## Storage and retrieval of ghost images in hot atomic vapor |

Optics Express, Vol. 20, Issue 5, pp. 5809-5816 (2012)

http://dx.doi.org/10.1364/OE.20.005809

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### Abstract

Ghost imaging is an imaging technique in which the image of an object is revealed only in the correlation measurement between two beams of light, whereas the individual measurements contain no imaging information. Here, we experimentally demonstrate storage and retrieval of ghost images in hot atomic rubidium vapor. Since ghost imaging requires (quantum or classical) multimode spatial correlation between two beams of light, our experiment shows that the spatially multimode correlation, a second-order correlation property of light, can indeed be preserved during the storage-retrieval process. Our work, thus, opens up new possibilities for quantum and classical two-photon imaging, all-optical image processing, and quantum communication.

© 2012 OSA

## 1. Introduction

1. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. **77**, 633–673 (2005). [CrossRef]

2. M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. **84**, 5094–5097 (2000). [CrossRef] [PubMed]

3. D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. **86**, 783–786 (2001). [CrossRef] [PubMed]

8. Y.-W. Cho and Y.-H. Kim, “Storage and retrieval of thermal light in warm atomic vapor,” Phys. Rev. A **82**, 033830 (2010). [CrossRef]

9. A. L. Alexander, J. J. Longdell, M. J. Sellars, and N. B. Manson, “Photon echoes produced by switching electric fields,” Phys. Rev. Lett. **96**, 043602 (2006). [CrossRef] [PubMed]

14. K. F. Reim, J. Nunn, V. O. Lorenz, B. J. Sussman, K. C. Lee, N. K. Langford, D. Jaksch, and I. A. Walmsley, “Towards high-speed optical quantum memories,” Nat. Photonics **4**, 218–221 (2010). [CrossRef]

15. D. V. Vasilyev, I. V. Sokolov, and E. S. Polzik, “Quantum memory for images: a quantum hologram,” Phys. Rev. A. **77**, 020302(R) (2008). [CrossRef]

16. P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, “Storage and retrieval of multimode transverse images in hot atomic rubidium vapor,” Phys. Rev. Lett. **100**, 123903 (2008). [CrossRef] [PubMed]

20. F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. **94**, 183602 (2005). [CrossRef] [PubMed]

21. A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. **94**, 063601 (2005). [CrossRef] [PubMed]

3. D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. **86**, 783–786 (2001). [CrossRef] [PubMed]

## 2. Experimental setup

^{2}

*S*

_{1/2}

*F*= 2 → 5

^{2}

*P*

_{1/2}

*F*′ = 2, is spatially and temporally matched with the signal beam inside the vapor cell for preparation and manipulation of the EIT medium. Note that both the bucket detector and the CCD individually do not exhibit any imaging information. The ghost image of the mask is revealed in the correlation measurement between the bucket detector and the CCD.

*E*(

_{out}*r⃗*) = ∫

_{i}*dr⃗*″

*(*

_{i}E_{in}*r⃗*′

*)*

_{i}*h*(

_{i}*r⃗*,

_{i}*r⃗*″

*), where*

_{i}*r⃗*″

*is the transverse position vector,*

_{i}*E*(

_{in}*r⃗*″

*) refers to the fields at the plane immediately after PBS1, and*

_{i}*h*(

_{i}*r⃗*,

_{i}*r⃗*″

*) is the impulse response function of each optical system. In the reference beam, an object (Mask with OCR-a character 5) is placed immediately after PBS1. Thus, the impulse response function is given as*

_{i}*h*

_{1}(

*r⃗*

_{1},

*r⃗*″

_{1}) =

*T*(

*r⃗*″

_{1})

*δ*(

*r⃗*

_{1}–

*r⃗*″

_{1}) where

*T*(

*r⃗*″

_{1}) is the complex transmission function of the object. In the signal beam, the optical system consists of a 4

*f*imaging system and the EIT medium (vapor cell). The impulse response function of the optical system without the EIT medium can be written as

*h*

_{2}(

*r⃗*

_{2},

*r⃗*″

_{2}) =

*δ*(

*r⃗*

_{2}+

*mr⃗*″

_{2}), where

*m*=

*f*

_{2}/

*f*

_{1}is the magnification factor. Note that due to the lensless ghost imaging effect [27

27. G. Scarcelli, V. Berardi, and Y. Shih, “Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?,” Phys. Rev. Lett. **96**, 063602 (2006). [CrossRef] [PubMed]

*r⃗*″

_{1}can be found by correlation measurement of the bucket detector and the CCD placed in the signal beam at the same distance from PBS1 at

*r⃗*″

_{2}. The ghost image plane

*r⃗*″

_{2}is then relayed to

*r⃗*

_{2}using the 4

*f*imaging system with

*m*= 0.667

## 3. Construction of ghost images

*G*(

*r⃗*

_{1},

*r⃗*

_{2}) = 〈Δ

*I*

_{1}(

*r⃗*

_{1})Δ

*I*

_{2}(

*r⃗*

_{2})〉, where 〈...〉 is time averaging and, for thermal light, it becomes [28

28. A. Gatti, E. Brambilla, M. Bache, and A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A **70**, 013802 (2004). [CrossRef]

*r⃗*″

_{1},

*r⃗*″

_{2}) =

*I*

_{0}

*δ*(

*r*″

_{1}–

*r⃗*″

_{2}) and this gives rise to

*G*(

*r⃗*

_{1},

*r⃗*

_{2}) ∝ |

*T*(

*r⃗*

_{1})|

^{2}|

*δ*(

*r⃗*

_{1}+

*mr⃗*

_{2})|

^{2}. Since the reference beam is detected by a bucket detector which has no spatial resolution, integration of

*G*(

*r⃗*

_{1},

*r⃗*

_{2}) over

*r⃗*

_{1}is necessary and this yields ∫

*dr⃗*

_{1}

*G*(

*r⃗*

_{1},

*r⃗*

_{2}) ∝ |

*T*(−

*mr⃗*

_{2})|

^{2}. Thus, in the absence of the EIT storage medium, we expect to observe an inverted ghost image with the magnification factor of

*m*.

## 4. Storage and retrieval of ghost images

*f*imaging system. The vapor cell was heated to 70 ∼ 80 °C, providing a sufficient rubidium vapor density of approximately 10

^{12}cm

^{−3}. As discussed earlier, the thermal light source and the coupling beam were locked to 5

^{2}

*S*

_{1/2}

*F*= 1 (|1〉) → 5

^{2}

*P*

_{1/2}

*F*′ = 2 (|3〉) and 5

^{2}

*S*

_{1/2}

*F*= 2 (|2〉) → 5

^{2}

*P*

_{1/2}

*F*′ = 2 (|3〉) transitions of Rubidium 87 D1 line, respectively. To ensure better transmission, both beams are slightly blue-detuned by 60 MHz. The FWHM EIT linewidth of 188 kHz was observed by tuning the frequency of the coupling beam. Note that the bandwidth of the thermal light, 1/

*τ*≈ 138 kHz, fits within the EIT spectrum. The power and the beam diameter of the signal beam are approximately 250

_{c}*μ*W and 2.5 mm, respectively, at the ghost object plane,

*r⃗*″

_{2}in Fig. 1(b). The power of the coupling beam is 25 mW with a 5 mm beam diameter.

*μ*s rectangular pulse as mentioned earlier and the coupling beam is turned on to prepare the EIT medium for storage. After the signal pulse has completely entered the vapor cell, the coupling beam is turned off, storing the signal beam in the EIT medium. After some storage duration (4

*μ*s ∼ 20

*μ*s), the coupling beam is temporally turned back on for 4

*μ*s and, during this time, the signal beam stored in the EIT medium is partially retrieved. The CCD is triggered so that the exposure window overlaps only with the retrieved signal.

*μ*s to 16

*μ*s and each ghost image is reconstructed from 5,000 shots of such measurements. It is apparent that transverse spatial multimode correlation between the twin speckle beams survives the storage-retrieval process. Also, the reconstructed ghost images are clearly identifiable without broadening by atomic diffusion.

31. K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “Optimization of thermal ghost imaging: high-order correlation vs. background subtraction,” Opt. Express **18**, 5562–5573 (2010). [CrossRef] [PubMed]

34. G. Brida, M. V. Chekhova, G. A. Fornaro, M. Genovese, E. D. Lopaeva, and I. Ruo Berchera, “Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light,” Phys. Rev. A **83**, 063807 (2011). [CrossRef]

31. K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “Optimization of thermal ghost imaging: high-order correlation vs. background subtraction,” Opt. Express **18**, 5562–5573 (2010). [CrossRef] [PubMed]

31. K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “Optimization of thermal ghost imaging: high-order correlation vs. background subtraction,” Opt. Express **18**, 5562–5573 (2010). [CrossRef] [PubMed]

