## Accessing photon bunching with a photon number resolving multi-pixel detector |

Optics Express, Vol. 19, Issue 10, pp. 9352-9363 (2011)

http://dx.doi.org/10.1364/OE.19.009352

Acrobat PDF (1137 KB)

### Abstract

In quantum optics and its applications, there is an urgent demand for photon-number resolving detectors. Recently, there appeared multi-pixel counters (MPPC) that are able to distinguish between 1,2,..10 photons. At the same time, strong coupling between different pixels (crosstalk) hinders their photon-number resolution. In this work, we suggest a method for `filtering out’ the crosstalk effect in the measurement of intensity correlation functions. The developed approach can be expanded to the analysis of higher-order intensity correlations by using just a single MPPC.

© 2011 OSA

## 1. Introduction

1. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature **409**(6816), 46–52 (2001). [CrossRef] [PubMed]

3. J. L. O’Brien, “Optical quantum computing,” Science **318**(5856), 1567–1570 (2007). [CrossRef] [PubMed]

4. P. Walther, J.-W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature **429**(6988), 158–161 (2004). [CrossRef] [PubMed]

5. M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature **429**(6988), 161–164 (2004). [CrossRef] [PubMed]

6. B. Lounis and M. Orrit, “Single-photon sources,” Rep. Prog. Phys. **68**(5), 1129–1179 (2005). [CrossRef]

7. S. Cova, A. Longoni, and A. Andreoni, “Towards picoseconds resolution with single-photon avalanche diodes,” Rev. Sci. Instrum. **52**(3), 408–412 (1981). [CrossRef]

8. R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics **3**(12), 696–705 (2009). [CrossRef]

9. S. Takeuchi, J. Kim, Y. Yamamoto, and H. H. Hogue, “Development of a high quantum-efficiency single-photon counting system,” Appl. Phys. Lett. **74**(8), 1063–1065 (1999). [CrossRef]

14. A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express **16**(5), 3032–3040 (2008). [CrossRef] [PubMed]

15. M. Bondani, A. Allevi, A. Agliati, and A. Andreoni, “Self-consistent characterization of light statistics,” J. Mod. Opt. **56**(2), 226–231 (2009). [CrossRef]

16. B. E. Kardynal, Z. L. Yuan, and A. J. Shields, “An avalanche-photodiode-based photon-number-resolving detector,” Nat. Photonics **2**(7), 425–428 (2008). [CrossRef]

17. D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, and I. A. Walmsley, “Fiber-assisted detection with photon number resolution,” Opt. Lett. **28**(23), 2387–2389 (2003). [CrossRef] [PubMed]

19. M. Mičuda, O. Haderka, and M. Ježek, “High-efficiency photon-number-resolving multichannel detector,” Phys. Rev. A **78**(2), 025804 (2008). [CrossRef]

20. Hamamatsu web-page http://jp.hamamatsu.com/.

*pixels*, are embedded in a single chip of several millimeter size with their outputs connected into a summation circuit. The chip is illuminated by a spatially diffused light spot (e.g. originating from the fiber), providing that the chance of two photons to hit the same pixel is negligible. The amplitude of MPPC output is proportional to the number of firing pixels, which, in an ideal case, is equivalent to the number of registered incident photons. Thus, the concept of MPPC resembles the traditional approach of separating an incoming pulse into multiple spatial modes, providing, however, a striking advantage in compactness and photon-number resolution.

25. M. Ramilli, A. Allevi, V. Chmill, M. Bondani, M. Caccia, and A. Andreoni, “Photon-number statistics with silicon photomultipliers,” J. Opt. Soc. Am. B **27**(5), 852–862 (2010). [CrossRef]

24. I. Rech, A. Ingargiola, R. Spinelli, I. Labanca, S. Marangoni, M. Ghioni, and S. Cova, “Optical crosstalk in single photon avalanche diode arrays: a new complete model,” Opt. Express **16**(12), 8381–8394 (2008). [CrossRef] [PubMed]

## 2. Theory

*l*-th order CF at zero time delay is defined aswhere

*Two-mode squeezed vacuum*state can be produced, for instance, via nondegenerate collinear parametric down conversion (PDC) in a nonlinear medium. In this case the joint state vector is a superposition of Fock-state products with the same photon numbers for signal

