What do ultracold fermi superfluids teach us about quark gluon and condensed matter
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What do ultracold fermi superfluids teach us about quark gluon and condensed matter

What Do Ultracold Fermi Superfluids Teach Us About Quark Gluon andCondensed Matter

Wichita, Kansas

March 2012


What do ultracold fermi superfluids teach us about quark gluon and condensed matter

Combine Quark Gluon Physics and Atomic Fermi Gases (+ High Tc) Superconductivity CollaboratorsQijin Chen (Zhejiang Univ)ChihChunChien, Yan He, HaoGuo, Dan WulinAlso John Thomas, Debbie Jin groups


Outline of talk

Outline of Talk

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

    Superconductors).

  • Summary of Ground-breaking experiments in cold gases.

  • A refresher course on superconductivity.

  • Controversy about “perfect fluidity” – anomalously low viscosity.


Superfluidity associated with at least nine nobel prizes

Superfluidity Associated with at Least Nine Nobel Prizes

  • 1913 Onnes for superconductivity-expt

  • 1972 Bardeen, Cooper, Schrieffer (BCS)-theory

  • 1987 Bednorz and Muller– high Tc- expt

  • 2001 BEC in trapped Bose gases-expt

  • 2003 Abrikosov, Leggett, Ginzburg- theory

  • 2008 Nambu– BCS theory in particle physics.

    ……..

    And still counting !


Impact on other subfields of fermionic superfluidity

Impact on Other Subfields of FermionicSuperfluidity

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

  • Dense Quark matter, color superconductivity in RHIC

  • Hadronicsuperfluidity in neutron stars.

  • Applications to accelerator magnets,MRI…


The essence of fermionic superfluidity

The Essence of FermionicSuperfluidity

Increased attraction

fermions

bosons

Attractive interactions turn fermions into “composite bosons” (or Cooper pairs).

These are then driven by statistics to Bose condense.


Remarkable tuning capability in cold gases via feshbach resonance

R

Remarkable Tuning Capability in Cold Gases via Feshbach Resonance

.

Tuneable attraction: with varying magnetic field.

Feshbach Resonance

BEC

BCS


What do ultracold fermi superfluids teach us about quark gluon and condensed matter

Magnetic-field Feshbach resonance

Magnetic Field

BEC– strong attraction

Unitary limit


Summary of trapped fermi gases

Summary of Trapped Fermi Gases

  • Mainly 40K and 6Li.

  • Highly dilute:

  • Number of atoms N=105-106.

  • Fermi temperature EF ~ 1 mK.

  • Cooled down to T~10-100 nK

  • Expts. explore crossover near unitarity


Interdisciplinary aspects of bcs bec crossover

Interdisciplinary aspects of BCS-BEC Crossover

  • 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.

  • 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


Dense quark matter and ultracold fermi gases

Dense Quark Matter and Ultracold Fermi Gases

.


What do ultracold fermi superfluids teach us about quark gluon and condensed matter

Energy Scales 0f Cold Gases and Quark-Gluon PlasmaSeparated by ~21 decades:See Physics today, May 2010 page 29

Deconfined quark-gluon plasmas

made in ultrarelativistic heavy ion collisions

T ~ 102 MeV ~ 1012 K (temperature of early universe at 1m sec)

Trapped cold atomic systems:

Bose-condensed and BCS fermion superfluid states

T ~ nanokelvin (traps are the coldest places in the universe!)


Dense quark matter and ultracold fermi gases1

Dense Quark Matter and Ultracold Fermi Gases

.

Phase Diagram for Fermi atomic superfluids

temperature


What do ultracold fermi superfluids teach us about quark gluon and condensed matter

Phase Diagram in quark-gluon plasma

Gordon Baym, T. Hatsuda

Quark-gluon plasma

tricritical point

Pseudogap?

chirally symmetric

(Bose-Einstein decondensation)

Hadronic matter:

Neutrons, protons, pions, …

BEC (?)

BCS paired quark matter

Chiral symmetry breaking

(color superconductivity)

(density)


Experiments in ultracold fermi gases

Experiments in Ultracold Fermi Gases

.


Complexity of cold gases

Complexity of Cold Gases

  • How can we prove superfluidity ?

  • How can we measure temperature?

  • How can we measure the pairing gap ?

  • How can we measure transport?

Example:Experimental Apparatus ofDuke Group


What do ultracold fermi superfluids teach us about quark gluon and condensed matter

First Generation Experiments:

Indirect Evidence for Superfluidity of Unitary gases: magnetic field sweeps to BEC

Jin et al, PRL 92, 040403 (2004)‏

Thomas et al,Science 307, 1296 (2005)

Observation of quantized Vortices at MIT

Zwierlein et al , Nature 435, 170404 (2005)‏


Second generation experiments radio frequency probes which measure pairing

Second Generation Experiments: Radio Frequency Probeswhich measure pairing

  • Note close analogy with photoemission

  • Paired atoms are excited to higher

    hyperfine level.

  • The trap is turned off and momentum distribution is measured after time of flight.

