What Do Ultracold Fermi What Do Ultracold Fermi Superfluids Teach Us About Superfluids Teach Us About

Quark Gluon andQuark Gluon andCondensed MatterCondensed Matter

Wichita, KansasWichita, KansasMarch 2012

Combine Quark Gluon Physics and Combine Quark Gluon Physics and Atomic Fermi Gases (+ High Tc) Atomic Fermi Gases (+ High Tc)

Superconductivity Superconductivity

CollaboratorsCollaboratorsQijin Chen (Zhejiang Univ)Qijin Chen (Zhejiang Univ)

ChihChun Chien, Yan He, Hao Guo, Dan WulinChihChun Chien, Yan He, Hao Guo, Dan WulinAlso John Thomas, Debbie Jin groups Also John Thomas, Debbie Jin groups

Outline of TalkOutline of Talk

Summary of what cold Fermi gases may Summary of what cold Fermi gases may have in common with quark gluon plasmas have in common with quark gluon plasmas (and high Tc(and high Tc

Superconductors).Superconductors).

Summary of Ground-breaking experiments Summary of Ground-breaking experiments in cold gases.in cold gases.

A refresher course on superconductivity.A refresher course on superconductivity.

ControversyControversy about “perfect fluidity” – about “perfect fluidity” – anomalously low viscosity.anomalously low viscosity.

Superfluidity Associated Superfluidity Associated with at Least Nine Nobel with at Least Nine Nobel

Prizes Prizes 1913 Onnes for superconductivity-expt1913 Onnes for superconductivity-expt 1972 Bardeen, Cooper, Schrieffer (BCS)-1972 Bardeen, Cooper, Schrieffer (BCS)-

theorytheory 1987 Bednorz and Muller– high Tc- expt1987 Bednorz and Muller– high Tc- expt 2001 BEC in trapped Bose gases-expt2001 BEC in trapped Bose gases-expt 2003 Abrikosov, Leggett, Ginzburg- theory2003 Abrikosov, Leggett, Ginzburg- theory 2008 Nambu– BCS theory in particle 2008 Nambu– BCS theory in particle

physics.physics.…………....

And still counting !And still counting !

Impact on Other Subfields Impact on Other Subfields of Fermionic Superfluidityof Fermionic Superfluidity

Pairing in Nuclear Physics– Bohr, Pairing in Nuclear Physics– Bohr, Mottelson, Pines.Mottelson, Pines.

Dense Quark matter, color Dense Quark matter, color superconductivity in RHICsuperconductivity in RHIC

Hadronic superfluidity in neutron Hadronic superfluidity in neutron starsstars..

Applications to accelerator Applications to accelerator magnets,MRI…magnets,MRI…

The Essence of Fermionic The Essence of Fermionic SuperfluiditySuperfluidity

fermions bosons

Attractive interactions turn fermions into “composite bosons” (or Cooper pairs).These are then driven by statistics to

Bose condense.

Increased attraction

Remarkable Tuning Remarkable Tuning Capability in Cold Gases Capability in Cold Gases via Feshbach Resonancevia Feshbach Resonance

..

BCSBEC

RFeshbach Resonance

Tuneable attraction: with varying magnetic field.

Magnetic Field

Magnetic-field Feshbach resonance

BEC– strong attraction

Unitary limit

Summary of Trapped Fermi Summary of Trapped Fermi GasesGases

Mainly Mainly 4040K and K and 66Li. Li. Highly dilute: Highly dilute: Number of atoms N=10Number of atoms N=1055-10-106.6.

Fermi temperature Fermi temperature EEFF ~ 1 ~ 1 mmK.K. Cooled down to Cooled down to TT~10-100 nK~10-100 nK Expts. explore crossover near Expts. explore crossover near

unitarityunitarity

Interdisciplinary aspects of Interdisciplinary aspects of BCS-BEC CrossoverBCS-BEC Crossover

AMO PerspectiveAMO Perspective– Can explore new states of – Can explore new states of matter. Crossover completely accessible via matter. Crossover completely accessible via magnetic fields.magnetic fields.

Condensed Matter perspectiveCondensed Matter perspective – Opportunity – Opportunity to explore bigger-than-BCS theory. Crossover to explore bigger-than-BCS theory. Crossover may be relevant to cuprate superconductors.may be relevant to cuprate superconductors.

Nuclear/Particle/AstrophysicsNuclear/Particle/Astrophysics –Unitary –Unitary scattering regime is prototype for strongly scattering regime is prototype for strongly interacting Fermi systems: neutron stars, interacting Fermi systems: neutron stars, quark-gluon plasmas, nuclear matter. quark-gluon plasmas, nuclear matter.

