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Strongly correlated phenomena in cavity QED

Fernando G.S.L. Brand ão 1,2 Michael J. Hartmann 1,2 Martin B. Plenio 1,2 1 Institute for Mathematical Sciences, Imperial College London 2 QOLS, Blackett Laboratory, Imperial College London. Strongly correlated phenomena in cavity QED.

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Strongly correlated phenomena in cavity QED

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  1. Fernando G.S.L. Brandão1,2 Michael J. Hartmann1,2 Martin B. Plenio1,2 1Institute for Mathematical Sciences, Imperial College London 2QOLS, Blackett Laboratory, Imperial College London Strongly correlated phenomena in cavity QED London, 04/05/2007

  2. Non-trivial joint dynamics for atoms and photons Cavity QED systems Strong Coupling:

  3. Atoms in different cavities can “talk” to each other mediated by the photons Photons in the same cavity can “talk” to each other mediated by the atoms Array of coupled cavities

  4. Summary • Photon nonlinearities EIT-based schemes Stark-shift based scheme • Bose-Hubbard models Polaritons in coupled array of cavities The photonic limit • Spin Chains Heisenberg model (XYZ)

  5. Summary • Photon nonlinearities EIT-based schemes Stark-shift based scheme • Bose-Hubbard models Polaritons in coupled array of cavities The photonic limit • Spin Chains Heisenberg model (XYZ)

  6. Kerr-type nonlinear interaction: Several applications Photon blockade Imamoğlu et at, PRL 79, 1467 (1997) nonlinear optics Boyd, Nonlinear Optics, (1992) Quantum nondemolition measurents Imoto et al , PRA 32, 2287 (1985) Optical quantum computing Turchette et al, PRL 75, 4710 (1995) etc… Photon-Photon interactions

  7. Photon-Photon interactions Natural Kerr interactions are far too small… • Kerr-type nonlinear interaction:

  8. Electromagnetically Induced Transparency nonlinearities 4 D 3 d h w g W w Imamoğlu et at, PRL 79, 1467 (1997) 2 1

  9. Electromagnetically Induced Transparency nonlinearities 3 d N x W g 2 1

  10. Electromagnetically Induced Transparency nonlinearities 3 d N x W g 2 1

  11. Electromagnetically Induced Transparency nonlinearities 3 d N x W g 2 1

  12. Electromagnetically Induced Transparency nonlinearities 4 D 3 d h W g 2 1

  13. Electromagnetically Induced Transparency nonlinearities 4 D 3 d Only dark state polaritons p0 couple to level 4! h W g 2 1

  14. Electromagnetically Induced Transparency nonlinearities 4 D 3 d h W g 2 1

  15. Electromagnetically Induced Transparency nonlinearities 4 D 3 d h W g 2 1

  16. Electromagnetically Induced Transparency nonlinearities We didn’t assume: 4 D 3 D >> d h h W g 2 1

  17. Example: Toroidal Microcavities Electromagnetically Induced Transparency nonlinearities Spillane et al, PRA 71, 013817 (2005) Aoki et al, Nature 443 671 (2006)

  18. Example: Toroidal Microcavities Electromagnetically Induced Transparency nonlinearities Spillane et al, PRA 71, 013817 (2005) Aoki et al, Nature 443 671 (2006)

  19. Could we find a simpler set-up producing a nonlinearity comparable with the EIT one?

  20. A.C. Stark shift nonlinearity 3 D1 D2 g L L 2 1

  21. A.C. Stark shift nonlinearity Dispersive regime: 3 D1 D2 g L L 2 1

  22. A.C. Stark shift nonlinearity

  23. Dispersive regime: A.C. Stark shift nonlinearity

  24. Dispersive regime: A.C. Stark shift nonlinearity

  25. A.C. Stark shift nonlinearity • Same strength as EIT scheme • - One level less

  26. Summary • Photon nonlinearities EIT-based schemes Stark-shift based scheme • Bose-Hubbard model Polaritons in coupled array of cavities The photonic limit • Spin Chains Heisenberg model (XYZ)

  27. Bose Hubbard Model Fisher et al, PRB 40, 546 (1989)

  28. Cold atoms in Optical Lattices Jaksch et al, PRL 81, 3108 (1998) Greiner et al, Nature 415, 39 (2002)

  29. Cold atoms in Optical Lattices Jaksch et al, PRL 81, 3108 (1998) Greiner et al, Nature 415, 39 (2002)

  30. The set-up

  31. The set-up Photons can hope from one cavity to a neighbouring one Yariv et al, Optics Lett. 24, 711 (1999)

  32. The polaritonic case 4 D 3 d h W g 2 1

  33. The polaritonic case 4 D 3 d h W g 2 1

  34. The polaritonic case

  35. The polaritonic case

  36. The polaritonic case

  37. real pred. Fabry-Perot: 160 5 x 103 Photonic bgc: 10 5.5 x 105 MCs @ Imperial: 40 ? Micro-toroid: 53 5 x 106 Spillane et al, PRA 2005 Soda et al, Nature Materials 2005

  38. The polaritonic case

  39. The photonic case a.c. Stark shift nonlinearity EIT nonlinearity

  40. The photonic case

  41. real pred. Fabry-Perot: 2.6 10 Photonic bgc: 0.1 4 x 103 MCs @ Imperial: 0.8 ? Micro-toroid: 2.6 1.25 x 105 Spillane et al, PRA 2005 Soda et al, Nature Materials 2005

  42. Summary • Photon nonlinearities EIT-based schemes Stark-shift based scheme • Photonic Bose-Hubbard models Polaritons in coupled array of cavities The photonic limit • Spin Chains Heisenberg model (XYZ)

  43. Spins Lattices Open questions in condensed-matter physics: high Tc superconductivity, frustration, etc… Applications in quantum information science: entanglement propagation, measurement-based quantum computation, etc…

  44. Spins Lattices: Heisenberg (XYZ) model

  45. Spins Lattices: Heisenberg (XYZ) model XX and YY interactions:

  46. Spins Lattices: Heisenberg (XYZ) model XX and YY interactions:

  47. Spins Lattices: Heisenberg (XYZ) model XX and YY interactions:

  48. Spins Lattices: Heisenberg (XYZ) model ZZ interactions + magnetic field:

  49. Spins Lattices: Heisenberg (XYZ) model Suzuki-Trotter Decomposition: +

  50. Cluster state generation

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