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
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
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




Pairing in Nuclear Physics– Bohr,
Mottelson, Pines.
Dense Quark matter, color
superconductivity in RHIC
Hadronic superfluidity in neutron stars.
Applications to accelerator magnets,MRI…
The Essence of Fermionic
Superfluidity
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
Feshbach
Resonance
BEC
R
Tuneable attraction:
with varying
magnetic field.
BCS
Magnetic-field Feshbach resonance
Magnetic Field
BEC– strong
attraction
Unitary limit
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




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
Energy Scales 0f Cold Gases and
Quark-Gluon Plasma
Separated 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 Gases
Phase Diagram for Fermi atomic
superfluids
temperature
.
Phase Diagram in quark-gluon plasma
Gordon Baym, T. Hatsuda
Quark-gluon
plasma
tricritical
point
Hadronic matter:
Neutrons, protons, pions, …
BEC (?)
Chiral symmetry breaking
Pseudogap?
chirally symmetric
(Bose-Einstein decondensation)
BCS paired quark matter
(color superconductivity)
(density)
.
Experiments in Ultracold Fermi
Gases
Complexity of Cold Gases



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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 of
Duke 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)
Second Generation Experiments:
Radio Frequency Probes
which measure pairing
RF

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.

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.
Via AdS/CFT:
 1 
s

4 kB
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
.
Theory Interlude

Number Equation

Zero chemical Potential

Noncondensed bosons
Number of condensed bosons
………………………………….
Statistical Basis of Ideal Bose
Condensation (BEC)
then determined.
Comparing T=0 BCS and Fermi Gas
Fermi Gas
BCS superconductor
excitation gap for fermions
No excitation gap
BCS-BEC Crossover– Tuneable
attractive interaction
BEC– strong
attraction
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

Pair chemical potential:
Leads to BCS gap equation for

Total ``number” of pairs

Noncondensed pairs:
………………………………….
Composite bosons
Ideal Point bosons
Excitations in BCS-BEC
Crossover
.
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
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
The two
predictions seem
to follow the
difference
between helium-3
and helium-4
Helium 3
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?
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.
Viscosity
/entropy
viscosity
Tc
John Thomas– Science 2011
Wide Impact of Cold Gases
RHIC physics
.
Perfect Fluids
Fermi
Gases
Spectroscopy
Transport
Scattering
Bad Metals
Hi Tc
cuprates
Conclusions



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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 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
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 :
v
F =  A v /d
Photoemission Analogue: Momentum
Resolved RF in K-40
Jin et al (2010)
.
Below Tc
Around Tc
Above Tc
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



Cooper pairs overlap
Molecules form from unpaired atoms – random
pairing
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 Ground-breaking experiments in cold gases.

Theory interlude.

Similarity of Spectroscopic, Transport and Scattering probes.

Controversies in cold gases, high Tc cuprates, and QGP viscosity
predictions.
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
Why BCS-BEC Crossover
may apply to High Tc Cuprates
 Pairs are anomalously small.
BEC
BCS

Tc is high. “Glue” is strong

Quasi 2 dimensional.

“Pseudogap” (normal state gap) very
prominent.
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.”
( 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
These distinguish condensed
and non-condensed pairs.
v
3. Neutron scattering and 2-photon Bragg
Unlike neutrons, Bragg measures
spin and charge scattering
SEPARATELY