OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 24 — Nov. 21, 2011
  • pp: 24228–24240

Quantum imaging with N-photon states in position space

E. Brainis  »View Author Affiliations


Optics Express, Vol. 19, Issue 24, pp. 24228-24240 (2011)
http://dx.doi.org/10.1364/OE.19.024228


View Full Text Article

Enhanced HTML    Acrobat PDF (1043 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We investigate the physics of quantum imaging with N > 2 entangled photons in position space. It is shown that, in paraxial approximation, the space-time propagation of the quantum state can be described by a generalized Huygens-Fresnel principle for the N-photon wave function. The formalism allows the initial conditions to be set on multiple reference planes, which is very convenient to describe the generation of multiple photon pairs in separate thin crystals. Applications involving state shaping and spatial entanglement swapping are developed.

© 2011 OSA

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(270.0270) Quantum optics : Quantum optics

ToC Category:
Quantum Optics

History
Original Manuscript: September 21, 2011
Revised Manuscript: October 29, 2011
Manuscript Accepted: November 1, 2011
Published: November 14, 2011

Citation
E. Brainis, "Quantum imaging with N-photon states in position space," Opt. Express 19, 24228-24240 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-24-24228


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. C. Lu, X. Zhou, O. Guhne, W. Gao, J. Zhang, Z. Yuan, A. Goebel, T. Yang, and J. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys.3, 91–95 (2007). [CrossRef]
  2. H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature466, 601–603 (2010). [CrossRef] [PubMed]
  3. E. Waks, E. Diamanti, and Y. Yamamoto, “Generation of photon number states,” New J. Phys.8, 4–8 (2006). [CrossRef]
  4. W.-B. Gao, C.-Y. Lu, X.-C. Yao, P. Xu, O. Gühne, A. Goebel, Y.-A. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys.6, 331–335 (2010). [CrossRef]
  5. T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the Standard Quantum Limit with Four-Entangled Photons,” Science316, 726–729 (2007). [CrossRef] [PubMed]
  6. R. Okamoto, H. F. Hofmann, T. Nagata, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit: phase super-sensitivity of N-photon interferometers,” New J. Phys.10, 073033 (2008). [CrossRef]
  7. J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multi-photon entanglement and interferometry,” to appear in Rev. Mod. Phys. (2011).
  8. S. P. Walborn, C. H. Monken, S. Pádua, and P. H. Souto Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep.495, 87–139 (2010). [CrossRef]
  9. L. Neves, S. Pádua, and C. Saavedra, “Controlled generation of maximally entangled qudits using twin photons,” Phys. Rev. A69, 042305 (2004). [CrossRef]
  10. L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett.94, 100501 (2005). [CrossRef] [PubMed]
  11. R. Shimizu, K. Edamatsu, and T. Itoh, “Quantum diffraction and interference of spatially correlated photon pairs and its Fourier-optical analysis,” Phys. Rev. A74, 013801 (2006). [CrossRef]
  12. W. H. Peeters, J. J. Renema, and M. P. van Exter, “Engineering of two-photon spatial quantum correlations behind a double slit,” Phys. Rev. A79, 043817 (2009). [CrossRef]
  13. G. Lima, A. Vargas, L. Neves, R. Guzmán, and C. Saavedra, “Manipulating spatial qudit states with programmable optical devices,” Opt. Express17, 10688–10696 (2009). [CrossRef] [PubMed]
  14. C. Bonato, S. Bonora, A. Chiuri, P. Mataloni, G. Milani, G. Vallone, and P. Villoresi, “Phase control of a path-entangled photon state by a deformable membrane mirror,” J. Opt. Soc. Am. B27, A175–A180 (2010). [CrossRef]
  15. A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: Exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett.85, 2733–2736 (2000). [CrossRef] [PubMed]
  16. P. Kok, A. N. Boto, D. S. Abrams, C. P. Williams, S. L. Braunstein, and J. P. Dowling, “Quantum-interferometric optical lithography: Towards arbitrary two-dimensional patterns,” Phys. Rev. A63, 063407 (2001). [CrossRef]
  17. D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett.74, 3600–3603 (1995). [CrossRef] [PubMed]
  18. 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–R3432 (1995). [CrossRef] [PubMed]
  19. T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Two-photon geometric optics,” Phys. Rev. A53, 2804–2815 (1996). [CrossRef] [PubMed]
  20. T. E. Keller, M. H. Rubin, Y. Shih, and L.-A. Wu, “Theory of the three-photon entangled state,” Phys. Rev. A57, 2076–2079 (1998). [CrossRef]
  21. J. Wen, E. Oh, and S. Du, “Tripartite entanglement generation via four-wave mixings: narrowband triphoton W state,” J. Opt. Soc. Am. B27, A11–A20 (2010). [CrossRef]
  22. J. Wen, M. H. Rubin, and Y. Shih, “Transverse correlations in multiphoton entanglement,” Phys. Rev. A76, 045802 (2007). [CrossRef]
