1. Rotating FFLO Superfluid in cold atom gases Niigata University, Youichi Yanase Tomohiro Yoshida 2012 Feb 13, GCOE シンポジウム「階層の連結」, Kyoto University

2. Group member (from 2009 Oct.) Tomohiro Yoshida Daisuke Maruyama Shuhei TakamatsuShunsuke Kawabe “Non-centrosymmetric Superconductivity” “Spin triplet Superconductivity” “FFLO Superfluid” Sr 2 RuO 4

3. Introduction to FFLO state

4. Standard theory of Superfluidity/SC J. BardeenL. N. CooperJ. R. Schrieffer Fermions + Attractive interaction BCS Theory (1957) Basic Assumption: Total momentum of Cooper pair is zero. Cooper pairs with q=0

5. Standard theory of Superfluidity/SC J. BardeenL. N. CooperJ. R. Schrieffer Fermions + Attractive interaction BCS Theory (1957) Cooper pairs with q=0 FFLO state Condensate of Cooper pairs with q=0 Theory: Fulde-Ferrell (1964), Larkin-Ovchinnikov (1964)

6.  (r)=  exp(iqx)  (r)=  cos(qx) Fulde-Ferrell stateLarkin-Ovchinnikov state Broken translation symmetryBroken inversion symmetry FFLO Superfluidity/Superconductivity Condesate of Cooper pairs with finite total momentum Under current, Non-centro. SC 3 He thin film, Superconductor Multi-component superconductor

7.  (r)=  exp(iqx)  (r)=  cos(qx) Fulde-Ferrell stateLarkin-Ovchinnikov state Broken translation symmetryBroken inversion symmetry FFLO Superfluidity/Superconductivity Condesate of Cooper pairs with finite total momentum Under current, Non-centro. SC 3 He thin film, Superconductor Multi-component superconductor

8.  (r)=  exp(iqx)  (r)=  cos(qx) Fulde-Ferrell stateLarkin-Ovchinnikov state Broken translation symmetryBroken inversion symmetry FFLO Superfluidity/Superconductivity Condesate of Cooper pairs with finite total momentum Under current, Non-centro. SC 3 He thin film, Superconductor Multi-component superconductor

9. Candidates (1) Superconductors in magnetic field CeCoIn 5, (TMTSF) 2 X ….. (2) Imbalanced cold Fermi gases (3) High density quark matter (Color superconductivity) FFLO Superfluidity/Superconductivity (4) 3 He thin film Theory: Fulde-Ferrell (1964), Larkin-Ovchinnikov (1964) (5) Stripe phase in Cuprates Condesate of Cooper pairs with finite total momentum MIT, Rice, Paris (2006-)

10. Why we couldn’t realize FFLO phase in SC for 40 years ? FFLO phase is suppressed by (2) Orbital pair-breaking effect Low dimension, Heavy effective mass We need a high quality single crystal (3) Fermi liquid correction (F 0 a < 0) (1) Disorder Strongly correlated electron systems Strongly correlated electron systems ???

11. (3) -(BETS) 2 X (4)  -(ET) 2 X (2) (TMTSF) 2 X Matsuda-Shimahara (2007) Radovan et al. (2003) Bianchi et al. (2003) Uji et al. (2006) Lortz et al. (2007) All of these compounds are close to AFQCP Fermi liquid correction, retardation effect, parity mixing … Yanase (2008) (1) CeCoIn 5 Clean and Pauli-limited SC Why we could find the FFLO phase ? Yonezawa et al. (2008)

12. BCS theory Miclea et al. (2006) CeCoIn 5 FFLO superconductivity near AFQCP 2D Hubbard model + ＦＬＥＸ Yanase (2008) Stable FFLO phase Antiferromagnetic QCP

13. FFLO phase in cold Fermi gases Y. Y. PRB (2009) T. Yoshida and Y. Y. PRA (2011)

14. Superfluid in cold atom gases E. A. CornellW. KetterleC. E. Wieman BEC in dilute Bose gas BEC in 87 Rb atoms Reduced temperature Superfluidity in Fermi gas

15. Advantages of cold Fermi gases Cold Fermi gasesSuperconductors T P T H BCS FFLO (2) No orbital pair-breaking effect Pure FFLO state without vortex Discussion with Machida and Mizushima (1) Disorder free (3) Attractive interaction Fermi liquid correction stabilizes FFLO

16. Disadvantage ? : Trap potential Harmonic trap Experiment ： Shin et al. (2006) No translation symmetry !! We cannot distinguish the FFLO state from phase separation Theory: Mizushima et al.

17. Toroidal trap C. Ryu et al. (2007) in NIST No translation symmetry but, rotation symmetry ! Our idea FFLO superfluid phase in the troidal trap

18. Model Lattice model in a trap potential Method BdG (M.F.A.), RSTA (Self-consistent 1-loop) Low density limitContinuum gas Trap potential Harmonic potential Toroidal potential

19. Imbalance: Order parameter Radial-FFLO No symmetry breaking Mean field theory (BdG equation) Rotation symmetry breaking !! Angular-FFLO

20. Local Population imbalance Radial-FFLO Angular-FFLO No symmetry breaking distinguished from phase separation !!

21. Beyond mean field theory (RSTA) RSTA = Real Space Self-consistent T-matrix Approximation = ～ = + Inhomogeneity: Exact fluctuation: 1-loop Mesoscopic fluctuation Thermal fluctuation History (1) Pseudogap in disordered high-Tc cuprates (2006) (2) Superconductor-Insulator transition in Diamond (2008)

22. Phase diagram in RSTA Angular-FFLO state is stable near BCS-BEC crossover !! BCS side near crossover

23. Rotating FFLO phases T. Yoshida and Y. Y. (2011) Spontaneous rotation symmetry breaking Intriguing effect of rotation

24. R Fermi gas Rotating FFLO phase in the toroidal trap One dimensional attractive Hubbard model quasi-1D model in BCS regionBdG equation Rotation Phase shift

25. T-  phase diagram Imbalanced gas (A-FFLO state) Balanced gas (BCS state)

26. Half quantum vortex state Half quantum vortex Half period of Little-Parks oscillation Imbalanced gas (A-FFLO state) Balanced gas (BCS state)

27. Blue line: balanced gas Red line ： imbalanced gas The mass current is half quantized in the A-FFLO superfluid state Half quantized mass current Rotation

28. Summary We can produce and observe the Angular-FFLO state!! Toroidal trap + Feshbach resonance Half quantum vortex state Study in future: (A) Trap geometry (B) Optical lattice (C) Dipole interaction Rotation

29. Summary We can produce and observe the Angular-FFLO state!! Toroidal trap + Feshbach resonance Rotation Thank you very much for your attentions Half quantum vortex state