The Nature of The Nature of the Pseudogap in the Pseudogap in Ultracold Fermi Ultracold Fermi

GasesGases

Univ. of WashingtonUniv. of Washington

May 2011

Pseudogap Pseudogap Discoveries Discoveries

Randeria Randeria group noted a pseudogap group noted a pseudogap was present in BCS-BEC crossover, was present in BCS-BEC crossover,

as a spin gap. (Varenna, ‘97): as a spin gap. (Varenna, ‘97):

““There would be no pseudogap in the There would be no pseudogap in the charge channel.”charge channel.”

““The pseudogap phase was associated The pseudogap phase was associated with spin-charge separation”with spin-charge separation”

LevinLevin group was first to see pseudogap group was first to see pseudogap in the spectral function.in the spectral function.

This was a quasi-particle gap.This was a quasi-particle gap.““No spin charge separation above Tc.”No spin charge separation above Tc.”The pseudogap would enter below Tc– The pseudogap would enter below Tc–

as pair excitations of condensate.as pair excitations of condensate.

1992, 95, 97

1997

Message to the skepticsMessage to the skeptics: :

The Role for Analytic Many Body Theories in Cold Atom FieldThe Role for Analytic Many Body Theories in Cold Atom Field

1.1. They connect different experiments, provide simple They connect different experiments, provide simple intuition and intuition and predictionspredictions..

2.2. They are more appropriate for the big picture than for They are more appropriate for the big picture than for precision studies.precision studies.

3.3. When done correctly, When done correctly, they do not involve inaccessible they do not involve inaccessible numerics, and respect conservation lawsnumerics, and respect conservation laws..

Inverse Penetration Depth

Predictions For difference structure

factor:

Condensed Matter theorists look at Condensed Matter theorists look at broad classes of experiments which broad classes of experiments which

may may challenge some of the challenge some of the “benchmarks”“benchmarks”

!

Helium 3Helium 4

Helium 3Helium 4

Viscosity much more sensitive to microscopics than thermodynamics

Very similar specific heat

Physical Picture of the Physical Picture of the PseudogapPseudogap

..

Due to stronger- than- BCS attraction pairs form at T* and condense at TcTc .

Non-condensed pairs appear below TcTc as pair excitations of the condensate.

Contrast with BCS

Crossover theory

Comparing Comparing Different Analytic Different Analytic

Crossover TheoriesCrossover Theories

Our Starting Point : Simple Our Starting Point : Simple Mean Field Ground StateMean Field Ground State

Why?Why?

This is the simplest ground state. This is the simplest ground state. Basis for Bogoliubov-de Gennes theory.Basis for Bogoliubov-de Gennes theory. Basis for unequal population theoriesBasis for unequal population theories.. No first order transitions.No first order transitions. Superfluid density is well behaved.Superfluid density is well behaved. Basis for Gor’kov theory.Basis for Gor’kov theory.

All Analytic Theories All Analytic Theories address finite temperature: address finite temperature:

via T-matrix scheme via T-matrix scheme Treat pair propagators (t) Treat pair propagators (t)

and particles (G). No higher and particles (G). No higher correlations.correlations.

Solve coupled equations for Solve coupled equations for two propagators: G and t. two propagators: G and t.

Here G depends on which Here G depends on which depends on t. depends on t.

Three different T-matrix Three different T-matrix approachesapproaches

NSR pair susceptibilityNSR pair susceptibility: :

BCS-LeggettBCS-Leggett::

Zwerger Zwerger

Single Particle Properties in Single Particle Properties in BCS-Leggett ApproachBCS-Leggett Approach

The self energyThe self energy::

The spectral function at different The spectral function at different T– showingT– showing

pseudogap effects.pseudogap effects.

Two Particle Properties Two Particle Properties Density and Spin Correlation Density and Spin Correlation

functionsfunctions 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 Comparison of TTc c

in Nozieres Schmitt-Rink scheme in Nozieres Schmitt-Rink scheme and present theory and present theory

Homogeneous Trap

Nozieres Schmitt-Rink

BCS-Leggett

Experiments from M. Ueda et al.

BCS-LeggettNozieres Schmitt-Rink

Comparison of Spectral Comparison of Spectral functions in the Normal functions in the Normal

statestate..

Nozieres Schmitt Rink Scheme:

BCS-Leggett Scheme:

Increasing temperature

BCS-Leggett emphasizes small q pairs. Appropriate nearer condensation.

Nozieres Schmitt Rink emphasizes all-q pairs. Appropriate at high T.

Comparison of Spectral Comparison of Spectral Functions with Drummond Functions with Drummond

GroupGroupBCS-Leggett Scheme:

Drummond (high T) Virial Approximation!

Comparison of Comparison of ThermodynamicsThermodynamics

Nozieres Schmitt-Rink scheme Nozieres Schmitt-Rink scheme (Drummond) and present theory(Drummond) and present theory

Homogeneous

Trap

Nozieres Schmitt-Rink

Trap

Homogeneous Experiments from M. Ueda et al.

Homogeneous Trap– courtesy of R. Hulet

Comparison of Density Profiles Comparison of Density Profiles with Strinati groupwith Strinati group

Strinati group NSR

BCS-Leggett approach

Non-monotonic in temperatureNon-monotonic in temperature

What is the evidence for a What is the evidence for a pseudogap in ultracold pseudogap in ultracold fermionic superfluids?fermionic superfluids?

Non-condensed pairs -> Smooth profiles at unitarityNon-condensed pairs -> Smooth profiles at unitarity

RF Spectroscopy and RF Spectroscopy and Pseudogap EffectsPseudogap Effects

0,0

0,4

0,0

0,4

-20 0 20 40

0,0

0,4

0,0

0,4

(d)

(c)

(a)

frac

tiona

l los

s in

|2>

RF frequency offset (kHz)

(b)

C. Chin et al, Science 305, 1128 (2004).

Temperature scale

set by theory (2006)

..

Above TcAround TcBelow Tc

Momentum Resolved RF and Momentum Resolved RF and Pseudogap EffectsPseudogap Effects

Effects of Pseudogap on Effects of Pseudogap on ViscosityViscosity

Lowers carrier number.Lowers carrier number. Carrier number increases with Carrier number increases with

temperature.temperature. Decreases number of fermions, due to Decreases number of fermions, due to

conversion to pairsconversion to pairs– lowering – lowering viscosityviscosity Homogeneou

s viscosity Experiment

Measure Viscosity in Traps Measure Viscosity in Traps by Breathing mode by Breathing mode

frequency and damping frequency and damping Theory and experiment in traps:

Low viscosity due to pseudogap and to bosonic degrees of freedom = perfect fluids. Analogue in cuprates = bad metals.

Duke Experiments

Tc

..

Schaefer et al argue that phonons dominate the physics.

We argue that phonons don’t contribute to viscosity in fermionic superfluids. Goldstone bosons don’t couple to transverse probes.

Thermodynamical Thermodynamical Controversy on Pseudogap: Controversy on Pseudogap:

Disagree with ENS GroupDisagree with ENS Group

Prescription for seeing the pseudogap: look for spin susceptibility and entropy suppression.

Pressure has T-squared dependence even in a BCS superfluid.

The pseudogap cannot be accessed by low T expts.

Spin Diffusion Controversy Spin Diffusion Controversy On Pseudogap. Disagree On Pseudogap. Disagree

with MIT groupwith MIT group..

If we follow experimental protocol for estimating the spin conductivity, we find (incorrectly) non-pseudogap behavior in spin susceptibility.

Spin diffusion coefficientSpin susceptibility with pgSpin conductivity with pg

Spin susceptibility

Without pg

How to think about Benchmarks when How to think about Benchmarks when there are Qualitative Puzzlesthere are Qualitative Puzzles

Viscosity much more sensitive to microscopics than thermodynamics!

Helium 3

Contrast with very similar Specific heat:

Helium 4

Helium 3Helium 4

Conclusions– We have Conclusions– We have argued since 2003 that argued since 2003 that

The pseudogap appears in cold gases near unitarity.The pseudogap appears in cold gases near unitarity. It is a quasi-particle gap appearing in the spectral It is a quasi-particle gap appearing in the spectral

function (1997)—not associated with spin charge function (1997)—not associated with spin charge separation.separation.

It manifests itself below Tc as non-condensed pair It manifests itself below Tc as non-condensed pair excitations of the condensate.excitations of the condensate.

It should be widely observable experimentally. It should be widely observable experimentally. (Varenna 2006).(Varenna 2006).

We have argued (since 1997) this pseudogap We have argued (since 1997) this pseudogap scenario applies to the cuprates.scenario applies to the cuprates.

Our claims met with enormous resistance from all Our claims met with enormous resistance from all quarters– until recently when everybody claims to quarters– until recently when everybody claims to have discovered the pseudogap!have discovered the pseudogap!

Review PapersReview Papers

1. Physics Reports 412, 1 (2005)- Relation between cuprates and cold gases.

2. Reports in Prog. In Physics 72, 2. Reports in Prog. In Physics 72, 122501(2009). Relation between 122501(2009). Relation between RF and photoemission.RF and photoemission.

Recent Transport PapersRecent Transport Papers1. (2010). ArXiv 1008.0423, ArXiv 1009.4678

2. (2011). ArXiv 1102.44982. (2011). ArXiv 1102.4498