  23. J. Wen, P. Xu, M. H. Rubin, and Y. Shih, “Transverse correlations in triphoton entanglement: Geometrical and physical optics,” Phys. Rev. A76, 023828 (2007). [CrossRef]
  24. J. Wen and M. H. Rubin, “Distinction of tripartite Greenberger-Horne-Zeilinger and W states entangled in time (or energy) and space,” Phys. Rev. A79, 025802 (2009). [CrossRef]
  25. J. Wen, S. Du, and M. Xiao, “Improving spatial resolution in quantum imaging beyond the Rayleigh diffraction limit using multiphoton W entangled states,” Phys. Lett. A374, 3908 – 3911 (2010). [CrossRef]
  26. B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A62, 043816 (2000). [CrossRef]
  27. A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett.87, 123602 (2001). [CrossRef] [PubMed]
  28. A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Entangled-photon Fourier optics,” J. Opt. Soc. Am. B19, 1174–1184 (2002). [CrossRef]
  29. M. Hawton, “Photon position operator with commuting components,” Phys. Rev. A59, 954–959 (1999). [CrossRef]
  30. M. Hawton and W. E. Baylis, “Photon position operators and localized bases,” Phys. Rev. A64, 012101 (2001). [CrossRef]
  31. M. Hawton, “Photon wave functions in a localized coordinate space basis,” Phys. Rev. A59, 3223–3227 (1999). [CrossRef]
  32. I. Bialynicki-Birula, “On the wave function of the photon,” Acta Phys. Pol. A86, 97–116 (1994).
  33. I. Bialynicki-Birula, “Photon wave function,” in Progress in Optics, vol. 36, E. Wolf, ed. (North-Holland, Elsevier, Amsterdam, 1996), chap. 5, pp. 248–294.
  34. J. E. Sipe, “Photon wave functions,” Phys. Rev. A52, 1875–1883 (1995). [CrossRef] [PubMed]
  35. Note that the quantum mechanical scalar product 〈Ψ(2)|Ψ(1)〉=∑h=±∫d3k[f±(2)(k)]*f±(1)(k)=∫d3r1∫d3r2[Ψ(2)(r2)]*⋅Ψ(1)(r1)𝒲(r1−r2) is evaluate using a double integral in the position representation with a non local kernel 𝒲 (ρ) = (h̄c2π2|ρ|2)−1.
  36. B. J. Smith and M. G. Raymer, “Two-photon wave mechanics,” Phys. Rev. A74, 062104 (2006). [CrossRef]
  37. B. J. Smith and M. G. Raymer, “Photon wave functions, wave-packet quantization of light, and coherence theory,” New J. Phys.9, 414 (2007). [CrossRef]
  38. J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, Englewood, 2005), 3rd ed.
  39. In [26,28], time is only introduced to account for the bandwidth of the continuous biphoton stream and compute coincidence rates in the slow detector limit.
  40. T. Legero, T. Wilk, M. Hennrich, G. Rempe, and A. Kuhn, “Quantum beat of two single photons,” Phys. Rev. Lett.93, 070503 (2004). [CrossRef] [PubMed]
  41. J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett.62, 2205–2208 (1989). [CrossRef] [PubMed]
  42. V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A79, 013827 (2009). [CrossRef]
  43. E. Brainis, C. Muldoon, L. Brandt, and A. Kuhn, “Coherent imaging of extended objects,” Opt. Commun.282, 465–472 (2009). [CrossRef]
  44. G. Taguchi, T. Dougakiuchi, N. Yoshimoto, K. Kasai, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Measurement and control of spatial qubits generated by passing photons through double slits,” Phys. Rev. A78, 012307 (2008). [CrossRef]
  45. M. A. Solis-Prosser and L. Neves, “Remote state preparation of spatial qubits,” Phys. Rev. A84, 012330 (2011). [CrossRef]
  46. S. P. Walborn, D. S. Ether, R. L. de Matos Filho, and N. Zagury, “Quantum teleportation of the angular spectrum of a single-photon field,” Phys. Rev. A76, 033801 (2007). [CrossRef]
  47. P. L. Saldanha and C. H. Monken, “Interaction between light and matter: a photon wave function approach,” New J. Phys.13, 073015 (2011). [CrossRef]
  48. J.-W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: Entangling photons that never interacted,” Phys. Rev. Lett.80, 3891–3894 (1998). [CrossRef]
  49. N. J. Cerf, M. Lévy, and G. V. Assche, “Quantum distribution of gaussian keys using squeezed states,” Phys. Rev. A63, 052311 (2001). [CrossRef]
  50. M. P. Almeida, S. P. Walborn, and P. H. Souto Ribeiro, “Experimental investigation of quantum key distribution with position and momentum of photon pairs,” Phys. Rev. A72, 022313 (2005). [CrossRef]
  51. L. Zhang, C. Silberhorn, and I. A. Walmsley, “Secure quantum key distribution using continuous variables of single photons,” Phys. Rev. Lett.100, 110504 (2008). [CrossRef] [PubMed]
  52. D. S. Tasca, R. M. Gomes, F. Toscano, P. H. Souto Ribeiro, and S. P. Walborn, “Continuous-variable quantum computation with spatial degrees of freedom of photons,” Phys. Rev. A83, 052325 (2011). [CrossRef]
  53. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys.3, 305–310 (2007). [CrossRef]
  54. B.-J. Pors, F. Miatto, G. W. ’t Hooft, E. R. Eliel, and J. P. Woerdman, “High-dimensional entanglement with orbital-angular-momentum states of light,” J. Opt.13, 064008 (2011). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited