Competing instabilities in ultracold Fermi gases

1. David Pekker(Harvard), MehrtashBabadi(Harvard), Lode Pollet(Harvard), RajdeepSensarma(Harvard/JQI Maryland), NikolajZinner(Harvard/Niels Bohr Institute), Antoine Georges (EcolePolytechnique), Eugene Demler(Harvard) Competing instabilities in ultracold Fermi gases Special thanks to W. Ketterle, G.B. Jo, and other members of the MIT group Details in arXiv:1005.2366 Harvard-MIT $$ NSF, AFOSR MURI, DARPA ARO

2. If time permits Superfluidity and Dimerization in a Multilayered System of Fermionic Dipolar Molecules A. Potter, E. Berg, D.W. Wang, B. Halperin, and E. Demler

3. Competing instabilities in strongly correlated electron systems 400 High Tc superconductors Organic materials. Bechgaard salts Heavy fermion materials 300 200 temperature (K) 100 0 doping This talk is also about competition between pairing and magnetism/CDW

4. Outline • Introduction. Stoner instability • Possible observation of Stoner instability in MIT experiments. G.B. Jo et al., Science (2009) • Dynamics of molecule formation near Feshbach resonance • Dynamical crossing of Stoner transition • Comparison of two instabilities • Interplay of Superfluidity and Dimerization in a • multilayered system of fermionic dipolar molecules

5. Stoner instability E. Stoner, Phil. Mag. 15:1018 (1933)

6. U N(0) = 1 Stoner model of ferromagnetism Spontaneous spin polarization decreases interaction energy but increases kinetic energy of electrons Mean-field criterion U – interaction strength N(0) – density of states at Fermi level Kanamori’s counter-argument: renormalization of U. then Theoretical proposals for observing Stoner instability with cold gases: Salasnich et. al. (2000); Sogo, Yabu (2002); Duine, MacDonald (2005); Conduit, Simons (2009); LeBlanck et al. (2009); … • Recent work on hard sphere potentials: Pilati et al. (2010); Chang et al. (2010)

7. Experiments were done dynamically. What are implications of dynamics? Why spin domains could not be observed? Earlier work by C. Salomon et al., 2003

8. Is it sufficient to consider effective model with repulsive interactions when analyzing experiments? Feshbach physics beyond effective repulsive interaction

9. V(x) Feshbach resonance Interactions between atoms are intrinsically attractive Effective repulsion appears due to low energy bound states Example: scattering length V0tunable by the magnetic field Can tune through bound state

10. Feshbach resonance Two particle bound state formed in vacuum Stoner instability BCS instability Molecule formation and condensation This talk: Prepare Fermi state of weakly interacting atoms. Quench to the BEC side of Feshbach resonance. System unstable to both molecule formation and Stoner ferromagnetism. Which instability dominates ?

11. Pair formation

12. Two-particle scattering in vacuum Microscopic Hamiltonian p k -k Schrödinger equation -p

13. T-matrix Lippman-Schwinger equation k k p p k p k p’ -k -p -p’ -p -k -p On-shell T-matrix. Universal low energy expression For positive scattering length bound state at appears as a pole in the T-matrix

14. Cooperon Two particle scattering in the presence of a Fermi sea p k -k Need to make sure that we do not include interaction effects on the Fermi liquid state in scattered state energy -p

15. Cooperon Grand canonical ensemble Define Cooperon equation

16. Cooperonvs T-matrix k k p p k p k p’ -k -p -p’ -p -k -p

17. Cooper channel response function Linear response theory Induced pairing field Response function Poles of the Cooper channel response function are given by

18. Cooper channel response function Linear response theory Poles of the response function, , describe collective modes • Time dependent dynamics When the mode frequency has negative imaginary part, the system is unstable

19. Pairing instability regularized BCS side • Instability rate coincides with the equilibrium gap • (Abrikosov, Gorkov, Dzyaloshinski) Instability to pairing even on the BEC side • Related work: Lamacraft, Marchetti, 2008

20. Pairing instability Intuition: two body collisions do not lead to molecule formation on the BEC side of Feshbach resonance. Energy and momentum conservation laws can not be satisfied. This argument applies in vacuum. Fermi sea prevents formation of real Feshbach molecules by Pauli blocking. Molecule Fermi sea

21. Pairing instability Time dependent variationalwavefunction Time dependence of uk(t) and vk(t) due to DBCS(t) For small DBCS(t):

22. Pairing instability From wide to narrow resonances Effects of finite temperature Three body recombination as in Shlyapnikov et al., 1996; Petrov, 2003; Esry 2005

23. Magnetic instability

24. Stoner instability. Naïve theory Linear response theory Spin response function Spin collective modes are given by the poles of response function Negative imaginary frequencies correspond to magnetic instability

25. RPA analysis for Stoner instability Self-consistent equation on response function Spin susceptibility for non-interacting gas RPA expression for the spin response function

26. Quench dynamics across Stoner instability Stoner criterion For U>Uc unstable collective modes Unstable modes determine characteristic lengthscale of magnetic domains

27. Stoner quench dynamics in D=3 Scaling near transition Growth rate of magnetic domains Unphysical divergence of the instability rate at unitarity Domain size

28. Stoner instability = + + + … Stoner instability is determined by two particle scattering amplitude Divergence in the scattering amplitude arises from bound state formation. Bound state is strongly affected by the Fermi sea. = + + + …

29. Stoner instability RPA spin susceptibility Interaction = Cooperon

30. Stoner instability Pairing instability always dominates over pairing If ferromagnetic domains form, they form at large q

31. Relation to experiments

32. Pairing instability vs experiments

33. Conclusions to part I Competition of pairing and ferromagnetism near Feshbach resonance Dynamics of competing orders is important for understanding experiments Simple model with repulsive interactions may not be sufficient Strong suppression of Stoner instability by Feshbach resonance physics + Pauli blocking Alternative interpretation of experiments based on pair formation

34. Superfluidity and Dimerization in a Multilayered System of Fermionic Dipolar Molecules A. Potter, E. Berg, D.W. Wang, B. Halperin, and E. Demler

35. Ultracold polar molecules - + + Experiments on polar molecules: Innsbruck, Yale, Harvard, UConn,… -

36. Instability of Unstructured Systems

37. Pairing in a multilayer system d Earlier theoretical work on polar molecules in layered systems: Shlyapnikov et al. (2003); Wang et al (2006); Santos et al. (2007); Collathet al. (2008); …

38. Pairing in a multilayer system Dimerization … … paired unpaired unpaired paired … … Interplay of two orders: superfluidity in individual bilayers and dimerization

39. Dimerization at mean-field level z+1 z

40. Effective Lattice Model Lattice Site Physical Layers & L

41. Effective lattice model: Ising degrees of freedom Effective lattice model: XY phase degrees of freedom

42. Lattice model: generic phase diagram Effective Ising/XY Lattice Model: Mean-field

43. Phase diagram If similar for layered system:

44. Light-Scattering Detection Dimerization Order Parameter: … Finite Confinement Strength Transverse Displacement: New Bragg Peaks @: … Correlation Measurements: Correlations:

45. Summary Competition between pairing and ferromagnetic instabilities in ultracold Fermi gases near Feshbach resonances D. Pekker et al., arXiv:1005.2366 Motivated by experiments of Jo et al., Science (2009) Superfluidity and Dimerization in a Multilayered System of Fermionic Dipolar Molecules A. Potter, E. Berg, D.W. Wang, B.I. Halperin, E. Demler Harvard-MIT $$ NSF, AFOSR MURI, DARPA

46. Summary of part II