Self-referenced hologram of a single photon beam

Wiktor Szadowiak, Sanjukta Kundu, Jerzy Szuniewicz, and Radek Lapkiewicz

Institute of Experimental Physics, Faculty of Physics, University of Warsaw, ul. Pasteura 5,02-093 Warszawa, Poland

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Abstract

Quantitative characterization of the spatial structure of single photons is essential for free-space quantum communication and quantum imaging. We introduce an interferometric technique that enables the complete characterization of a two-dimensional probability amplitude of a single photon. Importantly, in contrast to methods that use a reference photon for the phase measurement, our technique relies on a single photon interfering with itself. Our setup comprises of a heralded single-photon source with an unknown spatial phase and a modified Mach-Zehnder interferometer with a spatial filter in one of its arms. The spatial filter removes the unknown spatial phase and the filtered beam interferes with the unaltered beam passing through the other arm of the interferometer. We experimentally confirm the feasibility of our technique by reconstructing the spatial phase of heralded single photons using the lowest order interference fringes. This technique can be applied to the characterization of arbitrary pure spatial states of single photons.

The measurements of the spatial wavefunction of photons are important for applications in quantum imaging, metrology, communication, and computation. However, the indeterminate global phase of single photons was believed to constitute an obstacle for characterizing their spatial phase profile using classical interferometric techniques. Weak measurements, tomography, and two-photon interferometry have been used instead, but they are not as straightforward, robust, and precise as the classical holographic techniques. We demonstrate a novel approach to determining the spatial phase profile of a single photon beam based on self-referenced interferometry which relies on a single photon interfering with itself. We experimentally confirm the feasibility of our technique by reconstructing the two-dimensional spatial phase profile of single photons using the lowest-order interference fringes. Our technique does not require the generation of reference photons and coincidence detection and it can tolerate more losses than methods using two-photon interference. Owing to its simplicity, our method can facilitate quantum technology applications that rely on the spatial degree of freedom of photons.

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[1] G. M. Terriza, J. P. Torres and L. Torner, Twisted photons, Nature Physics 3, 305–310 (2007). DOI: 10.1038/​nphys607.
https:/​/​doi.org/​10.1038/​nphys607

[2] J. S. Lundeen, B. Sutherland, A. Patel, C. Stewart & C. Bamber, Direct measurement of the quantum wavefunction, Nature 474, 188–191 (2011). DOI: 10.1038/​nature10120.
https:/​/​doi.org/​10.1038/​nature10120

[3] R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, A. Zeilinger, Quantum entanglement of high angular momenta, Science 338, 640–643 (2012). DOI: 10.1126/​science.1227193.
https:/​/​doi.org/​10.1126/​science.1227193

[4] M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, Efficient separation of the orbital angular momentum eigenstates of ligh, Nat. Commun. 4, 2781 (2013). DOI: 10.1038/​ncomms3781.
https:/​/​doi.org/​10.1038/​ncomms3781

[5] S. Walborn, D. Lemelle, M. Almeida, P. Ribeiro, Quantum key distribution with higher-order alphabets using spatially encoded qudits, Phys. Rev. Lett. 96, 090501 (2006). DOI: 10.1103/​PhysRevLett.96.090501.
https:/​/​doi.org/​10.1103/​PhysRevLett.96.090501

[6] S. F. Pereira, Z. Y. Ou, and H. J. Kimble, Quantum communication with correlated nonclassical states, Phys. Rev. A 62, 042311 (2000). DOI: 10.1103/​PhysRevA.62.042311.
https:/​/​doi.org/​10.1103/​PhysRevA.62.042311

[7] R. Fickler, R. Lapkiewicz, M. Huber, M. P.J. Lavery, M. J. Padgett & A. Zeilinger, Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information, Nature Communications 5, 4502 (2014). DOI: 10.1038/​ncomms5502.
https:/​/​doi.org/​10.1038/​ncomms5502

[8] M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. R. Leeb, A. Zeilinger, Long distance quantum communication with entangled photons using satellites, IEEE J. Sel. Top. Quantum Electron 9, 1541 (2003). DOI: 10.1109/​JSTQE.2003.820918.
https:/​/​doi.org/​10.1109/​JSTQE.2003.820918

[9] M. Krenn, J. Handsteiner, M. Fink, R. Fickler, and A. Zeilinger. Twisted photon entanglement through turbulent air across Vienna, Proc. Natl Acad. Sci. USA 112, 14197–14201 (2015). DOI: 10.1073/​pnas.1517574112.
https:/​/​doi.org/​10.1073/​pnas.1517574112

[10] O. Lib, G. Hasson, Y. Bromberg, Real-time shaping of entangled photons by classical control and feedback, Science Advances 6, eabb6298 (2020). DOI: 10.1126/​sciadv.abb6298.
https:/​/​doi.org/​10.1126/​sciadv.abb6298

