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

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

1. Ghost Imaging and Interference with entangled photon pairs

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

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, 3600 (1995)

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

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

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.

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

Ghost Imaging and Interference with classically correlated light Phys. Rev. Lett. 89, 113601 (2002)

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

Phys. Rev. Lett. 92, 033601 (2004). Did not give the fringe equation

The angle between two peaks:

Experimental observation of ghost imaging with thermal light A.Valencia, G. Scarcelli, M D’Angelo and Y. Shih, quant-ph/0408001 v1 30 Jul 2004

The Double Slits

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%

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/0408021, 3 Aug 2004

Detector 1 is a bucket detector,

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

Ghost image with coherent Gaussian beam

In the input plane

Point by point projection

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

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

Different amplification factor

Ghost interference with coherent Gaussian beam

at For we have

For all angles we have This gives the interference fringes.

The angle between two peaks:

For small By refocusing Clear fringes can be obtained

z2 varies from satisfy to not satisfy image condition

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:

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.

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).

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

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.

The Ghost image and Interference with Blackbody Radiation

Ghost Interference with blackbody radiation

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

Sufficient Large

Ghost Image with Blackbody Radiation

Ghost Image with Blackbody Radiation

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

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

Fourth-order correlation function

The image at different positions

Image for different surface sizes

(a) (b) (c) with

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

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

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

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.