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Experiments With Entangled Photons

Experiments With Entangled Photons

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Experiments With Entangled Photons

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  1. Experiments With Entangled Photons Paulo Henrique Souto Ribeiro Instituto de Física - UFRJ Summer School of Optics Concépcion January/2010

  2. Quantum Optics Group at IF/UFRJ

  3. Group members Experiments: Prof. Paulo Henrique Souto Ribeiro Prof. Stephen Patrick Walborn Theory: Prof. Luiz Davidovich Prof. Nicim Zagury Prof. Ruynet Matos Filho Prof. Fabricio Toscano Msc and PhD students: Adriana Auyuanet Larrieu, Adriano H. de Oliveira Aragão, Bruno de Moura Escher , Bruno Taketani, Daniel Schneider Tasca, Gabriel Horacio Aguilar, Osvaldo Jimenez farias, Gabriela Barreto Lemos, Rafael Chaves.

  4. UFAL UFMG UFF UFRJ USP-SÃO PAULO

  5. Outline:

  6. Part I - Simultaneity in parametric down-conversion - Violation of a classical inequality - Consequences of simultaneity: i) localized one-photon state; ii) the Hong-Ou-Mandel interferometer iii) measurement of the tunneling time

  7. Parametric Down-conversion Espontaneous emission Twin Photons Stimulated emission

  8. Parametric Down-conversion

  9. Observation of simultaneity

  10. Observation of simultaneity

  11. Parametric down-conversion: quantum state Time evolution Time evolution operator Time integral

  12. Simultaneity in parametric down-conversion Quantum state for weak interaction

  13. Simultaneity in parametric down-conversion Quantum state including some approximations

  14. Simultaneity in parametric down-conversion Calculation of expectation values Electric field operator Intensity Coincidence

  15. Simultaneity in parametric down-conversion: very simple view

  16. Simultaneity in parametric down-conversion: very simple view Quantum state: simple version Electric field operator: plane wave, almost monochromatic Coincidence

  17. Simultaneity in parametric down-conversion: very simple view Plane wave pumping field

  18. Coincidence detection

  19. Coincidence detection

  20. Measurement of time delays s=168ps s=185ps

  21. Simultaneity in parametric down-conversion: very simple view + detection filters Plane wave pumping field

  22. Simultaneity in parametric down-conversion: very simple view + detection filters Interference filter: typical Dl = 10nm, Dw = 3.8 x 1013 Hz, Dt = 82 fs << 100ps

  23. Simultaneity in parametric down-conversion: very simple view + timing resolution

  24. Localized one photon state

  25. Localized one photon state

  26. Violation of a classical inequality

  27. Violation of a classical inequality

  28. Hong, Ou and Mandel Interferometer

  29. Hong, Ou and Mandel Interferometer: single mode approach Beam splitter Input-output relations

  30. Hong, Ou and Mandel Interferometer: single mode approach Two-photon input state Beam splitter Coincidence probability

  31. Hong, Ou and Mandel Interferometer

  32. Single-photon tunneling time

  33. Part II - Polarization entanglement - Bell’s inequalities - Entanglement measurement

  34. Polarization entanglement: generation Kwiat et al. PRL 75, 4337 (1995)

  35. Polarization entanglement: generation Kwiat et al. PRA 60, R773 (1999) White et al. PRL 83, 3103 (1999)

  36. Polarization entanglement: generation Kwiat et al. PRA 60, R773 (1999) White et al. PRL 83, 3103 (1999)

  37. Mixed states and entangled states Mixed state Pure entangled state

  38. Detection of entanglement:violation of the Bell inequality

  39. Bell inequality and Bell states Bell-CHSH inequality

  40. Bell inequality and Bell states Bell states for the photon polarization Coincidence rate for f+:

  41. Bell inequality and Bell states Bell states for the photon polarization Coincidence rate for f+:

  42. Bell inequality and Bell states Maximal violation

  43. Bell inequality and Bell states Maximal violation

  44. Bell inequality and Bell states Maximal violation

  45. Bell inequality and entanglement • Violation of a Bell inequality • Detects but does not quantify the • entanglement properly • - Some entangled states do not violate the • Bell inequality • Valid for dichotomic or dichotomized • systems

  46. Quantum state tomography Take a set of measurements : Reconstruction of the density matrix

  47. Quantum state tomography

  48. Quantum state tomography

  49. Quantum state tomography With r12 one can compute all quantities related to the system

  50. Direct measurement of entanglement Concurrency: