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Eugene Demler Harvard University

Simulations of strongly correlated electron systems using cold atoms. Main collaborators: Anatoli Polkovnikov Harvard/Boston University Ehud Altman Harvard/Weizmann Daw-Wei Wang Harvard/Tsing-Hua University Vladimir Gritsev Harvard Adilet Imambekov Harvard

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Eugene Demler Harvard University

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  1. Simulations of strongly correlated electron systems using cold atoms Main collaborators: Anatoli PolkovnikovHarvard/Boston University Ehud AltmanHarvard/Weizmann Daw-Wei Wang Harvard/Tsing-Hua University Vladimir GritsevHarvard Adilet Imambekov Harvard Ryan Barnett Harvard/Caltech Mikhail LukinHarvard Eugene Demler Harvard University

  2. Strongly correlated electron systems

  3. “Conventional” solid state materials Bloch theorem for non-interacting electrons in a periodic potential

  4. EF Consequences of the Bloch theorem B VH d Metals I Insulators and Semiconductors EF First semiconductor transistor

  5. “Conventional” solid state materials Electron-phonon and electron-electron interactions are irrelevant at low temperatures ky kx Landau Fermi liquid theory: when frequency and temperature are smaller than EF electron systems are equivalent to systems of non-interacting fermions kF Ag Ag Ag

  6. Non Fermi liquid behavior in novel quantum materials Violation of the Wiedemann-Franz law in high Tc superconductors Hill et al., Nature 414:711 (2001) UCu3.5Pd1.5 Andraka, Stewart, PRB 47:3208 (93) CeCu2Si2. Steglich et al., Z. Phys. B 103:235 (1997)

  7. Puzzles of high temperature superconductors Unusual “normal” state Maple, JMMM 177:18 (1998) Resistivity, opical conductivity, Lack of sharply defined quasiparticles, Nernst effect Mechanism of Superconductivity High transition temperature, retardation effect, isotope effect, role of elecron-electron and electron-phonon interactions Competing orders Role of magnetsim, stripes, possible fractionalization

  8. Applications of quantum materials:High Tc superconductors

  9. Applications of quantum materials: Ferroelectric RAM + + + + + + + + V _ _ _ _ _ _ _ _ FeRAM in Smart Cards Non-Volatile Memory HighSpeed Processing

  10. Modeling strongly correlated systems using cold atoms

  11. Bose-Einstein condensation Cornell et al., Science 269, 198 (1995) Ultralow density condensed matter system Interactions are weak and can be described theoretically from first principles

  12. Feshbach resonances • Rotating systems • Low dimensional systems • Atoms in optical lattices • Systems with long range dipolar interactions New Era in Cold Atoms Research Focus on Systems with Strong Interactions

  13. Feshbach resonance and fermionic condensates Greiner et al., Nature 426:537 (2003); Ketterle et al., PRL 91:250401 (2003) Ketterle et al., Nature 435, 1047-1051 (2005)

  14. One dimensional systems 1D confinement in optical potential Weiss et al., Science (05); Bloch et al., Esslinger et al., One dimensional systems in microtraps. Thywissen et al., Eur. J. Phys. D. (99); Hansel et al., Nature (01); Folman et al., Adv. At. Mol. Opt. Phys. (02) Strongly interacting regime can be reached for low densities

  15. Atoms in optical lattices Theory: Jaksch et al. PRL (1998) Experiment: Kasevich et al., Science (2001); Greiner et al., Nature (2001); Phillips et al., J. Physics B (2002) Esslinger et al., PRL (2004); and many more …

  16. Atoms in optical lattices Electrons in Solids Strongly correlated systems Simple metals Perturbation theory in Coulomb interaction applies. Band structure methods wotk Strongly Correlated Electron Systems Band structure methods fail. Novel phenomena in strongly correlated electron systems: Quantum magnetism, phase separation, unconventional superconductivity, high temperature superconductivity, fractionalization of electrons …

  17. New Era in Cold Atoms Research Focus on Systems with Strong Interactions Goals • Resolve long standing questions in condensed matter physics • (e.g. origin of high temperature superconductivity) • Resolve matter of principle questions • (e.g. existence of spin liquids in two and three dimensions) • Study new phenomena in strongly correlated systems • (e.g. coherent far from equilibrium dynamics)

  18. Outline • Introduction. Cold atoms in optical lattices. Bose Hubbard model • Two component Bose mixtures Quantum magnetism. Competing orders. Fractionalized phases • Fermions in optical lattices Pairing in systems with repulsive interactions. High Tc mechanism • Boson-Fermion mixtures Polarons. Competing orders • Interference experiments with fluctuating BEC Analysis of correlations beyond mean-field • Moving condensates in optical lattices Non equilibrium dynamics of interacting many-body systems Emphasis: detection and characterzation of many-body states

