## Spatial properties of twin-beam correlations at low- to high-intensity transition |

Optics Express, Vol. 22, Issue 11, pp. 13374-13379 (2014)

http://dx.doi.org/10.1364/OE.22.013374

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### Abstract

It is shown that spatial correlation functions measured for correlated photon pairs at the single-photon level correspond to speckle patterns visible at high intensities. This correspondence is observed for the first time in one experimental setup by using different acquisition modes of an intensified CCD camera in low and high intensity regimes. The behavior of intensity auto- and cross-correlation functions in dependence on pump-beam parameters including power and transverse profile is investigated.

© 2014 Optical Society of America

## 1. Introduction

1. L. Mandel and E. Wolf, *Optical Coherence and Quantum Optics* (Cambridge University, 1995). [CrossRef]

3. B. M. Jost, A. V. Sergienko, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Spatial correlations of spontaneously down-converted photon pairs detected with a single-photon-sensitive CCD camera,” Opt. Express **3**, 81–88 (1998). [CrossRef] [PubMed]

4. A. Mosset, F. Deveaux, G. Fanjoux, and E. Lantz, “Direct experimental characterization of the Bose-Einstein distribution of spatial fluctuations of spontaneous parametric down-conversion,” Eur. Phys. J. D **28**, 447–451 (2004). [CrossRef]

5. O. Haderka, J. Peřina Jr., and M. Hamar, “Simple direct measurement of nonclassical joint signal-idler photon-number statistics and the correlation area of twin photon beams,” J. Opt. B Quantum Semicl. Opt. **7**, S572–S576 (2005). [CrossRef]

7. C. H. Monken, P. H. Souto Ribeiro, and S. Padua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A **57**, 3123–3126 (1998). [CrossRef]

8. G. Molina-Terriza, S. Minardi, Y. Deyanova, C. I. Osorio, M. Hendrych, and J. P. Torres, “Control of the shape of the spatial mode function of photons generated in noncollinear spontaneous parametric down conversion,” Phys. Rev. A **72**, 065802 (2005). [CrossRef]

3. B. M. Jost, A. V. Sergienko, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Spatial correlations of spontaneously down-converted photon pairs detected with a single-photon-sensitive CCD camera,” Opt. Express **3**, 81–88 (1998). [CrossRef] [PubMed]

5. O. Haderka, J. Peřina Jr., and M. Hamar, “Simple direct measurement of nonclassical joint signal-idler photon-number statistics and the correlation area of twin photon beams,” J. Opt. B Quantum Semicl. Opt. **7**, S572–S576 (2005). [CrossRef]

6. M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera”,Nat. Commun. **3**, 984 (2012). [CrossRef] [PubMed]

9. T. P. Grayson and G. A. Barbosa, “Spatial properties of spontaneous parametric down-conversion and their effect on induced coherence without induced emission,” Phys. Rev. A **49**, 2948–2961 (1994). [CrossRef] [PubMed]

12. M. Hamar, J. Peřina Jr., O. Haderka, and V. Michálek, “Transverse coherence of photon pairs generated in spontaneous parametric downconversion,” Phys. Rev. A **81**, 043827 (2010). [CrossRef]

13. E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion,” Phys. Rev. A **69**, 023802 (2004). [CrossRef]

14. M. Bondani, A. Allevi, and A. Andreoni, “Ghost imaging by intense multimode twin beam,” Eur. Phys. J. Special Topics **203**, 151–161 (2012). [CrossRef]

15. O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric downconversion,” Phys. Rev. Lett. **93**, 243601 (2004). [CrossRef]

15. O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric downconversion,” Phys. Rev. Lett. **93**, 243601 (2004). [CrossRef]

*, Γ*

_{ss}*) and cross-correlation (XC, Γ*

_{ii}*, Γ*

_{si}*) functions [16*

_{is}16. G. Brida, M. Genovese, A. Meda, E. Predazzi, and I. Ruo Berchera, “Systematic study of the PDC speckle structure for quantum imaging applications,” Int. Journ. Quantum Inf. **7**, 139–147 (2009). [CrossRef]

17. G. Brida, M. Genovese, A. Meda, E. Predazzi, and I. Ruo Berchera, “Tailoring PDC speckle structure,” J. Mod. Opt. **56**, 201–208 (2009). [CrossRef]

*s*[

*i*] stands for a signal [idler] beam with intensity fluctuation Δ

*I*(

_{s}**r**

_{1}) [Δ

*I*(

_{i}**r**

_{2})] at position

**r**

_{1}[

**r**

_{2}] and 〈〉 denotes quantum (statistical) averaging. Although the two described intensity regimes together with their own experimental techniques differ considerably, the observed effects arise from the same nonlinear process. That is why it is important to compare quantitatively the observed coherence properties at single-photon and intense twin-beam regime.

