1. The Nature of the Pseudogap in Ultracold Fermi Gases Univ. of Washington May 2011

2. Pseudogap Discoveries 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. 1992, 95, 97 1997

3. 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. Inverse Penetration Depth Predictions For difference structure factor :

4. Condensed Matter theorists look at broad classes of experiments which may challenge some of the “benchmarks” ! Helium 3 Helium 4 Helium 3Helium 4 Viscosity much more sensitive to microscopics than thermodynamics Very similar specific heat

5. Physical Picture of the Pseudogap Physical Picture of the Pseudogap. Tc Due to stronger- than- BCS attraction pairs form at T* and condense at Tc. Tc Non-condensed pairs appear below Tc as pair excitations of the condensate. Contrast with BCS Crossover theory

6. Comparing Different Analytic Crossover Theories

7. Our Starting Point : Simple Mean Field Ground State Why? This is the simplest ground state. 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.

8. All Analytic Theories address finite temperature: via T-matrix scheme Treat pair propagators (t) and particles (G). No higher correlations. Treat pair propagators (t) and particles (G). No higher correlations. Solve coupled equations for two propagators: G and t. Solve coupled equations for two propagators: G and t. Here G depends on which depends on t. Here G depends on which depends on t.

9. Three different T-matrix approaches Three different T-matrix approaches NSR pair susceptibility: BCS-Leggett: Zwerger

10. Single Particle Properties in BCS-Leggett Approach The self energy : The self energy : The spectral function at different T– showing pseudogap effects.

11. 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!

12. Comparison of T c in Nozieres Schmitt-Rink scheme and present theory in Nozieres Schmitt-Rink scheme and present theory Homogeneous Trap Nozieres Schmitt- Rink BCS-Leggett Experiments from M. Ueda et al. BCS-Leggett Nozieres Schmitt- Rink

13. Comparison of Spectral functions in the Normal state. 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.

14. Comparison of Spectral Functions with Drummond Group BCS-Leggett Scheme : Drummond (high T) Virial Approximation !

15. Comparison of Thermodynamics Nozieres Schmitt-Rink scheme (Drummond) and present theory Nozieres Schmitt-Rink scheme (Drummond) and present theory Homogeneous Trap Nozieres Schmitt-Rink Trap Homogeneous Experiments from M. Ueda et al. Homogeneous Trap– courtesy of R. Hulet

16. Comparison of Density Profiles with Strinati group Strinati group NSR BCS-Leggett approach Non-monotonic in temperature

17. What is the evidence for a pseudogap in ultracold fermionic superfluids? Non-condensed pairs -> Smooth profiles at unitarity

18. RF Spectroscopy and Pseudogap Effects RF Spectroscopy and Pseudogap Effects C. Chin et al, Science 305, 1128 (2004 ). Temperature scale set by theory (2006)

19. . Above Tc Around Tc Below Tc Momentum Resolved RF and Pseudogap Effects

20. Effects of Pseudogap on Viscosity Lowers carrier number. Lowers carrier number. Carrier number increases with temperature. Carrier number increases with temperature. Decreases number of fermions, due to conversion to pairs – lowering viscosity Decreases number of fermions, due to conversion to pairs – lowering viscosity Homogeneous viscosity Experiment

21. Measure Viscosity in Traps by Breathing mode 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

22. . 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.

23. Thermodynamical Controversy on Pseudogap: Disagree 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.

24. Spin Diffusion Controversy On Pseudogap. Disagree with 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

25. How to think about Benchmarks when there are Qualitative Puzzles How to think about Benchmarks when there are Qualitative Puzzles Viscosity much more sensitive to microscopics than thermodynamics! Helium 3 Contrast with very similar Specific heat : Helium 4 Helium 3Helium 4

26. Conclusions– We have 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 function (1997)—not associated with spin charge separation. 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 manifests itself below Tc as non-condensed pair excitations of the condensate. It should be widely observable experimentally. (Varenna 2006). It should be widely observable experimentally. (Varenna 2006). We have argued (since 1997) this pseudogap scenario applies to the cuprates. 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!

27. 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