*(s)*and idler

*(i)*beams [26],In the case of degenerate collinear PDC, the signal and idler photons are indistinguishable, and the state produced is

*single-mode squeezed vacuum*, with the state vector given by a superposition of even-number Fock states,The index

*n*does not have to be the number of single modes, but may relate to the ensembles of many modes, accessed via multimode detection [26]. In this case, the probability amplitudes in Eq. (2a) and Eq. (2b) obey the Poissonian distribution, with

*B*is the inverse number of detected frequency and spatial modes, while

27. M. Avenhaus, K. Laiho, M. V. Chekhova, and C. Silberhorn, “Accessing higher order correlations in quantum optical states by time multiplexing,” Phys. Rev. Lett. **104**(6), 063602 (2010). [CrossRef] [PubMed]

*k*is the number of pixels having fired (

*m*, the average number of photons hitting a single pixel is

*m*(the binomial coefficient). The total number of pairwise coincidences is

*m*is

28. O. Haderka, J. Perina Jr, M. Hamar, and J. Perina, “Direct measurement and reconstruction of nonclassical features of twin beams generated in spontaneous parametric down-conversion,” Phys. Rev. A **71**(3), 033815 (2005). [CrossRef]

29. J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of sub-shot-noise correlations of spatial fluctuations in the photon-counting regime,” Phys. Rev. Lett. **101**(23), 233604 (2008). [CrossRef] [PubMed]

*k*-photon event from the dark noise only, which can be measured independently.

*k*-photon event would contain a contribution from the lower photon number events with the addition from the crosstalk. In reality, both real photocounts and dark counts would trigger crosstalk events. Thus the number of

*k*-photon events is given by

22. P. Eraerds, M. Legré, A. Rochas, H. Zbinden, and N. Gisin, “SiPM for fast photon-counting and multiphoton detection,” Opt. Express **15**(22), 14539–14549 (2007). [CrossRef] [PubMed]

23. I. Afek, A. Natan, O. Ambar, and Y. Silberberg, “Quantum state measurements using multipixel photon detectors,” Phys. Rev. A **79**(4), 043830 (2009). [CrossRef]

25. M. Ramilli, A. Allevi, V. Chmill, M. Bondani, M. Caccia, and A. Andreoni, “Photon-number statistics with silicon photomultipliers,” J. Opt. Soc. Am. B **27**(5), 852–862 (2010). [CrossRef]

23. I. Afek, A. Natan, O. Ambar, and Y. Silberberg, “Quantum state measurements using multipixel photon detectors,” Phys. Rev. A **79**(4), 043830 (2009). [CrossRef]

25. M. Ramilli, A. Allevi, V. Chmill, M. Bondani, M. Caccia, and A. Andreoni, “Photon-number statistics with silicon photomultipliers,” J. Opt. Soc. Am. B **27**(5), 852–862 (2010). [CrossRef]

*k*-photon events is given bywhere

*P*being the probability of the occurrence of one crosstalk photocount and

*q*the number of avalanches triggered by the impinging photons. A generalized model, which takes into account the higher-order crosstalk effects, has been considered in [25

**27**(5), 852–862 (2010). [CrossRef]

*P*in Eqs. (5a,5b) can be ignored. Thus the model simplifies to a linear one [22

22. P. Eraerds, M. Legré, A. Rochas, H. Zbinden, and N. Gisin, “SiPM for fast photon-counting and multiphoton detection,” Opt. Express **15**(22), 14539–14549 (2007). [CrossRef] [PubMed]

*k*-photon events that have been modified by the crosstalk and have become

*k*-photon events. In the linear model given by Eq. (5c), it is assumed that the largest nonlinear term in Eq. (5a), namely

*P*can be easily measured using some light source with known

## 3. Experiment

^{−3}. A lens with a focal length of f=750 mm was used to focus the pump beam into two 5mm long type-I BBO crystals, where PDC occurred. The crystals had oppositely directed axes in order to compensate for the spatial walk-off of the pump. After passing the BBO crystals the pump was eliminated by a UV mirror (UVM) whilst the PDC emission fluently passed through it. The collinear part of the PDC beam with the divergence equal to that of the pump was coupled into a single-mode optical fiber (SMF) by means of an achromatic lens f=6.24 mm, placed at a distance of 550 mm from the crystal. At the output of the fiber a collimated beam was formed by a lens with f=6.24 mm and addressed into an MPPC module (Hamamatsu, model C10751-02 with 400 pixels embedded in 1.5*1.5 mm chip). In order to ensure a relatively homogeneous illumination of the MPPC area, a lens (L) with f=400 mm was used to focus the beam onto the MPPC chip and provided a spot with the diameter 700 um. A fast digital oscilloscope (LeCroy Wave Runner, 2 GS/s sampling rate) was used to capture the analogue output from the MPPC (in a range 0-650 mV) and plot the histogram of its amplitude. The standard acquisition for each point was 10

^{6}shots of the pump laser.

