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Quantum ghost imaging with improved diffraction limit

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Abstract

Traditional quantum ghost imaging technique uses three-photon spontaneous parametric down-conversion for producing beams of entangled photons. Two main factors limiting the spatial resolution of ghost imaging techniques are the (usually small) angular range in which the phase-matching condition is satisfied and angular apertures of the optical elements. In this paper, we propose to use the spontaneous four-wave back-mixing process to obtain quantum ghost images due to its ability to weaken the requirements on the phase-matching condition. Thus, only angular apertures of the optical elements remain as the main limiting factor, in contrast to setups where three-photon processes are used. Therefore, the upper bound on spatial resolution is higher. As a result, an improvement in resolution can be expected, assuming that other factors remain the same. Two design options that provide these benefits are proposed.

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References

  1. Gatti, A., Brambilla, E., Bache, M., Lugiato, L.A.: Ghost imaging. In: M.I. Kolobov (ed.) Quantum Imaging, chap. 5, pp. 79–111. Springer (2007)

  2. Shapiro, J.H., Boyd, R.W.: The physics of ghost imaging. Quantum Inf. Process. 11, 949–993 (2012). https://doi.org/10.1007/s11128-011-0356-5

    Article  MATH  Google Scholar 

  3. Padgett, M.J., Boyd, R.W.: An introduction to ghost imaging: quantum and classical. Phil. Trans. R. Soc. A. 375, 20160233 (2017). https://doi.org/10.1098/rsta.2016.0233

    Article  ADS  Google Scholar 

  4. Klyshko, D.: Physical foundations of quantum electronics. World Scientific Publishing Company, Singapore (2011). https://doi.org/10.1142/7930

  5. Basset, M.G., Setzpfandt, F., Steinlechner, F., Beckert, E., Pertsch, T., Gräfe, M.: Perspectives for applications of quantum imaging. Laser Photon. Rev. 13(10), 1900097 (2019). https://doi.org/10.1002/lpor.201900097

    Article  Google Scholar 

  6. Yu, H., Lu, R., Han, S., Xie, H., Du, G., Xiao, T., Zhu, D.: Fourier-transform ghost imaging with hard X Rays. Phys. Rev. Lett. 117, 113901 (2016). https://doi.org/10.1103/PhysRevLett.117.113901

    Article  ADS  Google Scholar 

  7. Pelliccia, D., Rack, A., Scheel, M., Cantelli, V., Paganin, D.M.: Experimental X-ray ghost imaging. Phys. Rev. Lett. 117, 113902 (2016). https://doi.org/10.1103/PhysRevLett.117.113902

    Article  ADS  Google Scholar 

  8. Yu, Y., Wang, C., Liu, J., Wang, J., Cao, M., Wei, D., Gao, H., Li, F.: Ghost imaging with different frequencies through non-degenerated four-wave mixing. Opt. Express 24(16), 18290 (2016). https://doi.org/10.1364/OE.24.018290

    Article  ADS  Google Scholar 

  9. Belinsky, A.V.: Effect of defocusing on the quality of quantum ghost images. Quantum Electron. 50(10), 951–953 (2020). https://doi.org/10.1070/qel17330

    Article  ADS  Google Scholar 

  10. Monroy-Ruz, J., Garay-Palmett, K., U’ren, A.B.: Counter-propagating spontaneous four wave mixing: photon-pair factorability and ultra-narrowband single photons. New J. Phys. 18, 103026 (2016). https://doi.org/10.1088/1367-2630/18/10/103026

    Article  ADS  Google Scholar 

  11. Saravi, S., Pertsch, T., Setzpfandt, F.: Generation of counterpropagating path-entangled photon pairs in a single periodic waveguide. Phys. Rev. Lett. 118, 183603 (2017). https://doi.org/10.1103/PhysRevLett.118.183603

    Article  ADS  Google Scholar 

  12. Gatti, A., Brambilla, E.: Heralding pure single photons: a comparison between counterpropagating and copropagating twin photons. Phys. Rev. 97, 013838 (2018). https://doi.org/10.1103/PhysRevA.97.013838

    Article  Google Scholar 

  13. Zhang, Y., Spiniolas, R., Shinbrough, K., Fang, B., Cohen, O., Lorenz, V.O.: Dual-pump approach to photon-pair generation: demonstration of enhanced characterization and engineering capabilities. Opt. Express 27, 19050–19061 (2019). https://doi.org/10.1364/OE.27.019050

    Article  ADS  Google Scholar 

  14. Yu, H., Chen, F., He, Y., Pan, Q., Yu, D., Xie, J.: Nonlinear phase matching in parametric four-wave mixing process of Cs vapor. Optik 205, 163583 (2020). https://doi.org/10.1016/j.ijleo.2019.163583

    Article  ADS  Google Scholar 

  15. Belinsky, A.V.: The “paradox’’ of Karl Popper and its connection with the Heisenberg uncertainty principle and quantum ghost images. Moscow Univ. Phys. Bull. 73(5), 447–456 (2018). https://doi.org/10.3103/s0027134918050053

    Article  ADS  Google Scholar 

  16. Morris, P.A., Toninelli, E., Gregory, T., Aspden, R.S., Spalding, G., Boyd, R.W., Padgett, M.J.: Experimental limits of ghost diffraction: Popper’s thought experiment. Sci. Rep. 8(1), 13183 (2018). https://doi.org/10.1038/s41598-018-31429-y

    Article  ADS  Google Scholar 

  17. Moreau, P.A., Toninelli, E., Morris, P.A., Aspden, R.S., Gregory, T., Spalding, G., Boyd, R.W., Padgett, M.J.: Resolution limits of quantum ghost imaging. Opt. Express 26(6), 7528 (2018). https://doi.org/10.1364/oe.26.007528

    Article  ADS  Google Scholar 

  18. Balakin, D.A., Belinsky, A.V.: On the possibility of a significant improvement in the quality of a quantum ghost image by registering an additional image in the object channel. Quantum Electron. 49(10), 967–973 (2019). https://doi.org/10.1070/qel17039

    Article  ADS  Google Scholar 

  19. Balakin, D.A., Belinsky, A.V., Chirkin, A.S.: Object reconstruction from multiplexed quantum ghost images using reduction technique. Quantum Inf. Process. 18, 80 (2019). https://doi.org/10.1007/s11128-019-2193-x

    Article  ADS  MATH  Google Scholar 

  20. Zel’dovich, B.Y., Shkunov, V.V.: Wavefront reproduction in stimulated Raman scattering. Sov. J. Quantum Electron. 7(5), 610–615 (1977). https://doi.org/10.1070/qe1977v007n05abeh012572

    Article  ADS  Google Scholar 

  21. Zel’dovich, B.Y., Pilipetskiy, N.F., Shkunov, V.V.: Wave front conjugation. Nauka, Moscow (1985). (in Russian)

  22. Eichler, H.J., Mehl, O.: Phase conjugate mirrors. J. Nonlinear Optical Phys. Mater. 10(01), 43–52 (2001). https://doi.org/10.1142/s0218863501000425

    Article  ADS  Google Scholar 

  23. Lee, K.R., Lee, J., Park, J.H., Park, J.H., Park, Y.K.: One-wave optical phase conjugation mirror by actively coupling arbitrary light fields into a single-mode reflector. Phys. Rev. Lett. 115(15), 153902 (2015). https://doi.org/10.1103/physrevlett.115.153902

    Article  ADS  Google Scholar 

  24. Ganeev, R.A., Usmanov, T.: Nonlinear-optical parameters of various media. Quantum Electron. 37(7), 605–622 (2007). https://doi.org/10.1070/QE2007v037n07ABEH013367

    Article  ADS  Google Scholar 

  25. Belinsky, A.V.: Light wave compression in counter-propagating four-photon mixing in inhomogeneous pump field [in Russian]. J. Appl. Spectrosc. 50(3), 469–472 (1989)

    Google Scholar 

  26. Belinskiĭ, A.V., Chirkin, A.S.: Four-photon mixing and squeezed states in a resonator. Sov. J. Quantum Electron. 18(10), 1349–1351 (1988). https://doi.org/10.1070/qe1988v018n10abeh012582

    Article  ADS  Google Scholar 

  27. Kolobov, M.I., Sokolov, I.V.: Spatial behavior of squeezed states of light and quantum noise in optical images. JETP 69(6), 1097–1104 (1989)

    ADS  Google Scholar 

  28. Kolobov, M.I., Sokolov, I.V.: Squeezed states of light and noise-free optical images. Phys. Lett. A 140(3), 101–104 (1989). https://doi.org/10.1016/0375-9601(89)90498-2

    Article  ADS  Google Scholar 

  29. Chirkin, A.S., Makeev, E.V.: Simultaneous phase-sensitive parametric amplification and up-conversion of an optical image. J. Opt. B: Quantum Semiclassical Opt. 7(12), S500–S506 (2005). https://doi.org/10.1088/1464-4266/7/12/010

