Abstract

Phase-sensitive weak measurement systems have been receiving an increasing amount of attention. In this paper, we introduce a series of weak measurement working areas. By adjusting the pre-selection and post-selection states and the total phase difference between vertically polarized light and horizontally polarized light, the measurement of the weak value is amplified by several times in one system. Its applicability is verified in a label-free total internal reflection system. The original sensitivity and resolution are improved at different working areas, reaching 1.85 um/refractive index unit (RIU) and 6.808 × 10−7 RIU, respectively.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. 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] [PubMed]
  2. N. W. M. Ritchie, J. G. Story, and R. G. Hulet, “Realization Of a Measurement Of a “Weak Value”,” Phys. Rev. Lett. 66(9), 1107–1110 (1991).
    [Crossref] [PubMed]
  3. T. Denkmayr, H. Geppert, S. Sponar, H. Lemmel, A. Matzkin, J. Tollaksen, and Y. Hasegawa, “Observation of a quantum Cheshire Cat in a matter-wave interferometer experiment,” Nat. Commun. 5(1), 4492 (2014).
    [Crossref] [PubMed]
  4. O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
    [Crossref] [PubMed]
  5. J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86(1), 307–316 (2014).
    [Crossref]
  6. S. Pang and T. A. Brun, “Improving the precision of weak measurements by postselection measurement,” Phys. Rev. Lett. 115(12), 120401 (2015).
    [Crossref] [PubMed]
  7. A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71(5), 708–711 (1993).
    [Crossref] [PubMed]
  8. G. I. Viza, J. Martínez-Rincón, G. A. Howland, H. Frostig, I. Shomroni, B. Dayan, and J. C. Howell, “Weak-values technique for velocity measurements,” Opt. Lett. 38(16), 2949–2952 (2013).
    [Crossref] [PubMed]
  9. L. J. Salazar-Serrano, D. Janner, N. Brunner, V. Pruneri, and J. P. Torres, “Measurement of sub-pulse-width temporal delays via spectral interference induced by weak value amplification,” Phys. Rev. A 89(1), 012126 (2014).
    [Crossref]
  10. L. J. Salazar-Serrano, D. Barrera, W. Amaya, S. Sales, V. Pruneri, J. Capmany, and J. P. Torres, “Enhancement of the sensitivity of a temperature sensor based on fiber Bragg gratings via weak value amplification,” Opt. Lett. 40(17), 3962–3965 (2015).
    [Crossref] [PubMed]
  11. X. Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C. F. Li, and G. C. Guo, “Phase Estimation With Weak Measurement Using a White Light Source,” Phys. Rev. Lett. 111(3), 033604 (2013).
    [Crossref] [PubMed]
  12. P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, “Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification,” Phys. Rev. Lett. 102(17), 173601 (2009).
    [Crossref] [PubMed]
  13. G. Jayaswal, G. Mistura, and M. Merano, “Weak measurement of the Goos-Hänchen shift,” Opt. Lett. 38(8), 1232–1234 (2013).
    [Crossref] [PubMed]
  14. B. D. L. Bernardo, S. Azevedo, and A. Rosas, “Ultrasmall polarization rotation measurements via weak value amplification,” Phys. Lett. A 378(30-31), 2029–2033 (2014).
    [Crossref]
  15. D. Li, Z. Shen, Y. He, Y. Zhang, Z. Chen, and H. Ma, “Application of quantum weak measurement for glucose concentration detection,” Appl. Opt. 55(7), 1697–1702 (2016).
    [Crossref] [PubMed]
  16. Y. Zhang, D. Li, Y. He, Z. Shen, and Q. He, “Optical weak measurement system with common path implementation for label-free biomolecule sensing,” Opt. Lett. 41(22), 5409–5412 (2016).
    [Crossref] [PubMed]
  17. D. Li, Q. He, Y. He, M. Xin, Y. Zhang, and Z. Shen, “Molecular imprinting sensor based on quantum weak measurement,” Biosens. Bioelectron. 94, 328–334 (2017).
    [Crossref] [PubMed]
  18. N. Brunner and C. Simon, “Measuring Small Longitudinal Phase Shifts: Weak Measurements or Standard Interferometry?” Phys. Rev. Lett. 105(1), 010405 (2010).
    [Crossref] [PubMed]
  19. C. F. Li, J. S. Tang, Y. L. Li, and G. C. Guo, “Experimentally witnessing the initial correlation between an open quantum system and its environment,” Phys. Rev. A 83(6), 064102 (2011).
    [Crossref]
  20. P. D. Hale and G. W. Day, “Stability Of Birefringent Linear Retarders (Waveplates),” Appl. Opt. 27(24), 5146–5153 (1988).
    [Crossref] [PubMed]
  21. Y. Aharonov and L. Vaidman, “Properties Of a Quantum System during the Time Interval Between 2 Measurements,” Phys. Rev. A 41(1), 11–20 (1990).
    [Crossref] [PubMed]
  22. W. Lu and W. M. