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Optical proposals for controlled delayed-choice experiment based on weak cross-Kerr nonlinearities

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Abstract

Employing polarization modes of a photon, we propose two theoretical proposals to exhibit the wave–particle duality of the photon with the assistance of weak cross-Kerr nonlinearities. The first proposal is a classical controlled delayed-choice experiment (that is, Wheeler’s delayed-choice experiment), where we can observe selectively wave property or particle property of the photon relying on the experimenter’s selection, whereas the second proposal is a quantum controlled delayed-choice experiment, by which the mixture phenomenon of a wave and a particle will be exhibited. Both of them can be realized with near-unity probability and embody the charming characteristics of quantum mechanics. The employment of the mature techniques and simple operations (e.g., Homodyne measurement, classical feed forward, and single-photon transformations) provides the feasibility of the delayed-choice experiment proposals presented here.

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References

  1. Bohr, N.: The quantum postulate and the recent development of atomic theory. Nature 121(3050), 580–590 (1928)

    Article  ADS  MATH  Google Scholar 

  2. Bohr, N.: Quantum Theory and Measurement, pp. 9–49. Princeton University Press, Princeton (1984)

  3. Wheeler, J.A.: The Past and the Delayed-Choice Double-Slit Experiment. Academic Press, New York (1978)

    Book  Google Scholar 

  4. Wheeler, J.A.: Quantum Theory and Measurement, pp. 182–213. Princeton University Press, Princeton (1984)

  5. Zhu, X., Fang, X., Peng, X., Feng, M., Gao, K., Fei, D.: Experimental testing of complementarity for ensemble-averaged spin states. J. Phys. B 34(22), 4349–4357 (2001)

    Article  ADS  Google Scholar 

  6. Soumya Singha, R., Shukla, A., Mahesh, T.S.: NMR implementation of a quantum delayed-choice experiment. Phys. Rev. A 85(2), 022109 (2012)

    Article  ADS  Google Scholar 

  7. Xin, T., Li, H., Wang, B.-X., Long, G.-L.: Realization of an entanglement-assisted quantum delayed-choice experiment. Phys. Rev. A 92(2), 022126 (2015)

    Article  ADS  Google Scholar 

  8. Schmid, K., Becker, H., Dultz, W., Martienssen, W., Kempe, M., Schmitzer, H.: Interferometric optical path measurement of a glass wedge with single photons and biphotons. Opt. Lett. 32(15), 2257–2259 (2007)

    Article  ADS  Google Scholar 

  9. Ionicioiu, R., Terno, D.: Proposal for a quantum delayed-choice experiment. Phys. Rev. Lett. 107(23), 230406 (2011)

    Article  ADS  Google Scholar 

  10. Tang, J.-S., Li, Y.-L., Xu, X.-Y., Xiang, G.-Y., Li, C.-F., Guo, G.-C.: Realization of quantum Wheeler’s delayed-choice experiment. Nat. Photon. 6(9), 602–606 (2012)

    Article  ADS  Google Scholar 

  11. Guo, Q., Cheng, L.-Y., Wang, H.-F., Zhang, S.: Simple implementation of quantum delayed-choice experiment using conventional linear optical elements, pp. 1–10. ArXiv, Preprint (2013)

  12. Lee, J.-C., Lim, H.-T., Hong, K.-H., Jeong, Y.-C., Kim, M.S., Kim, Y.: Experimental demonstration of delayed-choice decoherence suppression. Nat. Commun. 5, 4522 (2014)

    ADS  Google Scholar 

  13. Jia, A.-A., Huang, J.-H., Zhang, T.-C., Zhu, S.-Y.: Influence of losses on the wave-particle duality. Phys. Rev. A 89(4), 042103 (2014)

    Article  ADS  Google Scholar 

  14. Ionicioiu, R., Jennewein, T., Mann, R.B., Terno, D.R.: Is wave-particle objectivity compatible with determinism and locality? Nat. Commun. 5, 3997 (2014)

    Article  ADS  Google Scholar 

  15. Long, G.-L., Qin, W., Yang, Z., Li, J.-L.: Realistic Interpretation of Quantum Mechanics and Encounter-Delayed-Choice Experiment. Arxiv Preprints, pp. 1–7 (2014)

  16. Sun, J., Sun, Y.-N., Li, C.-F., Guo, G.-C.: On delay of the delayed choice experiment. Chin. Phys. Lett. 32(9), 090302 (2015)

    Article  ADS  Google Scholar 

  17. de Almeida, N.G., Avelar, A.T., Cardoso, W.B.: A proposal to implement a quantum delayed choice experiment assisted by cavity QED. Phys. Lett. A 378(18–19), 1254–1257 (2014)

    Article  ADS  Google Scholar 

  18. Manning, A.G., Khakimov, R.I., Dall, R.G., Truscott, A.G.: Wheeler’s delayed-choice gedanken experiment with a single atom. Nat. Phys. 11(7), 539–542 (2015)

    Article  Google Scholar 

  19. Zheng, S.-B., Zhong, Y.-P., Kai, X., Wang, Q.-J., Wang, H., Shen, L.-T., Yang, C.-P., Martinis, J.M., Cleland, A.N., Han, S.-Y.: Quantum delayed-choice experiment with a beam splitter in a quantum superposition. Phys. Rev. Lett. 115(26), 260403 (2015)

    Article  ADS  Google Scholar 

  20. Jacques, V., Wu, E., Grosshans, F., Treussart, F., Grangier, P., Aspect, A., Roch, J.-F.: Experimental realization of Wheeler’s delayed-choice Gedanken experiment. Science 315(5814), 966–968 (2007)

    Article  ADS  MATH  Google Scholar 

  21. Jacques, V., Wu, E., Grosshans, F., Treussart, F., Grangier, P., Aspect, A., Roch, J.-F.: Delayed-choice test of quantum complementarity with interfering single photons. Phys. Rev. Lett. 100(22), 220402 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Gardiner, C.W., Zoller, P.: Quantum Noise. Springer Press, Berlin (2000)

    Book  MATH  Google Scholar 

  23. Nemoto, K., Munro, W.J.: Nearly deterministic linear optical Controlled-NOT gate. Phys. Rev. Lett. 93(25), 250502 (2004)

    Article  ADS  Google Scholar 

  24. Lin, Q., Li, J.: Quantum control gates with weak cross-Kerr nonlinearity. Phys. Rev. A 79(2), 022301 (2009)

    Article  ADS  Google Scholar 

  25. Simon, Marvin K.: Probability Distributions Involving Gaussian Random Variables, A Handbook for Engineers. Scientists and Mathematicians. Springer Press, New York (2006)

    Google Scholar 

  26. Siomau, M., Kamli, A.A., Moiseev, S.A., Sanders, B.C.: Entanglement creation with negative index metamaterials. Phys. Rev. A 85(5), 050303(R) (2012)

    Article  ADS  Google Scholar 

  27. Paik, H., Schuster, D.I., Bishop, L.S., Kirchmair, G., Catelani, G., Sears, A.P., Johnson, B.R., Reagor, M.J., Frunzio, L., Glazman, L.I., Girvin, S.M., Devoret, M.H., Schoelkopf, R.J.: Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Phys. Rev. Lett. 107(24), 240501 (2011)

    Article  ADS  Google Scholar 

  28. Hoi, I.-C., Kockum, A.F., Palomaki, T., Stace, T.M., Fan, B., Tornberg, L., Sathyamoorthy, S.R., Johansson, G., Delsing, P., Wilson, C.M.: Giant cross-Kerr effect for propagating microwaves induced by an artificial atom. Phys. Rev. Lett. 111(5), 053601 (2013)

    Article  ADS  Google Scholar 

  29. Lukin, M.D., Imamoglu, A.: Nonlinear optics and quantum entanglement of ultraslow single photons. Phys. Rev. Lett. 84(7), 1419–1422 (2000)

    Article  ADS  Google Scholar 

  30. Bajcsy, M., Zibrov, A.S., Lukin, M.D.: Stationary pulses of light in an atomic medium. Nature 426(6967), 638–641 (2003)

    Article  ADS  Google Scholar 

  31. Wang, Z.-B., Marzlin, K.-P., Sanders, B.C.: Large cross-phase modulation between slow copropagating weak pulses in \(^{\rm 87}\)Rb. Phys. Rev. Lett. 97(6), 063901 (2006)

  32. Chen, Y.-F., Wang, C.-Y., Wang, S.-H., Ite, A.: Low-light-level cross-phase-modulation based on stored light pulses. Phys. Rev. Lett. 96(4), 043603 (2006)

    Article  ADS  Google Scholar 

  33. Lo, H.-Y., Chen, Y.-C., Su, P.-C., Chen, H.-C., Chen, J.-X., Chen, Y.-C., Ite, A.Y., Chen, Y.-F.: Electromagnetically-induced-transparency-based cross-phase-modulation at attojoule levels. Phys. Rev. A 83(4), 041804(R) (2011)