String theory and AdS/CFT ConjectureString theory and AdS/CFT Conjecture: : Minimum shear viscosityMinimum shear viscosity

Dense Quark Matter and Dense Quark Matter and Ultracold Fermi GasesUltracold Fermi Gases

..

Deconfined quark-gluon plasmas made in ultrarelativistic heavy ion collisions

T ~ 102 MeV ~ 1012 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 Energy Scales 0f Cold Gases and and

Quark-Gluon PlasmaQuark-Gluon Plasma

Separated by ~21 decades:Separated by ~21 decades: See Physics today, May 2010 page 29See Physics today, May 2010 page 29

Dense Quark Matter and Dense Quark Matter and Ultracold Fermi GasesUltracold Fermi Gases

..

tem

per

atu

rePhase Diagram for Fermi Phase Diagram for Fermi

atomic superfluidsatomic superfluids

(color superconductivity)

Phase Diagram in quark-gluon plasmaGordon 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 Experiments in Ultracold Fermi GasesFermi Gases

..

Complexity of Cold GasesComplexity 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:Example:ExperimentalExperimental Apparatus of Apparatus ofDuke GroupDuke Group

First Generation Experiments:First Generation Experiments:

IndirectIndirect Evidence for Superfluidity of Evidence for Superfluidity of UnitaryUnitary gases: magnetic field sweeps to BECgases: magnetic field sweeps to BEC

Jin et al, PRL 92, 040403 (2004)Jin et al, PRL 92, 040403 (2004)

Observation of Observation of quantized Vortices at quantized Vortices at

MITMIT

Thomas et al,Science 307, 1296 Thomas et al,Science 307, 1296 (2005)(2005)

Zwierlein et al , Nature 435, Zwierlein et al , Nature 435, 170404 (2005)170404 (2005)

Second Generation Second Generation Experiments:Experiments: Radio Radio Frequency ProbesFrequency Probes

which measure pairingwhich measure pairing Note close analogy with Note close analogy with

photoemissionphotoemission Paired atoms are excited to higher Paired atoms are excited to higher

hyperfine level.hyperfine level. The trap is turned off and The trap is turned off and

momentum distribution is momentum distribution is measured after time of flight.measured after time of flight.

Energy vs momentum of initial Energy vs momentum of initial (paired) states is then inferred. (paired) states is then inferred.

RF

Third Generation:Third Generation: Transport ExperimentsTransport Experiments

See Physics today, May 2010 page 29See Physics today, May 2010 page 29 String theory and experiment suggest that in the String theory and experiment suggest that in the

quantum world the viscosity can only be so low.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 At the same time there is controversy about how the shear viscosity behaves at the lowest temperatures.shear viscosity behaves at the lowest temperatures.

Will be discussed in this talkWill be discussed in this talk..

B4

1

ks

Remarkable Similarity of Remarkable Similarity of Experimental Probes:Experimental Probes: Atomic Physics and Atomic Physics andCondensed matterCondensed matter

..

Theory InterludeTheory Interlude

..

Statistical Basis of Ideal Bose Statistical Basis of Ideal Bose Condensation (BECCondensation (BEC))

Number EquationNumber Equation

Zero chemical PotentialZero chemical Potential

Noncondensed bosonsNoncondensed bosons

…………………………………

.

Number of condensed bosons then determined.

Comparing T=0 BCS and Comparing T=0 BCS and Fermi GasFermi 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 Contrast Between BCS and BCS-BEC CrossoverBCS-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 TheoryBCS-BEC Crossover Theory

Pair chemical potentialPair chemical potential::

Total ``number” of pairsTotal ``number” of pairs

Noncondensed pairsNoncondensed pairs::

…………………………………

.Composite bosons Ideal Point bosons

Leads to BCS gap equation for

Excitations in BCS-BEC Excitations in BCS-BEC CrossoverCrossover

..

Understanding the Understanding the excitations is fundamental excitations is fundamental

to understanding the to understanding the physics: The excitations physics: The excitations

consist of non-condensed consist of non-condensed pairs and fermions.pairs and fermions.

Understanding “Perfect Understanding “Perfect Fluidity”– low viscosity– Fluidity”– low viscosity–

associated with associated with understanding understanding the the

excitations. excitations.

Recall the condensate has Recall the condensate has zero viscosityzero viscosity

..

Different Predictions for Different Predictions for Shear viscosity in cold Shear viscosity in cold

gasesgases 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 Difference Between Bosonic and Fermionic SuperfluidsFermionic 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?Which One is Right?To settle the issue turn To settle the issue turn to experiments which to experiments which

measure shear viscosity measure shear viscosity via damping of breathing via damping of breathing

mode.mode.

And the Answer is…..And the Answer is…..

Experiments Measure Experiments Measure Very Very Low Low Viscosity at the lowest Viscosity at the lowest temperatures temperatures as we predictas we predict..

