What Do Ultracold Fermi Superfluids Teach Us About Quark Gluon and Condensed Matter Wichita, Kansas March 2012

Combine Quark Gluon Physics and Atomic Fermi Gases (+ High Tc) Superconductivity Collaborators Qijin Chen (Zhejiang Univ) ChihChun Chien, Yan He, Hao Guo, Dan Wulin Also John Thomas, Debbie Jin groups

Outline of Talk Summary of what cold Fermi gases may have in common with quark gluon plasmas (and high Tc Summary of what cold Fermi gases may have in common with quark gluon plasmas (and high TcSuperconductors). Summary of Ground-breaking experiments in cold gases. Summary of Ground-breaking experiments in cold gases. A refresher course on superconductivity. A refresher course on superconductivity. Controversy about “perfect fluidity” – anomalously low viscosity. Controversy about “perfect fluidity” – anomalously low viscosity.

Superfluidity Associated with at Least Nine 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 2008 Nambu– BCS theory in particle physics Nambu– BCS theory in particle physics.…….. And still counting !

Impact on Other Subfields of Fermionic Superfluidity Pairing in Nuclear Physics– Bohr, Mottelson, Pines. Pairing in Nuclear Physics– Bohr, Mottelson, Pines. Dense Quark matter, color superconductivity in RHIC Dense Quark matter, color superconductivity in RHIC Hadronic superfluidity in neutron stars. Hadronic superfluidity in neutron stars. Applications to accelerator magnets,MRI… Applications to accelerator magnets,MRI…

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

Remarkable Tuning Capability in Cold Gases via Feshbach Resonance. BCS BEC R Feshbach Resonance Tuneable attraction: with varying magnetic field.

Magnetic Field Magnetic-field Feshbach resonance BEC– strong attraction Unitary limit

Summary of Trapped Fermi Gases Mainly 40 K and 6 Li. Mainly 40 K and 6 Li. Highly dilute: Highly dilute: Number of atoms N= Number of atoms N= Fermi temperature E F ~ 1 m K. Fermi temperature E F ~ 1 m K. Cooled down to T~ nK Cooled down to T~ nK Expts. explore crossover near unitarity Expts. explore crossover near unitarity

Interdisciplinary aspects of BCS-BEC Crossover AMO Perspective– Can explore new states of matter. Crossover completely accessible via magnetic fields. AMO Perspective– Can explore new states of matter. Crossover completely accessible via magnetic fields. Condensed Matter perspective – Opportunity to explore bigger-than-BCS theory. Crossover may be relevant to cuprate superconductors. Condensed Matter perspective – Opportunity to explore bigger-than-BCS theory. Crossover may be relevant to cuprate superconductors. Nuclear/Particle/Astrophysics –Unitary scattering regime is prototype for strongly interacting Fermi systems: neutron stars, quark-gluon plasmas, nuclear matter. Nuclear/Particle/Astrophysics –Unitary scattering regime is prototype for strongly interacting Fermi systems: neutron stars, quark-gluon plasmas, nuclear matter. String theory and AdS/CFT Conjecture: Minimum shear viscosity String theory and AdS/CFT Conjecture: Minimum shear viscosity

Dense Quark Matter and Ultracold Fermi Gases.

Deconfined quark-gluon plasmas made in ultrarelativistic heavy ion collisions T ~ 10 2 MeV ~ K (temperature of early universe at 1  sec) Trapped cold atomic systems: Bose-condensed and BCS fermion superfluid states T ~ nanokelvin (traps are the coldest places in the universe!) Energy Scales 0f Cold Gases and Quark-Gluon Plasma Separated by ~21 decades: See Physics today, May 2010 page 29

Dense Quark Matter and Ultracold Fermi Gases. temperature Phase Diagram for Fermi atomic superfluids

(color superconductivity) Phase Diagram in quark-gluon plasma Gordon Baym, T. Hatsuda Chiral symmetry breaking chirally symmetric (Bose-Einstein decondensation) Hadronic matter : Neutrons, protons, pions, … BEC (?) BCS paired quark matter (density) tricritical point Quark-gluon plasma Pseudogap?