    Article  ADS  Google Scholar 

  34. Shiau, B.-W., Wu, M.-C., Lin, C.-C., Chen, Y.-C.: Low-light-level cross-phase modulation with double slow light pulses. Phys. Rev. Lett. 106(19), 193006 (2011)

    Article  ADS  Google Scholar 

  35. Chen, Y.-H., Lee, M.-J., Hung, W., Chen, Y.-C., Chen, Y.-F., Ite, A.Y.: Demonstration of the interaction between two stopped light pulses. Phys. Rev. Lett. 108(17), 173603 (2012)

    Article  ADS  Google Scholar 

  36. Venkataraman, V., Saha, K., Gaeta, A.L.: Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing. Nat. Photon. 7(2), 138–141 (2012)

    Article  ADS  Google Scholar 

  37. Chen, Y.-H., Lee, M.-J., Wang, I.-C., Du, S., Chen, Y.-F., Chen, Y.-C., Ite, A.Y.: Coherent optical memory with high storage efficiency and large fractional delay. Phys. Rev. Lett. 110(8), 083601 (2013)

    Article  ADS  Google Scholar 

  38. Feizpour, A., Hallaji, M., Dmochowski, G., Steinberg, A.M.: Observation of the nonlinear phase shift due to single post-selected photons. Nat. Phys. 11(11), 905–909 (2015)

    Article  Google Scholar 

  39. Feizpour, A., Xing, X., Steinberg, A.M.: Amplifying single-photon nonlinearity using weak measurements. Phys. Rev. Lett. 107(13), 133603 (2011)

    Article  ADS  Google Scholar 

  40. Sefi, S., Vaibhav, V., van Loock, P.: Measurement-induced optical Kerr interaction. Phys. Rev. A 88(1), 012303 (2013)

    Article  ADS  Google Scholar 

  41. Bartkowiak, M., Wu, L.-A., Miranowicz, A.: Quantum circuits for amplification of Kerr nonlinearity via quadrature squeezing. J. Phys. B 47(14), 145501 (2014)

    Article  ADS  Google Scholar 

  42. Shapiro, J.: Single-photon Kerr nonlinearities do not help quantum computation. Phys. Rev. A 73(6), 062305 (2006)

    Article  ADS  Google Scholar 

  43. Shapiro, J.H., Razavi, M.: Continuous-time cross-phase modulation and quantum computation. New J. Phys. 9(1), 16 (2007)

    Article  ADS  Google Scholar 

  44. Kok, P., Nemoto, K., Ralph, T.C., Dowling, J.P., Milburn, G.J.: Linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79(1), 135–174 (2007)

    Article  ADS  Google Scholar 

  45. Matsuda, N., Shimizu, R., Mitsumori, Y., Kosaka, H., Edamatsu, K.: Observation of optical-fibre Kerr nonlinearity at the single-photon level. Nat. Photon. 3(2), 95–98 (2009)

    Article  ADS  MATH  Google Scholar 

  46. Gea-Banacloche, J.: Impossibility of large phase shifts via the giant Kerr effect with single-photon wave packets. Phys. Rev. A 81(4), 043823 (2010)

    Article  ADS  Google Scholar 

  47. Fan, B., Kockum, A.F., Combes, J., Johansson, G., Hoi, I., Wilson, C.M., Delsing, P., Milburn, G.J., Stace, T.M.: Breakdown of the cross-Kerr scheme for photon counting. Phys. Rev. Lett. 110(5), 053601 (2013)

    Article  ADS  Google Scholar 

  48. Imoto, N., Haus, H.A., Yamamoto, Y.: Quantum nondemolition measurement of the photon number via the optical Kerr effect. Phys. Rev. A 32(4), 2287–2292 (1985)

    Article  ADS  Google Scholar 

  49. Barrett, S.D., Kok, P., Nemoto, K., Beausoleil, R.G., Munro, W.J., Spiller, T.P.: Symmetry analyzer for nondestructive bell-state detection using weak nonlinearities. Phys. Rev. A 71(6), 060302(R) (2005)

    Article  ADS  Google Scholar 

  50. Munro, W.J., Nemoto, K., Spiller, T.P.: Weak nonlinearities: a new route to optical quantum computation. New J. Phys. 7(1), 137 (2005)

    Article  ADS  Google Scholar 

  51. Spiller, T.P., Nemoto, K., Braunstein, S.L., Munro, W.J., Van Loock, P.: Milburn., G.J.: Quantum computation by communication. New J. Phys. 8(2), 30 (2006)

    Article  ADS  Google Scholar 

  52. He, B., Ren, Y., Bergou, J.: Creation of high-quality long-distance entanglement with flexible resources. Phys. Rev. A 79(5), 052323 (2009)

