1 / 44

Two-Photon Fields: Coherence, Interference and Entanglement

Two-Photon Fields: Coherence, Interference and Entanglement. Anand Kumar Jha Indian Institute of Technology, Kanpur QIPA 2103, HRI, Allahabad. Outline. Introduction to one-photon coherence Parametric down-conversion Two-photon interference: Temporal, spatial and angular

emily-jenkins
Télécharger la présentation

Two-Photon Fields: Coherence, Interference and Entanglement

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Two-Photon Fields: Coherence, Interference and Entanglement Anand Kumar Jha Indian Institute of Technology, Kanpur QIPA 2103, HRI, Allahabad

  2. Outline Introduction to one-photon coherence Parametric down-conversion Two-photon interference: Temporal, spatial and angular Two-photon coherence and entanglement

  3. One-Photon Interference: “A photon interferes with itself ” - Dirac Necessary condition for interference: ( when I1= I2=C/2) Mandel and Wolf, Optical Coherence and Quantum Optics

  4. One-Photon Interference: “A photon interferes with itself ” - Dirac Necessary condition for interference: Mandel and Wolf, Optical Coherence and Quantum Optics

  5. Parametric down-conversion Leads to second-order nonlinear optical effects two-photon field

  6. Conservation laws and entanglement Entanglement in time and energy “Temporal” two-photon coherence Entanglement in position and momentum “Spatial” two-photon coherence Entanglement in angular position and orbital angular momentum “Angular” two-photon coherence Coherence length of pump laser:~ 10 cms. Coherence length of signal-idler field:~ c/Dw ~ 100 mm.

  7. Two-Photon Interference • Postponed Compensation Experiment • T. B. Pittman,PRL 77, 1917 (1996) • Hong-Ou-Mandel effect • C. K. Hong et al.,PRL 59, 2044 (1987) • Induced Coherence • X. Y. Zou et al., PRL 67, 318 (1991) • Frustrated two-photon Creation • T. J. Herzog et al.,PRL 72, 629 (1994)

  8. Two-Photon Interference: A two-photon interferes with itself T. J. Herzog et al., PRL 72, 629 (1994)

  9. Two-Photon Interference: A two-photon interferes with itself T. J. Herzog et al., PRL 72, 629 (1994)

  10. Two-Photon Interference: A two-photon interferes with itself two-photon path-length difference Jha, O’Sullivan, Chan, and Boyd et al., PRA 77, 021801(R) (2008)

  11. Two-Photon Interference: A two-photon interferes with itself two-photon path-length difference two-photon path-asymmetry length difference Jha, O’Sullivan, Chan, and Boyd et al., PRA 77, 021801(R) (2008)

  12. Two-Photon Interference: A two-photon interferes with itself two-photon path-length difference two-photon path-asymmetry length difference Jha, O’Sullivan, Chan, and Boyd et al., PRA 77, 021801(R) (2008)

  13. R. J. Glauber, Phys. Rev. 130, 2529 (1963) Two-Photon Interference: A two-photon interferes with itself two-photon path-length difference two-photon path-asymmetry length difference Jha, O’Sullivan, Chan, and Boyd et al., PRA 77, 021801(R) (2008)

  14. Two-Photon Interference: A two-photon interferes with itself two-photon path-length difference two-photon path-asymmetry length difference Necessary conditions for two-photon interference: ( when R1= R2=C/2) Jha, O’Sullivan, Chan, and Boyd et al., PRA 77, 021801(R) (2008)

  15. Two-Photon Interference: A two-photon interferes with itself two-photon path-length difference two-photon path-asymmetry length difference Case I : = 0 • ΔL plays the same role in two-photon interference • as Δl does in one-photon interference

  16. Two-Photon Interference: A two-photon interferes with itself two-photon path-length difference two-photon path-asymmetry length difference Case I : = 0 • ΔL’ has no one-photon analog • The curverepresents how coherence is lost due to an • increase in the two-photon path-length asymmetry difference ΔL’

  17. Hong-Ou-Mandel (HOM) Effect 1 2

  18. Hong-Ou-Mandel (HOM) Effect x 1 2x 2 ΔL = 0 ;ΔL’ = 2x

  19. Postponed Compensation Experiment 2D D 1(t-t) 2 (r-r) D

  20. Postponed Compensation Experiment 2D D 1(t-t) x x 2 (r-r) D ΔL = D ; ΔL’ = 2x

  21. Experimental Verification Jha, O’Sullivan, Chan, and Boyd et al., PRA 77, 021801(R) (2008)

  22. Experimental Verification • Hong-Ou-Mandel effect • C. K. Hong et al.,PRL 59, 2044 (1987) Jha, O’Sullivan, Chan, and Boyd et al., PRA 77, 021801(R) (2008)

  23. Two-photon transverse position vector : Two-photon position-asymmetry vector : Spatial Two-photon Interference (Gaussian Schell- model pump) Coincidence count rate: A. K. Jha and R.W. Boyd, PRA 81, 013828 (2010)

