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Phase separation in optical lattices in spin-dependent external potentials

Explore the effects of spin-dependent potentials and off-diagonal confinement on phase separation in quantum gases. Investigate tunabilities, dimensionality, and disorder in continuous/discrete systems of N~100-1000 atoms. Examine interactions through lasers and Feshbach resonance, and study external potential confinement methods. Analyze components and population imbalance dynamics in the Hubbard model to observe peak densities and disorder effects. Discuss phase diagrams and phase separation induced by external potentials, emphasizing the impact of spin-dependent trapping on interaction effects.

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Phase separation in optical lattices in spin-dependent external potentials

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  1. Phase separation in optical lattices in spin-dependent external potentials 高 先龙 • 合作者：陈阿海 Aug 5, 2010 第四届全国冷原子物理和量子信息青年学者学术讨论会

  2. Outline • Introduction • Motivation: spin-dependent potential • off-diagonal confinement • Some results • Conclusions

  3. Tunabilities in quantum gases Dimensionality Interaction External potential Continuous/discrete systems Disorder Components/population imbalance Static/dynamics

  4. Dimensionality N ~100-1000 atoms thanks to Markus Greiner

  5. Interaction D. Jaksch et al., PRL81, 3108 (98) Indirectly by lasers Directly by Feshbach resonance

  6. External potential d

  7. External potential confinement+interaction new methods demanded

  8. Continuous/discrete systems z potential along z Inhomogeneous 1D Gaudin/Yang model Observed by H. Moritz et al., PRL94, 210401 (2005)

  9. Confinement-induced resonance M. Olshanii, PRL81, 938 (98) G. Xianlong et al., PRA73, 033609 (06)

  10. Continuous/discrete systems t t U t t = Inhomogeneous 1D Hubbard model

  11. To observe the optical peak density: absorption images of expanded clouds

  12. Disorder ei D speckle intensity Billy et al., Nature453, 891(2008) Roati et al., Nature453, 895 (2008)

  13. Components/population imbalance

  14. Components/population imbalance

  15. Static/dynamics Quantum Newton’s cradle Kinoshita, Nature 440, 900 (2006)

  16. Spin-charge separation in 1D GXL et al., PRL(2008); GXL, PRB(2010)

  17. Outline • Introduction • Motivation: spin-dependent potential • off-diagonal confinement • Some results • Conclusions

  18. The Phase Diagram: Hubbard model n=Nf /Ns 2 Band insulator Band insulator Luttinger Liquid 1 Mott insulator Luther-Emery Liquid Luttinger Liquid 0 u=U/t E.H. Lieb and F.Y. Wu, Phys. Rev. Lett. 20, 1445 (1968)

  19. Phases induced by spin-independent external potential U＞０ U<０ See M. Rigol et al., PRL91, 130403 (2003) GXL et al., PRL98, 030404 (2007)

  20. To realize spin-dependent external potential * Potassium 40, DeMarco and Jin, Science 285, 1703(99) * Unequal masses Blume, PRA78, 013613(08) * Spin-dependent optical trap: asymmetrically detuning the laser frequencies with respect to the two hyperfine states Iskin and Williams, PRA77, 013605(08)

  21. Phase Separation induced by external potential

  22. Outline • Introduction • Motivation: spin-dependent potential • off-diagonal confinement • Some results • Conclusions

  23. The effects of interaction on phase separation P=0

  24. 3D Plots for

  25. Contour plot

  26. The effects of spin-dependent trapping on PS P=0 Weak interaction

  27. Strong interaction

  28. 3D Plots for u=5

  29. Contour plot

  30. Phase diagram for P=0

  31. Phase diagram for P=0.5

  32. The effects of trap ratio on Mott phase CAH & GXL, PRA81

  33. Phase diagram for Mott phase

  34. CAH & GXL, PRA81

  35. Phase separation for mass imbalance

  36. Diagonal confinement off-diagonal confinement

  37. Fermi-Hubbard model with ODC

  38. Density distribution with varying N CAH, GXL, in preparation

  39. Chemical potential

  40. Outline • Introduction • Motivation: spin-dependent potential • off-diagonal confinement • Some results • Conclusions

  41. Conclusions: * Fermions can be phase-separated in a spin-dependent external potential by repulsive interaction * Increase the trap imbalance, Mott phase ferromagnetic insulating phase * Critical U exists in the spin-dependent system

  42. Thanks for your attention!

  43. 尖峰山 1300m 470m 欢迎各位访问我校：浙江师范大学

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