Resolution of Quantum Imaging with Undetected Photons
1Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, Vienna A-1090, Austria
2Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, Boltzmanngasse 5, University of Vienna, Vienna A-1090, Austria
3Instituto de Física, Universidade Federal do Rio de Janeiro, Av. Athos da Silveira Ramos 149, Rio de Janeiro, CP: 68528, Brazil
4Physics Department, University of Massachusetts Boston, 100 Morrissey Boulevard, Boston MA 02125, USA
5Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Pasteura 5, Warsaw 02-093, Poland
6Department of Physics, Oklahoma State University, Stillwater, Oklahoma, USA
Published: | 2022-02-09, volume 6, page 646 |
Eprint: | arXiv:2010.07712v2 |
Doi: | https://doi.org/10.22331/q-2022-02-09-646 |
Citation: | Quantum 6, 646 (2022). |
Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.
Abstract
Quantum imaging with undetected photons is a recently introduced technique that goes significantly beyond what was previously possible. In this technique, images are formed without detecting the light that interacted with the object that is imaged. Given this unique advantage over the existing imaging schemes, it is now of utmost importance to understand its resolution limits, in particular what governs the maximal achievable spatial resolution.
We show both theoretically and experimentally that the momentum correlation between the detected and undetected photons governs the spatial resolution — a stronger correlation results in a higher resolution. In our experiment, the momentum correlation plays the dominating role in determining the resolution compared to the effect of diffraction. We find that the resolution is determined by the wavelength of the undetected light rather than the wavelength of the detected light. Our results thus show that it is in principle possible to obtain resolution characterized by a wavelength much shorter than the detected wavelength.

Popular summary
► BibTeX data
► References
[1] C. Bruschini, H. Homulle, I. M. Antolovic, S. Burri, and E. Charbon, ``Single-photon avalanche diode imagers in biophotonics: review and outlook'' Light Sci. Appl. 8, 87 (2019).
https://doi.org/10.1038/s41377-019-0191-5
[2] G. Lubin, R. Tenne, I. M. Antolovic, E. Charbon, C. Bruschini, and D. Oron, ``Quantum correlation measurement with single photon avalanche diode arrays'' Opt. Express 27, 32863–32882 (2019).
https://doi.org/10.1364/OE.27.032863
[3] A. Nomerotski ``Imaging and time stamping of photons with nanosecond resolution in Timepix based optical cameras'' Nucl. Instrum. Methods Phys. Res., Sect. A 937, 26–30 (2019).
https://doi.org/10.1016/j.nima.2019.05.034
[4] A. V. Burlakov, M. V. Chekhova, D. N. Klyshko, S. P. Kulik, A. N. Penin, Y. H. Shih, and D. V. Strekalov, ``Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions'' Phys. Rev. A 56, 3214–3225 (1997).
https://doi.org/10.1103/PhysRevA.56.3214
[5] A. Mosset, F. Devaux, and E. Lantz, ``Spatially Noiseless Optical Amplification of Images'' Phys. Rev. Lett. 94, 223603 (2005).
https://doi.org/10.1103/PhysRevLett.94.223603
[6] S. P. Walborn, C. H. Monken, S. Pádua, and P. H. S. Ribeiro, ``Spatial correlations in parametric down-conversion'' Phys. Rep. 495, 87–139 (2010).
https://doi.org/10.1016/j.physrep.2010.06.003
[7] P. A. Moreau, E. Toninelli, T. Gregory, and M. J. Padgett, ``Imaging with quantum states of light'' Nat. Rev. Phys. 1, 367–380 (2019).
https://doi.org/10.1038/s42254-019-0056-0
[8] M. Kutas, B. Haase, P. Bickert, F. Riexinger, D. Molter, and G. von Freymann, ``Terahertz quantum sensing'' Sci. Adv. 6, eaaz8065 (2020).
https://doi.org/10.1126/sciadv.aaz8065
[9] R. Nairand M. Tsang ``Far-Field Superresolution of Thermal Electromagnetic Sources at the Quantum Limit'' Phys. Rev. Lett. 117, 190801 (2016).