^{−3}. The laser pulse was tailored to mimic the profile and duration of the PDC pulse and its intensity was controlled by a half-wave plate (HWP) and a polarizing beam splitter (PBS). In relevant measurements the laser pulse was addressed into the optical path by a flipping mirror (FM1) and then was focused onto the MPPC chip with the same spot size as in the PDC experiment.

32. R. D. Younger, K. A. McIntosh, J. W. Chludzinski, D. C. Oakley, L. J. Mahoney, J. E. Funk, J. P. Donnelly, and S. Verghese, “Crosstalk Analsis of Integrated Geiger-mode Avalanche Photodiode Focal Plane Array,” Proc. SPIE **7320**, 73200Q–73200Q-12 (2009). [CrossRef]

## 4. Results and discussion

*P*being the only fitting parameter, is shown in Fig. 3 and Fig. 4 (black dashed trace, squares) and summarized in Table 1 . The value of the crosstalk probability was found to be

## 5. Conclusion

32. R. D. Younger, K. A. McIntosh, J. W. Chludzinski, D. C. Oakley, L. J. Mahoney, J. E. Funk, J. P. Donnelly, and S. Verghese, “Crosstalk Analsis of Integrated Geiger-mode Avalanche Photodiode Focal Plane Array,” Proc. SPIE **7320**, 73200Q–73200Q-12 (2009). [CrossRef]

## Acknowledgement

## References and links

1. | E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature |

2. | P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. |

3. | J. L. O’Brien, “Optical quantum computing,” Science |

4. | P. Walther, J.-W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature |

5. | M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature |

6. | B. Lounis and M. Orrit, “Single-photon sources,” Rep. Prog. Phys. |

7. | S. Cova, A. Longoni, and A. Andreoni, “Towards picoseconds resolution with single-photon avalanche diodes,” Rev. Sci. Instrum. |

8. | R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics |

9. | S. Takeuchi, J. Kim, Y. Yamamoto, and H. H. Hogue, “Development of a high quantum-efficiency single-photon counting system,” Appl. Phys. Lett. |

10. | J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett. |

11. | E. Waks, K. Inoue, E. Diamanti, and Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quant. |

12. | B. Cabrera, R. M. Clarke, P. Colling, A. J. Miller, S. Nam, and R. W. Romani, “Detection of single infrared, optical, and ultraviolet photons using superconducting transition edge sensors,” Appl. Phys. Lett. |

13. | D. Rosemberg, A. E. Lita, A. J. Miller, and S. W. Nam, “Noise-free high-efficiency photon-number-resolving detectors,” Phys. Rev. A |

14. | A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express |

15. | M. Bondani, A. Allevi, A. Agliati, and A. Andreoni, “Self-consistent characterization of light statistics,” J. Mod. Opt. |

16. | B. E. Kardynal, Z. L. Yuan, and A. J. Shields, “An avalanche-photodiode-based photon-number-resolving detector,” Nat. Photonics |

17. | D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, and I. A. Walmsley, “Fiber-assisted detection with photon number resolution,” Opt. Lett. |

18. | M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A |

19. | M. Mičuda, O. Haderka, and M. Ježek, “High-efficiency photon-number-resolving multichannel detector,” Phys. Rev. A |

20. | Hamamatsu web-page http://jp.hamamatsu.com/. |

21. | K. Yamamoto, K. Yamamura, K. Sato, S. Kamakura, T. Ota, H. Suzuki, and S. Ohsuka, “Development of Multi-Pixel Photon Counter (MPPC),” Nuclear Science Symposium Conference Record, 2007. NSS ’07. IEEE |