35. F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. **104**, 253603 (2010). [CrossRef] [PubMed]

*E*(

_{in}*r⃗*″

_{2}) at the ghost object plane is Fourier transformed by the lens (L1) and stored as the coherence between the atomic ground states |1〉 and |2〉 [2

2. M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. **84**, 5094–5097 (2000). [CrossRef] [PubMed]

*ρ*

_{12}evolves according to the diffusion equation where

*D*and Γ are the diffusion coefficient and the ground state decay rate, respectively. The field at the detection plane is then given as [16

16. P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, “Storage and retrieval of multimode transverse images in hot atomic rubidium vapor,” Phys. Rev. Lett. **100**, 123903 (2008). [CrossRef] [PubMed]

36. L. Zhao, T. Wang, Y. Xiao, and S. F. Yelin, “Image storage in hot vapors,” Phys. Rev. A **77**, 041802(R) (2008). [CrossRef]

*E*(

_{out}*r⃗*

_{2}) =

*E*(−

_{in}*mr⃗*

_{2}) exp(−(

*β*+ Γ)

*t*), where

_{s}*m*is the magnification of the 4

*f*imaging system,

*t*is the storage time, and

_{s}*β*=

*D*(2

*π*)

^{2}

*m*

^{2}(

*x*

^{2}+

*y*

^{2})/(

*λf*

_{1})

^{2}. Here,

*f*

_{1}is the focal length of the first lens L1. The retrieved signal field at the CCD plane is then given as

*∫ dr⃗*″

_{2}

*h*

_{2}(

*r⃗*

_{2},

*r⃗*″

_{2})

*E*(

_{in}*r⃗*″

_{2}) =

*E*(−

_{in}*mr⃗*

_{2}) exp(−(

*β*+ Γ)

*t*). The second-order correlation function is therefore given as

_{s}*G*(

*r⃗*

_{1},

*r⃗*

_{2}) ∝ |

*T*(

*r⃗*

_{1})|

^{2}|

*δ*(

*r⃗*

_{1}+

*mr⃗*

_{2})|

^{2}exp (−2(

*β*+ Γ)

*t*). The ghost image is obtained by integrating over

_{s}*r⃗*

_{1}This result shows that the ghost image can survive the storage-retrieval process while maintaining sharp edges although the overall “brightness” of the ghost image experiences exponential decay. Thus, as mentioned before, CNR of the ghost image can be improved by including more shots of measurements in ghost image reconstruction which is more or less equivalent to making a longer exposure in photography. We note that we could avoid the image degradation due to the atomic diffusion by storing the Fourier transformed image. Zero crossings in the Fourier transformed image is much insensitive to the atomic diffusion due to the destructive interference [16

16. P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, “Storage and retrieval of multimode transverse images in hot atomic rubidium vapor,” Phys. Rev. Lett. **100**, 123903 (2008). [CrossRef] [PubMed]

36. L. Zhao, T. Wang, Y. Xiao, and S. F. Yelin, “Image storage in hot vapors,” Phys. Rev. A **77**, 041802(R) (2008). [CrossRef]

37. A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. of Mod. Opt. **53**, 739–760 (2006). [CrossRef]

## 5. Conclusion

## Acknowledgments

## References and links

1. | M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. |

2. | M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. |

3. | D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. |

4. | M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature , |

5. | K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Storage and retrieval of a squeezed vacuum,” Phys. Rev. Lett. |

6. | H. Tanji, S. Ghosh, J. Simon, B. Bloom, and V. Vuletić, “Heralded single-magnon quantum memory for photon polarization states,” Phys. Rev. Lett. |

7. | Y.-W. Cho and Y.-H. Kim, “Atomic vapor quantum memory for a photonic polarization qubit,” Opt. Express |

8. | Y.-W. Cho and Y.-H. Kim, “Storage and retrieval of thermal light in warm atomic vapor,” Phys. Rev. A |

9. | A. L. Alexander, J. J. Longdell, M. J. Sellars, and N. B. Manson, “Photon echoes produced by switching electric fields,” Phys. Rev. Lett. |

10. | M. U. Staudt, S. R. Hastings-Simon, M. Nilsson, M. Afzelius, V. Scarani, R. Ricken, H. Suche, W. Sohler, W. Tittel, and N. Gisin, “Fidelity of an optical memory based on stimulated photon echoes,” Phys. Rev. Lett. |

