Fermi Condensates

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�� 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) = Â [ 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

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

G 40 Ps/

'B Ebinding

No condensate, much too fast for condensation !! Detecting a Fermi condensate

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 0.4 universal parameter S Figure: k a T e 2 F M. Randeria Tc,BCS c,BCS |

F 0.2

/T 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 scattering length 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. Viverit, S. Giorgini, L.P. Pitaevskii and S. Stringari, PRA 69, 013607 (2004) Kinetic energy

change in Ekin normalized to Ekin at a=0 5

4 Large effect! 0 0

kin 3 Ekin more than

E 1 doubles at /kFa=0 /

kin 2 E ' 1 0 1.0 0.5 0 -0.5 -1.0 -1.5 -2.0 BCS BEC 1/k 0 F a Two limits: exact theories

0.5 5 4 0 kin E 0 kin

3 / E kin /

E 0.1 ' kin 2 E ' 1 0 0.03 1.0 0.5 0 -0.5 -1 -2 -3 -4 -5 -6 1/k 0 1/k0 F a F a

Time-evolve wavefunction Calculate change due to of isolated molecule weak attractive interactions in the normal state

Theory: Murray Holland and Stefano Giorgini In between 4

3 0 0 kin

E 2 / kin

E 1 '

0 0.4 0.2 0 -0.2 -0.4 0 1/k a • Neither theory fits F • probe of pairing in crossover • future goal: compare to full crossover theory Varying T/TF

1.0 (T/T )0 = 0.11 F 0.8 0.13

0 0.20 F 0.6 0.3 0.5 / E 0.4 0.7 kin 1.0 E 0.2 ' 0 0.5 0 -0.5 -1.0 -1.5 1/k 0 F a

•TF is roughly constant but n changes Thanks:

Deborah Jin Cindy Regal Jayson Stewart

… I am starting a research group this summer, Markus Greiner PhD students and Deborah Jin Cindy Regal postdocs welcome … ICTP SCHOOL ON QUANTUM PHASE TRANSITIONS AND NON-EQUILIBRIUM PHENOMENA IN COLD ATOMIC GASES 2005 Correlations in atom shot noise

Markus Greiner

JILA, Group of D. Jin; Coworkers: C. Regal and J. Stewart NIST and the University of Colorado, Boulder Detecting atom-atom correlations New experimental systems show interesting atom-atom correlations:

• atom pair correlations:

kF spatial: in momentum space: molecules Cooper pairs

• in lattices:

Mott insulator: Anti-ferromagnetic phases:

• presently only the overall density distribution is measured in time-of-flight absorption imaging Æ no information about atom-atom correlations Photon pair detection in quantum optics

Parametric down conversion:

crystal correlation blue photon two red photons Æ entangled

practically all experiments detecting non-classical states of light are based on the detection of photon-photon correlations … papers too good to be published … ;-)

Proposal on the detection of correlations in atom shot noise by Ehud Altman et al., PRA 70, 013603 Atom shot-noise limited imaging Æ proposed by E. Altman, E. Demler, and M.D.Lukin, PRA 70, 013603 (2004)

• TOF absorption image 1.0

• take fit residual 0.5 • spatial filter to “bin” picture on variable transmission 0 length scale 110100 100 Pm spatial period (Pm)

Atom shot-noise 0.10 limited image: 0.08 0.06 0.04 measured noise at

noise (OD) OD=1, Poisson noise 0.02

100 Pm 0 background noise, 0102030 expected photon SN effective bin size (Pm) Spatial shot-noise correlations

• TOF absorption image in two spin states after molecule dissociation

mf = -9/2

mf = -7/2 Spatial shot-noise correlations

• TOF absorption image in two spin states after molecule dissociation

mf = -9/2

mf = -7/2 Finding shot-noise correlations

I GIGIINr(, )' Nr (, ) i 7/2 9/2 I 'I (7/2,9/2) ()' NrNr 7/2() 9/2 () r ~ 0.3 correlations 0.2

0.1 correlation 0 0.3 ~ 0.2 without molecules

0.1

0 correlation 0 S 2S 'I (rad) Finding shot-noise correlations

I GIGIINr(, )' Nr (, ) i 7/2 9/2 I (7/2,9/2) ()' NrNr 7/2() 9/2 () r

correlations

without molecules Shot-noise correlations in momentum space

• Correlations of atoms with equal momentum in opposite directions:

mf = -9/2

mf = -5/2 Noise correlations of nonlocal singlet pairs

M. Greiner et al., 'I PRL (2005)

correlation signal Future applications:

• Detect condensed pairs, should work in the BCS limit; Things to optimize: • switch off interaction • optimize ratio between relative and center of mass motion • optimize condensate fraction

• Pairs are entangled (singlet molecules) Æ EPR pairs Æ study Bell inequalities and entanglement Noise correlations in optical lattices

Æ Work by Simon Fölling, Fabrice Gerbier, Artur Widera, Olaf Mandel, Tatjana Gericke and Immanuel Bloch in Mainz Proposed by Ehud Altman et al.

Hanbury Brown Twiss Superfluid phase: (HBT) experiment: long range phase Measure correlations coherence of fluctuations

Mott insulator: no first order phase coherence Æ no interference pattern Noise correlations in optical lattices (Mainz)

Foelling et al., Nature (2005) Noise correlations in optical lattices (Mainz)

Fermions: anti correlations Æ peaks should be negative

Anti-ferromagnetic state: additional correlations peaks

Spin waves etc. … Thanks:

Deborah Jin Cindy Regal Jayson Stewart

… I am starting a research group this summer, Markus Greiner PhD students and Deborah Jin Cindy Regal postdocs welcome …