Experiments in Ultracold Fermi Gases Experiments in Ultracold Fermi Gases.

Complexity of Cold Gases How can we prove superfluidity ? How can we prove superfluidity ? How can we measure temperature? How can we measure temperature? How can we measure the pairing gap ? How can we measure the pairing gap ? How can we measure transport? How can we measure transport? Example: Experimental Apparatus of Duke Group

First Generation Experiments: Indirect Evidence for Superfluidity of Unitary gases: magnetic field sweeps to BEC Jin et al, PRL 92, (2004) ‏ Observation of quantized Vortices at MIT Observation of quantized Vortices at MIT Thomas et al,Science 307, 1296 (2005) Zwierlein et al, Nature 435, (2005) ‏

Second Generation Experiments: Radio Frequency Probes which measure pairing Note close analogy with photoemission Note close analogy with photoemission Paired atoms are excited to higher Paired atoms are excited to higher hyperfine level. The trap is turned off and momentum distribution is measured after time of flight. The trap is turned off and momentum distribution is measured after time of flight. Energy vs momentum of initial (paired) states is then inferred. Energy vs momentum of initial (paired) states is then inferred. RF

Third Generation: Transport Experiments See Physics today, May 2010 page 29 String theory and experiment suggest that in the quantum world the viscosity can only be so low. String theory and experiment suggest that in the quantum world the viscosity can only be so low. Via AdS/CFT: Via AdS/CFT: At the same time there is controversy about how the shear viscosity behaves at the lowest temperatures. At the same time there is controversy about how the shear viscosity behaves at the lowest temperatures. Will be discussed in this talk. Will be discussed in this talk.

Remarkable Similarity of Experimental Probes: Atomic Physics and Condensed matter.

Theory Interlude.

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.

Comparing T=0 BCS and Fermi Gas Fermi Gas No excitation gap BCS superconductor excitation gap for fermions

BCS-BEC Crossover– Tuneable attractive interaction BEC– strong attraction

Contrast Between BCS and BCS-BEC Crossover Contrast Between BCS and BCS-BEC Crossover. Due to stronger- than- BCS attraction pairs form at T* and condense at Tc. The pseudogap (pg) reflects preformed pairs above Tc. In BCS theory all energy scales are equal !

BCS-BEC Crossover Theory 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

Excitations in BCS-BEC Crossover Excitations in BCS-BEC Crossover. Understanding the excitations is fundamental to understanding the physics: The excitations consist of non-condensed pairs and fermions. Understanding the excitations is fundamental to understanding the physics: The excitations consist of non-condensed pairs and fermions.

Understanding “Perfect Fluidity”– low viscosity– associated with understanding the excitations. Recall the condensate has zero viscosity Understanding “Perfect Fluidity”– low viscosity– associated with understanding the excitations. Recall the condensate has zero viscosity.

Different Predictions for Shear viscosity in cold gases Different Predictions for Shear viscosity in cold gases Our prediction: We anticipate viscosity should not turn up at low temperatures. Excitations are gapped out. Quark Gluon Plasma (QCD) Predictions for viscosity– predict upturn at low T

Difference Between Bosonic and Fermionic Superfluids ! Helium 3 Helium 4 Helium 3 shows no upturn Helium 4 shows upturn The two predictions seem to follow the difference between helium-3 and helium-4 The Difference gets to the heart of the physics– the nature of lowest T excitations.

Which One is Right? To settle the issue turn to experiments which measure shear viscosity via damping of breathing mode.