12. M. Hamar, J. Peřina Jr., O. Haderka, and V. Michálek, “Transverse coherence of photon pairs generated in spontaneous parametric downconversion,” Phys. Rev. A **81**, 043827 (2010). [CrossRef]

## 2. Experimental setup

*θ*= 37°). Nearly degenerate photon pairs occurred at a cone layer with a vertex half-angle of 11.9°. A part of the cone layer was selected by a 40-nm-wide bandpass interference filter (IF) centered at 710 nm, that is close to frequency degeneracy. One part of the cone-layer (signal) was captured directly by the photocathode of the iCCD camera (Andor DH734, pixel size 13 × 13

*μ*m

^{2}) placed 38.5 cm behind the crystal, while the corresponding twin portion (idler) was directed to a different section of the photocathode using a dielectric mirror (M, see Fig. 1). An additional long-pass filter (EF) was used to cut scattered pumping photons. The camera was triggered by an electronic pulse derived from the laser pulse and set to 5 ns detection window (used both for low- and high-intensity measurement) to assure detection of PDC from a single pump pulse and to minimize noise. The power of the transmitted pump beam was monitored using a power-meter. Moreover, the pump beam diameter was measured in the horizontal and vertical directions using a scanning knife-edge. The pump beam was nearly elliptical with the vertical width reaching approximately 70% of the horizontal one. The pump power was changed by using a half-wave plate (HWP) followed by a polarizing beam splitter.

## 3. Results

12. M. Hamar, J. Peřina Jr., O. Haderka, and V. Michálek, “Transverse coherence of photon pairs generated in spontaneous parametric downconversion,” Phys. Rev. A **81**, 043827 (2010). [CrossRef]

5. O. Haderka, J. Peřina Jr., and M. Hamar, “Simple direct measurement of nonclassical joint signal-idler photon-number statistics and the correlation area of twin photon beams,” J. Opt. B Quantum Semicl. Opt. **7**, S572–S576 (2005). [CrossRef]

_{is,Θ}= (490 ± 52)

*μ*m in the horizontal direction (radial with respect to the cone section) and ΔΓ

_{is,Ψ}= (710 ± 52)

*μ*m in the vertical (azimuthal) one. The sequence was measured at the pump power

*P*= 20

_{p}*μ*W, which resulted in 8.9 mean idler detected photons and 10.5 mean signal detected photons. As our method naturally includes also the determination of effective quantum detection efficiency [18

18. J. Peřina Jr., O. Haderka, V. Michálek, and M. Hamar, “Absolute detector calibration using twin beams,” Opt. Lett. **37**, 2475–2477 (2012). [CrossRef]

*P*causes the transition from photon-counting to classical-intensity measurement and patterns with speckles [see Fig. 2(c)] occur in single-shot images for

_{p}*P*values larger than 20 mW. By setting a 4×4-hardware binning, we took a sequence of 1000 images for different pump powers and pump-beam sizes and processed them by computing intensity AC functions Γ

_{p}*and XC functions Γ*

_{ii}*at 100 randomly selected points in the fringe patterns close to the frequency degeneracy of the PDC process [for an example, see Fig. 2(d)]. This approach gives a better signal-to-noise ratio than taking the correlation of the whole image, as only a part of the image is covered by a significant light intensity. These correlation functions are conveniently characterized by their horizontal ΔΓ*

_{is}_{Θ}and vertical ΔΓ

_{Ψ}widths that depend on pump-beam parameters.

