Abstract

The state of the quantum system will inevitably be disturbed and changed in the testing process. Using interaction-free measurement (IFM), the information can be extracted without any interaction between objects and photons or particles. Here we present a novel approach that the refractive index can be measured accurately with “no-touch” measurement between testing materials and light beam. The design system is a non-traditional model of interaction-free measurement with an unbalanced Mach-Zehnder interferometer (UMZI), which is combined with the chain quantum Zeno effect and the technique for spatial separation of light field. We select two beams with different intensity distribution in cross-section and different frequency as the transmission source, and the refractive index of samples can be obtained from the contrast degree of two beams under the condition of a few beam splitters existing. The scheme could prevent the damage to the radiation-sensitive optical materials, and provide a new idea for the research and application of precision measurement.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. D. T. Delpy, M. Cope, P. Zee, S. Arridge, S. Wray, and J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33(12), 1433–1442 (1988).
    [Crossref]
  2. B. Lamine, C. Fabre, and N. Treps, “Quantum improvement of time transfer between remote clocks,” Phys. Rev. Lett. 101(12), 123601 (2008).
    [Crossref]
  3. N. Treps, N. Grossc, W. P. Bowen, C. Fabre, H. A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301(5635), 940–943 (2003).
    [Crossref]
  4. C. F. Li, X. Y. Xu, J. S. Tang, J. S. Xu, and G. C. Guo, “Ultrasensitive phase estimation with white light,” Phys. Rev. A 83(4), 044102 (2011).
    [Crossref]
  5. X. Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C. F. Li, and G. C. Guo, “Phase estimation with peak measurement using a white light source,” Phys. Rev. Lett. 111(3), 033604 (2013).
    [Crossref]
  6. A. Agarwal, K. K. Berggren, Y. J. van Staaden, and V. K. Goyal, “Reduced damage in electron microscopy by using interaction-free measurement and conditional reillumination,” Phys. Rev. A 99(6), 063809 (2019).
    [Crossref]
  7. Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60(14), 1351–1354 (1988).
    [Crossref]
  8. Y. Aharonov and L. Vaidman, “Complete description of a quantum system at a given time,” J,” J. Phys. A: Math. Gen. 24(10), 2315–2328 (1991).
    [Crossref]
  9. A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements,” Found Phys. 23(7), 987–997 (1993).
    [Crossref]
  10. M. Z. Renninger, Phys. 158, 417 (1960). This is written in German, a relatively clear discussion of the paper in English is given in J. G. Cramer, Rev. Mod. Phys. 58, 647 (1986).
  11. R. H. Dicke, “Interaction-free quantum measurements: A paradox?” Am. J. Phys. 49(10), 925–930 (1981).
    [Crossref]
  12. A. G. White, J. R. Mitchell, O. Nairz, and P. G. Kwiat, ““Interaction-free” imaging,”,” Phys. Rev. A 58(1), 605–613 (1998).
    [Crossref]
  13. A. Karlsson, G. Bjork, and E. Forsberg, “Interaction (energy exchange) free and quantum nondemolition measurements,” Phys. Rev. Lett. 80(6), 1198–1201 (1998).
    [Crossref]
  14. G. S. Paraoanu, “Interaction-free measurements with superconducting qubits,” Phys. Rev. Lett. 97(18), 180406 (2006).
    [Crossref]
  15. Y. Zhou and M. H. Yung, “Interaction-free measurement as quantum channel discrimination,” Phys. Rev. A 96(6), 062129 (2017).
    [Crossref]
  16. S. Durr and G. Rempe, “Can wave-particle duality be based on the uncertainty relation?” Am. J. Phys. 68(11), 1021–1024 (2000).
    [Crossref]
  17. D. M. Greenberger and A. Yasin, “Simultaneous wave and particle knowledge in a neutron interferometer,” Phys. Lett. A 128(8), 391–394 (1988).
    [Crossref]
  18. P. G. Kwait, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74(24), 4763–4766 (1995).
    [Crossref]
  19. G. L. Long, W. Qin, Z. Yang, and J. L. Li, “Realistic interpretation of quantum mechanics and encounter-delayed-choice experiment,” Sci. China: Phys., Mech. Astron. 61(3), 030311 (2018).
    [Crossref]
  20. T. G. Noh, “Counterfactual quantum cryptography,” Phys. Rev. Lett. 103(23), 230501 (2009).
    [Crossref]
  21. G. Brida, A. Cavanna, I. P. Degiovanni, M. Genovese, and P. Traina, “Experimental realization of counterfactual quantum cryptography,” Laser Phys. Lett. 9(3), 247–252 (2012).
    [Crossref]
  22. Y. Liu, L. Ju, X. L. Liang, S. B. Tang, G. L. Tu, L. Zhou, C. Z. Peng, K. Chen, T. Y. Chen, Z. B. Chen, and J. W. Pan, “Experimental demonstration of counterfactual quantum communication,” Phys. Rev. Lett. 109(3), 030501 (2012).
    [Crossref]
  23. H. Salih, Z. H. Li, M. Al-Amri, and M. Suhail Zubairy, “Protocol for direct counterfactual quantum communication,” Phys. Rev. Lett. 110(17), 170502 (2013).
    [Crossref]
  24. A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, “Asking photons where they have been,” Phys. Rev. Lett. 111(24), 240402 (2013).
    [Crossref]
  25. F. Li, J. X. Zhang, and S. Y. Zhu, “Numerical simulation of the effect of dissipation and phase fluctuation in a direct communication scheme,” J. Phys. B: At., Mol. Opt. Phys. 48(11), 115506 (2015).
    [Crossref]
  26. C. Liu, J. Liu, J. X. Zhang, and S. Y. Zhu, “Improvement of reliability in multi-interferometer-based counterfactual deterministic communication with dissipation compensation,” Opt. Express 26(3), 2261–2269 (2018).
    [Crossref]
  27. Y. Cao, Y. H. Li, Z. Cao, J. Yin, Y. A. Chen, H. L. Yin, T. Y. Chen, X. F. Ma, C. Z. Peng, and J. W. Pan, “Direct counterfactual communication via quantum Zeno effect,” Proc. Natl. Acad. Sci. 114(19), 4920–4924 (2017).
    [Crossref]
  28. J. Volz, R. Gehr, G. Dubois, J. Estève, and J. Reichel, “Measurement of the internal state of a single atom without energy exchange,” Nature 475(7355), 210–213 (2011).
    [Crossref]
  29. W. P. Putnam and M. F. Yanik, “Noninvasive electron microscopy with interaction-free quantum measurements,” Phys. Rev. A 80(4), 040902 (2009).
    [Crossref]
  30. E. H. Huntington, G. N. Milford, and C. Robilliard, “Demonstration of the spatial separation of the entangled quantum sidebands of an optical field,” Phys. Rev. A 71(4), 041802 (2005).
    [Crossref]

2019 (1)

A. Agarwal, K. K. Berggren, Y. J. van Staaden, and V. K. Goyal, “Reduced damage in electron microscopy by using interaction-free measurement and conditional reillumination,” Phys. Rev. A 99(6), 063809 (2019).
[Crossref]

2018 (2)

G. L. Long, W. Qin, Z. Yang, and J. L. Li, “Realistic interpretation of quantum mechanics and encounter-delayed-choice experiment,” Sci. China: Phys., Mech. Astron. 61(3), 030311 (2018).
[Crossref]

C. Liu, J. Liu, J. X. Zhang, and S. Y. Zhu, “Improvement of reliability in multi-interferometer-based counterfactual deterministic communication with dissipation compensation,” Opt. Express 26(3), 2261–2269 (2018).
[Crossref]

2017 (2)

Y. Cao, Y. H. Li, Z. Cao, J. Yin, Y. A. Chen, H. L. Yin, T. Y. Chen, X. F. Ma, C. Z. Peng, and J. W. Pan, “Direct counterfactual communication via quantum Zeno effect,” Proc. Natl. Acad. Sci. 114(19), 4920–4924 (2017).
[Crossref]

Y. Zhou and M. H. Yung, “Interaction-free measurement as quantum channel discrimination,” Phys. Rev. A 96(6), 062129 (2017).
[Crossref]

2015 (1)

F. Li, J. X. Zhang, and S. Y. Zhu, “Numerical simulation of the effect of dissipation and phase fluctuation in a direct communication scheme,” J. Phys. B: At., Mol. Opt. Phys. 48(11), 115506 (2015).
[Crossref]

2013 (3)

H. Salih, Z. H. Li, M. Al-Amri, and M. Suhail Zubairy, “Protocol for direct counterfactual quantum communication,” Phys. Rev. Lett. 110(17), 170502 (2013).
[Crossref]

A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, “Asking photons where they have been,” Phys. Rev. Lett. 111(24), 240402 (2013).
[Crossref]

X. Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C. F. Li, and G. C. Guo, “Phase estimation with peak measurement using a white light source,” Phys. Rev. Lett. 111(3), 033604 (2013).
[Crossref]

2012 (2)

G. Brida, A. Cavanna, I. P. Degiovanni, M. Genovese, and P. Traina, “Experimental realization of counterfactual quantum cryptography,” Laser Phys. Lett. 9(3), 247–252 (2012).
[Crossref]

Y. Liu, L. Ju, X. L. Liang, S. B. Tang, G. L. Tu, L. Zhou, C. Z. Peng, K. Chen, T. Y. Chen, Z. B. Chen, and J. W. Pan, “Experimental demonstration of counterfactual quantum communication,” Phys. Rev. Lett. 109(3), 030501 (2012).
[Crossref]

2011 (2)

J. Volz, R. Gehr, G. Dubois, J. Estève, and J. Reichel, “Measurement of the internal state of a single atom without energy exchange,” Nature 475(7355), 210–213 (2011).
[Crossref]

C. F. Li, X. Y. Xu, J. S. Tang, J. S. Xu, and G. C. Guo, “Ultrasensitive phase estimation with white light,” Phys. Rev. A 83(4), 044102 (2011).
[Crossref]

2009 (2)

W. P. Putnam and M. F. Yanik, “Noninvasive electron microscopy with interaction-free quantum measurements,” Phys. Rev. A 80(4), 040902 (2009).
[Crossref]

T. G. Noh, “Counterfactual quantum cryptography,” Phys. Rev. Lett. 103(23), 230501 (2009).
[Crossref]

2008 (1)

B. Lamine, C. Fabre, and N. Treps, “Quantum improvement of time transfer between remote clocks,” Phys. Rev. Lett. 101(12), 123601 (2008).
[Crossref]

2006 (1)

G. S. Paraoanu, “Interaction-free measurements with superconducting qubits,” Phys. Rev. Lett. 97(18), 180406 (2006).
[Crossref]

2005 (1)

E. H. Huntington, G. N. Milford, and C. Robilliard, “Demonstration of the spatial separation of the entangled quantum sidebands of an optical field,” Phys. Rev. A 71(4), 041802 (2005).
[Crossref]

2003 (1)

N. Treps, N. Grossc, W. P. Bowen, C. Fabre, H. A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301(5635), 940–943 (2003).
[Crossref]

2000 (1)

S. Durr and G. Rempe, “Can wave-particle duality be based on the uncertainty relation?” Am. J. Phys. 68(11), 1021–1024 (2000).
[Crossref]

1998 (2)

A. G. White, J. R. Mitchell, O. Nairz, and P. G. Kwiat, ““Interaction-free” imaging,”,” Phys. Rev. A 58(1), 605–613 (1998).
[Crossref]

A. Karlsson, G. Bjork, and E. Forsberg, “Interaction (energy exchange) free and quantum nondemolition measurements,” Phys. Rev. Lett. 80(6), 1198–1201 (1998).
[Crossref]

1995 (1)

P. G. Kwait, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74(24), 4763–4766 (1995).
[Crossref]

1993 (1)

A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements,” Found Phys. 23(7), 987–997 (1993).
[Crossref]

1991 (1)

Y. Aharonov and L. Vaidman, “Complete description of a quantum system at a given time,” J,” J. Phys. A: Math. Gen. 24(10), 2315–2328 (1991).
[Crossref]

1988 (3)

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60(14), 1351–1354 (1988).
[Crossref]

D. T. Delpy, M. Cope, P. Zee, S. Arridge, S. Wray, and J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33(12), 1433–1442 (1988).
[Crossref]

D. M. Greenberger and A. Yasin, “Simultaneous wave and particle knowledge in a neutron interferometer,” Phys. Lett. A 128(8), 391–394 (1988).
[Crossref]

1981 (1)

R. H. Dicke, “Interaction-free quantum measurements: A paradox?” Am. J. Phys. 49(10), 925–930 (1981).
[Crossref]

Agarwal, A.

A. Agarwal, K. K. Berggren, Y. J. van Staaden, and V. K. Goyal, “Reduced damage in electron microscopy by using interaction-free measurement and conditional reillumination,” Phys. Rev. A 99(6), 063809 (2019).
[Crossref]

Aharonov, Y.

Y. Aharonov and L. Vaidman, “Complete description of a quantum system at a given time,” J,” J. Phys. A: Math. Gen. 24(10), 2315–2328 (1991).
[Crossref]

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60(14), 1351–1354 (1988).
[Crossref]

Al-Amri, M.

H. Salih, Z. H. Li, M. Al-Amri, and M. Suhail Zubairy, “Protocol for direct counterfactual quantum communication,” Phys. Rev. Lett. 110(17), 170502 (2013).
[Crossref]

Albert, D. Z.

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60(14), 1351–1354 (1988).
[Crossref]

Arridge, S.

D. T. Delpy, M. Cope, P. Zee, S. Arridge, S. Wray, and J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33(12), 1433–1442 (1988).
[Crossref]

Bachor, H. A.

N. Treps, N. Grossc, W. P. Bowen, C. Fabre, H. A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301(5635), 940–943 (2003).
[Crossref]

Bar-Ad, S.

A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, “Asking photons where they have been,” Phys. Rev. Lett. 111(24), 240402 (2013).
[Crossref]

Berggren, K. K.

A. Agarwal, K. K. Berggren, Y. J. van Staaden, and V. K. Goyal, “Reduced damage in electron microscopy by using interaction-free measurement and conditional reillumination,” Phys. Rev. A 99(6), 063809 (2019).
[Crossref]

Bjork, G.

A. Karlsson, G. Bjork, and E. Forsberg, “Interaction (energy exchange) free and quantum nondemolition measurements,” Phys. Rev. Lett. 80(6), 1198–1201 (1998).
[Crossref]

Bowen, W. P.

N. Treps, N. Grossc, W. P. Bowen, C. Fabre, H. A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301(5635), 940–943 (2003).
[Crossref]

Brida, G.

G. Brida, A. Cavanna, I. P. Degiovanni, M. Genovese, and P. Traina, “Experimental realization of counterfactual quantum cryptography,” Laser Phys. Lett. 9(3), 247–252 (2012).
[Crossref]

Cao, Y.

Y. Cao, Y. H. Li, Z. Cao, J. Yin, Y. A. Chen, H. L. Yin, T. Y. Chen, X. F. Ma, C. Z. Peng, and J. W. Pan, “Direct counterfactual communication via quantum Zeno effect,” Proc. Natl. Acad. Sci. 114(19), 4920–4924 (2017).
[Crossref]

Cao, Z.

Y. Cao, Y. H. Li, Z. Cao, J. Yin, Y. A. Chen, H. L. Yin, T. Y. Chen, X. F. Ma, C. Z. Peng, and J. W. Pan, “Direct counterfactual communication via quantum Zeno effect,” Proc. Natl. Acad. Sci. 114(19), 4920–4924 (2017).
[Crossref]

Cavanna, A.

G. Brida, A. Cavanna, I. P. Degiovanni, M. Genovese, and P. Traina, “Experimental realization of counterfactual quantum cryptography,” Laser Phys. Lett. 9(3), 247–252 (2012).
[Crossref]

Chen, K.

Y. Liu, L. Ju, X. L. Liang, S. B. Tang, G. L. Tu, L. Zhou, C. Z. Peng, K. Chen, T. Y. Chen, Z. B. Chen, and J. W. Pan, “Experimental demonstration of counterfactual quantum communication,” Phys. Rev. Lett. 109(3), 030501 (2012).
[Crossref]

Chen, T. Y.

Y. Cao, Y. H. Li, Z. Cao, J. Yin, Y. A. Chen, H. L. Yin, T. Y. Chen, X. F. Ma, C. Z. Peng, and J. W. Pan, “Direct counterfactual communication via quantum Zeno effect,” Proc. Natl. Acad. Sci. 114(19), 4920–4924 (2017).
[Crossref]

Y. Liu, L. Ju, X. L. Liang, S. B. Tang, G. L. Tu, L. Zhou, C. Z. Peng, K. Chen, T. Y. Chen, Z. B. Chen, and J. W. Pan, “Experimental demonstration of counterfactual quantum communication,” Phys. Rev. Lett. 109(3), 030501 (2012).
[Crossref]

Chen, Y. A.

Y. Cao, Y. H. Li, Z. Cao, J. Yin, Y. A. Chen, H. L. Yin, T. Y. Chen, X. F. Ma, C. Z. Peng, and J. W. Pan, “Direct counterfactual communication via quantum Zeno effect,” Proc. Natl. Acad. Sci. 114(19), 4920–4924 (2017).
[Crossref]

Chen, Z. B.

Y. Liu, L. Ju, X. L. Liang, S. B. Tang, G. L. Tu, L. Zhou, C. Z. Peng, K. Chen, T. Y. Chen, Z. B. Chen, and J. W. Pan, “Experimental demonstration of counterfactual quantum communication,” Phys. Rev. Lett. 109(3), 030501 (2012).
[Crossref]

Cope, M.

D. T. Delpy, M. Cope, P. Zee, S. Arridge, S. Wray, and J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33(12), 1433–1442 (1988).
[Crossref]

Danan, A.

A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, “Asking photons where they have been,” Phys. Rev. Lett. 111(24), 240402 (2013).
[Crossref]

Degiovanni, I. P.

G. Brida, A. Cavanna, I. P. Degiovanni, M. Genovese, and P. Traina, “Experimental realization of counterfactual quantum cryptography,” Laser Phys. Lett. 9(3), 247–252 (2012).
[Crossref]

Delpy, D. T.

D. T. Delpy, M. Cope, P. Zee, S. Arridge, S. Wray, and J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33(12), 1433–1442 (1988).
[Crossref]

Dicke, R. H.

R. H. Dicke, “Interaction-free quantum measurements: A paradox?” Am. J. Phys. 49(10), 925–930 (1981).
[Crossref]

Dubois, G.

J. Volz, R. Gehr, G. Dubois, J. Estève, and J. Reichel, “Measurement of the internal state of a single atom without energy exchange,” Nature 475(7355), 210–213 (2011).
[Crossref]

Durr, S.

S. Durr and G. Rempe, “Can wave-particle duality be based on the uncertainty relation?” Am. J. Phys. 68(11), 1021–1024 (2000).
[Crossref]

Elitzur, A. C.

A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements,” Found Phys. 23(7), 987–997 (1993).
[Crossref]

Estève, J.

J. Volz, R. Gehr, G. Dubois, J. Estève, and J. Reichel, “Measurement of the internal state of a single atom without energy exchange,” Nature 475(7355), 210–213 (2011).
[Crossref]

Fabre, C.

B. Lamine, C. Fabre, and N. Treps, “Quantum improvement of time transfer between remote clocks,” Phys. Rev. Lett. 101(12), 123601 (2008).
[Crossref]

N. Treps, N. Grossc, W. P. Bowen, C. Fabre, H. A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301(5635), 940–943 (2003).
[Crossref]

Farfurnik, D.

A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, “Asking photons where they have been,” Phys. Rev. Lett. 111(24), 240402 (2013).
[Crossref]

Forsberg, E.

A. Karlsson, G. Bjork, and E. Forsberg, “Interaction (energy exchange) free and quantum nondemolition measurements,” Phys. Rev. Lett. 80(6), 1198–1201 (1998).
[Crossref]

Gehr, R.

J. Volz, R. Gehr, G. Dubois, J. Estève, and J. Reichel, “Measurement of the internal state of a single atom without energy exchange,” Nature 475(7355), 210–213 (2011).
[Crossref]

Genovese, M.

G. Brida, A. Cavanna, I. P. Degiovanni, M. Genovese, and P. Traina, “Experimental realization of counterfactual quantum cryptography,” Laser Phys. Lett. 9(3), 247–252 (2012).
[Crossref]

Goyal, V. K.

A. Agarwal, K. K. Berggren, Y. J. van Staaden, and V. K. Goyal, “Reduced damage in electron microscopy by using interaction-free measurement and conditional reillumination,” Phys. Rev. A 99(6), 063809 (2019).
[Crossref]

Greenberger, D. M.

D. M. Greenberger and A. Yasin, “Simultaneous wave and particle knowledge in a neutron interferometer,” Phys. Lett. A 128(8), 391–394 (1988).
[Crossref]

Grossc, N.

N. Treps, N. Grossc, W. P. Bowen, C. Fabre, H. A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301(5635), 940–943 (2003).
[Crossref]

Guo, G. C.

X. Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C. F. Li, and G. C. Guo, “Phase estimation with peak measurement using a white light source,” Phys. Rev. Lett. 111(3), 033604 (2013).
[Crossref]

C. F. Li, X. Y. Xu, J. S. Tang, J. S. Xu, and G. C. Guo, “Ultrasensitive phase estimation with white light,” Phys. Rev. A 83(4), 044102 (2011).
[Crossref]

Herzog, T.

P. G. Kwait, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74(24), 4763–4766 (1995).
[Crossref]

Huntington, E. H.

E. H. Huntington, G. N. Milford, and C. Robilliard, “Demonstration of the spatial separation of the entangled quantum sidebands of an optical field,” Phys. Rev. A 71(4), 041802 (2005).
[Crossref]

Ju, L.

Y. Liu, L. Ju, X. L. Liang, S. B. Tang, G. L. Tu, L. Zhou, C. Z. Peng, K. Chen, T. Y. Chen, Z. B. Chen, and J. W. Pan, “Experimental demonstration of counterfactual quantum communication,” Phys. Rev. Lett. 109(3), 030501 (2012).
[Crossref]

Karlsson, A.

A. Karlsson, G. Bjork, and E. Forsberg, “Interaction (energy exchange) free and quantum nondemolition measurements,” Phys. Rev. Lett. 80(6), 1198–1201 (1998).
[Crossref]

Kasevich, M. A.

P. G. Kwait, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74(24), 4763–4766 (1995).
[Crossref]

Kedem, Y.

X. Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C. F. Li, and G. C. Guo, “Phase estimation with peak measurement using a white light source,” Phys. Rev. Lett. 111(3), 033604 (2013).
[Crossref]

Kwait, P. G.

P. G. Kwait, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74(24), 4763–4766 (1995).
[Crossref]

Kwiat, P. G.

A. G. White, J. R. Mitchell, O. Nairz, and P. G. Kwiat, ““Interaction-free” imaging,”,” Phys. Rev. A 58(1), 605–613 (1998).
[Crossref]

Lam, P. K.

N. Treps, N. Grossc, W. P. Bowen, C. Fabre, H. A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301(5635), 940–943 (2003).
[Crossref]

Lamine, B.

B. Lamine, C. Fabre, and N. Treps, “Quantum improvement of time transfer between remote clocks,” Phys. Rev. Lett. 101(12), 123601 (2008).
[Crossref]

Li, C. F.

X. Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C. F. Li, and G. C. Guo, “Phase estimation with peak measurement using a white light source,” Phys. Rev. Lett. 111(3), 033604 (2013).
[Crossref]

C. F. Li, X. Y. Xu, J. S. Tang, J. S. Xu, and G. C. Guo, “Ultrasensitive phase estimation with white light,” Phys. Rev. A 83(4), 044102 (2011).
[Crossref]

Li, F.

F. Li, J. X. Zhang, and S. Y. Zhu, “Numerical simulation of the effect of dissipation and phase fluctuation in a direct communication scheme,” J. Phys. B: At., Mol. Opt. Phys. 48(11), 115506 (2015).
[Crossref]

Li, J. L.

G. L. Long, W. Qin, Z. Yang, and J. L. Li, “Realistic interpretation of quantum mechanics and encounter-delayed-choice experiment,” Sci. China: Phys., Mech. Astron. 61(3), 030311 (2018).
[Crossref]

Li, Y. H.

Y. Cao, Y. H. Li, Z. Cao, J. Yin, Y. A. Chen, H. L. Yin, T. Y. Chen, X. F. Ma, C. Z. Peng, and J. W. Pan, “Direct counterfactual communication via quantum Zeno effect,” Proc. Natl. Acad. Sci. 114(19), 4920–4924 (2017).
[Crossref]

Li, Z. H.

H. Salih, Z. H. Li, M. Al-Amri, and M. Suhail Zubairy, “Protocol for direct counterfactual quantum communication,” Phys. Rev. Lett. 110(17), 170502 (2013).
[Crossref]

Liang, X. L.

Y. Liu, L. Ju, X. L. Liang, S. B. Tang, G. L. Tu, L. Zhou, C. Z. Peng, K. Chen, T. Y. Chen, Z. B. Chen, and J. W. Pan, “Experimental demonstration of counterfactual quantum communication,” Phys. Rev. Lett. 109(3), 030501 (2012).
[Crossref]

Liu, C.

Liu, J.

Liu, Y.

Y. Liu, L. Ju, X. L. Liang, S. B. Tang, G. L. Tu, L. Zhou, C. Z. Peng, K. Chen, T. Y. Chen, Z. B. Chen, and J. W. Pan, “Experimental demonstration of counterfactual quantum communication,” Phys. Rev. Lett. 109(3), 030501 (2012).
[Crossref]

Long, G. L.

G. L. Long, W. Qin, Z. Yang, and J. L. Li, “Realistic interpretation of quantum mechanics and encounter-delayed-choice experiment,” Sci. China: Phys., Mech. Astron. 61(3), 030311 (2018).
[Crossref]

Ma, X. F.

Y. Cao, Y. H. Li, Z. Cao, J. Yin, Y. A. Chen, H. L. Yin, T. Y. Chen, X. F. Ma, C. Z. Peng, and J. W. Pan, “Direct counterfactual communication via quantum Zeno effect,” Proc. Natl. Acad. Sci. 114(19), 4920–4924 (2017).
[Crossref]

Milford, G. N.

E. H. Huntington, G. N. Milford, and C. Robilliard, “Demonstration of the spatial separation of the entangled quantum sidebands of an optical field,” Phys. Rev. A 71(4), 041802 (2005).
[Crossref]

Mitchell, J. R.

A. G. White, J. R. Mitchell, O. Nairz, and P. G. Kwiat, ““Interaction-free” imaging,”,” Phys. Rev. A 58(1), 605–613 (1998).
[Crossref]

Nairz, O.

A. G. White, J. R. Mitchell, O. Nairz, and P. G. Kwiat, ““Interaction-free” imaging,”,” Phys. Rev. A 58(1), 605–613 (1998).
[Crossref]

Noh, T. G.

T. G. Noh, “Counterfactual quantum cryptography,” Phys. Rev. Lett. 103(23), 230501 (2009).
[Crossref]

Pan, J. W.

Y. Cao, Y. H. Li, Z. Cao, J. Yin, Y. A. Chen, H. L. Yin, T. Y. Chen, X. F. Ma, C. Z. Peng, and J. W. Pan, “Direct counterfactual communication via quantum Zeno effect,” Proc. Natl. Acad. Sci. 114(19), 4920–4924 (2017).
[Crossref]

Y. Liu, L. Ju, X. L. Liang, S. B. Tang, G. L. Tu, L. Zhou, C. Z. Peng, K. Chen, T. Y. Chen, Z. B. Chen, and J. W. Pan, “Experimental demonstration of counterfactual quantum communication,” Phys. Rev. Lett. 109(3), 030501 (2012).
[Crossref]

Paraoanu, G. S.

G. S. Paraoanu, “Interaction-free measurements with superconducting qubits,” Phys. Rev. Lett. 97(18), 180406 (2006).
[Crossref]

Peng, C. Z.

Y. Cao, Y. H. Li, Z. Cao, J. Yin, Y. A. Chen, H. L. Yin, T. Y. Chen, X. F. Ma, C. Z. Peng, and J. W. Pan, “Direct counterfactual communication via quantum Zeno effect,” Proc. Natl. Acad. Sci. 114(19), 4920–4924 (2017).
[Crossref]

Y. Liu, L. Ju, X. L. Liang, S. B. Tang, G. L. Tu, L. Zhou, C. Z. Peng, K. Chen, T. Y. Chen, Z. B. Chen, and J. W. Pan, “Experimental demonstration of counterfactual quantum communication,” Phys. Rev. Lett. 109(3), 030501 (2012).
[Crossref]

Putnam, W. P.

W. P. Putnam and M. F. Yanik, “Noninvasive electron microscopy with interaction-free quantum measurements,” Phys. Rev. A 80(4), 040902 (2009).
[Crossref]

Qin, W.

G. L. Long, W. Qin, Z. Yang, and J. L. Li, “Realistic interpretation of quantum mechanics and encounter-delayed-choice experiment,” Sci. China: Phys., Mech. Astron. 61(3), 030311 (2018).
[Crossref]

Reichel, J.

J. Volz, R. Gehr, G. Dubois, J. Estève, and J. Reichel, “Measurement of the internal state of a single atom without energy exchange,” Nature 475(7355), 210–213 (2011).
[Crossref]

Rempe, G.

S. Durr and G. Rempe, “Can wave-particle duality be based on the uncertainty relation?” Am. J. Phys. 68(11), 1021–1024 (2000).
[Crossref]

Renninger, M. Z.

M. Z. Renninger, Phys. 158, 417 (1960). This is written in German, a relatively clear discussion of the paper in English is given in J. G. Cramer, Rev. Mod. Phys. 58, 647 (1986).

Robilliard, C.

E. H. Huntington, G. N. Milford, and C. Robilliard, “Demonstration of the spatial separation of the entangled quantum sidebands of an optical field,” Phys. Rev. A 71(4), 041802 (2005).
[Crossref]

Salih, H.

H. Salih, Z. H. Li, M. Al-Amri, and M. Suhail Zubairy, “Protocol for direct counterfactual quantum communication,” Phys. Rev. Lett. 110(17), 170502 (2013).
[Crossref]

Suhail Zubairy, M.

H. Salih, Z. H. Li, M. Al-Amri, and M. Suhail Zubairy, “Protocol for direct counterfactual quantum communication,” Phys. Rev. Lett. 110(17), 170502 (2013).
[Crossref]

Sun, K.

X. Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C. F. Li, and G. C. Guo, “Phase estimation with peak measurement using a white light source,” Phys. Rev. Lett. 111(3), 033604 (2013).
[Crossref]

Tang, J. S.

C. F. Li, X. Y. Xu, J. S. Tang, J. S. Xu, and G. C. Guo, “Ultrasensitive phase estimation with white light,” Phys. Rev. A 83(4), 044102 (2011).
[Crossref]

Tang, S. B.

Y. Liu, L. Ju, X. L. Liang, S. B. Tang, G. L. Tu, L. Zhou, C. Z. Peng, K. Chen, T. Y. Chen, Z. B. Chen, and J. W. Pan, “Experimental demonstration of counterfactual quantum communication,” Phys. Rev. Lett. 109(3), 030501 (2012).
[Crossref]

Traina, P.

G. Brida, A. Cavanna, I. P. Degiovanni, M. Genovese, and P. Traina, “Experimental realization of counterfactual quantum cryptography,” Laser Phys. Lett. 9(3), 247–252 (2012).
[Crossref]

Treps, N.

B. Lamine, C. Fabre, and N. Treps, “Quantum improvement of time transfer between remote clocks,” Phys. Rev. Lett. 101(12), 123601 (2008).
[Crossref]

N. Treps, N. Grossc, W. P. Bowen, C. Fabre, H. A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301(5635), 940–943 (2003).
[Crossref]

Tu, G. L.

Y. Liu, L. Ju, X. L. Liang, S. B. Tang, G. L. Tu, L. Zhou, C. Z. Peng, K. Chen, T. Y. Chen, Z. B. Chen, and J. W. Pan, “Experimental demonstration of counterfactual quantum communication,” Phys. Rev. Lett. 109(3), 030501 (2012).
[Crossref]

Vaidman, L.

X. Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C. F. Li, and G. C. Guo, “Phase estimation with peak measurement using a white light source,” Phys. Rev. Lett. 111(3), 033604 (2013).
[Crossref]

A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, “Asking photons where they have been,” Phys. Rev. Lett. 111(24), 240402 (2013).
[Crossref]

A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements,” Found Phys. 23(7), 987–997 (1993).
[Crossref]

Y. Aharonov and L. Vaidman, “Complete description of a quantum system at a given time,” J,” J. Phys. A: Math. Gen. 24(10), 2315–2328 (1991).
[Crossref]

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60(14), 1351–1354 (1988).
[Crossref]

van Staaden, Y. J.

A. Agarwal, K. K. Berggren, Y. J. van Staaden, and V. K. Goyal, “Reduced damage in electron microscopy by using interaction-free measurement and conditional reillumination,” Phys. Rev. A 99(6), 063809 (2019).
[Crossref]

Volz, J.

J. Volz, R. Gehr, G. Dubois, J. Estève, and J. Reichel, “Measurement of the internal state of a single atom without energy exchange,” Nature 475(7355), 210–213 (2011).
[Crossref]

Weinfurter, H.

P. G. Kwait, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74(24), 4763–4766 (1995).
[Crossref]

White, A. G.

A. G. White, J. R. Mitchell, O. Nairz, and P. G. Kwiat, ““Interaction-free” imaging,”,” Phys. Rev. A 58(1), 605–613 (1998).
[Crossref]

Wray, S.

D. T. Delpy, M. Cope, P. Zee, S. Arridge, S. Wray, and J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33(12), 1433–1442 (1988).
[Crossref]

Wyatt, J.

D. T. Delpy, M. Cope, P. Zee, S. Arridge, S. Wray, and J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33(12), 1433–1442 (1988).
[Crossref]

Xu, J. S.

C. F. Li, X. Y. Xu, J. S. Tang, J. S. Xu, and G. C. Guo, “Ultrasensitive phase estimation with white light,” Phys. Rev. A 83(4), 044102 (2011).
[Crossref]

Xu, X. Y.

X. Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C. F. Li, and G. C. Guo, “Phase estimation with peak measurement using a white light source,” Phys. Rev. Lett. 111(3), 033604 (2013).
[Crossref]

C. F. Li, X. Y. Xu, J. S. Tang, J. S. Xu, and G. C. Guo, “Ultrasensitive phase estimation with white light,” Phys. Rev. A 83(4), 044102 (2011).
[Crossref]

Yang, Z.

G. L. Long, W. Qin, Z. Yang, and J. L. Li, “Realistic interpretation of quantum mechanics and encounter-delayed-choice experiment,” Sci. China: Phys., Mech. Astron. 61(3), 030311 (2018).
[Crossref]

Yanik, M. F.

W. P. Putnam and M. F. Yanik, “Noninvasive electron microscopy with interaction-free quantum measurements,” Phys. Rev. A 80(4), 040902 (2009).
[Crossref]

Yasin, A.

D. M. Greenberger and A. Yasin, “Simultaneous wave and particle knowledge in a neutron interferometer,” Phys. Lett. A 128(8), 391–394 (1988).
[Crossref]

Yin, H. L.

Y. Cao, Y. H. Li, Z. Cao, J. Yin, Y. A. Chen, H. L. Yin, T. Y. Chen, X. F. Ma, C. Z. Peng, and J. W. Pan, “Direct counterfactual communication via quantum Zeno effect,” Proc. Natl. Acad. Sci. 114(19), 4920–4924 (2017).
[Crossref]

Yin, J.

Y. Cao, Y. H. Li, Z. Cao, J. Yin, Y. A. Chen, H. L. Yin, T. Y. Chen, X. F. Ma, C. Z. Peng, and J. W. Pan, “Direct counterfactual communication via quantum Zeno effect,” Proc. Natl. Acad. Sci. 114(19), 4920–4924 (2017).
[Crossref]

Yung, M. H.

Y. Zhou and M. H. Yung, “Interaction-free measurement as quantum channel discrimination,” Phys. Rev. A 96(6), 062129 (2017).
[Crossref]

Zee, P.

D. T. Delpy, M. Cope, P. Zee, S. Arridge, S. Wray, and J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33(12), 1433–1442 (1988).
[Crossref]

Zeilinger, A.

P. G. Kwait, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74(24), 4763–4766 (1995).
[Crossref]

Zhang, J. X.

C. Liu, J. Liu, J. X. Zhang, and S. Y. Zhu, “Improvement of reliability in multi-interferometer-based counterfactual deterministic communication with dissipation compensation,” Opt. Express 26(3), 2261–2269 (2018).
[Crossref]

F. Li, J. X. Zhang, and S. Y. Zhu, “Numerical simulation of the effect of dissipation and phase fluctuation in a direct communication scheme,” J. Phys. B: At., Mol. Opt. Phys. 48(11), 115506 (2015).
[Crossref]

Zhou, L.

Y. Liu, L. Ju, X. L. Liang, S. B. Tang, G. L. Tu, L. Zhou, C. Z. Peng, K. Chen, T. Y. Chen, Z. B. Chen, and J. W. Pan, “Experimental demonstration of counterfactual quantum communication,” Phys. Rev. Lett. 109(3), 030501 (2012).
[Crossref]

Zhou, Y.

Y. Zhou and M. H. Yung, “Interaction-free measurement as quantum channel discrimination,” Phys. Rev. A 96(6), 062129 (2017).
[Crossref]

Zhu, S. Y.

C. Liu, J. Liu, J. X. Zhang, and S. Y. Zhu, “Improvement of reliability in multi-interferometer-based counterfactual deterministic communication with dissipation compensation,” Opt. Express 26(3), 2261–2269 (2018).
[Crossref]

F. Li, J. X. Zhang, and S. Y. Zhu, “Numerical simulation of the effect of dissipation and phase fluctuation in a direct communication scheme,” J. Phys. B: At., Mol. Opt. Phys. 48(11), 115506 (2015).
[Crossref]

Am. J. Phys. (2)

R. H. Dicke, “Interaction-free quantum measurements: A paradox?” Am. J. Phys. 49(10), 925–930 (1981).
[Crossref]

S. Durr and G. Rempe, “Can wave-particle duality be based on the uncertainty relation?” Am. J. Phys. 68(11), 1021–1024 (2000).
[Crossref]

Found Phys. (1)

A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements,” Found Phys. 23(7), 987–997 (1993).
[Crossref]

J. Phys. A: Math. Gen. (1)

Y. Aharonov and L. Vaidman, “Complete description of a quantum system at a given time,” J,” J. Phys. A: Math. Gen. 24(10), 2315–2328 (1991).
[Crossref]

J. Phys. B: At., Mol. Opt. Phys. (1)

F. Li, J. X. Zhang, and S. Y. Zhu, “Numerical simulation of the effect of dissipation and phase fluctuation in a direct communication scheme,” J. Phys. B: At., Mol. Opt. Phys. 48(11), 115506 (2015).
[Crossref]

Laser Phys. Lett. (1)

G. Brida, A. Cavanna, I. P. Degiovanni, M. Genovese, and P. Traina, “Experimental realization of counterfactual quantum cryptography,” Laser Phys. Lett. 9(3), 247–252 (2012).
[Crossref]

Nature (1)

J. Volz, R. Gehr, G. Dubois, J. Estève, and J. Reichel, “Measurement of the internal state of a single atom without energy exchange,” Nature 475(7355), 210–213 (2011).
[Crossref]

Opt. Express (1)

Phys. Lett. A (1)

D. M. Greenberger and A. Yasin, “Simultaneous wave and particle knowledge in a neutron interferometer,” Phys. Lett. A 128(8), 391–394 (1988).
[Crossref]

Phys. Med. Biol. (1)

D. T. Delpy, M. Cope, P. Zee, S. Arridge, S. Wray, and J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33(12), 1433–1442 (1988).
[Crossref]

Phys. Rev. A (6)

C. F. Li, X. Y. Xu, J. S. Tang, J. S. Xu, and G. C. Guo, “Ultrasensitive phase estimation with white light,” Phys. Rev. A 83(4), 044102 (2011).
[Crossref]

A. Agarwal, K. K. Berggren, Y. J. van Staaden, and V. K. Goyal, “Reduced damage in electron microscopy by using interaction-free measurement and conditional reillumination,” Phys. Rev. A 99(6), 063809 (2019).
[Crossref]

A. G. White, J. R. Mitchell, O. Nairz, and P. G. Kwiat, ““Interaction-free” imaging,”,” Phys. Rev. A 58(1), 605–613 (1998).
[Crossref]

Y. Zhou and M. H. Yung, “Interaction-free measurement as quantum channel discrimination,” Phys. Rev. A 96(6), 062129 (2017).
[Crossref]

W. P. Putnam and M. F. Yanik, “Noninvasive electron microscopy with interaction-free quantum measurements,” Phys. Rev. A 80(4), 040902 (2009).
[Crossref]

E. H. Huntington, G. N. Milford, and C. Robilliard, “Demonstration of the spatial separation of the entangled quantum sidebands of an optical field,” Phys. Rev. A 71(4), 041802 (2005).
[Crossref]

Phys. Rev. Lett. (10)

T. G. Noh, “Counterfactual quantum cryptography,” Phys. Rev. Lett. 103(23), 230501 (2009).
[Crossref]

Y. Liu, L. Ju, X. L. Liang, S. B. Tang, G. L. Tu, L. Zhou, C. Z. Peng, K. Chen, T. Y. Chen, Z. B. Chen, and J. W. Pan, “Experimental demonstration of counterfactual quantum communication,” Phys. Rev. Lett. 109(3), 030501 (2012).
[Crossref]

H. Salih, Z. H. Li, M. Al-Amri, and M. Suhail Zubairy, “Protocol for direct counterfactual quantum communication,” Phys. Rev. Lett. 110(17), 170502 (2013).
[Crossref]

A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, “Asking photons where they have been,” Phys. Rev. Lett. 111(24), 240402 (2013).
[Crossref]

A. Karlsson, G. Bjork, and E. Forsberg, “Interaction (energy exchange) free and quantum nondemolition measurements,” Phys. Rev. Lett. 80(6), 1198–1201 (1998).
[Crossref]

G. S. Paraoanu, “Interaction-free measurements with superconducting qubits,” Phys. Rev. Lett. 97(18), 180406 (2006).
[Crossref]

P. G. Kwait, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74(24), 4763–4766 (1995).
[Crossref]

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60(14), 1351–1354 (1988).
[Crossref]

X. Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C. F. Li, and G. C. Guo, “Phase estimation with peak measurement using a white light source,” Phys. Rev. Lett. 111(3), 033604 (2013).
[Crossref]

B. Lamine, C. Fabre, and N. Treps, “Quantum improvement of time transfer between remote clocks,” Phys. Rev. Lett. 101(12), 123601 (2008).
[Crossref]

Proc. Natl. Acad. Sci. (1)

Y. Cao, Y. H. Li, Z. Cao, J. Yin, Y. A. Chen, H. L. Yin, T. Y. Chen, X. F. Ma, C. Z. Peng, and J. W. Pan, “Direct counterfactual communication via quantum Zeno effect,” Proc. Natl. Acad. Sci. 114(19), 4920–4924 (2017).
[Crossref]

Sci. China: Phys., Mech. Astron. (1)

G. L. Long, W. Qin, Z. Yang, and J. L. Li, “Realistic interpretation of quantum mechanics and encounter-delayed-choice experiment,” Sci. China: Phys., Mech. Astron. 61(3), 030311 (2018).
[Crossref]

Science (1)

N. Treps, N. Grossc, W. P. Bowen, C. Fabre, H. A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301(5635), 940–943 (2003).
[Crossref]

Other (1)

M. Z. Renninger, Phys. 158, 417 (1960). This is written in German, a relatively clear discussion of the paper in English is given in J. G. Cramer, Rev. Mod. Phys. 58, 647 (1986).

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Figures (8)

Fig. 1.
Fig. 1. Schematic diagram of the UMZI-based scheme for interaction-free measurement of refractive index. Here ${\hat{a}_{{\omega _0} + \omega }}$ and ${\hat{a}_{{\omega _0}\textrm{ - }\omega }}$ stand for the two beams, which have different intensity distribution in cross section and different frequency. PBS stands for the polarizing beam splitter, and λ/2 stands for the half-wave plate, which are used to adjust the intensity of lower arm precisely. Δl stands for the arm-length difference. HR stands for the high reflectivity mirror. BS1 and BS2 stands for the 50/50 beam splitter. The BSNs stand for the beam splitters, they have large reflectivity of cos2(π/2n) with n being the number of beam splitters. PZT stands for the piezoelectric transducer. As discussed in the text, the contrast degree of two beams on the CCD reflects the change of relative phase difference in the IFM system, that is, accurately reveals the refractive index of samples in the testing channel.
Fig. 2.
Fig. 2. Schematic setup of the UMZI for longitudinal-mode separation. Here ${\hat{a}_{\textrm{in}}}$ stands for the coherent field with two kinds of frequency, and ${\hat{v}_{\textrm{in}}}$ stands for the vacuum field. The additional HRs in the lower arm make the two optical paths different. F-P stands for the Fabry–Pérot cavity, and D1 are the beam detector.
Fig. 3.
Fig. 3. Transmission spectra of the F-P cavity of the two beams with 9.192 GHz frequency difference. (a) One of the two beams has been detected when locking the phase difference of two big MZIs to be φ=(2n + 1)π/2. (b) The overlapping two beams have been detected when locking the phase difference to be φ≠(2n + 1)π/2. (c) Another beam having a 9.192 GHz frequency difference has been detected when φ=-(2n + 1)π/2.
Fig. 4.
Fig. 4. Schematic setup of the “chained” quantum Zeno effect for IFM.
Fig. 5.
Fig. 5. The probability of Pdet and Pabs vs the number of BSN.
Fig. 6.
Fig. 6. The normalized intensity of two output of each M-Z interferometer.
Fig. 7.
Fig. 7. The contrast degree γ as function of ns with the thickness l = 0.5 mm, 1.0 mm, and 1.5 mm.
Fig. 8.
Fig. 8. The contrast degree γ as function of ns with the number of beam splitter n = 2, 3, and 4.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

W BS = ( i r BS t BS t BS i r BS ) , W in  =  ( e i φ 0 0 1 ) ,
W BS  1 ( δ a ^ in ( t ) δ v ^ in ( t ) )  =  ( δ a ^ r ( t ) δ v ^ t ( t ) ) t t W BS  2 W in ( δ a ^ r ( t t ) δ a ^ t ( t ) ) = ( δ a ^ 1 out ( t ) δ a ^ 2 out ( t ) ) ,
δ a ^ 1 out ( ω ) = 1 2 [ δ a ^ in ( ω ) ( 1 e i φ + i ω t ) ] + i 2 [ δ v ^ in ( ω ) ( 1 + e i φ + i ω t ) ] ,
δ a ^ 2 out ( ω ) = i 2 [ δ a ^ in ( ω ) ( e i φ + i ω t + 1 ) ] + 1 2 [ δ v ^ in ( ω ) ( e i φ + i ω t 1 ) ] .
δ a ^ 1 out  ( ω ) = δ a ^ in ( ω ) , δ a ^ 2 out  ( ω ) = i δ a ^ in ( ω ) ,
δ a ^ 1 out  ( ω ) = i δ v ^ in ( ω ) , δ a ^ 2 out  ( ω ) = δ v ^ in ( ω ) .
W BS  N  =  ( r BS  N t BS  N t BS  N r BS  N ) , W ϕ  =  ( e i ϕ 0 0 1 δ abs ) ,
W  = ( W BS  N W ϕ ) n 1 W BS  N = ( W 11 W 12 W 21 W 22 ) ,
P abs = j = 1 7 I ( b ^ 2 out  ) / I ( b ^ in ) 2 r BS  N 2 j ,
W ϕ  =  ( 1 0 0 e i ϕ + i k ( n s 1 ) l ) ,
W whole  = ( W BS  N W ϕ ) n 1 W BS  N ,
T in  =  ( 1 δ path 0 0 W 11 whole ) ,
T BS  =  ( 2 / 2 2 / 2 2 / 2 2 / 2 ) ,
T  =  T BS T in T BS  =  ( T 11 T 12 T 21 T 22 ) .
γ  =  | | T 21 | 2 | T 11 | 2 | T 21 | 2 + | T 11 | 2 | ,

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