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Quantum magnetism of ultracold atoms

Eugene Demler (Harvard) . Quantum magnetism of ultracold atoms. Theory collaborators: Robert Cherng, Adilet Imambekov, Vladimir Gritsev, Takuya Kitagawa, Mikhail Lukin, Susanne Pielawa, Joerg Schmiedmayer Experiments: Bloch et al., Schmiedmayer et al., Stamper-Kurn et al. Harvard-MIT.

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Quantum magnetism of ultracold atoms

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  1. Eugene Demler(Harvard) Quantum magnetism of ultracold atoms Theory collaborators: Robert Cherng, Adilet Imambekov, Vladimir Gritsev, Takuya Kitagawa, Mikhail Lukin, Susanne Pielawa, Joerg Schmiedmayer Experiments: Bloch et al.,Schmiedmayer et al., Stamper-Kurn et al. Harvard-MIT $$ NSF, AFOSR MURI, DARPA

  2. ? Ferromagnetismin itinerant systems Magnetism in condensed matter systems Stoner instability. Double exchange Frustrated magnetic systems Antiferromagnetism

  3. Quantum magnetism of ultracold atoms Familiar models, New questions Spin dynamics in 1d systems Luttinger model and nonequilibrium dynamics. New characterization: full distribution functions Ferromagnetic F=1 spinor condensates Quantum Hall ferromagnets in disguise. Skyrmion crystal phases

  4. Spin dynamics in 1d systems:Ramsey interference experiments arXiv:0912.4643 T. Kitagawa, S. Pielawa, A. Imambekov, J.Schmiedmayer, V. Gritsev, E. Demler

  5. 1 Working with N atoms improves the precision by . t 0 Ramsey interference Atomic clocks and Ramsey interference:

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

  7. Ramsey Interference with 1d BEC 1d systems in microchips 1d systems in optical lattices Two component BEC in microchip • Ramsey interference in 1d tubes: • Widera et al., • PRL 100:140401 (2008) Treutlein et.al, PRL 2004, also Schmiedmayer, Van Druten

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

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

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

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

  12. 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!

  13. Distribution function of fringe contrastas a probe of many-body dynamics Short segments Radius = Amplitude Angle = Phase Long segments

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

  15. Long segments Short segments l =110 mm l =20 mm Expt Theory Data: Schmiedmayer et al., unpublished

  16. Skyrmion crystals in ferromagnetic F=1 spinor condensates R. Cherng, Ph.D. Thesis

  17. Spinor condensates. F=1 Three component order parameter: mF=-1,0,+1 Contact interaction depends on relative spin orientation When g2>0 interaction is antiferromagnetic. Example 23Na Favors condensation into mF=0 state (or its rotation) When g2<0 interaction is ferromagnetic. Example 87Rb Favors condensation into mF=1 state (or its rotation)

  18. Spin textures in ferromagnetic Rb condensates mF=-1 Imbalanced (non-equilibrium) Initial populations mF=-1 Equal (equilibrium) Initial populations mF=0 mF=0 mF=+1 mF=+1 Vengalattore et al., PRL (2008)

  19. Spin textures: checkerboard pattern Equal populations Spectrum in Momentum Space Transverse Longitudinal Vengalattore et al., PRL (2008)

  20. q Magnetic dipolar interactions in spinor condensates Comparison of contact and dipolar interactions. Typical value a=100aB For 87Rb m=mB and e=0.007 Interaction of F=1 atoms Spin dependent interactions in 87Rb are small A. Widera, I. Bloch et al., New J. Phys. 8:152 (2006) a2-a0= -1.07 aB

  21. Energy scales B F High energy scales Precession (115 kHz) • Spin independent S-wave scattering (gsn=215 Hz) Quasi-2D geometry Low energy scales Spin dependent S-wave scattering (gsn=8 Hz) Quadratic Zeeman (1 Hz) Dipolar interaction (gdn = 1 Hz)

  22. Dipolar interactions Fast Larmor precession strongly modifies effective dipolar interactions Fourier components of effective interaction (in-plane field)

  23. Instabilities of ferromagnetic F=1 Rb condensate due to dipolar interactions Theory: unstable modes in the regime corresponding to Berkeley experiments. Cherng, Demler, PRL (2009) Experiments. Vengalattore et al. PRL (2008)

  24. From microscopic Hamiltonian to effective low energy theory Dipolar and quadratic Zeeman Fixed density Maximally polarized • Lamacraft, PRA (2008) Low energy manifold Magnetization Condensate phase Superfluid velocity

  25. Mermin-Ho relation Magnetization Skyrmion density Superfluid velocity Superfluid velocity Divergence flow Mermin-Ho Skyrmion density

  26. Non-linear sigma model Low-energy Lagrangian Superfluid flow related to skyrmion density Superfluid kinetic energy Spin Stiffness Skyrmion interaction (Log)

  27. Magnetic crystals in spinor condensates

  28. Effective Hamiltonian Spin dependent interactions Skyrmion interaction Interaction strengths

  29. Minimal energy spin texture

  30. Find all spin groups consistent with constraints • Intrinsic constraints • Zero net skyrmion charge • Maximally polarized magnetization • Explicit symmetry breaking via external field • D2 point group • SG = p2mm, p2mg, p2gg • Phenomenological constraints • Rectangular lattice • No easy-axis or easy plane • Zero net magnetization

  31. Minimal energy spin texture

  32. Understanding spin textures

  33. Skyrmions in ferromagnets Spin space Real space Radial coordinate Azimuthal coordinate ~ Ordinary ferromagnets. Equations of motion Single skyrmion solution Spinor ferromagnets. Equations of motion

  34. Exact solutions for spinor condensates Spin space Real space Stereographic coordinates Holomorphic coordinates Separation of variables static solution ansatz

  35. Single skyrmion solutions Ordinary ferromagnet Spinor condensate ferromagnet

  36. Lattice of skyrmions Ordinary ferromagnet Spinor condensate ferromagnet

  37. Spin textures: skyrmion lattice Skyrmion lattice solution without dipolar interactions Equal populations Transverse Longitudinal

  38. Spin textures Skyrmion lattice solution with dipolar interactions Equal populations Transverse Longitudinal

  39. Quantum magnetism of ultracold atoms New questions, interesting physics Harvard-MIT Spin dynamics in 1d systems Luttinger model and nonequilibrium dynamics. New characterization: full distribution functions Ferromagnetic F=1 spinor condensates Quantum Hall ferromagnets in disguise. Skyrmion crystal phases

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