11. | M. P. Hedges, J. J. Longdell, Y. Li, and M. J. Sellars, “Efficient quantum memory for light,” Nature |

12. | C. Clausen, I. Usmani, F. Bussires, N. Sangouard, M. Afzelius, H. de Riedmatten, and N. Gisin, “Quantum storage of photonic entanglement in a crystal,” Nature |

13. | M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. |

14. | K. F. Reim, J. Nunn, V. O. Lorenz, B. J. Sussman, K. C. Lee, N. K. Langford, D. Jaksch, and I. A. Walmsley, “Towards high-speed optical quantum memories,” Nat. Photonics |

15. | D. V. Vasilyev, I. V. Sokolov, and E. S. Polzik, “Quantum memory for images: a quantum hologram,” Phys. Rev. A. |

16. | P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, “Storage and retrieval of multimode transverse images in hot atomic rubidium vapor,” Phys. Rev. Lett. |

17. | M. Shuker, O. Firstenberg, R. Pugatch, A. Ron, and N. Davison, “Storing images in warm atomic vapor,” Phys. Rev. Lett. |

18. | G. Heinze, A. Rudolf, F. Beil, and T. Halfmann, “Storage of images in atomic coherences in a rare-earth-ion-doped solid,” Phys. Rev. A |

19. | T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A |

20. | F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. |

21. | A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. |

22. | G. Brida, M. Genovese, and I. R. Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics |

23. | R. E. Meyers, K. S. Deacon, and Y. Shih, “Ghost-imaging experiment by measuring reflected photons,” Phys. Rev. A |

24. | J. Cheng and S. Han, “Incoherent coincidence imaging and its applicability in X-ray diffraction,” Phys. Rev. Lett. |

25. | P. Clemente, V. Durán, V. Torres-Company, E. Tajahuerce, and J. Lancis, “Optical encryption based on computational ghost imaging,” Opt. Lett. |

26. | V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science |

27. | G. Scarcelli, V. Berardi, and Y. Shih, “Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?,” Phys. Rev. Lett. |

28. | A. Gatti, E. Brambilla, M. Bache, and A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A |

29. | The cross correlation for the ghost imaging is calculated by the following equation, |

30. | A delay/pulse generator (SRS, DG535) provides the synchronization pulses for the CCD (JAI, CM-030-GE), the digitizer (NI, PCI-5114), and the two acousto-optic modulators used in the experiment. Each “measurement” is then repeated at 1.5 Hz. |

31. | K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “Optimization of thermal ghost imaging: high-order correlation vs. background subtraction,” Opt. Express |

32. | K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “High-order thermal ghost imaging,” Opt. Lett. |

33. | B. I. Erkmen and J. H. Shapiro, “Signal-to-noise ratio of Gussian-state ghost imaging,” Phys. Rev. A |

34. | G. Brida, M. V. Chekhova, G. A. Fornaro, M. Genovese, E. D. Lopaeva, and I. Ruo Berchera, “Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light,” Phys. Rev. A |

35. | F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. |

36. | L. Zhao, T. Wang, Y. Xiao, and S. F. Yelin, “Image storage in hot vapors,” Phys. Rev. A |

37. | A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. of Mod. Opt. |

**OCIS Codes**

(030.1640) Coherence and statistical optics : Coherence

(270.1670) Quantum optics : Coherent optical effects

(270.5585) Quantum optics : Quantum information and processing

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: January 5, 2012

Revised Manuscript: February 12, 2012

Manuscript Accepted: February 13, 2012

Published: February 24, 2012

**Citation**

Young-Wook Cho, Joo-Eon Oh, and Yoon-Ho Kim, "Storage and retrieval of ghost images in hot atomic vapor," Opt. Express **20**, 5809-5816 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-5-5809

