2011.8.5 兰州

1. Connecting two important issues in cold atoms--Origin of strong interaction and Existence of itinerant Ferromagnetism 崔晓玲 清华大学高等研究院 2011.8.5 兰州 Collaborator:Tin-Lun Ho(Ohio State University)

2. Strongly interacting Fermi gas (1999-2011) • Strong attraction: highest superfluid Tc～TF Origin? Any way to achieve stronger? • Strong repulsion: itinerant Ferromagnetism Exist or not? Connecting two issues: The answers are both strongly indicated by two-body solutions

3. Part I Narrow Feshbach Resonance--- alternative way to achieve strong interaction Tin-Lun Ho and XL Cui, arxiv: 1105.4627

4. 2nd closed-channel molecule 2: weak coupling  narrow FR 1st closed-channel molecule: strong coupling wide FR Wide vs. Narrow Feshbach resonance Many cold atomic isotopes across both wide and narrow resonance For example, Li-6 s-wave FR: E=0, two atoms in open channel Emergence of bound states:

5. Wide vs. Narrow Feshbach resonance s-wave scattering length: (with E-dependence) narrow wide strong E-dependence weak E-dependence as, r* single as : effective range

6. weak interaction strong interaction (universality) Phase shift (i) wide:

7. Phase shift in narrow resonance: (i) strong k-dependence (ii) pi-shift within Phase shift (ii) narrow:

8. Two-body spectrum free levels 2nd molecule in narrow FR 1st molecule in wide FR

9. Two-body spectrum free levels

10. Interaction effect studied by High-T Virial expansion fugacity: upper branch &lower branch upper: bound state excluded lower: bound stateincluded

11. Interaction effect studied by High-T Virial expansion Comparison between narrow and wide: Narrow Wide anti-symmetric Interaction across wide resonance!

12. Interaction effect studied by High-T Virial expansion Comparison between narrow and wide: Narrow Wide

13. Interaction effect studied by High-T Virial expansion Comparison between narrow and wide: Narrow New features in Narrow FR:(i)interaction effect gained far from resonance(ii) stronger attraction achieved at resonance than in wide FR------ a bran-new class of universality!(iii) strongly asymmetric around resonance

14. Conclusions for Part I • Basic features of narrow resonance • Strong E-dependence of scattering length • Energy scale of resonance width << Fermi energy • Physical consequences • Interaction effect observed far from resonance • New generation of universality at resonance Experiment on Narrow Resonance: easy accessible in experiment: many samples, high-T… preliminary results been achieved in Penn State (K. O’Hara group) and Innsbruck (R. Grimm)

15. Part II Existence of Itinerant Ferromagnetism--- where to look for? 1,2,3D? wide or narrow resonance? XL Cui and Tin-Lun Ho, to be published

16. a. 1933, oldest Stoner theory: (Hartree-Fork approx) Stoner criterion for onset of FM: A long-standing problem : Whether itinerant Ferromagnetism will show up in spin-1/2 fermions due to strong repulsive interaction?

17. Science 325, 1521 (2009) b. 2009, experiment at MIT: Inconsistence: • based on mean-field calculation in a trap, which predict large domain structure • not able to observe any domain

18. c. 2009-now, theoretical studies: Duine and MacDonald, PRL 95 230403. (2005) : 2nd perturbation Zhai, PRA 80, 051605 (R) (2009) Cui and Zhai, PRA 81, 041602(2010): variational approach Pilati et al, PRL 105 030405 (2010 ): QMC Chang et al, PANS 108,51 (2011): QMC Heiselberg, arxiv 1012.4569: Jastrow wf Barth and Zwerger, arxiv: 1101.5594: fermion-boson mapping Zhou, Ceperley and Zhang, arxiv:1103.3534: lattice ED He and Huang, arxiv:1106.1345: diagrammatic approach ……