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

RF


Third generation transport experiments see physics today may 2010 page 29

Third Generation:Transport ExperimentsSee Physics today, May 2010 page 29

  • String theory and experiment suggest that in the quantum world the viscosity can only be so low.

  • Via AdS/CFT:

  • At the same time there is controversy about how the shear viscosity behaves at the lowest temperatures.

    Will be discussed in this talk.


Remarkable similarity of experimental probes atomic physics and condensed matter

Remarkable Similarity of Experimental Probes: Atomic Physics andCondensed matter

.


Theory interlude

Theory Interlude

.


Statistical basis of ideal bose condensation bec

Statistical Basis of Ideal Bose Condensation (BEC)

………………………………….

  • Number Equation

  • Zero chemical Potential

  • Noncondensed bosons

Number of condensed bosons then determined.


Comparing t 0 bcs and fermi gas

Comparing T=0 BCS and Fermi Gas

Fermi Gas

BCS superconductor

excitation gap for fermions

No excitation gap


What do ultracold fermi superfluids teach us about quark gluon and condensed matter

BCS-BEC Crossover– Tuneable attractive interaction

BEC– strong attraction


Contrast between bcs and bcs bec crossover

Contrast Between BCS and BCS-BEC Crossover

.

In BCS theory all energy scales are equal !

Due to stronger- than- BCS attraction pairs form at T* and condense at Tc.

The pseudogap (pg) reflects preformed pairs above Tc.


Bcs bec crossover theory

BCS-BEC Crossover Theory

Composite bosons

Ideal Point bosons

………………………………….

  • Pair chemical potential:

  • Total ``number” of pairs

  • Noncondensed pairs:

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.


What do ultracold fermi superfluids teach us about quark gluon and condensed matter

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

Difference Between Bosonic and FermionicSuperfluids

Helium 3

The two predictions seem to follow the difference between helium-3 and helium-4

Helium 4

!

Helium 4 shows upturn

Helium 3 shows no upturn

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 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

And the Answer is…..Experiments Measure Very Low Viscosity at the lowest temperatures as we predict.

Viscosity /entropy

viscosity

Tc

John Thomas– Science 2011


Wide impact of cold gases

Wide Impact of Cold Gases

.

RHIC physics

Perfect Fluids

Bad Metals

Fermi Gases

Hi Tc cuprates

Spectroscopy

Transport

Scattering


Conclusions

Conclusions

  • BCS-BEC crossover theory presents opportunity to generalize the paradigm of condensed matter theories = BCS theory.

  • Can be studied in ultracold Fermi gases.

  • 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.


Outline of talk1

Outline of Talk

  • 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.

  • Theory interlude.

  • Similarity of Spectroscopic, Transport and Scattering probes.

  • Controversies in cold gases and QGP viscosity predictions.


Review papers

Review Papers

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

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


What do ultracold fermi superfluids teach us about quark gluon and condensed matter

Shear viscosity :

F =  A v /d

v


What do ultracold fermi superfluids teach us about quark gluon and condensed matter

Photoemission Analogue: Momentum Resolved RF in K-40Jin et al (2010)

.

Above Tc

Below Tc

Around Tc


Measure viscosity by breathing mode frequency and damping

Measure Viscosity by Breathing mode frequency and damping

Theory and experiment

Duke Experiment

Low viscosity due to pseudogap and to bosonic degrees of freedom = perfect fluids. Analogue in cuprates = bad metals.


Text here

Text Here

  • Cooper pairs overlap

  • Molecules form from unpaired atoms – random pairing

  • What really happened during the projection?


Revisiting outline of talk

Revisiting Outline of Talk

  • 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.

  • Theory interlude.

  • Similarity of Spectroscopic, Transport and Scattering probes.

  • Controversies in cold gases, high Tccuprates, and QGP viscosity predictions.


Comparing our viscosity predictions and experiment

Comparing Our Viscosity Predictions and Experiment

Homogeneous theory

Tc

Theory and experiment in traps:

Low viscosity due to pseudogap and to bosonic degrees of freedom = perfect fluids. Analogue in cuprates = bad metals.


The cuprates and ultracold fermi gases

The Cuprates and Ultracold Fermi Gases

.


Why bcs bec crossover may apply to high tc cuprates

Why BCS-BEC Crossover may apply to High TcCuprates

  • Pairs are anomalously small.

  • Tc is high. “Glue” is strong

  • Quasi 2 dimensional.

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

BEC

BCS

cuprates


Similarity of phase diagrams

Similarity of Phase diagrams

.

BCS-BEC on d-wave paired lattice

Cuprates

Tc vanishes in the fermionic regime– pair localization


A supporting quote

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.”

    ( Summary article --Nature Phys. 2006).


1 photoemission and rf spectroscopy

1. Photoemission and RF Spectroscopy

These detect the presence of pairing, based on fits to

2. Conductivity and Shear Viscosity

These distinguish condensed and non-condensed pairs.

v

3. Neutron scattering and 2-photon Bragg

Unlike neutrons, Bragg measures spin and charge scattering SEPARATELY


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