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What Do High Tc Superconductors Teach Us About Ultracold Superfluids and Vice Versa? Fermi National Laboratory Jan 2007

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Cold Atom Collaborators: Qijin Chen (Johns Hopkins, UC ) J. Stajic (U Chicago; LANL) Yan He (U. Chicago) ChihChun Chien (U. Chicago) J.E. Thomas, J. Kinast, A. Turlapov (Duke) D.S. Jin, C. Regal and M. Greiner (JILA) M. Holland, M. Chiofalo, J. Milstein(JILA)

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Impact of Superfluidity and Superconductivity 2007 is 50 th anniversary of BCS Theory! Festivities planned in Urbana for coming October

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Superfluidity Associated with at Least Eight Nobel Prizes 8 Nobel prizes : 1913 Onnes for superconductivity-expt 1913 Onnes for superconductivity-expt 1972 Bardeen, Cooper, Schrieffer (BCS)-theory 1972 Bardeen, Cooper, Schrieffer (BCS)-theory 1987 Bednorz and Muller– high Tc- expt 1987 Bednorz and Muller– high Tc- expt 2001 BEC in trapped Bose gases-expt 2001 BEC in trapped Bose gases-expt 2003 Abrikosov, Leggett, Ginzburg- theory 2003 Abrikosov, Leggett, Ginzburg- theory …….. And Still counting !

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Impact on Other Subfields of Fermionic Superfluidity Pairing in Nuclear Physics– Bohr, Mottelson, Pines. Pairing in Nuclear Physics– Bohr, Mottelson, Pines. Higgs mechanism in Particle Physics. Higgs mechanism in Particle Physics. Dense QCD, color superconductivity in RHIC Dense QCD, color superconductivity in RHIC Hadronic superfluidity in neutron stars. Hadronic superfluidity in neutron stars. Applications to accelerator physics. Applications to accelerator physics.

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The Essence of Fermionic Superfluidity fermionsbosons Attractive interactions turn fermions into “ composite bosons ” (or Cooper pairs). These are then driven by statistics to Bose condense. Increased attraction

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What is this talk about ? 1. BCS theory and Bose Condensation (BEC) can be treated in one “master” theory (of fermion superfluids) with continuous evolution from one to another. 2. Ultracold gases are the best way to see this evolution. 3. But the same phenomenon may be present in high Tc cuprates.

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Remarkable Tuning Capability in Cold Gases via Feshbach Resonance. molecules → ← BB > Scattering length BCS BEC Unitary limit

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Ultracold Fermi Gases Tuning the attractive interaction via Magnetic Field allows us to study 1. Most general form of fermionic superfluidity. 2. Unitary scattering prototypes for other subdisciplines. BEC BCS Strong attraction Weak attraction

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High Tc Cuprates– also candidates for BCS-BEC Crossover BEC BCS “The size of the cuprate pairs (from 10-30 puts us in the intermediate regime of the so- called BCS-BEC crossover” A. J. Leggett 2006 (Nature Physics). See Also T. D. Lee in 1987.

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Three Part Talk Ground-breaking experiments in cold gases. Ground-breaking experiments in cold gases. Theory interlude. Theory interlude. Expts. on novel, common aspects of cold gases and high Tc cuprates. Expts. on novel, common aspects of cold gases and high Tc cuprates.

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Part 1: Proving Superfluidity Much easier on the Bose side of resonance! Part 1: Proving Superfluidity Much easier on the Bose side of resonance! Observation of BEC in Fermi gases first reported by Jin et al, Nature 426 (2003). Simultaneously by Grimm et al, Science 302 (2003).

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First Generation Evidence for superfluidity of Unitary gases: early 2004 : Phase Diagram from JILA First Generation Evidence for superfluidity of Unitary gases: early 2004 : Phase Diagram from JILA. Based on rapid sweep to Bose gas regime. Jin et al, PRL 92

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Sweep Basis for Jin ’ s experiments. molecules → ← BB > BCS BEC Unitary limit Adiabatic sweep (sets temperature) Quick sweep

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Second Generation Experiments; Thermodynamical Evidence for Phase Transition near unitarity. Our Collaboration with Duke Group: John Thamas, Joe Kinast, Andrey Turlapov--- Feb 2005 Science 307, 1296

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Third Generation Experiments Vortices Seen at MIT-- April 2005 Vortices “ visible ” after sweep to BEC because of density depletion at the core. Zwierlein et al, Nature 435, 170404 (2005)

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Part 2 THEORY INTERLUDE: BCS, BEC and BCS-BEC Crossover

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What is Ground State for BCS-BEC Crossover ? Chemical potential varies when attraction strength tuned arbitrarily: Same as in BCS:

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What is Novel about BCS-BEC Crossover? Answer: Finite T effects Pairs form at one temperature T* Pairs form at one temperature T* Pairs condense at lower temperature Tc Pairs condense at lower temperature Tc New form of condensate excitation — pair excitations New form of condensate excitation — pair excitations BCS Unitary BEC

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What is special about BCS Theory? Pairs form and condense at the same temperature Tc And this special case works magnificently, except for high Tc cuprates!

