Stochastic Resonances in Photon Number Resolving Detectors

Shree Krishnamoorthy, Harish Ravishankar, Pradeep K. Kumar, Anil Prabhakar


The photon number statistics of a coherent optical pulse will typically follow a Poissonian distribution. At low photon numbers, a gated avalanche photo-detector (GAPD) is used to detect the presence of photons in each optical pulse. GAPDs use a thresholding logic, but suffer from after-pulsing effects. The efficiency of a GAPD was characterized and its after-pulses were analyzed by looking at the detection patterns obtained. The GAPD was found to show evidence of stochastic resonance which affected the dark noise of the detector. We post-process the detected bit patterns to eliminate the resonances and estimate the true dark count of the detector. The GAPD was then used with a recirculating optical loop to build a multi-photon resolving detector (MPRD). In the MPRD, the probability of detection at consecutive loop round trip times were used to estimate the mean photon number. We quantify these statistics and establish a reliable measure of photon number at an optical power of -94 dBm. The digital electronics was able to store data for 224 optical pulses, making the statistical analysis meaningful.


  1. Ben-Michael, R., Itzler, M. A., Nyman, B., and Entwistle, M. (2006). Afterpulsing in InGaAs/InP single photon avalanche photodetectors. In Dig. LEOS Summer Top. Meet., pages 15-16, Quebec City. IEEE.
  2. Bennett, C. H., Brassard, G., et al. (1984). Quantum cryptography: Public key distribution and coin tossing. In Proc. IEEE Int. Conf. Computers, Systems and Signal Processing, Bangalore, volume 175-179, Bangalore. New York, IEEE.
  3. Blasej, K., Prochazka, I., and Kodet, J. (2014). Photon counting detector for high-repetition-rate optical time transfer providing extremely high data yield. Optical Engineering, 53:081903.
  4. Bloch, M., McLaughlin, S. W., Merolla, J. M., and Patois, F. (2007). Frequency-coded quantum key distribution. Opt. Lett., 32:301-303.
  5. Cova, S., Ghioni, M., Lotito, A., Rech, I., and Zappa, F. (2004). Evolution and prospects for single-photon avalanche diodes and quenching circuits. J. Mod. Optic, 51(9-10):1267-1288.
  6. Fitch, M., Jacobs, B., Pittman, T., and Franson, J. (2003). Photon-number resolution using time-multiplexed single-photon detectors. Phys. Rev. A, 68(4):043814.
  7. Gammaitoni, L. (1995). Stochastic resonance and the dithering effect in threshold physical systems. Phys. Rev. E, 52(5):4691.
  8. Haderka, O., Hamar, M., and Per?ina Jr, J. (2004). Experimental multi-photon-resolving detector using a single avalanche photodiode. Eur. Phys. J. D - Atomic, Molecular, Optical and Plasma Physics, 28:149-154.
  9. Hadfield, R. H. (2009). Single-photon detectors for optical quantum information applications. Nat. photonics, 3(12):696-705.
  10. Inoue, K., Waks, E., and Yamamoto, Y. (2003). Differentialphase-shift quantum key distribution using coherent light. Phy. Rev. A, 68:022317.
  11. Kolb, K. (2014). Signal-to-noise ratio of geiger-mode avalanche photodiode single-photon counting detectors. Optical Engineering, 53(8):081904-081904.
  12. Kumar, P., Thevan, S., and Prabhakar, A. (2009). Optimization of gated photodetection for quantum key distribution. In SPIE Europe Optics and Optoelec. Conf., Prague. SPIE.
  13. Lo, H.-K. and Chau, H. F. (1999). Unconditional security of quantum key distribution over arbitrarily long distances. Science, 283(5410):2050-2056.
  14. McDonnell, M. D., Stocks, N. G., Pearce, C. E. M., and Abbott, D. (2008). Stochastic resonance: from suprathreshold stochastic resonance to stochastic signal quantization. Cambridge University Press, Cambridge.
  15. McIntyre, R. (1966). Multiplication noise in uniform avalanche diodes. IEEE Trans. Electron Devices, ED13(1):164-168.
  16. Mogilevtsev, D. (2010). Calibration of single-photon detectors using quantum statistics. Phys. Rev. A, 82(2):021807.
  17. Norbert, L. and Mika, J. (2002). Quantum key distribution with realistic states: photon-number statistics in the photon-number splitting attack. New J. of Phys., 4(1):44.
  18. Ravi, H. and Prabhakar, A. (2011). Coherent state statistics from time-resolved photon counting. In SPIE OPTO, pages 79600S-79600S, San Francisco. SPIE.
  19. Tosi, A., Mora, A. D., Zappa, F., and Cova, S. (2009). Single-photon avalanche diodes for the near-infrared range: detector and circuit issues. J. Mod. Optic, 56(2- 3):299-308.
  20. Valerio, S., Helle, B. P., Nicolas, C., Miloslav, D., Norbert, L., and Momtchil, P. (2009). The security of practical quantum key distribution. Rev. of Mod. Phys., 81(3):1301.

Paper Citation

in Harvard Style

Krishnamoorthy S., Ravishankar H., K. Kumar P. and Prabhakar A. (2015). Stochastic Resonances in Photon Number Resolving Detectors . In Proceedings of the 3rd International Conference on Photonics, Optics and Laser Technology - Volume 2: PHOTOPTICS, ISBN 978-989-758-093-2, pages 40-46. DOI: 10.5220/0005335800400046

in Bibtex Style

author={Shree Krishnamoorthy and Harish Ravishankar and Pradeep K. Kumar and Anil Prabhakar},
title={Stochastic Resonances in Photon Number Resolving Detectors},
booktitle={Proceedings of the 3rd International Conference on Photonics, Optics and Laser Technology - Volume 2: PHOTOPTICS,},

in EndNote Style

JO - Proceedings of the 3rd International Conference on Photonics, Optics and Laser Technology - Volume 2: PHOTOPTICS,
TI - Stochastic Resonances in Photon Number Resolving Detectors
SN - 978-989-758-093-2
AU - Krishnamoorthy S.
AU - Ravishankar H.
AU - K. Kumar P.
AU - Prabhakar A.
PY - 2015
SP - 40
EP - 46
DO - 10.5220/0005335800400046