1. Quantum Imaging MURI Kick-Off Meeting Rochester, June 9-10, 2005 - Entangled state and thermal light - Foundamental and applications

2. Momentum (p 1 ) Momentum (p 2 ) Optical Projection (Chinese shadow, x -ray, … ) No image plane is defined.

3. Point (object Plane) Point (image plane) Optical Imaging: Position (x 1 )Position (x 2 ) and Image lens: Geometric optics

4. Spatial Resolution Image Plane Point (object plane)Spot (image plane) Imaging lens: finite size  function somb-function

5. S.C X2X2 X2X2 D2D2 D1D1 Two-Photon Imaging X2X2 X2X2 C.C

6. “Ghost” Imaging with entangled photon pairs Point x 1 (object plane)Point x 2 (image plane)

7. “Ghost” Image and “Ghost” Interference EPR Experiment in momentum-position PRL, 74, 3600 (1995); PRA, 52, R3429 (1995). SoSo SiSi

8. Classical: never! - classical statistical measurements

9. (1)No interaction between two distant quanta; (2) No action-at-a-distance between individual measurements. To EPR: the two quanta are independent as well as the measurements, so that Space-like separated measurement events. * *

10. Classically correlated systems: one may consider building an ensemble of particle-pairs to force each pair with and, so that. In this case, however,

11. Quantum: yes! - EPR : if the two quanta are entangled Although

12. Can quantum mechanical physical reality be considered complete? Einstein, Poldosky, Rosen, Phys. Rev. 47, 777 (1935). (2) Pointed out an surprising phenomenon: the momentum (position) for neither subsystem is determinate; however, if one particle is measured to have a certain momentum (posit- ion), the momentum (position) of its “twin” is determined with certainty, despite the distance between them! (1)Proposed the entangled two-particle state according to the principle of quantum superposition:

13. The apparent contradiction deeply troubled Einstein. While one sees the measurement on (p 1 +p 2 ) and (x 1 -x 2 ) of two individual particles satisfy the EPR  -function and believes the classical inequality, one might easily be trapped into considering either there is a violation of the uncertainty principle or there exists action-at-a-distance.

14. Violation of the uncertainty principle ? (p 1 +p 2 ) and (x 1 -x 2 ) are not conjugate variables !!!! Simultaneously !

16. Conjugate Variables:

17. EPR  -function: -- perfect entangled system EPR Inequality: -- non-perfect entangled system Although:

18. Observation: Believing: Conclusion: (Violation of the …) Then, why Einstein … ?

19. The interpretation ? Quantum entanglement

20. Two-photon is not two photons ! Classical: Two Wavepackets Entanglement: A non-factorable 2-D Wavepacket

21. Biphoton State: Spontaneous Parametric Down Conversion Two-photon Pure State The signal (idler) photon can have any energy (momentum), however, if one of the photons is measured at certain energy (momentum) its twin must be at a certain energy (momentum).

22. Operational approach: Pure state:

23. SPDC A biphoton Effective Two-photon wavefunction

24. Field Operators: : Green’s function (optical transfer function). determined by the experimental setup. The calculation of G (2) is lengthy but straightforward: It is the two-photon coherent superposition made it possible! Two-photon imaging

25. Although questions regarding fundamental issues of quantum theory still exist, quantum entanglement has indeed brought up a novel concept or technology in nonlocal position- ing and timing measurements with high accuracy, even beyond the classical limit.

26. Can “ghost” image be simulated classically ? Image but not projection!!! Question:

27. Yes Experimentally Thermal Light Imaging

28. Magic Mirror and Ghost Imaging

29. Experimental Result: Ghost image of a double-slit. A. Valencia, G. Scarcelli, M. D'Angelo, and Y.H. Shih, Phys. Rev. Lett. 94, 063601 (2005). M = 2.15 (M theory = 2.16); V = 12 % (V theory =16.5%)

30. Measurement on the image plan.

31. Two-photon thermal light Imaging: Incoherent imaging:

32. Magic Mirror ?

33. Measurement on the mirror plan.

34. It is useful !

35. A “Ghost” Camera in Space (Nonlocal)

36. A “Magic Mirror” for X-ray 3-D Imaging

37. It is fundamentally interesting !! Where it comes from ? Remember: thermal light is chaotic ! 50% momentum-momentum, position-position EPR correlation

38. It comes from Hanbeury Brown - Twiss … ??? It comes from “photon bunching” … ??? We are not satisfied !

39. The physics behind ???

40. f Fourier Transform Plane “Two-photon” film Slit A Slit B Fourier transform function (  or  ) ? Different Input State

41. Correlated Lasers f A product of two independent first-order-pattern.

42. SPDC f 0 0 + 2 =

43. Thermal + 0 0 + 222 =+

44. Quantum lithography (ultra-resolution: beyond classical limit)

45. Fourier Transform One Fourier Transform Two Optical Lithography

46. Fourier Transform One Fourier Transform Two Optical Lithography Laser

47. Fourier Transform One Fourier Transform Two Optical Lithography SPDC

48. Fourier Transform One Fourier Transform Two Optical Lithography Thermal

49. Two-photon diffraction and quantum lithography Experiment: M. D’Angelo, et al, PRL, 87, 013602 (2001). Theory: A.N. Boto, et al. PRL 85, 2733 (2000).

50. SPDC two-photon at Classical laser light at Experimental Data

51. It is the result of two-photon coherent superposition. It measures the second-order correlation between the object plane and the image plane, defined by the Gaussian thin lens equation. The published measurement was on the Fourier transform plane (far-field). PRL, 87, 013602 (2001).

52. Diffraction of a pair Classical diffraction Double (super) Spatial Resolution on the Image Plane Super-resolution:

53. “Ghost” Shadow (Projection) Bennink et al. PRL 89, 113601 (2002)