[11] H. Sasada and M. Okamoto, Transverse-mode beam splitter of a light beam and its application to quantum cryptography, Phys. Rev. A 68, 012323 (2003). DOI: 10.1103/​PhysRevA.68.012323.
https:/​/​doi.org/​10.1103/​PhysRevA.68.012323

[12] S. Leedumrongwatthanakun, L. Innocenti, H. Defienne, T. Juffmann, A. Ferraro, M. Paternostro, S. Gigan, Programmable linear quantum networks with a multimode fibre, Nat. Photonics 14, 139–142 (2020). DOI: 10.1038/​s41566-019-0553-9.
https:/​/​doi.org/​10.1038/​s41566-019-0553-9

[13] A. F. Abouraddy, G. Di Giuseppe, T. M. Yarnall, M. C. Teich, and B. E. A. Saleh, Implementing one-photon three-qubit quantum gates using spatial light modulators, Phys. Rev. A 86, 050303(R) (2012). DOI: 10.1103/​PhysRevA.86.050303.
https:/​/​doi.org/​10.1103/​PhysRevA.86.050303

[14] T. Ono, R. Okamoto & S. Takeuchi, An entanglement-enhanced microscope, Nature Communications 4, 2426 (2013). DOI: 10.1038/​ncomms3426.
https:/​/​doi.org/​10.1038/​ncomms3426

[15] P. A. Moreau, E. Toninelli, T. Gregory & M. J. Padgett, Imaging with quantum states of light, Nature Reviews Physics 1, 367–380 (2019). DOI: 10.1038/​s42254-019-0056-0.
https:/​/​doi.org/​10.1038/​s42254-019-0056-0

[16] Z. I. Borja, C. S. Gutiérrez, R. R. Alarcón, H. C. Ramírez, and A. B. U’Ren, Experimental demonstration of full-field quantum optical coherence tomography, Photon. Res. 8, 51-56 (2020). DOI: 10.1364/​PRJ.8.000051.
https:/​/​doi.org/​10.1364/​PRJ.8.000051

[17] R. S. Aspden, D. S. Tasca, R. W. Boyd & M. J. Padgett, EPR-based ghost imaging using a single-photon-sensitive camera, New J. Phys. 15, 073032 (2013). DOI: 10.1088/​1367-2630/​15/​7/​073032.
https:/​/​doi.org/​10.1088/​1367-2630/​15/​7/​073032

[18] G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz & A. Zeilinger, Quantum imaging with undetected photons, Nature 512, 409–412 (2014). DOI: 10.1038/​nature13586.
https:/​/​doi.org/​10.1038/​nature13586

[19] A. F. Abouraddy, P. R. Stone, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, Entangled-Photon Imaging of a Pure Phase Object, Phys. Rev. Lett. 93, 213903 (2004). DOI: 10.1103/​PhysRevLett.93.213903.
https:/​/​doi.org/​10.1103/​PhysRevLett.93.213903

[20] R. Fickler, M. Krenn, R. Łapkiewicz, S. Ramelow and A. Zeilinger, Real-time imaging of quantum entanglement, Sci. Rep. 3, 1914 (2013). DOI: 10.1038/​srep01914.
https:/​/​doi.org/​10.1038/​srep01914

[21] P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd and M. J. Padgett, Imaging with a small number of photons, Nature Commun. 6, 5913 (2015). DOI: 10.1038/​ncomms6913.
https:/​/​doi.org/​10.1038/​ncomms6913

[22] V. Giovannetti, S. Lloyd, and L. Maccone, Quantum Metrology, Phys. Rev. Lett. 96, 010401 (2006). DOI: 10.1103/​PhysRevLett.96.010401.
https:/​/​doi.org/​10.1103/​PhysRevLett.96.010401

[23] M. Parniak, S. Borówka, K. Boroszko, W. Wasilewski, K. Banaszek, and R. D. Dobrzański, Beating the Rayleigh Limit Using Two-Photon Interference, Phys. Rev. Lett. 121, 250503 (2018). DOI: 10.1103/​PhysRevLett.121.250503.
https:/​/​doi.org/​10.1103/​PhysRevLett.121.250503

[24] M. Tsang, R. Nair, and X. Lu, Quantum Theory of Superresolution for Two Incoherent Optical Point Sources, Phys. Rev. X 6, 031033 (2016). DOI: 10.1103/​PhysRevX.6.031033.
https:/​/​doi.org/​10.1103/​PhysRevX.6.031033

[25] R. Chrapkiewicz, M. Jachura, K. Banaszek and W. Wasilewski, Hologram of a single photon, Nat. Photonics 10, 576–579 (2016). DOI: 10.1038/​nphoton.2016.129.
https:/​/​doi.org/​10.1038/​nphoton.2016.129

