# Counting of Hong-Ou-Mandel Bunched Optical Photons Using a Fast Pixel Camera

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## Abstract

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## 1. Introduction

## 2. Single-Photon Counting Detectors

## 3. Counting of Bunched Single Photons in a Fast Camera

#### Tpx3Cam Fast Camera

^{2}. The processing electronics in each pixel records the time of arrival (ToA) of hits that cross a preset threshold with 1.6 ns resolution and stores it as time code in a memory inside the pixel. The information about time-over-threshold (ToT), which is related to the deposited energy in each pixel, is also stored. The readout is data driven with pixel dead time of only 475 ns + ToT, which allows multi-hit functionality at the pixel level and fast, 80 Mpix/sec, throughput.

^{TM}assembly [46], which integrates an intensifier, its power supply and relay optics to project the light flashes from the intensifier output screen directly onto the optical sensor in the camera. The image intensifier is a vacuum device with a photocathode followed by a micro-channel plate (MCP) and fast scintillator P47. The quantum efficiency (QE) of the GaAs photocathode in the intensifier (Photonis) is about 30% at 810 nm. The MCP efficiency in this intensifier is close to 100%. A second intensifier with a hi-QE green photocathode was used in series after the first intensifier to ensure efficient detection of the hits. The gains of both intensifiers were optimised to provide the maximum photon detection efficiency while avoiding saturation. Similar configurations of the intensified Tpx3Cam have been used previously for characterization of quantum networks [47,48], quantum target detection [49] and lifetime imaging [50] studies.

## 4. Experimental Setup

## 5. Data Analysis

## 6. Theory: SPDC Bi-Photon Spectrum and Hong-Ou-Mandel Effect

## 7. Results

## 8. Discussion and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AOM | acousto-optic modulator |

CW | continuous wave |

MCP | micro-channel plate |

MKID | microwave kinetic inductance device |

PDE | photon detection efficiency |

PMF | polarization maintaining fiber |

QE | quantum efficiency |

SiPM | silicon photomultiplier |

SNSPD | superconducting nanowire single photon detector |

SPDC | spontaneous parametric down conversion |

TES | transition edge sensor |

## References

- Ollivier, H.; Maillette de Buy Wenniger, I.; Thomas, S.; Wein, S.C.; Harouri, A.; Coppola, G.; Hilaire, P.; Millet, C.; Lemaître, A.; Sagnes, I.; et al. Reproducibility of high-performance quantum dot single-photon sources. ACS Photonics
**2020**, 7, 1050–1059. [Google Scholar] [CrossRef] - Saffman, M.; Walker, T.G. Creating single-atom and single-photon sources from entangled atomic ensembles. Phys. Rev. A
**2002**, 66, 06540. [Google Scholar] [CrossRef] [Green Version] - Firstenberg, O.; Adams, C.S.; Hofferberth, S. Nonlinear quantum optics mediated by Rydberg interactions. J. Phys. B At. Mol. Opt.
**2016**, 49, 152003. [Google Scholar] [CrossRef] - Ma, L.; Tang, X.; Slattery, O.T. Optical quantum memory and its applications in quantum communication systems. J. Res. Natl. Inst. Stan.
**2020**, 125, 125002. [Google Scholar] [CrossRef] - Scriminich, A.; Namazi, M.; Flament, M.; Gera, S.; Sagona-Stophel, S.; Vallone, G.; Villoresi, P.; Figueroa, E. Hong-Ou-Mandel interference between two weak coherent pulses retrieved from room-temperature quantum memories. In Proceedings of the Quantum Information and Measurement (QIM), Rome, Italy, 4–6 April 2019. [Google Scholar] [CrossRef]
- Chen, Y.A.; Chen, S.; Yuan, Z.S.; Zhao, B.; Chuu, C.S.; Schmiedmayer, J.; Pan, J.W. Memory-built-in quantum teleportation with photonic and atomic qubits. Nat. Phys.
**2008**, 4, 103–107. [Google Scholar] [CrossRef] - Motes, K.R.; Olson, J.P.; Rabeaux, E.J.; Dowling, J.P.; Olson, S.J.; Rohde, P.P. Linear Optical Quantum Metrology with Single Photons: Exploiting Spontaneously Generated Entanglement to Beat the Shot-Noise Limit. Phys. Rev. Lett.
**2015**, 114, 170802. [Google Scholar] [CrossRef] [Green Version] - Jeffrey, E.; Peters, N.A.; Kwiat, P.G. Towards a periodic deterministic source of arbitrary single-photon states. New J. Phys.
**2004**, 6, 100. [Google Scholar] [CrossRef] - Ramelow, S.; Mech, A.; Giustina, M.; Gröblacher, S.; Wieczorek, W.; Beyer, J.; Lita, A.; Calkins, B.; Gerrits, T.; Nam, S.W.; et al. Highly efficient heralding of entangled single photons. Opt. Express
**2013**, 21, 6707–6717. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Hong, C.K.; Ou, Z.Y.; Mandel, L. Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett.
**1987**, 59, 2044–2046. [Google Scholar] [CrossRef] [Green Version] - Hadfield, R.H. Single-photon detectors for optical quantum information applications. Nat. Photonics
**2009**, 3, 696–705. [Google Scholar] [CrossRef] - Seitz, P.; Theuwissen, A.J. (Eds.) Single-Photon Imaging; Springer: Berlin, Germany, 2011. [Google Scholar] [CrossRef] [Green Version]
- Migdall, A.; Polyakov, S.V.; Fan, J.; Bienfang, J.C. (Eds.) Single-Photon Generation and Detection; Experimental Methods in the Physical Sciences; Academic Press: Cambridge, MA, USA, 2013; Volume 45. [Google Scholar]
- Zhang, L.; Neves, L.; Lundeen, J.S.; Walmsley, I.A. A characterization of the single-photon sensitivity of an electron multiplying charge-coupled device. J. Phys. B At. Mol. Opt.
**2009**, 42, 114011. [Google Scholar] [CrossRef] [Green Version] - Avella, A.; Ruo-Berchera, I.; Degiovanni, I.P.; Brida, G.; Genovese, M. Absolute calibration of an EMCCD camera by quantum correlation, linking photon counting to the analog regime. Opt. Lett.
**2016**, 41, 1841. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Moreau, P.A.; Toninelli, E.; Gregory, T.; Padgett, M.J. Imaging with quantum states of light. Nat. Rev. Phys.
**2019**, 1, 367–380. [Google Scholar] [CrossRef] [Green Version] - Gasparini, L.; Bessire, B.; Unternährer, M.; Stefanov, A.; Boiko, D.; Perenzoni, M.; Stoppa, D. SUPERTWIN: Towards 100kpixel CMOS quantum image sensors for quantum optics applications. In Proceedings of the Quantum Sensing and Nano Electronics and Photonics XIV, San Francisco, CA, USA, 27 January 2017. [Google Scholar]
- Perenzoni, M.; Pancheri, L.; Stoppa, D. Compact SPAD-Based Pixel Architectures for Time-Resolved Image Sensors. Sensors
**2016**, 16, 745. [Google Scholar] [CrossRef] [PubMed] - Lee, M.J.; Charbon, E. Progress in single-photon avalanche diode image sensors in standard CMOS: From two-dimensional monolithic to three-dimensional-stacked technology. Jpn. J. Appl. Phys.
**2018**, 57, 1002A3. [Google Scholar] [CrossRef] - Jiang, L.A.; Dauler, E.A.; Chang, J.T. Photon-number-resolving detector with 10 bits of resolution. Phys. Rev. A
**2007**, 75, 062325. [Google Scholar] [CrossRef] - Morimoto, K.; Ardelean, A.; Wu, M.L.; Ulku, A.C.; Antolovic, I.M.; Bruschini, C.; Charbon, E. Megapixel time-gated SPAD image sensor for 2D and 3D imaging applications. Optica
**2020**, 7, 346. [Google Scholar] [CrossRef] - Brida, G.; Caspani, L.; Gatti, A.; Genovese, M.; Meda, A.; Berchera, I.R. Measurement of Sub-Shot-Noise Spatial Correlations without Background Subtraction. Phys. Rev. Lett.
**2009**, 102, 213602. [Google Scholar] [CrossRef] [Green Version] - Brida, G.; Degiovanni, I.P.; Florio, A.; Genovese, M.; Giorda, P.; Meda, A.; Paris, M.G.A.; Shurupov, A. Experimental Estimation of Entanglement at the Quantum Limit. Phys. Rev. Lett.
**2010**, 104, 100501. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Reichert, M.; Sun, X.; Fleischer, J.W. Quality of spatial entanglement propagation. Phys. Rev. A
**2017**, 95, 063836. [Google Scholar] [CrossRef] [Green Version] - Jost, B.M.; Sergienko, A.V.; Abouraddy, A.F.; Saleh, B.E.A.; Teich, M.C. Spatial correlations of spontaneously down-converted photon pairs detected with a single-photon-sensitive CCD camera. Opt. Express
**1998**, 3, 81–88. [Google Scholar] [CrossRef] [PubMed] - Jachura, M.; Chrapkiewicz, R. Shot-by-shot imaging of Hong–Ou–Mandel interference with an intensified sCMOS camera. Opt. Lett.
**2015**, 40, 1540–1543. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Fickler, R.; Krenn, M.; Lapkiewicz, R.; Ramelow, S.; Zeilinger, A. Real-Time Imaging of Quantum Entanglement. Sci. Rep.
**2013**, 3, 1914. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Just, F.; Filipenko, M.; Cavanna, A.; Michel, T.; Gleixner, T.; Taheri, M.; Vallerga, J.; Campbell, M.; Tick, T.; Anton, G.; et al. Detection of non-classical space-time correlations with a novel type of single-photon camera. Opt. Express
**2014**, 22, 17561–17572. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Vallerga, J.; Tremsin, A.; DeFazio, J.; Michel, T.; Alozy, J.; Tick, T.; Campbell, M. Optical MCP image tube with a quad Timepix readout: Initial performance characterization. J. Instrum.
**2014**, 9, C05055. [Google Scholar] [CrossRef] [Green Version] - Tremsin, A.; Vallerga, J. Unique capabilities and applications of Microchannel Plate (MCP) detectors with Medipix/Timepix readout. Radiat. Meras.
