Title: What Do High Tc Superconductors Teach Us About Ultracold Superfluids and Vice Versa
1What Do High Tc Superconductors Teach Us About
Ultracold Superfluids and Vice Versa?
- Fermi National Laboratory
Jan 2007
2Cold Atom CollaboratorsQijin 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. Milstein(JILA)
3Impact of Superfluidity and Superconductivity
2007 is 50 th anniversary of BCS Theory!
Festivities planned in Urbana for coming October
4Superfluidity 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 !
5Impact 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.
6The 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.
7What 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.
8Remarkable Tuning Capability in Cold Gases via
Feshbach Resonance
Scattering length
BEC
BCS
Unitary limit
9Ultracold Fermi Gases
Strong attraction
Weak attraction
BEC
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 subdisciplines.
10High Tc Cuprates also candidates for BCS-BEC
Crossover
BEC
BCS
The size of the cuprate pairs (from 10-30
puts us in the intermediate regime of the
so-called BCS-BEC crossover A. J. Leggett 2006
(Nature Physics). See Also
T. D. Lee in 1987.
11Three Part Talk
- Ground-breaking experiments in cold gases.
- Theory interlude.
- Expts. on novel, common aspects of cold gases
and high Tc cuprates.
12 Part 1 Proving SuperfluidityMuch 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).
13First Generation Evidence forsuperfluidity of
Unitary gases early 2004Phase Diagram from
JILA
Jin et al, PRL 92
Based on rapid sweep to Bose gas regime.
14Sweep Basis for Jins experiments
BEC
BCS
Unitary limit
Adiabatic sweep (sets temperature)
Quick sweep
15Second 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
16Third 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.
17Part 2 THEORY INTERLUDE BCS, BEC and
BCS-BEC Crossover
18What is Ground State for BCS-BEC Crossover ?
Same as in BCS
Chemical potential varies when attraction
strength tuned arbitrarily
19What is Novel about BCS-BEC Crossover? Answer
Finite T effects
- Pairs form at one temperature T
- Pairs condense at lower temperature Tc
- New form of condensate excitationpair excitations
20What 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!
21 More Rationale for Applying BCS-BEC Crossover to
high Tc
- Pseudogap (normal state gap) visible.
Cuprates
Compare with BCS
22Statistical Basis of Ideal Bose Condensation
(BEC)
.
- Number Equation
- Zero chemical Potential
- Noncondensed bosons
Number of condensed bosons then
determined.
23BCS-BEC Crossover Theory
Composite bosons
Ideal Point bosons
.
- Pair chemical potential
- Total number of pairs
- Noncondensed pairs
Leads to BCS gap equation for
24Part 3The Unitary Gas Looking for the Novel
Form of Superfluidity Via pseudogap effects
and pair excitations
25Backdground 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.
26Density Profiles and Pseudogap Effects
PRL 95, 260405 (2005)
Condensate Noncondensed pairs Fermions
Pair excitations smooth out profilesmaking it
hard to tell if system is normal or superfluid.
27Thermodynamics and Pseudogap effects
Energy vs T
Duke data
In data, T appears as temperature where 2 curves
meet
Science 307, 1296 (2005)
28 RF Spectroscopy and Pseudogap Effects
C. Chin et al, Science 305, 1128 (2004).
ntermediate T
Temperature scale set by theory
29Latest Excitement Fermionic Superfluidity
withImbalanced Spin Populations
Two groups Rice and MIT
30Rationale for the interest
- Interest from other sub-fields of physics
- -(QCD) dense quark matter
- -inside neutron stars
- -nuclear physics
- Search for the elusive Fulde Ferrell-Larkin
Ovchinnikov (FFLO) phase - - Another holy grail in
condensed matter -
31Population Imbalance Phase Diagram at Unitarity
Experiments at MIT and Rice seem to confirm
this phase diagram.
PS phase separation Polarization is in Fermi gas
outside superfluid core.
pgpseudogap
In Sarma phase, polarization is in normal
k-space region. See related F.
Wilczek papers.
32Last But Not Least..BCS-BEC Crossover and High
Tc Cuprates
33Cuprate Phase Diagram
- Apply crossover theory to d-wave latttice case
Fit T(x)
Theory
Pairs localize and Tc vanishes well before BEC.
34 Evidence for pair excitations in underdoped
cuprates
Understanding universality in Penetration depth
vs temperature.
Theory
UBC experiments
Note that fermionic gap is highly non-universal
35Conclusions
- 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
- 1. With optical lattices can test
Hubbard models, RVB, - 2. Lots yet to explore in population
imbalance expts. - May find the FFLO?
-
-
-
36Comparison with Rice data
Rice Expt
Theory
Density
Difference
Note polarization partly carried by noncondensed
pairs pseudogap effect.
37Comparison with Rice data
Rice data
Theory
38Comparison with MIT Data
Theory
Experiment
39Comparison with Rice data near unitarity
theory
expt
density
difference
Note polarization appears just outside superfluid
core.
40Comparison with MIT at in the near- BEC
theory
MIT data
Above Tc
Below Tc
See clear signatures of superfluidity!