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Quantum Phase Transition: Superfluid to Insulator

Explore the quantum phase transition from a superfluid to an insulator, with applications in trapped ultracold atoms and cuprate superconductors. This talk discusses Bose-Einstein condensation, the theory of the transition, and experimental tests in cuprates.

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Quantum Phase Transition: Superfluid to Insulator

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  1. The quantum phase transition between a superfluid and an insulator: applications to trapped ultracold atoms and the cuprate superconductors.

  2. The quantum phase transition between a superfluid and an insulator: applications to trapped ultracold atoms and the cuprate superconductors. Leon Balents (UCSB) Lorenz Bartosch (Harvard) Anton Burkov (Harvard) Predrag Nikolic (Harvard) Subir Sachdev (Harvard) Krishnendu Sengupta (HRI, India) Talk online at http://sachdev.physics.harvard.edu

  3. Outline • Bose-Einstein condensation and superfluidity. • The superfluid-insulator quantum phase transition. • The cuprate superconductors, and their proximity to a superfluid-insulator transition. • Landau-Ginzburg-Wilson theory of the superfluid-insulator transition. • Beyond the LGW paradigm: continuous quantum transitions with multiple order parameters. • Experimental tests in the cuprates.

  4. I. Bose-Einstein condensation and superfluidity

  5. Superfluidity/superconductivity occur in: • liquid 4He • metals Hg, Al, Pb, Nb, Nb3Sn….. • liquid 3He • neutron stars • cuprates La2-xSrxCuO4, YBa2Cu3O6+y…. • M3C60 • ultracold trapped atoms • MgB2

  6. The Bose-Einstein condensate: A macroscopic number of bosons occupy the lowest energy quantum state Such a condensate also forms in systems of fermions, where the bosons are Cooper pairs of fermions:

  7. Velocity distribution function of ultracold 87Rb atoms M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman and E. A. Cornell, Science269, 198 (1995)

  8. Excitations of the superfluid: Vortices

  9. Observation of quantized vortices in rotating 4He E.J. Yarmchuk, M.J.V. Gordon, and R.E. Packard, Observation of Stationary Vortex Arrays in Rotating Superfluid Helium, Phys. Rev. Lett. 43, 214 (1979).

  10. Observation of quantized vortices in rotating ultracold Na J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, Observation of Vortex Lattices in Bose-Einstein Condensates, Science 292, 476 (2001).

  11. Quantized fluxoids in YBa2Cu3O6+y J. C. Wynn, D. A. Bonn, B.W. Gardner, Yu-Ju Lin, Ruixing Liang, W. N. Hardy, J. R. Kirtley, and K. A. Moler, Phys. Rev. Lett. 87, 197002 (2001).

  12. Outline • Bose-Einstein condensation and superfluidity. • The superfluid-insulator quantum phase transition. • The cuprate superconductors, and their proximity to a superfluid-insulator transition. • Landau-Ginzburg-Wilson theory of the superfluid-insulator transition. • Beyond the LGW paradigm: continuous quantum transitions with multiple order parameters. • Experimental tests in the cuprates.

  13. II. The superfluid-insulator quantum phase transition

  14. Velocity distribution function of ultracold 87Rb atoms M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman and E. A. Cornell, Science269, 198 (1995)

  15. Apply a periodic potential (standing laser beams) to trapped ultracold bosons (87Rb) M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature415, 39 (2002).

  16. Momentum distribution function of bosons Bragg reflections of condensate at reciprocal lattice vectors M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature415, 39 (2002).

  17. Superfluid-insulator quantum phase transition at T=0 V0=10Er V0=3Er V0=0Er V0=7Er V0=13Er V0=14Er V0=16Er V0=20Er

  18. Bosons at filling fraction f = 1 Weak interactions: superfluidity Strong interactions: Mott insulator which preserves all lattice symmetries M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature415, 39 (2002).

