Transcript What Do High Tc Superconductors Teach Us About Ultracold Fermi National

What Do High Tc Superconductors
Teach Us About Ultracold
Superfluids and Vice Versa?
Fermi National
Laboratory
Jan 2007
Cold Atom Collaborators:
Qijin Chen (Johns Hopkins,
UC)
J. Stajic (U Chicago; LANL)
Yan He (U. Chicago)
ChihChun Chien (U. Chicago)
J.E. Thomas, J. Kinast, A. Turlapov
(Duke)
D.S. Jin, C. Regal and M. Greiner
(JILA)
M. Holland, M. Chiofalo, J.
Impact of Superfluidity and
Superconductivity
2007 is 50 th anniversary of BCS
Theory!
Festivities planned in Urbana for coming October
Superfluidity Associated with at
Least Eight Nobel Prizes
8 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
……..

And Still counting !
Impact on Other Subfields of
Fermionic Superfluidity

Pairing in Nuclear Physics– Bohr,
Mottelson, Pines.
Higgs mechanism in Particle Physics.
Dense QCD, color superconductivity in
RHIC
Hadronic superfluidity in neutron stars.

Applications to accelerator physics.

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
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.
What is this talk about ?
1.
BCS theory and Bose Condensation (BEC) can
be treated in one “master” theory (of fermion
superfluids) with continuous evolution from one
to another.
2.
Ultracold gases are the best way to see
this evolution.
3.
But the same phenomenon may be present in
high Tc cuprates.
Remarkable Tuning Capability in
Cold Gases via Feshbach Resonance
.
Scattering length
BEC
BCS
Unitary limit
molecules
→←
> DB
Ultracold Fermi Gases
Strong
attraction
BEC
Weak attraction
BCS
Tuning the attractive interaction via Magnetic
Field allows us to study
1. Most general form of fermionic superfluidity.
2. Unitary scattering prototypes for other
High Tc Cuprates– also
candidates for BCS-BEC
Crossover
BEC
BCS
“The size of the cuprate pairs (from 1030
puts us in the intermediate
regime of the so-called BCS-BEC
crossover” A. J. Leggett 2006 (Nature
Physics).
Three Part Talk

Ground-breaking experiments in cold gases.

Theory interlude.

Expts. on novel, common aspects of cold
gases and high Tc cuprates.
Part 1:
Proving
Superfluidity
Much easier on the Bose side of
resonance!
Observation of BEC in Fermi gases
first reported by Jin et al, Nature
426 (2003).
Simultaneously by Grimm et al,
Science 302
(2003).
First Generation Evidence for
superfluidity of Unitary gases: early
2004:
.
Phase Diagram
from JILA
Jin et al, PRL 92
Based on rapid sweep to Bose gas regime.
Sweep Basis for Jin’s experiments
.
BEC
Unitary limit
BCS
→←
Adiabatic sweep
(sets temperature)
Quick sweep
molecules
> DB
Second Generation Experiments;
Thermodynamical Evidence for
Phase Transition near unitarity
.
Science 307, 1296
Our Collaboration with Duke Group: John Thamas, Joe Kinast,
Andrey Turlapov--- Feb 2005
Third Generation Experiments
Vortices Seen at
MIT-- April 2005
Zwierlein et al , Nature 435, 170404 (2005)
Vortices “visible” after sweep to BEC
because of density depletion at the core.
Part 2
THEORY INTERLUDE:
BCS, BEC and BCS-BEC Crossover
What is Ground State for BCSBEC Crossover ?
Same as in
BCS:
Chemical potential varies
when attraction strength
tuned arbitrarily:
What is Novel about BCS-BEC
Crossover? Answer: Finite T effects

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Pairs form at one temperature T*
Pairs condense at lower temperature Tc
New form of condensate excitation—pair
excitations
BCS
Unitary
BEC
What is special about BCS
Theory?
Pairs form and condense at the same
temperature Tc
And this special case works magnificently, except for
high Tc cuprates!
More Rationale for Applying
BCS-BEC Crossover to high Tc

“Pseudogap” (normal state gap)
visible.
Cuprates:
Compare with BCS:
Statistical Basis of Ideal
Bose Condensation (BEC)
………………………………….

Number Equation

Zero chemical Potential

Noncondensed bosons
Number of condensed bosons
then
BCS-BEC Crossover Theory

………………………………….
Composite bosons
Pair chemical potential:
Leads to BCS gap equation for

Total ``number” of pairs

Noncondensed pairs:
Ideal Point bosons
Part 3:
The Unitary Gas: Looking for
the Novel Form of
Superfluidity:
Via pseudogap effects and pair
excitations
Backdground: what goes on
inside a trap?

Particle density peaked at trap
center.

Gap decreases from center to edge:
bosonic excitations in middle,
fermionic excitations at edge.
Density Profiles and Pseudogap Effects
PRL 95, 260405 (2005)
Condensate Noncondensed pairs Fermions
Pair excitations smooth out
profiles—making it hard to tell
if system is normal or
superfluid.
Thermodynamics and Pseudogap
effects
Energy vs
T
Theory and expt.
Duke data
In data, T* appears as temperature where 2 curves meet
Science 307, 1296 (2005)
RF Spectroscopy and Pseudogap
Effects
C. Chin et al, Science
305, 1128 (2004).
0,4
fractional loss in |2>
(a)
0,0
Temperature scale set
(b)
0,4
by theory
0,0
(c)
0,4
0,0
0,4
(d)
0,0
-20
0
20
40
RF frequency offset (kHz)
atest Excitement: Fermionic Superfluidity
with
Imbalanced Spin Populations
Two groups: Rice and MIT
Rationale for the interest

Interest from other sub-fields of physics:
-(QCD) dense quark matter
-inside neutron stars
-nuclear physics

Search for the elusive Fulde FerrellLarkin Ovchinnikov (FFLO) phase
- Another “holy grail” in condensed
matter
Population Imbalance Phase
Diagram at Unitarity
.
Experiments at MIT and
Rice seem to confirm
this phase diagram.
PS= phase separation
Polarization is in Fermi
pg=pseudogap
gas outside superfluid
core.
In “Sarma” phase, polarization is in normal kspace region.
See related F. Wilczek papers.
Last But Not Least…..BCS-BEC
Crossover and High Tc Cuprates
Cuprate Phase Diagram
Apply crossover theory to d-wave
latttice case
Fit T*(x)
Theory
Pairs localize and Tc vanishes well before BEC.
Evidence for pair excitations
in underdoped cuprates
.
Understanding universality in Penetration depth vs temperature.
UBC experiments
Theory
Note that fermionic gap is highly non-universal
Conclusions
 Cold
gases present opportunity to explore
bigger-than-BCS theory (ie., rewrite the texts),
 Possibly relevant to high Tc,
 Strong interest from other subdisciplines
 Future: More “exotic” phenomena in cold gases:
RVB,…
expts.
1.
With optical lattices can test Hubbard models,
2.
Lots yet to explore in
May find the FFLO?
population imbalance
Comparison with Rice data
Rice Expt
Theory
Density
Difference
Note polarization partly carried by noncondensed pairs
= pseudogap effect.
Comparison with Rice data
Theory
.
Rice data
Comparison with MIT Data
.
Experiment
Theory
Comparison with Rice data –near
unitarity
theory
.
expt
density
difference
Note polarization appears just
outside superfluid core.
Comparison with MIT at
in the near- BEC
.
theory
MIT data
Above Tc
Below Tc
See clear signatures of superfluidity!