https://doi.org/10.1103/PhysRevLett.117.190801
[10] M. Parniak, S. Borówka, K. Boroszko, W. Wasilewski, K. Banaszek, and R. Demkowicz-Dobrza ński, ``Beating the Rayleigh Limit Using Two-Photon Interference'' Phys. Rev. Lett. 121, 250503 (2018).
https://doi.org/10.1103/PhysRevLett.121.250503
[11] O. S. Magaña-Loaizaand R. W. Boyd ``Quantum imaging and information'' Rep. Prog. Phys. 82, 124401 (2019).
https://doi.org/10.1088/1361-6633/ab5005
[12] G. Brida, M. Genovese, and I. R. Berchera, ``Experimental realization of sub-shot-noise quantum imaging'' Nat. Photon. 4, 227–230 (2010).
https://doi.org/10.1038/nphoton.2010.29
[13] J. Sabines-Chesterking, A. R. McMillan, P. A. Moreau, S. K. Joshi, S. Knauer, E. Johnston, J. G. Rarity, and J. C. F. Matthews, ``Twin-beam sub-shot-noise raster-scanning microscope'' Opt. Express 27, 30810–30818 (2019).
https://doi.org/10.1364/OE.27.030810
[14] G. T. Garces, H. M. Chrzanowski, S. Daryanoosh, V. Thiel, A. L. Marchant, R. B. Patel, P. C. Humphreys, A. Datta, and I. A. Walmsley, ``Quantum-enhanced stimulated emission detection for label-free microscopy'' Appl. Phys. Lett. 117, 024002 (2020).
https://doi.org/10.1063/5.0009681
[15] O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, ``Superresolution microscopy with quantum emitters'' Nano Lett. 13, 5832–5836 (2013).
https://doi.org/10.1021/nl402552m
[16] A. Classen, J. von Zanthier, M. O. Scully, and G. S. Agarwal, ``Superresolution via structured illumination quantum correlation microscopy'' Optica 4, 580–587 (2017).
https://doi.org/10.1364/OPTICA.4.000580
[17] M. Unternährer, B. Bessire, L. Gasparini, M. Perenzoni, and A. Stefanov, ``Super-resolution quantum imaging at the Heisenberg limit'' Optica 5, 1150–1154 (2018).
https://doi.org/10.1364/OPTICA.5.001150
[18] R. Tenne, U. Rossman, B. Rephael, Y. Israel, A. Krupinski-Ptaszek, R. Lapkiewicz, Y. Silberberg, and D. Oron, ``Super-resolution enhancement by quantum image scanning microscopy'' Nat. Photon. 13, 116–122 (2019).
https://doi.org/10.1038/s41566-018-0324-z
[19] D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, ``Observation of two-photon “ghost” interference and diffraction'' Phys. Rev. Lett. 74, 3600 (1995).
https://doi.org/10.1103/PhysRevLett.74.3600
[20] T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, ``Optical imaging by means of two-photon quantum entanglement'' Phys. Rev. A 52, R3429 (1995).
https://doi.org/10.1103/PhysRevA.52.R3429
[21] R. S. Bennink, S. J. Bentley, and R. W. Boyd, ``“Two-photon” coincidence imaging with a classical source'' Phys. Rev. Lett. 89, 113601 (2002).
https://doi.org/10.1103/PhysRevLett.89.113601
[22] A. Gatti, E. Brambilla, and L. Lugiato, ``Quantum imaging'' Progress in Optics 51, 251–348 (2008).
https://doi.org/10.1016/S0079-6638(07)51005-X
[23] R. S. Aspden, D. S. Tasca, R. W. Boyd, and M. J. Padgett, ``EPR-based ghost imaging using a single-photon-sensitive camera'' New J. Phys. 15, 073032 (2013).
https://doi.org/10.1088/1367-2630/15/7/073032
[24] G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, ``Quantum imaging with undetected photons'' Nature 512, 409–412 (2014).
https://doi.org/10.1038/nature13586
[25] M. Lahiri, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, ``Theory of quantum imaging with undetected photons'' Phys. Rev. A 92, 013832 (2015).
https://doi.org/10.1103/PhysRevA.92.013832
[26] G. B. Lemos, V. Borish, S. Ramelow, R. Lapkiewicz, G. D. Cole, and A. Zeilinger, ``Quantum Imaging with Undetected Photons'' US Patent 9,557.262 B2; EP Patent 2 887 137 B1.
[27] D. A. Kalashnikov, A. V. Paterova, S. P. Kulik, and L. A. Krivitsky, ``Infrared spectroscopy with visible light'' Nat. Photon. 10, 98–101 (2016).
https://doi.org/10.1038/nphoton.2015.252
[28] A. Vallés, G. Jiménez, L. J. Salazar-Serrano, and J. P. Torres, ``Optical sectioning in induced coherence tomography with frequency-entangled photons'' Phys. Rev. A 97, 023824 (2018).
https://doi.org/10.1103/PhysRevA.97.023824
[29] A. V. Paterova, H. Yang, C. An, D. A. Kalashnikov, and L. A. Krivitsky, ``Tunable optical coherence tomography in the infrared range using visible photons'' Quantum Sci. Technol. 3, 025008 (2018).
https://doi.org/10.1088/2058-9565/aab567
[30] X. Y. Zou, L. J. Wang, and L. Mandel, ``Induced coherence and indistinguishability in optical interference'' Phys. Rev. Lett. 67, 318 (1991).
https://doi.org/10.1103/PhysRevLett.67.318
[31] L. J. Wang, X. Y. Zou, and L. Mandel, ``Induced coherence without induced emission'' Phys. Rev. A 44, 4614 (1991).
https://doi.org/10.1103/PhysRevA.44.4614
[32] R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, ``Quantum and Classical Coincidence Imaging'' Phys. Rev. Lett. 92, 033601 (2004).
https://doi.org/10.1103/PhysRevLett.92.033601
[33] K. W. C. Chan, M. N. O'Sullivan, and R. W. Boyd, ``Two-color ghost imaging'' Phys. Rev. A 79, 033808 (2009).
https://doi.org/10.1103/PhysRevA.79.033808
[34] P. A. Moreau, E. Toninelli, P. A. Morris, R. S. Aspden, T. Gregory, G. Spalding, R. W. Boyd, and M. J. Padgett, ``Resolution limits of quantum ghost imaging'' Opt. Express 26, 7528–7536 (2018).
https://doi.org/10.1364/OE.26.007528
[35] A. Hochrainer, M. Lahiri, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, ``Quantifying the momentum correlation between two light beams by detecting one'' Proc. Natl. Acad. Sci. USA 114, 1508–1511 (2017).
https://doi.org/10.1073/pnas.1620979114
[36] M. Lahiri, A. Hochrainer, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, ``Twin-photon correlations in single-photon interference'' Phys. Rev. A 96, 013822 (2017).
https://doi.org/10.1103/PhysRevA.96.013822
[37] H. M. Wisemanand K. Mølmer ``Induced coherence with and without induced emission'' Phys. Lett. A 270, 245–248 (2000).
https://doi.org/10.1016/S0375-9601(00)00314-5
[38] M. Lahiri, A. Hochrainer, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, ``Nonclassicality of induced coherence without induced emission'' Phys. Rev. A 100, 053839 (2019).
https://doi.org/10.1103/PhysRevA.100.053839
[39] C. H. Monken, P. H. S. Ribeiro, and S. Pádua, ``Transfer of angular spectrum and image formation in spontaneous parametric down-conversion'' Phys. Rev. A 57, 3123 (1998).
https://doi.org/10.1103/PhysRevA.57.3123
[40] A. A. Harmsand A. Zeilinger ``A new formulation of total unsharpness in radiography'' Phys. Med. Biol. 22, 70 (1977).
https://doi.org/10.1088/0031-9155/22/1/009
[41] G. D. Boreman ``Modulation transfer function in optical and electro-optical systems'' SPIE press Bellingham, WA (2001).
[42] M. Bornand E. Wolf ``Principles of optics'' Cambridge University Press (1999).
[43] J. W. Goodman ``Introduction to Fourier optics'' Roberts Company Publishers (2005).
[44] A. Schori, C. Bömer, D. Borodin, S. P. Collins, B. Detlefs, M. M. Sala, S. Yudovich, and S. Shwartz, ``Parametric down-conversion of x rays into the optical regime'' Phys. Rev. Lett. 119, 253902 (2017).
https://doi.org/10.1103/PhysRevLett.119.253902
[45] A. V. Paterova, S. M. Maniam, H. Yang, G. Grenci, and L. A. Krivitsky, ``Hyperspectral infrared microscopy with visible light'' Sci. Adv. 6, eabd0460 (2020).
https://doi.org/10.1126/sciadv.abd0460
[46] I. Kviatkovsky, H. M. Chrzanowski, E. G. Avery, H. Bartolomaeus, and S. Ramelow, ``Microscopy with undetected photons in the mid-infrared'' Sci. Adv. 6, eabd0264 (2020).
https://doi.org/10.1126/sciadv.abd0264
[47] A. V. Paterova, H. Yang, Z. S. D. Toa, and L. A. Krivitsky, ``Quantum imaging for the semiconductor industry'' Appl. Phys. Lett. 117, 054004 (2020).
https://doi.org/10.1063/5.0015614
[48] A. V. Paterova, D. A. Kalashnikov, E. Khaidarov, H. Yang, T. W. W. Mass, R. Paniagua-Domı́nguez, A. I. Kuznetsov, and L. A. Krivitsky, ``Non-linear interferometry with infrared metasurfaces'' Nanophotonics 10, 1775–1784 (2021).
https://doi.org/10.1515/nanoph-2021-0011
[49] M. Gilaberte Basset, A. Hochrainer, S. Töpfer, F. Riexinger, P. Bickert, J. R. León-Torres, F. Steinlechner, and M. Gräfe, ``Video-Rate Imaging with Undetected Photons'' Laser Photonics Rev. 15, 2000327 (2021).
https://doi.org/10.1002/lpor.202000327
Cited by
[1] Mayukh Lahiri, Balakrishnan Viswanathan, and Gabriela Barreto Lemos, Frontiers in Optics + Laser Science 2022 (FIO, LS) FM3B.6 (2022) ISBN:978-1-957171-17-3.
[2] Andres Vega, Elkin A. Santos, Jorge Fuenzalida, Marta Gilaberte Basset, Thomas Pertsch, Markus Gräfe, Sina Saravi, and Frank Setzpfandt, "Fundamental resolution limit of quantum imaging with undetected photons", Physical Review Research 4 3, 033252 (2022).
[3] Nathan R. Gemmell, Jefferson Flórez, Emma Pearce, Olaf Czerwinski, Chris C. Phillips, Rupert F. Oulton, and Alex S. Clark, "Loss-Compensated and Enhanced Midinfrared Interaction-Free Sensing with Undetected Photons", Physical Review Applied 19 5, 054019 (2023).
[4] Evelyn A. Ortega, Jorge Fuenzalida, Mirela Selimovic, Krishna Dovzhik, Lukas Achatz, Sören Wengerowsky, Rodrigo F. Shiozaki, Sebastian Philipp Neumann, Martin Bohmann, and Rupert Ursin, "Spatial and spectral characterization of photon pairs at telecommunication wavelengths from type-0 spontaneous parametric downconversion", Journal of the Optical Society of America B 40 1, 165 (2023).
[5] Gewei Qian, Xingqi Xu, Shun-An Zhu, Chenran Xu, Fei Gao, V. V. Yakovlev, Xu Liu, Shi-Yao Zhu, and Da-Wei Wang, "Quantum Induced Coherence Light Detection and Ranging", Physical Review Letters 131 3, 033603 (2023).
[6] Felix Riexinger, Mirco Kutas, Björn Haase, Michael Bortz, and Georg von Freymann, "General Simulation Method for Quantum‐Sensing Systems", Laser & Photonics Reviews 17 6, 2200945 (2023).