  24. Coherence and entanglement

  25. Laguerre-Gauss basis Angular Fourier Relationship Angular position l=2 l=0 l=1 Barnett and Pegg, PRA 41, 3427 (1990) Franke-Arnold et al., New J. Phys. 6, 103 (2004) Forbes, Alonso, and Siegman J. Phys. A 36, 707 (2003) Allen et al., PRA 45, 8185 (1992)

  26. Angular One-Photon Interference OAM-mode distribution: E. Yao et al., Opt. Express 14, 13089 (2006) A. K. Jha, et al.,PRA 78, 043810 (2008) Jha, Agarwal, and Boyd, PRA84, 063847 (2011)

  27. Angular Two-Photon Interference State of the two photons produced by PDC:

  28. Angular Two-Photon Interference State of the two photons produced by PDC: State of the two photons after the aperture:

  29. Concurrence W. K. Wootters, PRL 80, 2245 (1998) Angular Two-Photon Interference State of the two photons produced by PDC: State of the two photons after the aperture: Coincidence count rate: Visibility:

  30. Concurrence W. K. Wootters, PRL 80, 2245 (1998) Angular Two-Photon Interference State of the two photons produced by PDC: State of the two photons after the aperture: Coincidence count rate: Visibility: Concurrence of the two-qubit state: A. K. Jha et al., PRL 104, 010501 (2010)

  31. Angular Two-Photon Interference State of the two photons produced by PDC: State of the two photons after the aperture: Coincidence count rate: Visibility: Concurrence of the two-qubit state: A. K. Jha et al., PRL 104, 010501 (2010)

  32. Angular Two-Photon Interference State of the two photons produced by PDC: State of the two photons after the aperture: Coincidence count rate: Visibility: Concurrence of the two-qubit state: A. K. Jha et al., PRL 104, 010501 (2010)

  33. Angular Two-Photon Interference Coincidence count rate: Visibility: Concurrence of the two-qubit state: A. K. Jha et al., PRL 104, 010501 (2010)

  34. Angular Two-Photon Interference Coincidence count rate: Visibility: Concurrence of the two-qubit state: Jha, Agarwal, and Boyd, PRA84, 063847 (2011) A. K. Jha et al., PRL 104, 010501 (2010)

  35. Summary • A unified description of two-photon interference effects in terms of two-photon • path length difference (DL) and two-photon path-asymmetry length difference (DL’). • Coherence properties of the source (pump) field get completely transferred to the • down-converted entangled photons. • Does similar transfer occur in other nonlinear optical processes, such as four-wave mixing, that produce entangled photons? (working in collaboration with Dr. SaikatGhosh) • The coherence measure of two-photon fields provide a physically intuitive way • of quantifying two-photon entanglement. • Do the coherence measures of multi-photon field, in general, provide a physically intuitive way of quantifying multi-photon, high-dimensional entanglement?

  36. Acknowledgments • Robert Boyd, University of Rochester, USA • Emil Wolf, University of Rochester, USA • Miles Padgett University of Glasgow, Scotland, UK • Steve Barnett, University of Glasgow, Scotland, UK • Jonathan Leach, Heriott-Watt University, Scotland, UK • Collaborators at IIT Kanpur: Saikat Ghosh, Harshwardhan • Wanare, V Subrahmanyam • Group members: Niharika Singh (postdoc), Umesh Kumar and • Prashant Kumar (undergraduates).

  37. Angular One-Photon Interference

  38. Angular One-Photon Interference

  39. Some One-Photon Interference Effects Jha, O’Sullivan, Chan, and Boyd et al., PRA 77, 021801(R) (2008)

  40. Induced Coherence • X. Y. Zou et al., PRL 67, 318 (1991) Some One-Photon Interference Effects P.W. Milonni et al., PRA 53, 4556 (1996)

  41. Induced Coherence • X. Y. Zou et al., PRL 67, 318 (1991) Set of all possible mutually exclusive events One-photon interference profile at a given detection point is the sum of two-photon interference profiles Some One-Photon Interference Effects P.W. Milonni et al., PRA 53, 4556 (1996)

  42. Induced Coherence • X. Y. Zou et al., PRL 67, 318 (1991) Some One-Photon Interference Effects P.W. Milonni et al., PRA 53, 4556 (1996) • Fringes observed at detector • But only uniform intensity is observed at • detector because of the cancellation • due to out-of-phase fringe patterns: Rsiand Rti Fringes observed at both the detectors

  43. Angular Two-Photon Interference Concurrence of the two-qubit state: Jha, Agarwal, and Boyd, PRA83, 053829 (2011) A. K. Jha et al., PRL 104, 010501 (2010)

  44. Angular Two-Photon Interference Concurrence of the two-qubit state: A. K. Jha et al., PRL 104, 010501 (2010) Jha, Agarwal, and Boyd, PRA83, 053829 (2011)

More Related