**2020**, 130, 106228. [Google Scholar] [CrossRef] - Nomerotski, A. Imaging and time stamping of photons with nanosecond resolution in Timepix based optical cameras. Nucl. Instrum. Meth. A
**2019**, 937, 26–30. [Google Scholar] [CrossRef] [Green Version] - John, J.J.; Brouard, M.; Clark, A.; Crooks, J.; Halford, E.; Hill, L.; Lee, J.W.L.; Nomerotski, A.; Pisarczyk, R.; Sedgwick, I.; et al. PImMS, a fast event-triggered monolithic pixel detector with storage of multiple timestamps. J. Instrum.
**2012**, 7, C08001. [Google Scholar] [CrossRef] [Green Version] - Divochiy, A.; Marsili, F.; Bitauld, D.; Gaggero, A.; Leoni, R.; Mattioli, F.; Korneev, A.; Seleznev, V.; Kaurova, N.; Minaeva, O.; et al. Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths. Nat. Photonics
**2008**, 2, 302–306. [Google Scholar] [CrossRef] [Green Version] - Zhu, D.; Colangelo, M.; Chen, C.; Korzh, B.A.; Wong, F.N.C.; Shaw, M.D.; Berggren, K.K. Resolving Photon Numbers Using a Superconducting Nanowire with Impedance-Matching Taper. Nano Lett.
**2020**. [Google Scholar] [CrossRef] [Green Version] - Korzh, B.; Zhao, Q.Y.; Allmaras, J.P.; Frasca, S.; Autry, T.M.; Bersin, E.A.; Beyer, A.D.; Briggs, R.M.; Bumble, B.; Colangelo, M.; et al. Demonstration of sub-3 ps temporal resolution with a superconducting nanowire single-photon detector. Nat. Photonics
**2020**, 14, 250–255. [Google Scholar] [CrossRef] [Green Version] - Cabrera, B.; Clarke, R.M.; Colling, P.; Miller, A.J.; Nam, S.; Romani, R.W. Detection of single infrared, optical, and ultraviolet photons using superconducting transition edge sensors. Appl. Phys. Lett.
**1998**, 73, 735–737. [Google Scholar] [CrossRef] - Lita, A.E.; Miller, A.J.; Nam, S.W. Counting near-infrared single-photons with 95% efficiency. Opt. Express
**2008**, 16, 3032. [Google Scholar] [CrossRef] [PubMed] - Day, P.K.; LeDuc, H.G.; Mazin, B.A.; Vayonakis, A.; Zmuidzinas, J. A broadband superconducting detector suitable for use in large arrays. Nature
**2003**, 425, 817–821. [Google Scholar] [CrossRef] [PubMed] - Mazin, B.A.; O’Brien, K.; McHugh, S.; Bumble, B.; Moore, D.; Golwala, S.; Zmuidzinas, J. ARCHONS: A highly multiplexed superconducting optical to near-IR camera. In Ground-Based and Airborne Instrumentation for Astronomy III; McLean, I.S., Ramsay, S.K., Takami, H., Eds.; SPIE: Paris, France, 2010. [Google Scholar] [CrossRef] [Green Version]
- Kok, P.; Munro, W.J.; Nemoto, K.; Ralph, T.C.; Dowling, J.P.; Milburn, G.J. Linear optical quantum computing with photonic qubits. Rev. Mod. Phys.
**2007**, 79, 135–174. [Google Scholar] [CrossRef] [Green Version] - O’Brien, J.L. Optical Quantum Computing. Science
**2007**, 318, 1567–1570. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Fisher-Levine, M.; Nomerotski, A. TimepixCam: A fast optical imager with time-stamping. J. Instrum.
**2016**, 11, C03016. [Google Scholar] [CrossRef] - Zhao, A.; Beuzekom, M.V.; Bouwens, B.; Byelov, D.; Chakaberia, I.; Cheng, C.; Maddox, E.; Nomerotski, A.; Svihra, P.; Visser, J.; et al. Coincidence velocity map imaging using Tpx3Cam, a time stamping optical camera with 1.5 ns timing resolution. Rev. Sci. Instrum.
**2017**, 88, 113104. [Google Scholar] [CrossRef] - Nomerotski, A.; Chakaberia, I.; Fisher-Levine, M.; Janoska, Z.; Takacs, P.; Tsang, T. Characterization of TimepixCam, a fast imager for the time-stamping of optical photons. J. Instrum.
**2017**, 12, C01017. [Google Scholar] [CrossRef] - Poikela, T.; Plosilab, J.; Westerlundb, T.; Campbellc, M.; De Gasparic, M.; Llopartc, X.; Gromovd, V.; Kluitd, R. Timepix3: A 65K channel hybrid pixel readout chip with simultaneous ToA/ToT and sparse readout. J. Instrum.
**2014**, 9, C05013. [Google Scholar] [CrossRef] - Cricket. Available online: https://www.photonis.com/product/hi-qephotocathodes (accessed on 19 June 2020).
- Ianzano, C.; Svihra, P.; Flament, M.; Hardy, A.; Cui, G.; Nomerotski, A.; Figueroa, E. Fast camera spatial characterization of photonic polarization entanglement. Sci. Rep.
**2020**, 10. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Nomerotski, A.; Katramatos, D.; Stankus, P.; Svihra, P.; Cui, G.; Gera, S.; Flament, M.; Figueroa, E. Spatial and temporal characterization of polarization entanglement. Int. J. Quantum Inf.
**2020**, 18, 1941027. [Google Scholar] [CrossRef] - Zhang, Y.; England, D.; Nomerotski, A.; Svihra, P.; Ferrante, S.; Hockett, P.; Sussman, B. Multidimensional quantum-enhanced target detection via spectrotemporal-correlation measurements. Phys. Rev. A
**2020**, 101, 053808. [Google Scholar] [CrossRef] - Sen, R.; Hirvonen, L.M.; Zhdanov, A.; Svihra, P.; Andersson-Engels, S.; Nomerotski, A.; Papkovsky, D. New luminescence lifetime macro-imager based on a Tpx3Cam optical camera. Biomed. Opt. Express
**2020**, 11, 77–88. [Google Scholar] [CrossRef] [PubMed] - Turecek, D.; Jakubek, J.; Soukup, P. USB 3.0 readout and time-walk correction method for Timepix3 detector. J. Instrum.
**2016**, 11, C12065. [Google Scholar] [CrossRef] - Ou, Z.Y.J. Multi-Photon Quantum Interference; Springer International Publishing: Cham, Switzerland, 2007. [Google Scholar]
- Cialdi, S.; Castelli, F.; Paris, M.G. Properties of entangled photon pairs generated by a CW laser with small coherence time: Theory and experiment. J. Mod. Opt.
**2009**, 56, 215–225. [Google Scholar] [CrossRef] - Franson, J.D. Nonlocal cancellation of dispersion. Phys. Rev. A
**1992**, 45, 3126–3132. [Google Scholar] [CrossRef] [PubMed] - Steinberg, A.M.; Kwiat, P.G.; Chiao, R.Y. Dispersion cancellation and high-resolution time measurements in a fourth-order optical interferometer. Phys. Rev. A
**1992**, 45, 6659–6665. [Google Scholar] [CrossRef] - Steinberg, A.M.; Kwiat, P.G.; Chiao, R.Y. Dispersion cancellation in a measurement of the single-photon propagation velocity in glass. Phys. Rev. Lett.
**1992**, 68, 2421–2424. [Google Scholar] [CrossRef] - Rarity, J.G.; Tapster, P.R. Fourth-order interference in parametric downconversion. J. Opt. Soc. Am. B
**1989**, 6, 1221–1226. [Google Scholar] [CrossRef] - Orlov, D.; Ruardij, T.; Pinto, S.D.; Glazenborg, R.; Kernen, E. High collection efficiency MCPs for photon counting detectors. J. Instrum.
**2018**, 13, C01047. [Google Scholar] [CrossRef] [Green Version] - Orlov, D.A.; Glazenborg, R.; Ortega, R.; Kernen, E. UV/visible high-sensitivity MCP-PMT single-photon GHz counting detector for long-range lidar instrumentations. Ceas Space J.
**2019**, 11, 405–411. [Google Scholar] [CrossRef] - Xia, T.; Lichtman, M.; Maller, K.; Carr, A.W.; Piotrowicz, M.J.; Isenhower, L.; Saffman, M. Randomized Benchmarking of Single-Qubit Gates in a 2D Array of Neutral-Atom Qubits. Phys. Rev. Lett.
**2015**, 114, 100503. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Graham, T.M.; Kwon, M.; Grinkemeyer, B.; Marra, Z.; Jiang, X.; Lichtman, M.T.; Sun, Y.; Ebert, M.; Saffman, M. Rydberg-Mediated Entanglement in a Two-Dimensional Neutral Atom Qubit Array. Phys. Rev. Lett.
**2019**, 123, 230501. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Schematic illustration of the Hong-Ou-Mandel (HOM) effect. Left: Two near-simultaneous photons with similar wavelength impinge on a beam splitter (BS), and the outputs are registered on two detectors, D1 and D2. When the photons’ arrival is simultaneous, making them indistinguishable, the HOM interference effect causes both photons to exit one side of the splitter or the other, inhibiting the outcome with one photon going to each detector. Right: The signature of the HOM effect is a drop in the rate of coincident detections at D1 and D2, as the photon arrival times become identical. This is typically observed as an “HOM dip” in coincidences as a function of some relative time delay at the BS input.