[26] A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, Quantum state reconstruction of the single-photon Fock state, Phys. Rev. Lett. 87, 050402 (2001). DOI: 10.1103/​PhysRevLett.87.050402.
https:/​/​doi.org/​10.1103/​PhysRevLett.87.050402

[27] B. Stoklasa, L. Motka, J. Rehacek, Z. Hradil and L. L. Sánchez-Soto, Wavefront sensing reveals optical coherence, Nature Commun. 5, 3275 (2014). DOI: 10.1038/​ncomms4275.
https:/​/​doi.org/​10.1038/​ncomms4275

[28] J. E. Sipe, Photon wave functions, Phys. Rev. A. 52, 1875 (1995). DOI: 10.1103/​PhysRevA.52.1875.
https:/​/​doi.org/​10.1103/​PhysRevA.52.1875

[29] I. B. Birula, Photon Wave Function, Progress in Optics 36, 245-294 (1996). DOI: 10.1016/​S0079-6638(08)70316-0.
https:/​/​doi.org/​10.1016/​S0079-6638(08)70316-0

[30] B. J. Smith, B. Killett, M. G. Raymer, I. A. Walmsley, and K. Banaszek, Measurement of the transverse spatial quantum state of light at the single-photon level, Opt. Lett. 30, 24, 3365-3367 (2005). DOI: 10.1364/​OL.30.003365.
https:/​/​doi.org/​10.1364/​OL.30.003365

[31] A. I. Lvovsky and M. G. Raymer, Continuous-variable optical quantum-state tomography, Rev. Mod. Phys. 81, 299 (2009). DOI: 10.1103/​RevModPhys.81.299.
https:/​/​doi.org/​10.1103/​RevModPhys.81.299

[32] N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, Measuring Entangled Qutrits and Their Use for Quantum Bit Commitment, Phys. Rev. Lett. 93, 053601 (2004). DOI: 10.1103/​PhysRevLett.93.053601.
https:/​/​doi.org/​10.1103/​PhysRevLett.93.053601

[33] D. F. McAlister, M. Beck, L. Clarke, A. Mayer, and M. G. Raymer, Optical phase retrieval by phase-space tomography and fractional-order Fourier transforms, Opt. Lett. 20,1181-1183 (1995). DOI: 10.1364/​OL.20.001181.
https:/​/​doi.org/​10.1364/​OL.20.001181

[34] M. Mirhosseini, O. S. Magaña-Loaiza, S. M. H. Rafsanjani, and R. W. Boyd, Compressive Direct Measurement of the Quantum Wave Function, Phys. Rev. Lett. 113, 090402 (2014). DOI: 10.1103/​PhysRevLett.113.090402.
https:/​/​doi.org/​10.1103/​PhysRevLett.113.090402

[35] Z. Shi, M. Mirhosseini, J. Margiewicz, M. Malik, F. Rivera, Z. Zhu, and R. W. Boyd, Scan-free direct measurement of an extremely high-dimensional photonic state, Optica 2, 388-392 (2015). DOI: 10.1364/​OPTICA.2.000388.
https:/​/​doi.org/​10.1364/​OPTICA.2.000388

[36] C.C. Leary, L.A. Baumgardner, and M.G. Raymer, Stable mode sorting by two-dimensional parity of photonic transverse spatial states, Optics Express 17, 2435-2452 (2009). DOI: 10.1364/​OE.17.002435.
https:/​/​doi.org/​10.1364/​OE.17.002435

[37] C. K. Hong, Z. Y. Ou, and L. Mandel, Measurement of subpicosecond time intervals between two photons by interference, Phys. Rev. Lett. 59, 2044-2046 (1987). DOI: 10.1103/​PhysRevLett.59.2044.
https:/​/​doi.org/​10.1103/​PhysRevLett.59.2044

[38] G. Popescu, T. Ikeda, Ramachandra R. Dasari, and M. S. Feld, Diffraction phase microscopy for quantifying cell structure and dynamics, Optics Letters 31, Issue 6, 775-777 (2006). DOI: 10.1364/​OL.31.000775.
https:/​/​doi.org/​10.1364/​OL.31.000775

[39] D. Gabor, A new microscopic principle, Nature 161, 777–778 (1948). DOI: 10.1038/​161777a0.
https:/​/​doi.org/​10.1038/​161777a0

[40] R. J. Collier, C. B. Burckhardt and L. H. Lin, Optical Holography (Academic, 1971).

[41] J. Mertz, Introduction to Optical Microscopy, 1st Edition, Roberts and company publishers, 217-220 (2019).