22. | P. Eraerds, M. Legré, A. Rochas, H. Zbinden, and N. Gisin, “SiPM for fast photon-counting and multiphoton detection,” Opt. Express |

23. | I. Afek, A. Natan, O. Ambar, and Y. Silberberg, “Quantum state measurements using multipixel photon detectors,” Phys. Rev. A |

24. | I. Rech, A. Ingargiola, R. Spinelli, I. Labanca, S. Marangoni, M. Ghioni, and S. Cova, “Optical crosstalk in single photon avalanche diode arrays: a new complete model,” Opt. Express |

25. | M. Ramilli, A. Allevi, V. Chmill, M. Bondani, M. Caccia, and A. Andreoni, “Photon-number statistics with silicon photomultipliers,” J. Opt. Soc. Am. B |

26. | D. N. Klyshko, |

27. | M. Avenhaus, K. Laiho, M. V. Chekhova, and C. Silberhorn, “Accessing higher order correlations in quantum optical states by time multiplexing,” Phys. Rev. Lett. |

28. | O. Haderka, J. Perina Jr, M. Hamar, and J. Perina, “Direct measurement and reconstruction of nonclassical features of twin beams generated in spontaneous parametric down-conversion,” Phys. Rev. A |

29. | J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of sub-shot-noise correlations of spatial fluctuations in the photon-counting regime,” Phys. Rev. Lett. |

30. | H. Otono, S. Yamashita, T. Yoshioka, H. Oide, T. Suehiro, and H. Hano, “Study of MPPC at liquid nitrogen temperature,” Proceedings of International Workshop on New Photon-Detectors PD07 007 (2007). |

31. | M. Akiba, K. Tsujino, K. Sato, and M. Sasaki, “Multipixel silicon avalanche photodiode with ultralow dark count rate at liquid nitrogen temperature,” Opt. Express |

32. | R. D. Younger, K. A. McIntosh, J. W. Chludzinski, D. C. Oakley, L. J. Mahoney, J. E. Funk, J. P. Donnelly, and S. Verghese, “Crosstalk Analsis of Integrated Geiger-mode Avalanche Photodiode Focal Plane Array,” Proc. SPIE |

**OCIS Codes**

(270.0270) Quantum optics : Quantum optics

(270.5290) Quantum optics : Photon statistics

(270.5570) Quantum optics : Quantum detectors

(040.1345) Detectors : Avalanche photodiodes (APDs)

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: February 17, 2011

Revised Manuscript: April 1, 2011

Manuscript Accepted: April 1, 2011

Published: April 28, 2011

**Citation**

Dmitry A. Kalashnikov, Si Hui Tan, Maria V. Chekhova, and Leonid A. Krivitsky, "Accessing photon bunching with a photon number resolving multi-pixel detector," Opt. Express **19**, 9352-9363 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-10-9352