    Article  ADS  Google Scholar 

  30. Huttner, B., Serulnik, S., Ben-Aryeh, Y.: Quantum analysis of light propagation in a parametric amplifier. Phys. Rev. A 42(9), 5594–5600 (1990). https://doi.org/10.1103/physreva.42.5594

    Article  ADS  Google Scholar 

  31. Toren, M., Ben-Aryeh, Y.: The problem of propagation in quantum optics, with applications to amplification, coupling of EM modes and distributed feedback lasers. Quantum Opt.: J. Euro. Opt. Soc. Part B 6(5), 425–444 (1994). https://doi.org/10.1088/0954-8998/6/5/006

    Article  ADS  Google Scholar 

  32. Yariv, A., Pepper, D.M.: Amplified reflection, phase conjugation, and oscillation in degenerate four-wave mixing. Opt. Lett. 1(1), 16 (1977). https://doi.org/10.1364/ol.1.000016

    Article  ADS  Google Scholar 

  33. Klyshko, D.N.: Transverse photon bunching and two-photon processes in the field of parametrically scattered light. Zh. Eksp. Teor. Phys. 83, 1313–1323 (1982)

    Google Scholar 

  34. Klyshko, D.N.: A simple method of preparing pure states of an optical field, of implementing the Einstein-Podolsky-Rosen experiment, and of demonstrating the complementarity principle. Sov. Phys. Usp. 31, 74–85 (1988). https://doi.org/10.1070/PU1988v031n01ABEH002537

    Article  ADS  Google Scholar 

  35. Simonov, A.N., Larichev, A.V., Shibaev, V.P., Stakhanov, A.I.: High-quality correction of wavefront distortions using low-power phase conjugation in azo dye containing LC polymer. Opt. Commun. 197(1–3), 175–185 (2001). https://doi.org/10.1016/s0030-4018(01)01425-0

    Article  ADS  Google Scholar 

  36. Simonov, A.N., Larichev, A.V., Shibaev, V.P., Stakhanov, A.I.: Compensation of dynamic phase distortions in the phase conjugation system based on the film of azocontaining liquid-crystalline polymer. Opt. Spectrosc. 92(4), 536–543 (2002). https://doi.org/10.1134/1.1473593

    Article  ADS  Google Scholar 

  37. Li, G., Eralp, M., Thomas, J., Tay, S., Schülzgen, A., Norwood, R.A., Peyghambarian, N.: All-optical dynamic correction of distorted communication signals using a photorefractive polymeric hologram. Appl. Phys. Lett. 86(16), 161103 (2005). https://doi.org/10.1063/1.1898432

    Article  ADS  Google Scholar 

  38. Tyson, R.: Wavefront correction. Principles of Adaptive Optics, chap. 6, pp. 177–196. CRC Press, Boca Raton, FL (2011)

  39. Maldonado, J.L., Herrera-Ambriz, V.M., Rodríguez, M., Ramos-Ortíz, G., Meneses-Nava, M.A., Barbosa-García, O., Santillan, R., Farfán, N.: Reversible holography and optical phase conjugation for image formation/correction using highly efficient organic photorefractive polymers. J. Appl. Res. Technol. 13(6), 537–542 (2015). https://doi.org/10.1016/j.jart.2015.10.007

    Article  Google Scholar 

  40. Balakin, D.A., Belinsky, A.V.: Control of a quantum ghost image by spatial pumping phase modulation. J. Opt. Soc. Am. B. 38(12), 3705–3711 (2021). https://doi.org/10.1364/josab.433600

    Article  ADS  Google Scholar 

  41. Belinskiĭ, A.V., Klyshko, D.N.: Two-photon optics: diffraction, holography, and transformation of two-dimensional signals. JETP 78(3), 259–262 (1994)

    ADS  Google Scholar 

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Correspondence to Dmitriy A. Balakin.

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The authors are grateful to Sergey A. Magnitskiy, Anatoly S. Chirkin and Mikhail Smagin for help with the text. The authors thank the anonymous reviewers for their valuable suggestions and constructive comments.

The authors acknowledge the support by the Russian Foundation for Basic Research under the Project Number 18-01-00598-A.

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Balakin, D.A., Belinsky, A.V. Quantum ghost imaging with improved diffraction limit. Quantum Inf Process 21, 251 (2022). https://doi.org/10.1007/s11128-022-03602-w

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