[42] W. Szadowiak, S. Kundu, J. Szuniewicz, and R. Lapkiewicz, Self-referenced Measurement of the Spatial Structure of a Single Photon Beam, Frontiers in Optics + Laser Science APS/​DLS, OSA Technical Digest (Optical Society of America, 2019), paper FTu6A.6. DOI: 10.1364/​FIO.2019.FTu6A.6.
https:/​/​doi.org/​10.1364/​FIO.2019.FTu6A.6

[43] W. Szadowiak, S. Kundu, J. Szuniewicz, and R. Lapkiewicz, Self-referenced hologram of a single photon beam, Rochester Conference on Coherence and Quantum Optics (CQO-11), OSA Technical Digest (Optical Society of America, 2019), paper W6A.27. DOI: 10.1364/​CQO.2019.W6A.27.
https:/​/​doi.org/​10.1364/​CQO.2019.W6A.27

[44] N. Trautmann, G. P. Ferenczi, S. Croke, S. M. Barnett, Holographic quantum imaging: Reconstructing spatial properties via two-particle interference, Journal of Optics 19, 5 (2017). DOI: 10.1088/​2040-8986/​aa67b6.
https:/​/​doi.org/​10.1088/​2040-8986/​aa67b6

[45] L. Mandel, Quantum effects in one-photon and two-photon interference, Rev. Mod. Phys. 71, S274 (1999). DOI: 10.1103/​RevModPhys.71.S274.
https:/​/​doi.org/​10.1103/​RevModPhys.71.S274

[46] P. Grangier, G. Roger and A. Aspect, Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter: A New Light on Single-Photon Interferences, Europhys. Lett. 1, 173-179 (1986). DOI: 10.1209/​0295-5075/​1/​4/​004.
https:/​/​doi.org/​10.1209/​0295-5075/​1/​4/​004

[47] C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C Wong and J. H. Shapiro, High-flux source of polarization-entangled photons from a periodically poled ${\mathrm{KTiOPO}}_{4}$ parametric down-converter, Phys. Rev. A 69, Issue 1, 013807 (2004). DOI: 10.1103/​PhysRevA.69.013807.
https:/​/​doi.org/​10.1103/​PhysRevA.69.013807

[48] M. Jachura and R. Chrapkiewicz, Shot-by-shot imaging of Hong–Ou–Mandel interference with an intensified sCMOS camera, Opt. Lett. 40, 1540–1543 (2015). DOI: 10.1364/​OL.40.001540.
https:/​/​doi.org/​10.1364/​OL.40.001540

[49] J. Goodman, Introduction to Fourier Optics, 3rd Edition, Roberts & Company Publishers, pages 248-249 (2005).

[50] R. Chrapkiewicz, W. Wasilewski, and K. Banaszek, High-fidelity spatially resolved multiphoton counting for quantum imaging applications, Opt. Lett. 39, 5090-5093 (2014). DOI: 10.1364/​OL.39.005090.
https:/​/​doi.org/​10.1364/​OL.39.005090

[51] W. J. Bates, A wavefront shearing interferometer, Proc. Phys. Soc. 59, 940 (1947). DOI: 10.1088/​0959-5309/​59/​6/​303.
https:/​/​doi.org/​10.1088/​0959-5309/​59/​6/​303

[52] R. S. Aspden, M. J. Padgett, Light in a twist: Orbital angular momentum, Frontiers in Modern Optics 190, 149 (2016). DOI: 10.3254/​978-1-61499-647-7-149.
https:/​/​doi.org/​10.3254/​978-1-61499-647-7-149

[53] S. M. Barnett, M. Babiker and M. J. Padgett, Optical orbital angular momentum, Phil. Trans. R. Soc. A 375, 20150444 (2017). DOI: 10.1098/​rsta.2015.0444.
https:/​/​doi.org/​10.1098/​rsta.2015.0444

[54] A. Davis, V. Theil, M. Karpinski and B. J. Smith, Measuring the Single-Photon Temporal-Spectral Wave Function, Phys. Rev. Lett. 121, 083602 (2018). DOI: 10.1103/​PhysRevLett.121.083602.
https:/​/​doi.org/​10.1103/​PhysRevLett.121.083602

[55] E. M. Rasel, M. K. Oberthaler, H. Batelaan, J. Schmiedmayer, and A. Zeilinger, Atom Wave Interferometry with Diffraction Gratings of Light, Phys. Rev. Lett. 75, 2633 (1995). DOI: 10.1103/​PhysRevLett.75.2633.
https:/​/​doi.org/​10.1103/​PhysRevLett.75.2633

[56] M. Arndt, A. Ekers, W. Klitzing and H. Ulbricht, Focus on modern frontiers of matter wave optics and interferometry, New J. of Phys. 14, 125006 (2012). DOI: 10.1088/​1367-2630/​14/​12/​125006.
https:/​/​doi.org/​10.1088/​1367-2630/​14/​12/​125006

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