The Nature of the
Pseudogap in
Ultracold Fermi Gases
Univ. of Washington
May
2011
Pseudogap Discoveries
1992,
95,
97
1997
Randeria group noted a pseudogap was
present in BCS-BEC crossover, as a
spin gap. (Varenna, ‘97):
“There would be no pseudogap in the
charge channel.”
“The pseudogap phase was associated
with spin-charge separation”
Levin group was first to see pseudogap
in the spectral function.
This was a quasi-particle gap.
“No spin charge separation above Tc.”
The pseudogap would enter below Tc–
as pair excitations of condensate.
Message to the skeptics:
The Role for Analytic Many Body Theories
in Cold Atom Field
1. They connect different experiments,
provide simple intuition and predictions.
2.
They are more appropriate for the big
picture than for precision studies.
3. When done correctly, they do not
involve inaccessible numerics, and
respect conservation laws.
Predictions For difference
structure factor:
Inverse Penetration
Depth
Condensed Matter theorists look at
broad classes of experiments which may
challenge some of the “benchmarks”
Viscosity much
more sensitive to
microscopics than
thermodynamics
Very similar
specific heat
Helium 4
Helium 4
Helium 3
Helium 3
Physical Picture of the
Pseudogap
.
Contrast with BCS
Crossover theory
Due to stronger- than- BCS attraction
pairs form at T* and condense at Tc .
Non-condensed pairs appear below Tc as
pair excitations of the condensate.
Comparing Different
Analytic Crossover
Theories
Our Starting Point : Simple
Mean Field Ground State
Why?
This is the simplest ground state.
 Basis for Bogoliubov-de Gennes theory.

 Basis for unequal population
theories.
 No first order transitions.
 Superfluid density is well
behaved.
 Basis for Gor’kov theory.
All Analytic Theories
address finite temperature:
via T-matrix scheme
Treat pair propagators (t) and
particles (G). No higher
correlations.
 Solve coupled equations for
two propagators: G and t.
 Here G depends on
which
depends on t.

Three different T-matrix
approaches
NSR pair susceptibility:
BCS-Leggett:
Zwerger
Single Particle Properties in
BCS-Leggett Approach

The self energy:
The spectral function at different T– showing
pseudogap effects.
Two Particle Properties
Density and Spin Correlation
functions
Charge “sees” coherence – distinguishes between
condensed and non-condensed pairs.
Spin “sees” pairing– cannot distinguish
between condensed and non-condensed
pairs
Demonstrable agreement with sum rules. Following
Nambu!
Comparison of Tc

in Nozieres Schmitt-Rink scheme
and present theory
Homogeneous
Trap
BCS-Leggett
Nozieres SchmittRink
Nozieres SchmittBCS-Leggett
Rink
Experiments from M. Ueda
et al.
Comparison of Spectral
functions in the Normal state
.
Increasing temperature
Nozieres Schmitt
Rink Scheme:
BCS-Leggett
Scheme:
BCS-Leggett emphasizes small q pairs. Appropriate nearer
condensation.
Nozieres Schmitt Rink emphasizes all-q pairs. Appropriate
at high T.
Comparison of Spectral
Functions with Drummond
Group
Drummond (high T)
Virial Approximation!
BCS-Leggett Scheme:
Comparison of
Thermodynamics

Nozieres Schmitt-Rink scheme
(Drummond) and present theory
Trap– courtesy of R. Hulet
Homogeneous
Nozieres Schmitt-Rink
Trap
Trap
Homogeneous
Homogeneous Experiments
from M. Ueda et al.
Comparison of Density Profiles with
Strinati group
Strinati group NSR
BCS-Leggett approach
Non-monotonic in temperature
What is the evidence for a
pseudogap in ultracold
fermionic superfluids?
Non-condensed pairs -> Smooth profiles at unitarity
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 by theory
(2006)
(b)
0,4
0,0
(c)
0,4
0,0
0,4
(d)
0,0
-20
0
20
40
RF frequency offset (kHz)
Momentum Resolved RF and
Pseudogap Effects
.
Below Tc
Around Tc
Above Tc
Effects of Pseudogap on
Viscosity



Lowers carrier number.
Carrier number increases with
temperature.
Decreases number of fermions, due to
conversion to pairs– lowering viscosity
Homogeneous
viscosity
Experiment
Measure Viscosity in Traps
by Breathing mode frequency
and damping
Duke Experiments
Theory and experiment in
traps:
Tc
Low viscosity due to pseudogap and to bosonic degrees of
freedom = perfect fluids. Analogue in cuprates = bad metals.
We argue that phonons don’t
contribute to viscosity in fermionic
superfluids. Goldstone bosons
don’t couple to transverse probes.
.
Schaefer et al argue that phonons dominate the physics.
Thermodynamical Controversy
on Pseudogap: Disagree with
ENS Group
Pressure has Tsquared dependence
even in a BCS
superfluid.
The pseudogap
cannot be accessed
by low T expts.
Prescription for
seeing the
pseudogap: look for
spin susceptibility
and entropy
suppression.
Spin Diffusion Controversy On
Pseudogap. Disagree with
MIT group
.
Spin conductivity with pg
Spin susceptibility with pg
Spin diffusion coefficient
Spin susceptibility
If we follow
experimental protocol
for estimating the
spin conductivity, we
find (incorrectly) nonpseudogap behavior
in spin susceptibility.
Without pg
How to think about Benchmarks when
there are Qualitative Puzzles
Viscosity much more sensitive to
microscopics than thermodynamics!
Helium 4
Contrast with very
similar Specific heat:
Helium 4
Helium 3
Helium 3
Conclusions– We have
argued since 2003 that





The pseudogap appears in cold gases near
unitarity.
It is a quasi-particle gap appearing in the
spectral function (1997)—not associated with
spin charge separation.
It manifests itself below Tc as non-condensed
pair excitations of the condensate.
It should be widely observable experimentally.
(Varenna 2006).
We have argued (since 1997) this pseudogap
scenario applies to the cuprates.
Our claims met with enormous resistance from all
quarters– until recently when everybody claims
to have discovered the pseudogap!
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.
Recent Transport Papers
1. (2010). ArXiv 1008.0423, ArXiv
1009.4678
2. (2011). ArXiv 1102.4498