[7] Cherrie S. J. Lee, Andrius Zukauskas, and Carlota Canalias, "Large-aperture periodically poled Rb-doped KTP with a short-period via coercive field engineering", Optical Materials Express 13 8, 2203 (2023).
[8] Isaac Nape, Bereneice Sephton, Pedro Ornelas, Chane Moodley, and Andrew Forbes, "Quantum structured light in high dimensions", APL Photonics 8 5, 051101 (2023).
[9] Mirco Kutas, Björn Erik Haase, Felix Riexinger, Joshua Hennig, Patricia Bickert, Tobias Pfeiffer, Michael Bortz, Daniel Molter, and Georg von Freymann, "Quantum Sensing with Extreme Light", Advanced Quantum Technologies 5 6, 2100164 (2022).
[10] Jorge Fuenzalida, Marta Gilaberte Basset, Sebastian Töpfer, Juan P. Torres, and Markus Gräfe, "Experimental quantum imaging distillation with undetected light", Science Advances 9 35, eadg9573 (2023).
[11] Felix Riexinger, Mirco Kutas, Björn Haase, Patricia Bickert, Daniel Molter, Michael Bortz, and Georg von Freymann, "General simulation method for spontaneous parametric down- and parametric up-conversion experiments", SciPost Physics Core 6 1, 022 (2023).
[12] Armin Hochrainer, Mayukh Lahiri, Manuel Erhard, Mario Krenn, and Anton Zeilinger, "Quantum indistinguishability by path identity and with undetected photons", Reviews of Modern Physics 94 2, 025007 (2022).
[13] Bochen Wang, Yansheng Bao, Zhengyong Li, Changyong Tian, and Yong-Chun Liu, "Frequency-angular spectrum of entangled photon pairs generated by focused pump", Optik 289, 171283 (2023).
[14] Gabriela Barreto Lemos, Mayukh Lahiri, Sven Ramelow, Radek Lapkiewicz, and William N. Plick, "Quantum imaging and metrology with undetected photons: tutorial", Journal of the Optical Society of America B 39 8, 2200 (2022).
[15] Santiago Lopez-Huidobro, Mohammad Noureddin, Maria V. Chekhova, and Nicolas Y. Joly, "Tunable fiber source of entangled UV-C and infrared photons", Optics Letters 48 13, 3423 (2023).
[16] Paul Kinsler, Martin W McCall, Rupert F Oulton, and Alex S Clark, "The surprising persistence of time-dependent quantum entanglement", New Journal of Physics 24 10, 103037 (2022).
[17] Elkin A. Santos, Thomas Pertsch, Frank Setzpfandt, and Sina Saravi, "Subdiffraction Quantum Imaging with Undetected Photons", Physical Review Letters 128 17, 173601 (2022).
[18] Marta Gilaberte Basset, Armin Hochrainer, Sebastian Töpfer, Felix Riexinger, Patricia Bickert, Josué Ricardo León-Torres, Fabian Steinlechner, and Markus Gräfe, "Video-Rate Imaging with Undetected Photons", Laser & Photonics Reviews 15 6, 2000327 (2021).
[19] Balakrishnan Viswanathan, Gabriela Barreto Lemos, and Mayukh Lahiri, "Resolution limit in quantum imaging with undetected photons using position correlations", Optics Express 29 23, 38185 (2021).
[20] Balakrishnan Viswanathan, Gabriela Barreto Lemos, and Mayukh Lahiri, "Position correlation enabled quantum imaging with undetected photons", Optics Letters 46 15, 3496 (2021).
[21] Inna Kviatkovsky, Helen M. Chrzanowski, and Sven Ramelow, "Mid-infrared microscopy via position correlations of undetected photons", Optics Express 30 4, 5916 (2022).
The above citations are from Crossref's cited-by service (last updated successfully 2023-09-27 20:52:57) and SAO/NASA ADS (last updated successfully 2023-09-27 20:52:58). The list may be incomplete as not all publishers provide suitable and complete citation data.
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.