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### References

- M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys.77, 633–673 (2005). [CrossRef]
- M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett.84, 5094–5097 (2000). [CrossRef] [PubMed]
- D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett.86, 783–786 (2001). [CrossRef] [PubMed]
- M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature, 438, 837–841 (2005). [CrossRef] [PubMed]
- K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Storage and retrieval of a squeezed vacuum,” Phys. Rev. Lett.100, 093601 (2008). [CrossRef] [PubMed]
- H. Tanji, S. Ghosh, J. Simon, B. Bloom, and V. Vuletić, “Heralded single-magnon quantum memory for photon polarization states,” Phys. Rev. Lett.103, 043601 (2009). [CrossRef] [PubMed]
- Y.-W. Cho and Y.-H. Kim, “Atomic vapor quantum memory for a photonic polarization qubit,” Opt. Express18, 25786 (2010). [CrossRef] [PubMed]
- Y.-W. Cho and Y.-H. Kim, “Storage and retrieval of thermal light in warm atomic vapor,” Phys. Rev. A82, 033830 (2010). [CrossRef]
- A. L. Alexander, J. J. Longdell, M. J. Sellars, and N. B. Manson, “Photon echoes produced by switching electric fields,” Phys. Rev. Lett.96, 043602 (2006). [CrossRef] [PubMed]
- M. U. Staudt, S. R. Hastings-Simon, M. Nilsson, M. Afzelius, V. Scarani, R. Ricken, H. Suche, W. Sohler, W. Tittel, and N. Gisin, “Fidelity of an optical memory based on stimulated photon echoes,” Phys. Rev. Lett.98, 113601 (2007). [CrossRef] [PubMed]
- M. P. Hedges, J. J. Longdell, Y. Li, and M. J. Sellars, “Efficient quantum memory for light,” Nature465, 1052–1056 (2010). [CrossRef] [PubMed]
- C. Clausen, I. Usmani, F. Bussires, N. Sangouard, M. Afzelius, H. de Riedmatten, and N. Gisin, “Quantum storage of photonic entanglement in a crystal,” Nature469, 508–511 (2011). [CrossRef] [PubMed]
- M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun.2, 174 (2011). [CrossRef] [PubMed]
- K. F. Reim, J. Nunn, V. O. Lorenz, B. J. Sussman, K. C. Lee, N. K. Langford, D. Jaksch, and I. A. Walmsley, “Towards high-speed optical quantum memories,” Nat. Photonics4, 218–221 (2010). [CrossRef]
- D. V. Vasilyev, I. V. Sokolov, and E. S. Polzik, “Quantum memory for images: a quantum hologram,” Phys. Rev. A.77, 020302(R) (2008). [CrossRef]
- P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, “Storage and retrieval of multimode transverse images in hot atomic rubidium vapor,” Phys. Rev. Lett.100, 123903 (2008). [CrossRef] [PubMed]
- M. Shuker, O. Firstenberg, R. Pugatch, A. Ron, and N. Davison, “Storing images in warm atomic vapor,” Phys. Rev. Lett.100, 223601 (2008). [CrossRef] [PubMed]
- G. Heinze, A. Rudolf, F. Beil, and T. Halfmann, “Storage of images in atomic coherences in a rare-earth-ion-doped solid,” Phys. Rev. A81, 011401(R) (2010).
- T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A52, R3429 (1995). [CrossRef] [PubMed]
- F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett.94, 183602 (2005). [CrossRef] [PubMed]
- A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett.94, 063601 (2005). [CrossRef] [PubMed]
- G. Brida, M. Genovese, and I. R. Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics4, 227–230 (2010). [CrossRef]
- R. E. Meyers, K. S. Deacon, and Y. Shih, “Ghost-imaging experiment by measuring reflected photons,” Phys. Rev. A77, 041801(R) (2008). [CrossRef]
- J. Cheng and S. Han, “Incoherent coincidence imaging and its applicability in X-ray diffraction,” Phys. Rev. Lett.92, 093903 (2004). [CrossRef] [PubMed]
- P. Clemente, V. Durán, V. Torres-Company, E. Tajahuerce, and J. Lancis, “Optical encryption based on computational ghost imaging,” Opt. Lett.35, 2391–2393 (2010). [CrossRef] [PubMed]
- V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science321, 544–547 (2008). [CrossRef] [PubMed]
- G. Scarcelli, V. Berardi, and Y. Shih, “Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?,” Phys. Rev. Lett.96, 063602 (2006). [CrossRef] [PubMed]
- A. Gatti, E. Brambilla, M. Bache, and A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A70, 013802 (2004). [CrossRef]
- The cross correlation for the ghost imaging is calculated by the following equation, G(r→)=∑iNΔIiΔJi(r→), where ΔIi=Ii−1N∑iNIi and ΔJi(r→)=Ji(r→)−1N∑iNJi(r→) are fluctuations of photodetector and CCD output signals, respectively.
- A delay/pulse generator (SRS, DG535) provides the synchronization pulses for the CCD (JAI, CM-030-GE), the digitizer (NI, PCI-5114), and the two acousto-optic modulators used in the experiment. Each “measurement” is then repeated at 1.5 Hz.
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