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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 andCondensed Matter

Wichita, Kansas

March 2012

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

- 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.

- 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 !

- Pairing in Nuclear Physics– Bohr, Mottelson, Pines.
- Dense Quark matter, color superconductivity in RHIC
- Hadronicsuperfluidity in neutron stars.
- Applications to accelerator magnets,MRI…

Increased attraction

fermions

bosons

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

These are then driven by statistics to Bose condense.

R

.

Tuneable attraction: with varying magnetic field.

Feshbach Resonance

BEC

BCS

Magnetic-field Feshbach resonance

Magnetic Field

BEC– strong attraction

Unitary limit

- 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

- 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

.

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!)

.

Phase Diagram for Fermi atomic superfluids

temperature

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)

.

- 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

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)

- 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

- 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.

.

.

………………………………….

- Number Equation
- Zero chemical Potential
- Noncondensed bosons

Number of condensed bosons then determined.

Fermi Gas

BCS superconductor

excitation gap for fermions

No excitation gap

BCS-BEC Crossover– Tuneable attractive interaction

BEC– strong attraction

.

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.

Composite bosons

Ideal Point bosons

………………………………….

- Pair chemical potential:
- Total ``number” of pairs
- Noncondensed pairs:

Leads to BCS gap equation for

.

Understanding the excitations is fundamental to understanding the physics: The excitations consist of non-condensed pairs and fermions.

.

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

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.

To settle the issue turn to experiments which measure shear viscosity via damping of breathing mode.

Viscosity /entropy

viscosity

Tc

John Thomas– Science 2011

.

RHIC physics

Perfect Fluids

Bad Metals

Fermi Gases

Hi Tc cuprates

Spectroscopy

Transport

Scattering

- 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.

- 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.

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.

Shear viscosity :

F = A v /d

v

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

.

Above Tc

Below Tc

Around Tc

Theory and experiment

Duke Experiment

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

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

- 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.

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.

.

- Pairs are anomalously small.
- Tc is high. “Glue” is strong
- Quasi 2 dimensional.
- “Pseudogap” (normal state gap) very prominent.

BEC

BCS

cuprates

.

BCS-BEC on d-wave paired lattice

Cuprates

Tc vanishes in the fermionic regime– pair localization

- 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).

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