    Article  ADS  Google Scholar 

  53. Xia, Y., Song, J., Lu, P.-M., Song, H.-S.: Efficient implementation of the two-qubit controlled phase gate with cross-Kerr nonlinearity. J. Phys. B At. Mol. Opt. Phys. 44(2), 025503 (2011)

  54. Guo, Q., Bai, J., Cheng, L.-Y., Shao, X.-Q., Wang, H.-F., Zhang, S.: Simplified optical quantum-information processing via weak cross-Kerr nonlinearities. Phys. Rev. A 83(5), 054303 (2011)

    Article  ADS  Google Scholar 

  55. Wang, X.-W., Zhang, D.-Y., Tang, S.-Q., Xie, L.-J., Wang, Z.-Y., Kuang, L.-M.: Photonic two-qubit parity gate with tiny cross-Kerr nonlinearity. Phys. Rev. A 85(5), 052326 (2012)

    Article  ADS  Google Scholar 

  56. Xiu, X.-M., Dong, L., Shen, H.-Z., Gao, Y.-J., Yi, X.X.: Construction scheme of a two-photon polarization controlled arbitrary phase gate mediated by weak cross-phase modulation. J. Opt. Soc. Am. B 30(3), 589–597 (2013)

    Article  ADS  Google Scholar 

  57. Louis, S.G.R., Nemoto, K., Munro, W.J., Spiller, T.P.: The efficiencies of generating cluster states with weak nonlinearities. New J. Phys. 9(6), 193 (2007)

    Article  ADS  Google Scholar 

  58. Louis, S., Nemoto, K., Munro, W., Spiller, T.: Weak nonlinearities and cluster states. Phys. Rev. A 75(4), 042323 (2007)

    Article  ADS  Google Scholar 

  59. Dong, L., Wang, J.-X., Li, Q.-Y., Shen, H.-Z., Dong, H.-K., Xiu, X.-M., Gao, Y.-J., Hiap, C.H.: Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities. Phys. Rev. A 93(1), 012308 (2016)

    Article  ADS  Google Scholar 

  60. Sheng, Y.-B., Deng, F.-G., Zhou, H.-Y.: Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity. Phys. Rev. A 77(4), 042308 (2008)

    Article  ADS  Google Scholar 

  61. Li, X.-H.: Deterministic polarization-entanglement purification using spatial entanglement. Phys. Rev. A 82(4), 044304 (2010)

    Article  ADS  Google Scholar 

  62. Sheng, Y.-B., Deng, F.-G.: Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement. Phys. Rev. A 81(3), 032307 (2010)

    Article  ADS  Google Scholar 

  63. Sheng, Y.-B., Deng, F.-G.: One-step deterministic polarization-entanglement purification using spatial entanglement. Phys. Rev. A 82(4), 044305 (2010)

    Article  ADS  Google Scholar 

  64. Wang, C., Zhang, Y., Jin, G.-S.: Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities. Phys. Rev. A 84(9), 032307 (2011)

    Article  ADS  Google Scholar 

  65. Deng, F.-G.: Efficient multipartite entanglement purification with the entanglement link from a subspace. Phys. Rev. A 84(11), 052312 (2011)

    Article  ADS  Google Scholar 

  66. Zhou, L., Sheng, Y.-B.: Recyclable amplification protocol for the single-photon entangled state. Laser Phys. Lett. 12(4), 045203 (2015)

    Article  ADS  Google Scholar 

  67. Dong, L., Wang, J.-X., Li, Q.-Y., Shen, H.-Z., Dong, H.-K., Xiu, X.-M., Gao, Y.-J.: Single logical qubit information encoding scheme with the minimal optical decoherence-free subsystem. Opt. Lett. 41(5), 1030–1033 (2016)

    Article  ADS  Google Scholar 

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Acknowledgements

This study was supported by the National Natural Science Foundation of China (Grant Nos. 11674037, 11544013, 11305016, 61301133, 11271055) and the Program for Liaoning Excellent Talents in University of China (LNET Grant No. LJQ2014124).

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  1. College of Mathematics and Physics, Bohai University, Jinzhou, 121013, China

    Li Dong, Yan-Fang Lin, Qing-Yang Li, Xiao-Ming Xiu, Hai-Kuan Dong & Ya-Jun Gao

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  1. Li Dong
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Dong, L., Lin, YF., Li, QY. et al. Optical proposals for controlled delayed-choice experiment based on weak cross-Kerr nonlinearities. Quantum Inf Process 16, 122 (2017). https://doi.org/10.1007/s11128-017-1574-2

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