much longer near resonance than in BEC limit. Boulder School 2004 Mapping out a phase diagram repulsive E a F 40 μs/G 4000 μs/G > ΔB attractive T/TF molecules Boulder School 2004 BCS-BEC Crossover 0.20 N0/N 0-0.020 0.15 0.010 0.025 FF 0.050 0.075 0.10 0.100 T/TT/T 0.125 0.05 0.150 0.175 0 -2 -1 0 1 1/(k a) F ← BCS (atoms) BEC (molecules) → C. Regal, M. Greiner, and D. S. Jin, PRL 92, 040403 (2004) Boulder School 2004 BCS-BEC Crossover 0.20 N0/N 0-0.020 0.15 0.010 0.025 F 0.050 0.075 0.10 0.100 T/T 0.125 0.05 0.150 0.175 0 -2 -1 0 1 ←BCS 1/(k a) BEC→ F Cooper pairs: diatomic molecules: collective, many-body effect two-body effect weakly bound tightly bound (pairing in momentum-space) (pairing in real space) pair size >> n-1/3 pair size << n-1/3 Tc/TF << 1 Tc/TF ~ 1 Tpairing = Tc Tpairing >> Tc Fermion excitations Boson excitations Boulder School 2004 BCS-BEC crossover Predict a smooth connection between BCS and BEC 0.6 BEC BEC BCS 0.4 BCS F / T c T 0.2 J. R. Engelbrecht et al., A. Perali et al., PRB 55, 15153 (1997) cond-mat/0311309 0 -2 -1 0 1 2 ← BCS 1/(k a) BEC → ← BCS BEC → (atoms) F (molecules) (atoms) (molecules) partial list: Eagles, Leggett, Nozieres and Schmitt-Rink, Randeria, Haussman, Strinati, Holland, Timmermans, Griffin, Levin, … Boulder School 2004 Measuring the excitation spectrum Utilize tunable interaction to a measure spectrum: B 1/ν Æ dissociate pairs of atoms pert Bpert by modulating B-field B0 t tpert ΔB Ebinding B(t)=B0 +Bpert sin(ωt) collective excitations: Grimm, Thomas rf measurement at crossover: Grimm Boulder School 2004 Excitation spectrum: BEC side dissociation threshold: molecule binding energy EB /h 0.5 Δ B=-801 m G ) -2 0.0 2 -491 m G single particle excitation spectrum: 0 (kHz ms mG -367 m G 5 tilde • molecule dissociation N 0 -119 m G 5 0 1 10 100 f (k H z) Boulder School 2004 Excitation spectrum: BCS side collective excitation pair dissociation ΔB=5 mG ) 5 excitation spectrum -2 0 Æ shows pairing 1 253 mG Æcontaining information about (kHz ms mG 0 crossover regime, tilde 378 mG no theoretical model 1 N available yet 0 626 mG 0.05 0.00 1 10 100 f (kHz) Boulder School 2004 Exctitation spectrum 100 maximumν position 80 max νthreshold position 60 0 (kHz) 40 ν 20 0 • BEC side: dissociation threshold 20 according to molecule 15 binding energy 10 • BCS side: nonzero (kHz) ν maximum Æ pairing 5 0 -800 -400 0 400 800 ΔB (mG) Boulder School 2004 Conclusion ¾ 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 ! • “Cooper pairs” with strong interactions • “BEC” with extremely weakly bound molecules Next… Many opportunities for further experimental and theoretical work ... Boulder School 2004 Current group members: M. Greiner J. Goldwin S. Inouye C. Regal J. Smith M. Olsen Boulder School 2004 The End. Boulder School 2004