19. c. 2009-now, theoretical studies: Duine and MacDonald, PRL 95 230403. (2005) : 2nd perturbation Zhai, PRA 80, 051605 (R) (2009) Cui and Zhai, PRA 81, 041602(2010): variational approach Pilati et al, PRL 105 030405 (2010 ): QMC Chang et al, PANS 108,51 (2011): QMC Heiselberg, arxiv 1012.4569: Jastrow wf Barth and Zwerger, arxiv: 1101.5594: fermion-boson mapping Zhou, Ceperley and Zhang, arxiv:1103.3534: lattice ED He and Huang, arxiv:1106.1345: diagrammatic approach …… Supportive! d. INT and DAPAR meeting, Apr-June 2011, MIT announcement : “Absence of Itinerant Ferromagnetism in repulsive Fermi gas” spin susceptibility is measured which never signals the FM transition!!

20. One definite approach to FM: 1D system, g1D<0 side，upper branch! Another possible approach to FM: 2D system, kFa2D>>1 ，upper branch! • Now, though the existence of FM in 3D is still under debate, it seems that nature does NOT prefer FM ! • Then, is there any place for the cold atom community to find Itinerant FM? Yes!

21. Repulsive upper-branch in 1D---BA solution (i) Bose gas: Crossover from Tonks-Girardeau to super-TG regime Astrakharchik et al, PRL. 95, 190407 (2005): DMC M. T. Batchelor et al, J. Stat. Mech. 10, L10001 (2005): BA E. Haller et al., Science 325, 1224 (2009): sTG realized in Innsbruck (ii) Fermi gas: Crossover from Fermionic TG to sTG regime Guan and Chen, PRL 105, 175301(2010): BA Definition of 1D upper-branch from BA: the BAEs also have real solutions for c <0, which, however, correspond to some highly excited states of attractive Fermi systems. The FSTG state corresponds to the lowest real solutions of BAEs with c <0.

22. Repulsive upper-branch in 1D---BA solution Guan and Chen, PRL 105, 175301(2010)

23. Energy of fully polarized Fermi gas! Repulsive upper-branch in 1D---BA solution Guan and Chen, PRL 105, 175301(2010)

24. Repulsive upper-branch in 1D---BA solution lower branch

25. Repulsive upper-branch in 1D---BA solution transition to FM By switching B across quasi-1Dresonance to g<0 side, equal and uniform spin mixtures relax to FM state due to large spin fluctuations, and form domains.

26. Without Bethe Ansatz, any other general approach to predict FM in 1D? Yes!

27. From Hellman-Feynman theorem: E always increases with -1/g1D! Understanding FM transition from Tan’s contact 1D contact: Barth and Zwerger, arxiv: 1101.5594

28. Understanding FM transition from Tan’s contact increased E with -1/g + degenerate energy with FM at g=infty (fermionize) FM emerges right at g=infty, and is favored at g<0 (upper branch)

29. Any other physically-transparent way to judge the existence of FM besides 1D? Yes! from a two-body perspective • qualitative argument • reproduce established results in 1D and 3D • make predictions to many other systems eg: 1D/ 3D narrow resonance, and 2D.

30. Existence of Itinerant Ferromagnetism from the two-body perspective Narrow abg<0,gbg<0 Narrow abg>0,gbg>0 Wide 1D Y Y or N N 3D N N N 2D Y or N

31. Application in 1D (I) wide resonance: Yes identical fermions FM ground state

32. Application in 1D (II) narrow resonance, abg<0:Yes for EF<<B; No otherwise

33. Application in 3D wide resonance: No RHS: lowest bound state turn to scattering state, no s-wave upper-branch any more!

34. Application in 2D Yes for kFa2d>>1 (but easily decay to lower branch) No for kFa2d<<1

35. 3D 2D 1D × √ Existence of FM: maybe remain to be examined by experiment !! Conclusions for Part II • Existence of Itinerant Ferromagnetism from existing studies • 3D No (announced recently by MIT experiment) • 1D Yes (supported by BA solution) • Understanding the result from other method and further predictions • Tan’s adiabatic theorem (using Contact) • Two-body spectrum FM depend on the dimension, resonance width, background interaction, and size of Fermi cloud

36. Thanks for attending!