*P*, as shown in Fig. 3. The width ΔΓ of intensity XC function both in the radial [Fig. 3(a)] and azimuthal [Fig. 3(b)] directions is systematically larger than the corresponding width of the intensity AC function. This occurs probably due to the geometry of our experiment which is not perfectly far-field as we do not use any imaging to simplify the setup. The drop in AC function widths ΔΓ occurring for low pump powers

_{p}*P*(below 30 mW) reflects insufficient coherence inside the field observed for not sufficiently intense stimulated process. The width of the XC function Γ

_{p}*remains large in this region, as the coherence between the signal and idler fields (XC) originates in spontaneously generated photon pairs whereas the internal coherence (AC) of both emitted beams arises from stimulated emission in the nonlinear process [19*

_{is}19. X. Y. Zou, L. J. Wang, and L. Mandel, “Induced coherence and indistinguishability in optical interference,” Phys. Rev. Lett. **67**, 318–321 (1991). [CrossRef] [PubMed]

*measured at the single-photon level (*

_{is}*P*= 20

_{p}*μ*W). We can see that its value coincides well with the widths ΔΓ

*of the correlation functions obtained by classical-intensity measurements. This gives an experimental evidence that the correlation functions obtained in single-photon and classical-intensity measurements represent the same physical phenomenon of PDC though observed at different physical conditions. Whereas the twin beams at single-photon level are described by highly nonclassical multi-mode Fock states with completely random optical phases, the intense twin beams are well described by multi-mode classical coherent states whose well defined phase properties inside individual modes manifest themselves with the occurrence of speckles [13*

_{is}13. E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion,” Phys. Rev. A **69**, 023802 (2004). [CrossRef]

## 4. Conclusion

## Acknowledgments

## References and links

1. | L. Mandel and E. Wolf, |

2. | A. A. Malygin, A. N. Penin, and A. V. Sergienko, “Spatiotemporal grouping of photons in spontaneous parametric scattering of light,” Dokl. Akad. Nauk SSSR |

3. | B. M. Jost, A. V. Sergienko, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Spatial correlations of spontaneously down-converted photon pairs detected with a single-photon-sensitive CCD camera,” Opt. Express |

4. | A. Mosset, F. Deveaux, G. Fanjoux, and E. Lantz, “Direct experimental characterization of the Bose-Einstein distribution of spatial fluctuations of spontaneous parametric down-conversion,” Eur. Phys. J. D |

5. | O. Haderka, J. Peřina Jr., and M. Hamar, “Simple direct measurement of nonclassical joint signal-idler photon-number statistics and the correlation area of twin photon beams,” J. Opt. B Quantum Semicl. Opt. |

6. | M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera”,Nat. Commun. |

7. | C. H. Monken, P. H. Souto Ribeiro, and S. Padua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A |

8. | G. Molina-Terriza, S. Minardi, Y. Deyanova, C. I. Osorio, M. Hendrych, and J. P. Torres, “Control of the shape of the spatial mode function of photons generated in noncollinear spontaneous parametric down conversion,” Phys. Rev. A |

9. | T. P. Grayson and G. A. Barbosa, “Spatial properties of spontaneous parametric down-conversion and their effect on induced coherence without induced emission,” Phys. Rev. A |

10. | A. Joobeur, B. E. A. Saleh, and M. C. Teich, “Spatiotemporal coherence properties of entangled light beams generated by parametric down-conversion,” Phys. Rev. A |

11. | A. Joobeur, B. E. A. Saleh, T. S. Larchuk, and M. C. Teich, “Coherence properties of entangled light beams generated by parametric down-conversion: theory and experiment,” Phys. Rev. A |

12. | M. Hamar, J. Peřina Jr., O. Haderka, and V. Michálek, “Transverse coherence of photon pairs generated in spontaneous parametric downconversion,” Phys. Rev. A |

13. | E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion,” Phys. Rev. A |

14. | M. Bondani, A. Allevi, and A. Andreoni, “Ghost imaging by intense multimode twin beam,” Eur. Phys. J. Special Topics |

15. | O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric downconversion,” Phys. Rev. Lett. |

16. | G. Brida, M. Genovese, A. Meda, E. Predazzi, and I. Ruo Berchera, “Systematic study of the PDC speckle structure for quantum imaging applications,” Int. Journ. Quantum Inf. |

17. | G. Brida, M. Genovese, A. Meda, E. Predazzi, and I. Ruo Berchera, “Tailoring PDC speckle structure,” J. Mod. Opt. |

18. | J. Peřina Jr., O. Haderka, V. Michálek, and M. Hamar, “Absolute detector calibration using twin beams,” Opt. Lett. |

19. | X. Y. Zou, L. J. Wang, and L. Mandel, “Induced coherence and indistinguishability in optical interference,” Phys. Rev. Lett. |

20. | J. Peřina Jr., “Spatial properties of entangled photon pairs generated in nonlinear layered structures,” Phys. Rev. A |

