The Nature of the Pseudogap in Ultracold Fermi Gases

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

2. Pseudogap Discoveries 1992, 95, 97 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. 1997

3. Message to the skeptics: The Role for Analytic Many Body Theories in Cold Atom Field They connect different experiments, provide simple intuition and predictions. They are more appropriate for the big picture than for precision studies. When done correctly, they do not involve inaccessible numerics, andrespect conservation laws. Predictions For difference structure factor: Inverse Penetration Depth

4. 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 3 Helium 4 ! Helium 4 Helium 3

5. 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.

6. Comparing Different Analytic Crossover Theories

7. 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.

8. 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.

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

10. Single Particle Properties in BCS-Leggett Approach • 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 Tc • in Nozieres Schmitt-Rink scheme and present theory Homogeneous Trap BCS-Leggett Nozieres Schmitt-Rink BCS-Leggett Nozieres Schmitt-Rink Experiments from M. Ueda et al.

13. 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.

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

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

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 ultracoldfermionicsuperfluids? Non-condensed pairs -> Smooth profiles at unitarity

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

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

20. 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

21. 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.

22. 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.

23. Thermodynamical Controversy on Pseudogap: Disagree with ENS Group Pressure has T-squared 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.

24. Spin Diffusion Controversy On Pseudogap. Disagree with MIT group . Spin conductivity with pg Spin susceptibility with pg Spin diffusion coefficient Spin susceptibility Without pg If we follow experimental protocol for estimating the spin conductivity, we find (incorrectly) non-pseudogap behavior in spin susceptibility.

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

26. 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!

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