## Photon counts statistics of squeezed and multimode thermal states of light on multiplexed on–off detectors |

JOSA B, Vol. 31, Issue 10, pp. B8-B13 (2014)

http://dx.doi.org/10.1364/JOSAB.31.0000B8

Enhanced HTML Acrobat PDF (609 KB)

### Abstract

Photon number resolving detectors can be highly useful for studying the statistics of multiphoton quantum states of light. In this work we study the counts statistics of different states of light measured on multiplexed on–off detectors. We put special emphasis on artificial nonclassical features of the statistics obtained. We show new ways to derive analytical formulas for counts statistics and their moments. Using our approach we are the first, to the best of our knowledge, to derive statistics moments for multimode thermal states measured on multiplexed on–off detectors. We use them to determine empirical Mandel parameters and recently proposed sub-binomial parameters suitable for tests of nonclassicality of the measured states. Additionally, we investigate sub-Poissonian and superbunching properties of the two-mode squeezed state measured on a pair of multiplexed detectors, and we present results of the Fano factor and second-order correlation function for these states.

© 2014 Optical Society of America

**OCIS Codes**

(040.5570) Detectors : Quantum detectors

(270.5290) Quantum optics : Photon statistics

(270.6570) Quantum optics : Squeezed states

**History**

Original Manuscript: May 1, 2014

Revised Manuscript: July 5, 2014

Manuscript Accepted: July 17, 2014

Published: August 20, 2014

**Citation**

Radosław Chrapkiewicz, "Photon counts statistics of squeezed and multimode thermal states of light on multiplexed on–off detectors," J. Opt. Soc. Am. B **31**, B8-B13 (2014)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-31-10-B8

Sort: Year | Journal | Reset

### References

- V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004). [CrossRef]
- V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222–229 (2011). [CrossRef]
- R. Demkowicz-Dobrzanski, J. Kolodynski, and M. Guta, “The elusive Heisenberg limit in quantum-enhanced metrology,” Nat. Commun. 3, 1063 (2012). [CrossRef]
- M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429, 161–164 (2004). [CrossRef]
- I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328, 879–881 (2010). [CrossRef]
- D. F. Walls, “Squeezed states of light,” Nature 306, 141–146 (1983). [CrossRef]
- The LIGO Scientific Collaboration, “A gravitational wave observatory operating beyond the quantum shot-noise limit,” Nat. Phys. 7, 962–965 (2011). [CrossRef]
- G. Brida, M. Genovese, and I. R. Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010). [CrossRef]
- H. Paul, P. Törmä, T. Kiss, and I. Jex, “Photon chopping: new way to measure the quantum state of light,” Phys. Rev. Lett. 76, 2464–2467 (1996). [CrossRef]
- K. Banaszek and I. A. Walmsley, “Photon counting with a loop detector,” Opt. Lett. 28, 52–54 (2003). [CrossRef]
- J. Rehacek, Z. Hradil, O. Haderka, J. Perina, and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67, 061801 (2003). [CrossRef]
- D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499–1515 (2004). [CrossRef]
- I. Afek, A. Natan, O. Ambar, and Y. Silberberg, “Quantum state measurements using multipixel photon detectors,” Phys. Rev. A 79, 043830 (2009). [CrossRef]
- O. Haderka, J. Perina, and M. Hamar, “Direct measurement and reconstruction of nonclassical features of twin beams generated in spontaneous parametric down-conversion,” Phys. Rev. A 71, 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, 233604 (2008). [CrossRef]
- G. Brida, L. Ciavarella, I. P. Degiovanni, M. Genovese, L. Lolli, M. G. Mingolla, F. Piacentini, M. Rajteri, E. Taralli, and M. G. A. Paris, “Quantum characterization of superconducting photon counters,” New J. Phys. 14, 085001 (2012). [CrossRef]
- A. Allevi, M. Bondani, and A. Andreoni, “Photon-number correlations by photon-number resolving detectors,” Opt. Lett. 35, 1707–1709 (2010). [CrossRef]
- M. Lamperti, A. Allevi, M. Bondani, and R. Machulka, “Optimal sub-Poissonian light generation from twin beams by photon-number resolving detectors,” J. Opt. Soc. Am. B 31, 20–25 (2014). [CrossRef]
- A. Allevi, M. Lamperti, M. Bondani, J. Perina, V. Michalek, O. Haderka, and R. Machulka, “Characterizing the nonclassicality of mesoscopic optical twin-beam states,” Phys. Rev. A 88, 063807 (2013). [CrossRef]
- R. Machulka, O. Haderka, J. Perina, M. Lamperti, A. Allevi, and M. Bondani, “Spatial properties of twin-beam correlations at low- to high-intensity transition,” arXiv:1405.1190 (2014).
- T. J. Bartley, G. Donati, X.-M. Jin, A. Datta, M. Barbieri, and I. A. Walmsley, “Direct observation of sub-binomial light,” Phys. Rev. Lett. 110, 173602 (2013). [CrossRef]
- A. I. Lvovsky, R. Ghobadi, A. Chandra, A. S. Prasad, and C. Simon, Observation of micro-macro entanglement of light,” Nat. Phys. 9, 541–544, 2013. [CrossRef]
- H. Lee, U. Yurtsever, P. Kok, G. M. Hockney, C. Adami, S. L. Braunstein, and J. P. Dowling, “Towards photostatistics from photon-number discriminating detectors,” J. Mod. Opt. 51, 1517–1528 (2004). [CrossRef]
- J. S. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. L. Pregnell, C. Silberhorn, T. C. Ralph, J. Eisert, M. B. Plenio, and I. A. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2008). [CrossRef]
- J. Sperling, W. Vogel, and G. S. Agarwal, “True photocounting statistics of multiple on-off detectors,” Phys. Rev. A 85, 023820 (2012). [CrossRef]
- R. Chrapkiewicz, W. Wasilewski, and K. Banaszek, “High-fidelity spatially resolved multiphoton counting for quantum imaging applications,” arXiv:1405.4400 (2014).
- J. Sperling, W. Vogel, and G. S. Agarwal, “Sub-binomial light,” Phys. Rev. Lett. 109, 093601 (2012). [CrossRef]
- T. Kiesel and W. Vogel, “Complete nonclassicality test with a photon-number resolving detector,” Phys. Rev. A 86, 032119 (2012). [CrossRef]
- J. Sperling, W. Vogel, and G. S. Agarwal, “Correlation measurements with on-off detectors,” Phys. Rev. A 88, 043821 (2013). [CrossRef]
- V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008). [CrossRef]
- V. Boyer, A. Marino, and P. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100, 143601 (2008). [CrossRef]
- C. F. McCormick, V. Boyer, E. Arimondo, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32, 178–180 (2007). [CrossRef]
- R. Chrapkiewicz and W. Wasilewski, “Generation and delayed retrieval of spatially multimode Raman scattering in warm rubidium vapors,” Opt. Express 20, 29540 (2012). [CrossRef]
- M. Dabrowski, R. Chrapkiewicz, and W. Wasilewski, “Hamiltonian design in readout from room-temperature Raman quantum memory,” arXiv:1406.6489 (2014).
- E. W. Weisstein, “Stirling number of the second kind,” MathWorld—A Wolfram Web Resource, http://mathworld.wolfram.com/SecondKind.html .
- D. A. Kalashnikov, S.-H. Tan, and L. A. Krivitsky, “Crosstalk calibration of multi-pixel photon counters using coherent states,” Opt. Express 20, 5044–5051 (2012). [CrossRef]
- D. A. Kalashnikov, S.-H. Tan, T. S. Iskhakov, M. V. Chekhova, and L. A. Krivitsky, “Measurement of two-mode squeezing with photon number resolving multipixel detectors,” Opt. Lett. 37, 2829–2831 (2012). [CrossRef]
- A. Feito, J. S. Lundeen, H. Coldenstrodt-Ronge, J. Eisert, M. B. Plenio, and I. A. Walmsley, “Measuring measurement: theory and practice,” New J. Phys. 11, 093038 (2009). [CrossRef]
- J. W. Goodman, Statistical Optics (Wiley, 2000).
- T. S. Iskhakov, A. M. Pérez, K. Y. Spasibko, M. V. Chekhova, and G. Leuchs, “Superbunched bright squeezed vacuum state,” Opt. Lett. 37, 1919–1921 (2012). [CrossRef]
- P. Hong, J. Liu, and G. Zhang, “Two-photon superbunching of thermal light via multiple two-photon path interference,” Phys. Rev. A 86, 013807 (2012). [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.

« Previous Article | Next Article »

OSA is a member of CrossRef.