**OCIS Codes**

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

(230.5160) Optical devices : Photodetectors

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: March 25, 2014

Revised Manuscript: May 2, 2014

Manuscript Accepted: May 5, 2014

Published: May 27, 2014

**Citation**

Radek Machulka, Ondřej Haderka, Jan Peřina, Marco Lamperti, Alessia Allevi, and Maria Bondani, "Spatial properties of twin-beam correlations at low- to high-intensity transition," Opt. Express **22**, 13374-13379 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-11-13374

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### References

- L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995). [CrossRef]
- A. A. Malygin, A. N. Penin, A. V. Sergienko, “Spatiotemporal grouping of photons in spontaneous parametric scattering of light,” Dokl. Akad. Nauk SSSR 281, 308–313 (1985).
- B. M. Jost, A. V. Sergienko, A. F. Abouraddy, B. E. A. Saleh, M. C. Teich, “Spatial correlations of spontaneously down-converted photon pairs detected with a single-photon-sensitive CCD camera,” Opt. Express 3, 81–88 (1998). [CrossRef] [PubMed]
- A. Mosset, F. Deveaux, G. Fanjoux, E. Lantz, “Direct experimental characterization of the Bose-Einstein distribution of spatial fluctuations of spontaneous parametric down-conversion,” Eur. Phys. J. D 28, 447–451 (2004). [CrossRef]
- O. Haderka, J. Peřina, M. Hamar, “Simple direct measurement of nonclassical joint signal-idler photon-number statistics and the correlation area of twin photon beams,” J. Opt. B Quantum Semicl. Opt. 7, S572–S576 (2005). [CrossRef]
- M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera”,Nat. Commun. 3, 984 (2012). [CrossRef] [PubMed]
- C. H. Monken, P. H. Souto Ribeiro, S. Padua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A 57, 3123–3126 (1998). [CrossRef]
- G. Molina-Terriza, S. Minardi, Y. Deyanova, C. I. Osorio, M. Hendrych, J. P. Torres, “Control of the shape of the spatial mode function of photons generated in noncollinear spontaneous parametric down conversion,” Phys. Rev. A 72, 065802 (2005). [CrossRef]
- T. P. Grayson, G. A. Barbosa, “Spatial properties of spontaneous parametric down-conversion and their effect on induced coherence without induced emission,” Phys. Rev. A 49, 2948–2961 (1994). [CrossRef] [PubMed]
- A. Joobeur, B. E. A. Saleh, M. C. Teich, “Spatiotemporal coherence properties of entangled light beams generated by parametric down-conversion,” Phys. Rev. A 50, 3349–3361 (1994). [CrossRef] [PubMed]
- A. Joobeur, B. E. A. Saleh, T. S. Larchuk, M. C. Teich, “Coherence properties of entangled light beams generated by parametric down-conversion: theory and experiment,” Phys. Rev. A 53, 4360–4371 (1996). [CrossRef] [PubMed]
- M. Hamar, J. Peřina, O. Haderka, V. Michálek, “Transverse coherence of photon pairs generated in spontaneous parametric downconversion,” Phys. Rev. A 81, 043827 (2010). [CrossRef]
- E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion,” Phys. Rev. A 69, 023802 (2004). [CrossRef]
- M. Bondani, A. Allevi, A. Andreoni, “Ghost imaging by intense multimode twin beam,” Eur. Phys. J. Special Topics 203, 151–161 (2012). [CrossRef]
- O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric downconversion,” Phys. Rev. Lett. 93, 243601 (2004). [CrossRef]
- G. Brida, M. Genovese, A. Meda, E. Predazzi, I. Ruo Berchera, “Systematic study of the PDC speckle structure for quantum imaging applications,” Int. Journ. Quantum Inf. 7, 139–147 (2009). [CrossRef]
- G. Brida, M. Genovese, A. Meda, E. Predazzi, I. Ruo Berchera, “Tailoring PDC speckle structure,” J. Mod. Opt. 56, 201–208 (2009). [CrossRef]
- J. Peřina, O. Haderka, V. Michálek, M. Hamar, “Absolute detector calibration using twin beams,” Opt. Lett. 37, 2475–2477 (2012). [CrossRef]
- X. Y. Zou, L. J. Wang, L. Mandel, “Induced coherence and indistinguishability in optical interference,” Phys. Rev. Lett. 67, 318–321 (1991). [CrossRef] [PubMed]
- J. Peřina, “Spatial properties of entangled photon pairs generated in nonlinear layered structures,” Phys. Rev. A 84, 053840 (2011). [CrossRef]

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