��� ���� � �� ������ �� ������� ����� ����������� ��� ��������������� ��������� �� ���� ������ ����� �� � �� ���� ���� ����� ����������� ��������� ��� ������ ������� ���������� �� �������� �� �������� ��� ICTP SCHOOL ON QUANTUM PHASE TRANSITIONS AND NON-EQUILIBRIUM PHENOMENA IN COLD ATOMIC GASES 2005 Fermi condensates Markus Greiner JILA, Group of D. Jin; Coworkers: C. Regal and J. Stewart NIST and the University of Colorado, Boulder Highly controlled many-body quantum systems Weakly interacting Bose gases: Coherence, superfluid flow, vortices … Strongly correlated Bose systems: Superfluid to Mott insulator transition Fermionic superfluidity: BCS-BEC crossover physics • Condensed matter physics studied with an atomic physics system Outline: • Fermionic superfluidity; The tools: trapping, cooling, probing; • Controlling interactions; Molecular Bose-Einstein condensate; Fermi condensate: Generalized Cooper pairs in the BCS-BEC crossover; • Probing the fermion momentum distribution • Detecting atom-atom correlations via atom shot noise; Bosons Fermions integer spin half-integer spin <1,2 = <2,1 <1,2 = -<2,1 Æ Bosonic Æ Pauli exclusion enhancement principle EF= kbTF spin n spin p 1995: Bose-Einstein condensation 1999: Fermi sea of atoms e.g. 87Rb, 23Na, H, 39K … 40K, 6Li photons, liquid 4He electrons, protons, neutrons Pairing and Superfluidity Æ Spin is additive: Fermions can pair up and form effective bosons: <(1,…,N) =  [ I(1,2) I(3,4) … I(N-1,N) ] spin n spin p 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, Leggett, Nozieres and Schmitt-Rink, Randeria, Strinati, Zwerger, Holland, Timmermans, Griffin, Levin … Cooling a gas of fermionic 40K atoms 1. Laser cooling and trapping of 40K 300 K to 1 mK a109 atoms 2. Magnetic trapping and evaporative cooling n spin 1 mK to 10 PK spin p a109 ψ 107 atoms Cooling a gas of fermionic 40K atoms 3. Optical trapping and evaporative cooling 10 µK to 50 nK 107 ψ 105 atoms ¾ can confine any spin-state ¾ can apply arbitrary B-field Quantum degeneracy momentum distributions EF= kbTF T/TF=0.77 T=0 spin n kF spin p 1.4 T/TF=0.27 1.2 data Fermi gas fit 1.0 Gauss fit 0.8 T/T = 0.1 F 0.6 0.4 T/TF=0.11 0.2 Optical depth 0.0 0 1020304050 radius (arb) Controlling interaction Magnetic Feshbach resonance Turning the knob: a new molecular bound state appears as B is varied R V(R) internuclear separation R 202 G 200 G 204 G B-field Controlling interaction Magnetic Feshbach resonance: a new molecular bound state appears as B is varied V(R) R R R R 'B Ebinding molecular New bound state leads to binding energy divergence of scattering properties Æ Levinson Theorem Divergence of scattering length a Interactions between two free atoms are characterized by the a > 0 repulsive s-wave scattering length, a Large |a| ĺ strong interactions 'B Ebinding a < 0 attractive Broad feshbach resonance a Broad Feshbach resonance: K: width 22 MHz, approx. 5000 x EF Æ very strong coupling between open and closed channel Æ small closed channel occupancy 2 'B E = V(R) binding 2 mK a R EZ closed Æ well described as single channel channel problem Measurement of scattering length 3000 ) a o a 2000 1000 0 a > 0 repulsive -1000 -2000 scattering length ( scattering -3000 215 220 225 230 B (gauss) 'B Ebinding close to resonance: a < 0 attractive two-body binding energy 2 E = binding 2 mK a Creating molecules a V(R) Creating molecules by adiabatically ramping across R R the Feshbach resonance free atoms 'B Ebinding Theory: bound Timmermans et al., Phys. Rep. 315, 199 (1999), Abeelen et al., PRL83, 1550 (1999) molecules Mies et al., PRA 61, 022721 (2000), Ho et al., cond-mat/0306187 Experiment: coh. osc. atom/molecules Rb85: Donley et al., Nature 417, 529 (2002). Creating molecules ) 3 750 a measured 500 molecule 250 number 0 N molecule (10 molecule N 220 224 228 free atoms B (G) hold 'B Ebinding 40K: C. Regal et al. Nature 424, 47 … and quickly also with other bound Fermionic and Bosonic species: 6Li: Hulet (Houston), Salomon (Paris) molecules Grimm (Innsbruck), Ketterle (Boston) Cs: Grimm (Innsbruck) Rb: Rempe (Munich) Na: Ketterle (Boston) Molecule binding energy a V(R) Measurement of the R R molecular binding energy by rf-spectroscopy 0 -100 'B Ebinding -200 -300 (kHz) -400 'Q -500 220 221 222 223 224 C. Regal et al. Nature 424, 47 B (gauss) Molecule properties a • extremely weakly bound • large, molecule size § a • but: ridiculously stable close to Feshbach resonance free atoms 'B Ebinding C. A. Regal, M. Greiner, and D. S. Jin, condmat/0308606 (2003) size of molecule Interaction: theory prediction: changes D.S. Petrov, C. Salomon, G.V. Shlyapnikov, condmat/0309010 (2003) (accepted at PRL) Timescale of B-ramp a 1) Fast with respect to two-body physics atoms atoms 'B Ebinding Å 2 Ps/G molecules Timescale of B-ramp a 2) Adiabatic with respect to two-body physics atoms 'B Ebinding Å 40 Ps/G molecules up to 90% conversion efficiency Timescale of B-ramp a 2) Adiabatic with respect E to two-body physics F …but fast with respect to many body physics atoms 'B Ebinding Å 40 Ps/G molecules Timescale of B-ramp a 3) Adiabatic with respect E to two-body physics F and adiabatic with respect to many body physics atoms 'B Ebinding Å 4000 Ps/G molecules Timescale of B-ramp a 3) Adiabatic with respect E to two-body physics F and adiabatic with respect to many body physics atoms 'B Ebinding Å 4000 Ps/G Cubizolles et al., PRL 91, 240401 (2003); molecules BEC L. Carr et al., cond-mat/0308306 Molecular Bose-Einstein condensate A molecular BEC a emerges from a Fermi sea! T/TF= 0.19 0.06 Time of flight absorption image 'B M. Greiner, C. A. Regal, and D. S. Jin, Nature 426, 537 (2003) profile 6Li: Jochim et al., Science 302: 2101(2003), M. Zwierlein et al., Phys. Rev. Lett. 91, 250401 (2003). T. Bourdel et al., cond-mat/0403091 Molecular Bose-Einstein condensate A molecular BEC emerges from a Fermi sea! T/TF= 0.19 0.06 Æ timescale for many-body adiabaticity is 100x slower than for two-body adiabaticity Condensation of pairs of fermionic atoms Molecule or BEC side of a Atom or BCS side of Feshbach resonance: Feshbach resonance: BEC of molecules no two-body molecules Æ condensate of pairs of fermionic atoms BCSÆ 'B Ebinding Resonance superfluidity: Holland, Griffin, … Detecting a Fermi condensate 2) rapidly ramping across a 1) adiabatically ramping into the the Feshbach resonance regime with strong to project atoms pair wise attractive interactions onto molecules Æ fast compared to many body physics G 4000 s/G 40 Ps/ P 'B Ebinding Æ immediately probe Æ resonance condensation molecule momentum of fermionic atom pairs distribution Detecting a Fermi condensate condensate of pairs a of fermionic atoms ! G 4000 s/G 40 Ps/ P 'B Ebinding Æ immediately probe molecule momentum distribution Detecting a Fermi condensate a G 40 Ps/ 'B Ebinding No condensate, much too fast for condensation !! Detecting a Fermi condensate a G 4000 s/G 40 Ps/ P 'B Ebinding Condensate, requires condensate of fermionic atom pairs on BCS side! Fermionic condensate condensate of pairs a of fermionic atoms ! 'B=0.12 0.25 0.55 G T/TF=0.08 3x105 'B Ebinding 2x105 1x105 molecules N 0 -0.5 0.0 0.5 'B (gauss) Fermionic condensate 0.15 condensate a T/TF=0.08 fraction / N 0.10 0 N 0.05 0 -0.5 0 0.5 'B (gauss) 3x105 'B Ebinding 2x105 1x105 molecules N 0 -0.5 0.0 0.5 'B (gauss) BCS-BEC crossover F T / BEC T BCS of of molecules Cooper pairs before sweep Temperature inverse interaction strength 1/(kFa) Æ universal parameter S Figure: 0.4 k a T e 2 F M. Randeria Tc,BCS c,BCS | F /T 0.2 BEC-BCS crossover c T theory for example: Eagles, Leggett, Nozieres et al., Randeria, 0 Holland et al., Timmermans 1 0-1 et al., Ohashi et al., Stajic et al. … 1/kFa BCS-BEC crossover 1.0 gap at T=0 in BCS theory F E / two-body molecular ' binding energy 0.1 Figure: J. R. Engelbrecht et al., PRB 55, 15153 (1997) a) 2 1 0 -1 -2 1/(kF F T/T Temperature inverse interaction strength 1/(kFa) Probing atom momentum distribution rapidly switching off interactions before TOF expansion: Æ pairs dissociate, momentum distribution of fermions is measured 40K Feshbach resonance 10 a=0 ) 2000 0 5 0.002 ms/G 1000 B (gauss) ' large a 0 0 on -1000 a=0 trap off -2000 scattering length (a 190 200 210 220 0 102030405060 B (gauss) time (ms) BCS-BEC crossover theory Homogeneous gas, T=0: Momentum distribution broadens because of pairing 1.0 0.8 a=infinity a=0 ) 0.6 F 0.4 k/k ( n 0.2 0 0 0.5 1.0 1.5 2.0 2.5 k/k F M. Marini, F. Pistolesi, G. C. Strinati, Euro. Phys. J. B 1, 151 (1998) Momentum distributions of trapped gas T=0, mean-field theory Experiment 1.0 1.0 a=0 0.8 1 0.8 T = 0.12 TF /kFa=-0.66 OD 1 /k a=0 OD 0.6 F 0.6 1 /kFa=0.59 0.4 0.4 normalized 0.2 0.2 normalized 0 0 0 0.5 1.0 1.5 2.0 2.5 0 0.5 1.0 1.5 2.0 2.5 k/k 0 k/k 0 F F L.