1. Many-body quench dynamics in ultracold atoms Surprising applications to recent experiments $$ NSF, AFOSR MURI, DARPA Harvard-MIT Eugene Demler (Harvard)

2. Outline Competition between pairing and ferromagnetic instabilities in ultracold Fermi gases near Feshbach resonances Motivated by experiments, Jo et al., Science (2009) Ramsey interference experiments in 1d Probing many-body decoherence with quantum noise Motivated by experiments Widera et al., PRL (2008) Hofferberth et al., Nature (2007) + unpublished Vienna experiments

3. Competition between pairing and ferromagnetic instabilities in ultracold Fermi gases near Feshbach resonances arXiv:1005.2366 D. Pekker, M. Babadi, R. Sensarma, N. Zinner, L. Pollet, M. Zwierlein, E. Demler

4. Stoner model of ferromagnetism Spontaneous spin polarization decreases interaction energy but increases kinetic energy of electrons Mean-field criterion U N(0) = 1 U – interaction strength N(0) – density of states at Fermi level Theoretical proposals for observing Stoner instability with ultracold Fermi gases: Salasnich et. al. (2000); Sogo, Yabu (2002); Duine, MacDonald (2005); Conduit, Simons (2009); LeBlanck et al. (2009); … Existence of Stoner type ferromagnetism in a single band model is still a subject of debate

5. Experiments were done dynamically. What are implications of dynamics? Why spin domains could not be observed?

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

7. Feshbach resonance Interactions between atoms are intrinsically attractive Effective repulsion appears due to low energy bound states Example: scattering length V(x) V 0 tunable by the magnetic field Can tune through bound state

8. Feshbach resonance Two particle bound state formed in vacuum BCS instability Stoner 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 ?

9. Many-body instabilities Imaginary frequencies of collective modes Magnetic Stoner instability Pairing instability =+++ …

10. Many body instabilities near Feshbach resonance: naïve picture Pairing (BCS) Stoner (BEC) EF=EF= Pairing (BCS)Stoner (BEC)

11. Pairing instability regularized bubble is UV divergent To keep answers finite, we must tune together: upper momentum cut-off interaction strength U Instability to pairing even on the BEC side Change from bare interaction to the scattering length

12. 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

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

14. Stoner instability RPA spin susceptibility Interaction = Cooperon

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

16. Pairing instability vs experiments

17. Conclusions to part I Competition of pairing and ferromagnetism near Feshbach resonance Dynamics of competing orders is important for understanding experiments Simple model with contact 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

18. Ramsey interference in one dimensional systems: The full distribution function of fringe contrast as a probe of many-body dynamics T. Kitagawa, S. Pielawa, A. Imambekov, J.Schmiedmayer, V. Gritsev, E. Demler arXiv:0912.4643

19. Working with N atoms improves the precision by. Ramsey interference t 0 1 Atomic clocks and Ramsey interference:

20. Ramsey Interference with BEC Single mode approximation time Amplitude of Ramsey fringes Interactions should lead to collapse and revival of Ramsey fringes

21. 1d systems in microchips Treutlein et.al, PRL 2004 Two component BEC in microchip Ramsey Interference with 1d BEC 1d systems in optical lattices Ramsey interference in 1d tubes: A.Widera et al., B. PRL 100:140401 (2008)

22. Ramsey interference in 1d condensates Collapse but no revivals A. Widera, et al, PRL 2008

23. Ramsey interference in 1d condensates A. Widera, et al, PRL 2008 Only partial revival after spin echo! Spin echo experiments Expect full revival of fringes

24. Spin echo experiments in 1d tubes Single mode approximation does not apply. Need to analyze the full model

25. Ramsey interference in 1d Time evolution Technical noise could also lead to the absence of echo Need “smoking gun” signatures of many-body decoherece Luttinger liquid provides good agreement with experiments. A. Widera et al., PRL 2008. Theory: V. Gritsev

26. Distribution Probing spin dynamics using distribution functions Distribution contains information about all the moments → It can probe the system Hamiltonian Joint distribution function can also be obtained!

27. Distribution function of fringe contrast as a probe of many-body dynamics Short segments Long segments Radius = Amplitude Angle = Phase

28. Distribution function of fringe contrast as a probe of many-body dynamics Preliminary results by J. Schmiedmayer’s group Splitting one condensate into two.

29. Short segments Long segments l =20 mm l =110 mm ExptTheory Data: Schmiedmayer et al., unpublished

30. Summary of Part II Suggested unique signatures of the multimode decoherence of Ramsey fringes in 1d Ramsey interferometer combined with study of distribution function is a useful tool to probe many-body dynamics Harvard-MIT