**Figure 2.**Two photons coming out of a single-mode fiber, focused on to the fast pixel camera and registered individually.

**Figure 3.**The sketch of the experimental setup. Pump beam produced by continuous-wave (CW) narrow-band ($\mathsf{\Delta}{\lambda}_{\mathrm{p}}\approx 0.7\phantom{\rule{4pt}{0ex}}\mathrm{nm}$) laser tuned to the wavelength of (${\lambda}_{\mathrm{p}}=405\phantom{\rule{3.33333pt}{0ex}}\mathrm{nm}$) (spontaneous parametric down-conversion (SPDC) source). The created SPDC photons are coupled to polarization-maintaining fibers (PMF), where input polarization of photons in both arms is controlled by polarization plates P

_{1,2}. In the delay module, one can tune an optical path difference between the two legs using a motorized translation stage with 0.3 μm minimal step and dynamic range of 10 mm. Photon counts are recorded with the intensified Tpx3Cam fast camera.

**Figure 4.**Left: photograph of the HOM interferometer with optical delay and beam splitter. Right: photograph of Tpx3Cam with two fibers pointing to the intensifier photocathode.

**Figure 6.**Left: distribution of number of pixels in the cluster. Right: distribution of time-over-threshold (ToT) for the brightest pixel in the cluster, in ns, corresponding to the pixel intensity.

**Figure 7.**Left: distribution of measured time difference between photons registered in fiber 1 and fiber 2. Right: distribution of measured time difference between two photons in fiber 1. The distributions are fit with a double Gaussian function and a constant, see the text for detail.

**Figure 8.**Six examples of two clusters in a single fiber (fiber 2) separated by less than 100 ns. The hits are shown as boxed pairs of heatmaps in time-over-threshold (ToT) representation (left graph in the boxed pair of graphs) and time of arrival (ToA) representation (right graph).

**Figure 9.**Distribution of distances between the photon pairs in the same fiber for fiber 1 (red) and fiber 2 (blue).

**Figure 10.**Number of coincidences between two different fibers (fiber 1&2) and within the same fibers (fiber 1, fiber 2), shown for experimental data and corresponding fits as function of the delay between two photons. The delay is expressed in mm (bottom horizontal scale) and in fs (top horizontal scale). The HOM dip is obvious around the delay value of 0.18 mm.

**Figure 11.**Sum of two-photon coincidence rates in single fibers and between two fibers as function of the delay.

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**MDPI and ACS Style**

Nomerotski, A.; Keach, M.; Stankus, P.; Svihra, P.; Vintskevich, S.
Counting of Hong-Ou-Mandel Bunched Optical Photons Using a Fast Pixel Camera. *Sensors* **2020**, *20*, 3475.
https://doi.org/10.3390/s20123475

**AMA Style**

Nomerotski A, Keach M, Stankus P, Svihra P, Vintskevich S.
Counting of Hong-Ou-Mandel Bunched Optical Photons Using a Fast Pixel Camera. *Sensors*. 2020; 20(12):3475.
https://doi.org/10.3390/s20123475

**Chicago/Turabian Style**

Nomerotski, Andrei, Michael Keach, Paul Stankus, Peter Svihra, and Stephen Vintskevich.
2020. "Counting of Hong-Ou-Mandel Bunched Optical Photons Using a Fast Pixel Camera" *Sensors* 20, no. 12: 3475.
https://doi.org/10.3390/s20123475