Abstract
One of the most surprising consequences of quantum mechanics is the nonlocal correlation of a multiparticle system measured by joint-detection of distant particle-detectors. Ghost imaging is one of such phenomena. Traditionally, taking a photograph of an object requires facing a camera to the object. With ghost imaging, however, we can image the object by pointing a CCD camera or CCD array toward the light source, rather than the object. Ghost imaging is reproduced at the quantum level by a natural, non-factorizable, point-to-point image-forming correlation between the object and image planes. Two types of ghost imaging have been experimentally demonstrated since 1995. Type-one ghost imaging uses entangled photon pairs as the light source. The type-one nonfactorizable image-forming correlation is the result of a nonlocal constructive–destructive interference among a large number of biphoton amplitudes, a nonclassical entity corresponding to different yet indistinguishable alternatives for the entangled photon pair to produce a joint-detection event between distant photodetectors. Type-two ghost imaging uses chaotic-thermal light. The type-two nonfactorizable image-forming correlation is caused by the superposition between paired two-photon amplitudes, or the symmetrized effective two-photon wavefunction, corresponding to two different yet indistinguishable alternatives of triggering a joint-detection event by two independent photons. The multiphoton interference nature of ghost imaging determines its peculiar features: (1) it is nonlocal; (2) its imaging resolution differs from that of classical imaging; and (3) the type-two ghost image is turbulence-free. Ghost imaging has attracted a great deal of attention, perhaps due to these interesting and useful features. Achieving these features, the realization of nonlocal multiphoton interference is necessary. Classical simulations, such as the man-made factorizable speckle-to-speckle correlation, do not have such properties.
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Notes
- 1.
Any fluctuation of the refraction index or phase disturbance in the optical path has no influence on the quality of the type-two ghost image.
- 2.
A factorizable correlation function G (2)(r 1, t 1; r 2, t 2) = G (1)(r 1, t 1) G (1)(r 2, t 2) characters independent radiations at space-time (r 1, t 1) and (r 2, t 2). In ghost imaging, the light on the object plane and the light at the CCD array is described by a nonfactorizeable point-to-point image-forming function, indicating nontrivial statistical correlation between the two measured intensities.
- 3.
The ghost imaging experiment is thus considered a demonstration of the historical Einstein–Podolsky–Rosen (EPR) experiment.
- 4.
Similar to the HBT correlation, the contrast of the near-field partial point-to-point image-forming function is 50%, i.e., two to one ratio between the maximum value and the constant background, see (14.33).
- 5.
There exist a number of definitions for classical light and for quantum light. One of the commonly accepted definitions considers thermal light classical because its positive P-function.
- 6.
Similar to the far-field HBT correlation, the contrast of the “near-surface-field” point-to-point image-forming function is 50%, i.e., a two to one ratio between the maximum value and the constant background.
- 7.
The concept of “near-field” was defined by Fresnel to be distinct from the Fraunhofer far-field. The Fresnel near-field is different from the “near-surface-field”, that considers a distance of a few wavelengths from a surface.
- 8.
We cannot help but stop to ask: What has been preventing this simple move from far-field to near-field for half a century? The hand-waving argument of intensity fluctuation correlation may have played a role.
- 9.
The original publications of Gatti et al.. choose m = 2f ∕ 2f = 1 with 1 ∕ 2f + 1 ∕ 2f = 1 ∕ f to image the speckles of the source onto the object plane and the ghost image plane.
- 10.
The angular size of Sun is about 0. 53 ∘ . To achieve a compatible image spatial resolution, a traditional camera must have a lens of 92-meter diameter when taking pictures at 10 kilometers.
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Acknowledgments
The author thanks M. D’Angelo, G. Scarcelli, J.M. Wen, T.B. Pittman, M.H. Rubin, and L.A. Wu for helpful discussions. This work is partially supported by AFOSR and ARO-MURI program.
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Shih, Y. (2012). The Physics of Ghost Imaging. In: Cohen, L., Poor, H., Scully, M. (eds) Classical, Semi-classical and Quantum Noise. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6624-7_14
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