  19. Atoms in optical lattices. Bose Hubbard model

  20. U t Bose Hubbard model tunneling of atoms between neighboring wells repulsion of atoms sitting in the same well

  21. Bose Hubbard model. Mean-field phase diagram M.P.A. Fisher et al., PRB40:546 (1989) N=3 Mott 4 Superfluid N=2 Mott 0 2 N=1 Mott 0 Superfluid phase Weak interactions Mott insulator phase Strong interactions

  22. Bose Hubbard model Set . Hamiltonian eigenstates are Fock states 2 4

  23. Bose Hubbard Model. Mean-field phase diagram N=3 Mott 4 Superfluid N=2 Mott 2 N=1 Mott 0 Mott insulator phase Particle-hole excitation Tips of the Mott lobes

  24. Normalization Interaction energy Kinetic energy z – number of nearest neighbors Gutzwiller variational wavefunction

  25. Phase diagram of the 1D Bose Hubbard model. Quantum Monte-Carlo study Batrouni and Scaletter, PRB 46:9051 (1992)

  26. Optical lattice and parabolic potential N=3 4 N=2 MI SF 2 N=1 MI 0 Jaksch et al., PRL 81:3108 (1998)

  27. Mott insulator Superfluid t/U Superfluid to Insulator transition Greiner et al., Nature 415:39 (2002)

  28. Time of flight experiments Quantum noise interferometry of atoms in an optical lattice Second order coherence

  29. Second order coherence in the insulating state of bosons.Hanburry-Brown-Twiss experiment Theory: Altman et al., PRA 70:13603 (2004) Experiment: Folling et al., Nature 434:481 (2005)

  30. Hanburry-Brown-Twiss stellarinterferometer

  31. Hanburry-Brown-Twissinterferometer

  32. Bosons at quasimomentum expand as plane waves with wavevectors Second order coherence in the insulating state of bosons First order coherence: Oscillations in density disappear after summing over Second order coherence: Correlation function acquires oscillations at reciprocal lattice vectors

  33. Second order coherence in the insulating state of bosons.Hanburry-Brown-Twiss experiment Theory: Altman et al., PRA 70:13603 (2004) Experiment: Folling et al., Nature 434:481 (2005)

  34. Effect of parabolic potential on the second order coherence Experiment: Spielman, Porto, et al., Theory: Scarola, Das Sarma, Demler, cond-mat/0602319 Width of the correlation peak changes across the transition, reflecting the evolution of Mott domains

  35. Width of the noise peaks

  36. Interference of an array of independent condensates Hadzibabic et al., PRL 93:180403 (2004) Smooth structure is a result of finite experimental resolution (filtering)

  37. - on site repulsion - nearest neighbor repulsion Extended Hubbard Model Checkerboard phase: Crystal phase of bosons. Breaks translational symmetry

  38. Extended Hubbard model. Mean field phase diagram van Otterlo et al., PRB 52:16176 (1995) Hard core bosons. Supersolid – superfluid phase with broken translational symmetry

  39. Extended Hubbard model. Quantum Monte Carlo study Hebert et al., PRB 65:14513 (2002) Sengupta et al., PRL 94:207202 (2005)

  40. Dipolar bosons in optical lattices Goral et al., PRL88:170406 (2002)

  41. How to detect a checkerboard phase Correlation Function Measurements

  42. Magnetism in condensed matter systems

  43. Ferromagnetism Magnetic needle in a compass Magnetic memory in hard drives. Storage density of hundreds of billions bits per square inch.

  44. I N(0) = 1 Stoner model of ferromagnetism Spontaneous spin polarization decreases interaction energy but increases kinetic energy of electrons Mean-field criterion I – interaction strength N(0) – density of states at the Fermi level

  45. Antiferromagnetism Maple, JMMM 177:18 (1998) High temperature superconductivity in cuprates is always found near an antiferromagnetic insulating state

  46. = S S AF AF = ( + ) ( - ) t t = Antiferromagnetism Antiferromagnetic Heisenberg model = ( + ) Antiferromagnetic state breaks spin symmetry. It does not have a well defined spin

  47. ? Spin liquid states Alternative to classical antiferromagnetic state: spin liquid states Properties of spin liquid states: • fractionalized excitations • topological order • gauge theory description Systems with geometric frustration

  48. Spin liquid behavior in systems with geometric frustration Kagome lattice Pyrochlore lattice SrCr9-xGa3+xO19 ZnCr2O4 A2Ti2O7 Ramirez et al. PRL (90) Broholm et al. PRL (90) Uemura et al. PRL (94) Ramirez et al. PRL (02)

  49. Engineering magnetic systems using cold atoms in an optical lattice

  50. Spin interactions using controlled collisions Experiment: Mandel et al., Nature 425:937(2003) Theory: Jaksch et al., PRL 82:1975 (1999)

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