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What Do High Tc Superconductors Teach Us About Ultracold Superfluids and Vice Versa

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What Do High Tc Superconductors Teach Us About Ultracold Superfluids and ... J.E. Thomas, J. Kinast, A. Turlapov (Duke) D.S. Jin, C. Regal and M. Greiner (JILA) ... – PowerPoint PPT presentation

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Title: What Do High Tc Superconductors Teach Us About Ultracold Superfluids and Vice Versa


1
What Do High Tc Superconductors Teach Us About
Ultracold Superfluids and Vice Versa?
  • Fermi National Laboratory

Jan 2007
2
Cold 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)

3
Impact of Superfluidity and Superconductivity
2007 is 50 th anniversary of BCS Theory!
Festivities planned in Urbana for coming October
4
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 !

5
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.

6
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.
7
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.
8
Remarkable Tuning Capability in Cold Gases via
Feshbach Resonance
  • .

Scattering length
BEC
BCS
Unitary limit
9
Ultracold 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.
10
High 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.
11
Three 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).
13
First Generation Evidence forsuperfluidity of
Unitary gases early 2004Phase Diagram from
JILA
  • .

Jin et al, PRL 92
Based on rapid sweep to Bose gas regime.
14
Sweep Basis for Jins experiments
  • .

BEC
BCS
Unitary limit
Adiabatic sweep (sets temperature)
Quick sweep
15
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
16
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.
17
Part 2 THEORY INTERLUDE BCS, BEC and
BCS-BEC Crossover
18
What is Ground State for BCS-BEC Crossover ?
Same as in BCS

Chemical potential varies when attraction
strength tuned arbitrarily
19
What 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

20
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!
21
More Rationale for Applying BCS-BEC Crossover to
high Tc
  • Pseudogap (normal state gap) visible.


Cuprates
Compare with BCS
22
Statistical Basis of Ideal Bose Condensation
(BEC)
.
  • Number Equation
  • Zero chemical Potential
  • Noncondensed bosons

Number of condensed bosons then
determined.
23
BCS-BEC Crossover Theory
Composite bosons
Ideal Point bosons
.
  • Pair chemical potential
  • Total number of pairs
  • Noncondensed pairs

Leads to BCS gap equation for
24
Part 3The Unitary Gas Looking for the Novel
Form of Superfluidity Via pseudogap effects
and pair excitations
25
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.

26
Density 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.
27
Thermodynamics and Pseudogap effects
  • Theory and
    expt.

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
29
Latest Excitement Fermionic Superfluidity
withImbalanced Spin Populations
Two groups Rice and MIT
30
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 Ferrell-Larkin
    Ovchinnikov (FFLO) phase
  • - Another holy grail in
    condensed matter

31
Population 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.
32
Last But Not Least..BCS-BEC Crossover and High
Tc Cuprates
33
Cuprate 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
35
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
  • 1. With optical lattices can test
    Hubbard models, RVB,
  • 2. Lots yet to explore in population
    imbalance expts.
  • May find the FFLO?

36
Comparison with Rice data
Rice Expt
Theory
Density
Difference
Note polarization partly carried by noncondensed
pairs pseudogap effect.
37
Comparison with Rice data
Rice data
Theory
  • .

38
Comparison with MIT Data
Theory
Experiment
  • .

39
Comparison with Rice data near unitarity
theory
  • .

expt
density
difference
Note polarization appears just outside superfluid
core.
40
Comparison with MIT at in the near- BEC
  • .

theory
MIT data
Above Tc
Below Tc
See clear signatures of superfluidity!
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