  19. Bosons at filling fraction f= 1 Weak interactions: superfluidity

  20. Bosons at filling fraction f= 1 Weak interactions: superfluidity

  21. Bosons at filling fraction f= 1 Weak interactions: superfluidity

  22. Bosons at filling fraction f= 1 Weak interactions: superfluidity

  23. Bosons at filling fraction f= 1 Strong interactions: insulator

  24. Bosons at filling fraction f= 1/2 Weak interactions: superfluidity

  25. Bosons at filling fraction f= 1/2 Weak interactions: superfluidity

  26. Bosons at filling fraction f= 1/2 Weak interactions: superfluidity

  27. Bosons at filling fraction f= 1/2 Weak interactions: superfluidity

  28. Bosons at filling fraction f= 1/2 Weak interactions: superfluidity

  29. Bosons at filling fraction f= 1/2 Strong interactions: insulator

  30. Bosons at filling fraction f= 1/2 Strong interactions: insulator

  31. Bosons at filling fraction f= 1/2 Strong interactions: insulator Insulator has “density wave” order

  32. Bosons on the square lattice at filling fraction f=1/2 ? Insulator Charge density wave (CDW) order Superfluid Interactions between bosons

  33. Bosons on the square lattice at filling fraction f=1/2 ? Insulator Charge density wave (CDW) order Superfluid Interactions between bosons

  34. Bosons on the square lattice at filling fraction f=1/2 ? Insulator Valence bond solid (VBS) order Superfluid Interactions between bosons N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989).

  35. Bosons on the square lattice at filling fraction f=1/2 ? Insulator Valence bond solid (VBS) order Superfluid Interactions between bosons N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989).

  36. Bosons on the square lattice at filling fraction f=1/2 ? Insulator Valence bond solid (VBS) order Superfluid Interactions between bosons N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989).

  37. Bosons on the square lattice at filling fraction f=1/2 ? Insulator Valence bond solid (VBS) order Superfluid Interactions between bosons N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989).

  38. Bosons on the square lattice at filling fraction f=1/2 ? Insulator Valence bond solid (VBS) order Superfluid Interactions between bosons N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989).

  39. Bosons on the square lattice at filling fraction f=1/2 ? Insulator Valence bond solid (VBS) order Superfluid Interactions between bosons N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989).

  40. Bosons on the square lattice at filling fraction f=1/2 ? Insulator Valence bond solid (VBS) order Superfluid Interactions between bosons N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989).

  41. Bosons on the square lattice at filling fraction f=1/2 ? Insulator Valence bond solid (VBS) order Superfluid Interactions between bosons N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989).

  42. Bosons on the square lattice at filling fraction f=1/2 ? Insulator Valence bond solid (VBS) order Superfluid Interactions between bosons N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989).

  43. Outline • Bose-Einstein condensation and superfluidity. • The superfluid-insulator quantum phase transition. • The cuprate superconductors, and their proximity to a superfluid-insulator transition. • Landau-Ginzburg-Wilson theory of the superfluid-insulator transition. • Beyond the LGW paradigm: continuous quantum transitions with multiple order parameters. • Experimental tests in the cuprates.

  44. III. The cuprate superconductors and their proximity to a superfluid-insulator transition

  45. La2CuO4 La O Cu

  46. La2CuO4 Mott insulator: square lattice antiferromagnet

  47. La2-dSrdCuO4 Superfluid: condensate of paired holes

  48. The cuprate superconductor Ca2-xNaxCuO2Cl2 T. Hanaguri, C. Lupien, Y. Kohsaka, D.-H. Lee, M. Azuma, M. Takano, H. Takagi, and J. C. Davis, Nature430, 1001 (2004).

  49. The cuprate superconductor Ca2-xNaxCuO2Cl2 Evidence that holes can form an insulating state with period  4 modulation in the density T. Hanaguri, C. Lupien, Y. Kohsaka, D.-H. Lee, M. Azuma, M. Takano, H. Takagi, and J. C. Davis, Nature430, 1001 (2004).

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