Tc

John Thomas– Science 2011

viscosity

Viscosity /entropy

Wide Impact of Cold Wide Impact of Cold GasesGases

..

Transport

Spectroscopy

RHIC physics

Hi Tc cuprates

Bad MetalsPerfect FluidsFermi GasesScattering

ConclusionsConclusions BCS-BEC crossover theory presents BCS-BEC crossover theory presents

opportunity to generalize the paradigm opportunity to generalize the paradigm of condensed matter theories = BCS of condensed matter theories = BCS theory.theory.

Can be studied in ultracold Fermi gases.Can be studied in ultracold Fermi gases. Also may be relevant to the high Also may be relevant to the high

temperature superconductors and temperature superconductors and quark-gluon plasmas.quark-gluon plasmas.

Can address paradoxes in both cuprates Can address paradoxes in both cuprates and dense quark matter using Fermi and dense quark matter using Fermi gases.gases.

Outline of TalkOutline of Talk Summary of what cold Fermi gases may have in Summary of what cold Fermi gases may have in

common with high temperature superconductors common with high temperature superconductors and quark gluon plasmas.and quark gluon plasmas.

Summary of Ground-breaking experiments in cold Summary of Ground-breaking experiments in cold gases.gases.

Theory interlude.Theory interlude.

Similarity of Spectroscopic, Transport and Similarity of Spectroscopic, Transport and Scattering probes. Scattering probes.

ControversiesControversies in cold gases and QGP viscosity in cold gases and QGP viscosity predictionspredictions..

Review PapersReview Papers

1. Physics Reports 412, 1 (2005)- Relation between cuprates and cold gases.

2. Reports in Prog. In Physics 72, 2. Reports in Prog. In Physics 72, 122501(2009). Relation between 122501(2009). Relation between RF and photoemission.RF and photoemission.

vv

Shear viscosity Shear viscosity ::

F = F = A v /d A v /d

..

Above TcAround TcBelow Tc

Photoemission Analogue: Photoemission Analogue: Momentum Resolved RF in K-40Momentum Resolved RF in K-40

Jin et al (2010)Jin et al (2010)

Measure Viscosity by Measure Viscosity by Breathing mode frequency Breathing mode frequency

and dampingand 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 Text Here

Cooper pairs overlapCooper pairs overlap Molecules form from unpaired atoms Molecules form from unpaired atoms

– random pairing– random pairing What really happened during the What really happened during the

projection?projection?

Revisiting Outline of Revisiting Outline of TalkTalk

Summary of what cold Fermi gases may have in Summary of what cold Fermi gases may have in common with high temperature superconductors common with high temperature superconductors and quark gluon plasmas.and quark gluon plasmas.

Summary of Ground-breaking experiments in cold Summary of Ground-breaking experiments in cold gases.gases.

Theory interlude.Theory interlude.

Similarity of Spectroscopic, Transport and Similarity of Spectroscopic, Transport and Scattering probes. Scattering probes.

ControversiesControversies in cold gases, high Tc cuprates, and in cold gases, high Tc cuprates, and QGP viscosity predictions.QGP viscosity predictions.

Comparing Our Viscosity Comparing Our Viscosity Predictions and ExperimentPredictions 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 The Cuprates and Ultracold Fermi GasesFermi Gases

..

Why BCS-BEC Crossover Why BCS-BEC Crossover may apply to High Tc may apply to High Tc

CupratesCupratesPairs are anomalously small.Pairs are anomalously small.

Tc is high. “Glue” is strongTc is high. “Glue” is strong

Quasi 2 dimensional.Quasi 2 dimensional.

““Pseudogap” (normal state gap) Pseudogap” (normal state gap) very prominent.very prominent.

BEC BCS

cuprates

Similarity of Phase Similarity of Phase diagramsdiagrams

..

Cuprates

BCS-BEC on d-wave paired lattice

Tc vanishes in the fermionic regime– pair localization

A Supporting QuoteA Supporting Quote

A. LeggettA. Leggett: “The small size of the : “The small size of the cuprate pairs puts us in the cuprate pairs puts us in the intermediate regime of the so-called intermediate regime of the so-called BCS-BEC crossover.” BCS-BEC crossover.”

( Summary article --Nature Phys. 2006).( Summary article --Nature Phys. 2006).

1. Photoemission and 1. Photoemission and RF RF Spectroscopy Spectroscopy

These detect the presence of pairing, based on fits to

2. Conductivity and Shear 2. Conductivity and Shear ViscosityViscosity

vv

These distinguish condensed and non-condensed pairs.

3. Neutron scattering and 2-3. Neutron scattering and 2-photon Braggphoton Bragg

Unlike neutrons, Bragg measures spin and charge scattering SEPARATELY