1. Quantum and Classical Coincidence Imaging and Interference
Shiyao Zhu and Yangjian Cai
Physics Department
Hong Kong Baptist University

2. 1. Ghost Imaging and Interference with Entangled Photon Pairs
2. Ghost Imaging and Interference with Laser beam --- Coherent Gaussian Beam
(Classically Correlated Light)
3. Ghost Image with Blackbody Radiation
4.Comparison and Conclusion

3. 1. Ghost Imaging and Interference with entangled photon pairs

4. Y. H. Shih，Phys. Rev. Lett. 74, 3600 (1995)
Ghost Imaging and Interference
with entangled photon pairs
Y. H. Shih，Phys. Rev. Lett. 74, (1995)

6. hs(i) are the response functions of the signal and idler paths
For a thin planar crystal under quasi-monochromatic conditions, the biphoton state is written as:
The positive-frequency portions of the signal and idler electric field are expressed as:
hs(i) are the response functions of the signal and idler paths
B.E.A.Saleh, Physics Review A,043816, 2000
Y. H. Shih，Phys. Rev. Lett. 74, (1995)

7. The fourth-order correlation function
are the response functions of the signal and idler (the first and second) paths.

8. Y. H. Shih et al，Phys. Rev. A 52, R3429 (1995)z
Y. H. Shih et al，Phys. Rev. A 52, R3429 (1995)

10. What is the Ghost Image?
The object in one path, while the image in another path in coincident counting.
2. The position and magnification of the image determined by both paths.

11. 2. Ghost Imaging and Interference with Classically correlated light (Coherent Gaussian Beam) Laser beam

12. Ghost Imaging and Interference with classically correlated light
Phys. Rev. Lett. 89, (2002)

13. Boyd et al. PRL 92, 033601 (2004) No image equation

14. Phys. Rev. Lett. 92, (2004).
Did not give the fringe equation

15. The angle between two peaks:

16. Experimental observation of ghost imaging with thermal light
A.Valencia, G. Scarcelli, M D’Angelo and Y. Shih, quant-ph/ v1 30 Jul 2004

17. The Double Slits

18. Assume
where N is the number of distinct features in the object plane. In experiment, detector one is point-like detector
and is fixed at x1=0, the visibility for a single slit is about 26%, for a double slit is about 12%

19. D. Magatti, F. Ferri, A. Gatti, M. Bache, E. Brambilla, and L. A
D. Magatti, F. Ferri, A. Gatti, M. Bache, E. Brambilla, and L.A. Lugiato, quant-ph/ , 3 Aug 2004

22. Detector 1 is a bucket detector,

23. Analytical Derivation for the Ghost Imaging and Interference with Coherent Gaussian Beams

24. Ghost image with coherent Gaussian beam

25. In the input plane

27. Point by point projection

28. A point-to-point image. Is it a real Ghost Imaging?

31. Small waist width: Small spots on the object and on the detector 2.
For large waist width, the spots can become small through focusing.

32. Different amplification factor

33. Ghost interference with coherent Gaussian beam

34. at
For we have

36. For all angles we have
This gives the interference fringes.

38. The angle between two peaks:

39. For small
By refocusing
Clear fringes can be obtained

40. z2 varies from satisfy to not satisfy image condition

41. Comparison Difference: Similarity:
Ghost image and interference can be generated with entangled photon pairs and coherent Gaussian beams both with high visibility and good quality.
Difference:

42. Image The Function of Lens Quantum case: Imaging Coherent case: Focusing (both paths)
Interference
Quantum case: No Lens needed.
Classical Case: Lens needs for focusing.

43. Equation for image formation:
Coherent Gaussian beams: basically determined by
path one where the object is. First order-correlation
Entangled photon pairs: both paths. Second order
(b) Correlation:
Coherent Gaussian beams: Probability correlation, (intensity-intensity (particle-particle) correlation).
Entangled photon pairs: Probability amplitude correlation (electric field amplitude correlation).

44. Can classical light produce a real ghost image?
In above, we see that classical coherent field could not form the real ghost image.
Can classical light produce a real ghost image?
YES, Blackbody Radiation

45. Can it produce a real ghost image?
3. Blackbody Radiation
Blackbody Radiation is also a Classical source.
Can it produce a real ghost image?
YES.

46. The Ghost image and Interference with Blackbody Radiation

47. Ghost Interference with blackbody radiation

48. Y. H. Shih，Phys. Rev. Lett. 74, 3600 (1995)
Ghost Imaging and Interference
with entangled photon pairs
Y. H. Shih，Phys. Rev. Lett. 74, (1995)

49. Sufficient Large

50. Ghost Image with Blackbody Radiation

51. Ghost Image with Blackbody Radiation

52. Y. H. Shih et al，Phys. Rev. A 52, R3429 (1995)z
Y. H. Shih et al，Phys. Rev. A 52, R3429 (1995)

53. For sufficient high temperature T in one-dimension
High temperature, small

54. Fourth-order correlation function

55. The image at different positions

56. Image for different surface sizes

57. (a)
(b)
(c)
with

58. Quality and visibility of image
(a) (b) with

59. Difference Interference entangled photon blackbody radiation Image
Visibility Entangled photon pairs (high) Blackbody radiation (low)

60. Wave function of entangled photon pares
Comparison between entangled photon pairs and blackbody
Wave function of entangled photon pares
Fourth order correlation
Blackbody radiation
Fourth order correlation

61. Conclusion
Ghost image and interference can be generated with blackbody radiation.
Difference between Ghost image with entangled photons and blackbody radiation:
(a) Equation for imaging: -z1 replaced with z1,
(b) Low visibility for blackbody radiation.
The quality and visibility of the image with blackbody radiation is determined by the surface size and temperature (correlation length) of the blackbody.