And the Answer is….. Experiments Measure Very Low Viscosity at the lowest temperatures as we predict. Tc John Thomas– Science 2011 viscosity Viscosity /entropy

Wide Impact of Cold Gases. Transport Spectroscopy RHIC physics Hi Tc cuprates Bad Metals Perfect Fluids Fermi Gases Scattering

Conclusions BCS-BEC crossover theory presents opportunity to generalize the paradigm of condensed matter theories = BCS theory. BCS-BEC crossover theory presents opportunity to generalize the paradigm of condensed matter theories = BCS theory. Can be studied in ultracold Fermi gases. Can be studied in ultracold Fermi gases. Also may be relevant to the high temperature superconductors and quark-gluon plasmas. Also may be relevant to the high temperature superconductors and quark-gluon plasmas. Can address paradoxes in both cuprates and dense quark matter using Fermi gases. Can address paradoxes in both cuprates and dense quark matter using Fermi gases.

Outline of Talk Summary of what cold Fermi gases may have in common with high temperature superconductors and quark gluon plasmas. Summary of what cold Fermi gases may have in common with high temperature superconductors and quark gluon plasmas. Summary of Ground-breaking experiments in cold gases. Summary of Ground-breaking experiments in cold gases. Theory interlude. Theory interlude. Similarity of Spectroscopic, Transport and Scattering probes. Similarity of Spectroscopic, Transport and Scattering probes. Controversies in cold gases and QGP viscosity predictions. Controversies in cold gases and QGP viscosity predictions.

Review Papers 1. Physics Reports 412, 1 (2005)- Relation between cuprates and cold gases. 2. Reports in Prog. In Physics 72, (2009). Relation between RF and photoemission.

v Shear viscosity  : F =  A v /d

. Above Tc Around Tc Below Tc Photoemission Analogue: Momentum Resolved RF in K-40 Jin et al (2010)

Measure Viscosity by Breathing mode frequency and damping Theory and experiment Low viscosity due to pseudogap and to bosonic degrees of freedom = perfect fluids. Analogue in cuprates = bad metals. Duke Experiment

Text Here Cooper pairs overlap Cooper pairs overlap Molecules form from unpaired atoms – random pairing Molecules form from unpaired atoms – random pairing What really happened during the projection? What really happened during the projection?

Revisiting Outline of Talk Summary of what cold Fermi gases may have in common with high temperature superconductors and quark gluon plasmas. Summary of what cold Fermi gases may have in common with high temperature superconductors and quark gluon plasmas. Summary of Ground-breaking experiments in cold gases. Summary of Ground-breaking experiments in cold gases. Theory interlude. Theory interlude. Similarity of Spectroscopic, Transport and Scattering probes. Similarity of Spectroscopic, Transport and Scattering probes. Controversies in cold gases, high Tc cuprates, and QGP viscosity predictions. Controversies in cold gases, high Tc cuprates, and QGP viscosity predictions.

Comparing Our Viscosity Predictions and Experiment Theory and experiment in traps: Low viscosity due to pseudogap and to bosonic degrees of freedom = perfect fluids. Analogue in cuprates = bad metals. Homogeneous theory Tc

The Cuprates and Ultracold Fermi Gases.

Why BCS-BEC Crossover may apply to High Tc Cuprates Why BCS-BEC Crossover may apply to High Tc Cuprates  Pairs are anomalously small. Tc is high. “Glue” is strong Tc is high. “Glue” is strong Quasi 2 dimensional. Quasi 2 dimensional. “Pseudogap” (normal state gap) very prominent. “Pseudogap” (normal state gap) very prominent. BECBCS cuprates

Similarity of Phase diagrams. Cuprates BCS-BEC on d-wave paired lattice Tc vanishes in the fermionic regime– pair localization

A Supporting Quote A. Leggett: “The small size of the cuprate pairs puts us in the intermediate regime of the so-called BCS-BEC crossover.” A. Leggett: “The small size of the cuprate pairs puts us in the intermediate regime of the so-called BCS-BEC crossover.” ( Summary article --Nature Phys. 2006). ( Summary article --Nature Phys. 2006).

1. Photoemission and RF Spectroscopy These detect the presence of pairing, based on fits to 2. Conductivity and Shear Viscosity v These distinguish condensed and non-condensed pairs. 3. Neutron scattering and 2-photon Bragg Unlike neutrons, Bragg measures spin and charge scattering SEPARATELY