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More Rationale for Applying BCS- BEC Crossover to high Tc More Rationale for Applying BCS- BEC Crossover to high Tc “Pseudogap” (normal state gap) visible. “Pseudogap” (normal state gap) visible. Compare with BCS: Cuprates:

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Statistical Basis of Ideal Bose Condensation (BEC) Number Equation Number Equation Zero chemical Potential Zero chemical Potential Noncondensed bosons Noncondensed bosons …………………………………. Number of condensed bosons then determined.

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BCS-BEC Crossover Theory Pair chemical potential: Pair chemical potential: Total ``number” of pairs Total ``number” of pairs Noncondensed pairs : Noncondensed pairs : …………………………………. Composite bosons Ideal Point bosons Leads to BCS gap equation for

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Part 3: The Unitary Gas: Looking for the Novel Form of Superfluidity: Via pseudogap effects and pair excitations

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Backdground: what goes on inside a trap? Particle density peaked at trap center. Particle density peaked at trap center. Gap decreases from center to edge: bosonic excitations in middle, fermionic excitations at edge. Gap decreases from center to edge: bosonic excitations in middle, fermionic excitations at edge.

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Density Profiles and Pseudogap Effects Condensate Noncondensed pairs Fermions Pair excitations smooth out profiles—making it hard to tell if system is normal or superfluid. PRL 95, 260405 (2005)

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Thermodynamics and Pseudogap effects Theory and expt. Theory and expt. In data, T* appears as temperature where 2 curves meet Duke data Energy vs T Science 307, 1296 (2005)

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RF Spectroscopy and Pseudogap Effects RF Spectroscopy and Pseudogap Effects ntermediate Tntermediate T C. Chin et al, Science 305, 1128 (2004). Temperature scale set by theory

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Latest Excitement: Fermionic Superfluidity with Imbalanced Spin Populations Two groups: Rice and MIT

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Rationale for the interest Interest from other sub-fields of physics: Interest from other sub-fields of physics: -(QCD) dense quark matter -(QCD) dense quark matter -inside neutron stars -inside neutron stars -nuclear physics -nuclear physics Search for the elusive Fulde Ferrell- Larkin Ovchinnikov (FFLO) phase Search for the elusive Fulde Ferrell- Larkin Ovchinnikov (FFLO) phase - Another “holy grail” in condensed matter - Another “holy grail” in condensed matter

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Population Imbalance Phase Diagram at Unitarity. In “Sarma” phase, polarization is in normal k-space region. See related F. Wilczek papers. pg=pseudogap PS= phase separation Polarization is in Fermi gas outside superfluid core. Experiments at MIT and Rice seem to confirm this phase diagram.

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Last But Not Least…..BCS-BEC Crossover and High Tc Cuprates

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Cuprate Phase Diagram Apply crossover theory to d-wave latttice case Theory Fit T*(x) Pairs localize and Tc vanishes well before BEC.

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Evidence for pair excitations in underdoped cuprates Evidence for pair excitations in underdoped cuprates. Note that fermionic gap is highly non-universal Theory Understanding universality in Penetration depth vs temperature. UBC experiments

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Conclusions Cold gases present opportunity to explore bigger-than- BCS theory (ie., rewrite the texts), Possibly relevant to high Tc, Strong interest from other subdisciplines Future: More “exotic” phenomena in cold gases: 1. With optical lattices can test Hubbard models, RVB,… 1. With optical lattices can test Hubbard models, RVB,… 2. Lots yet to explore in population imbalance expts. 2. Lots yet to explore in population imbalance expts. May find the FFLO? May find the FFLO?

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Comparison with Rice data Density Difference Note polarization partly carried by noncondensed pairs = pseudogap effect. Rice ExptTheory

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Comparison with Rice data. Theory Rice data

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Comparison with MIT Data. Experiment Theory

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Comparison with Rice data –near unitarity. density difference Note polarization appears just outside superfluid core. expt theory

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Comparison with MIT at in the near- BEC. MIT data Above Tc Below Tc See clear signatures of superfluidity! theory

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