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### References

- E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001). [CrossRef] [PubMed]
- P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79(1), 135–175 (2007). [CrossRef]
- J. L. O’Brien, “Optical quantum computing,” Science 318(5856), 1567–1570 (2007). [CrossRef] [PubMed]
- P. Walther, J.-W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429(6988), 158–161 (2004). [CrossRef] [PubMed]
- M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429(6988), 161–164 (2004). [CrossRef] [PubMed]
- B. Lounis and M. Orrit, “Single-photon sources,” Rep. Prog. Phys. 68(5), 1129–1179 (2005). [CrossRef]
- S. Cova, A. Longoni, and A. Andreoni, “Towards picoseconds resolution with single-photon avalanche diodes,” Rev. Sci. Instrum. 52(3), 408–412 (1981). [CrossRef]
- R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics 3(12), 696–705 (2009). [CrossRef]
- S. Takeuchi, J. Kim, Y. Yamamoto, and H. H. Hogue, “Development of a high quantum-efficiency single-photon counting system,” Appl. Phys. Lett. 74(8), 1063–1065 (1999). [CrossRef]
- J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett. 74(7), 902–904 (1999). [CrossRef]
- E. Waks, K. Inoue, E. Diamanti, and Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quant. 9(6), 1502–1511 (2003). [CrossRef]
- B. Cabrera, R. M. Clarke, P. Colling, A. J. Miller, S. Nam, and R. W. Romani, “Detection of single infrared, optical, and ultraviolet photons using superconducting transition edge sensors,” Appl. Phys. Lett. 73(6), 735 (1998). [CrossRef]
- D. Rosemberg, A. E. Lita, A. J. Miller, and S. W. Nam, “Noise-free high-efficiency photon-number-resolving detectors,” Phys. Rev. A 71(6), 061803 (2005). [CrossRef]
- A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16(5), 3032–3040 (2008). [CrossRef] [PubMed]
- M. Bondani, A. Allevi, A. Agliati, and A. Andreoni, “Self-consistent characterization of light statistics,” J. Mod. Opt. 56(2), 226–231 (2009). [CrossRef]
- B. E. Kardynal, Z. L. Yuan, and A. J. Shields, “An avalanche-photodiode-based photon-number-resolving detector,” Nat. Photonics 2(7), 425–428 (2008). [CrossRef]
- D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, and I. A. Walmsley, “Fiber-assisted detection with photon number resolution,” Opt. Lett. 28(23), 2387–2389 (2003). [CrossRef] [PubMed]
- M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68(4), 043814 (2003). [CrossRef]
- M. Mičuda, O. Haderka, and M. Ježek, “High-efficiency photon-number-resolving multichannel detector,” Phys. Rev. A 78(2), 025804 (2008). [CrossRef]
- Hamamatsu web-page http://jp.hamamatsu.com/ .
- K. Yamamoto, K. Yamamura, K. Sato, S. Kamakura, T. Ota, H. Suzuki, and S. Ohsuka, “Development of Multi-Pixel Photon Counter (MPPC),” Nuclear Science Symposium Conference Record, 2007. NSS ’07. IEEE 2, 1511–1515 (2007).
- P. Eraerds, M. Legré, A. Rochas, H. Zbinden, and N. Gisin, “SiPM for fast photon-counting and multiphoton detection,” Opt. Express 15(22), 14539–14549 (2007). [CrossRef] [PubMed]
- I. Afek, A. Natan, O. Ambar, and Y. Silberberg, “Quantum state measurements using multipixel photon detectors,” Phys. Rev. A 79(4), 043830 (2009). [CrossRef]
- I. Rech, A. Ingargiola, R. Spinelli, I. Labanca, S. Marangoni, M. Ghioni, and S. Cova, “Optical crosstalk in single photon avalanche diode arrays: a new complete model,” Opt. Express 16(12), 8381–8394 (2008). [CrossRef] [PubMed]
- M. Ramilli, A. Allevi, V. Chmill, M. Bondani, M. Caccia, and A. Andreoni, “Photon-number statistics with silicon photomultipliers,” J. Opt. Soc. Am. B 27(5), 852–862 (2010). [CrossRef]
- D. N. Klyshko, Photons and Nonlinear Optics (Gordon and Breach, New York, 1988).
- M. Avenhaus, K. Laiho, M. V. Chekhova, and C. Silberhorn, “Accessing higher order correlations in quantum optical states by time multiplexing,” Phys. Rev. Lett. 104(6), 063602 (2010). [CrossRef] [PubMed]
- O. Haderka, J. Perina, M. Hamar, and J. Perina, “Direct measurement and reconstruction of nonclassical features of twin beams generated in spontaneous parametric down-conversion,” Phys. Rev. A 71(3), 033815 (2005). [CrossRef]
- J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of sub-shot-noise correlations of spatial fluctuations in the photon-counting regime,” Phys. Rev. Lett. 101(23), 233604 (2008). [CrossRef] [PubMed]
- H. Otono, S. Yamashita, T. Yoshioka, H. Oide, T. Suehiro, and H. Hano, “Study of MPPC at liquid nitrogen temperature,” Proceedings of International Workshop on New Photon-Detectors PD07 007 (2007).
- M. Akiba, K. Tsujino, K. Sato, and M. Sasaki, “Multipixel silicon avalanche photodiode with ultralow dark count rate at liquid nitrogen temperature,” Opt. Express 17(19), 16885–16897 (2009). [CrossRef] [PubMed]
- R. D. Younger, K. A. McIntosh, J. W. Chludzinski, D. C. Oakley, L. J. Mahoney, J. E. Funk, J. P. Donnelly, and S. Verghese, “Crosstalk Analsis of Integrated Geiger-mode Avalanche Photodiode Focal Plane Array,” Proc. SPIE 7320, 73200Q–73200Q-12 (2009). [CrossRef]

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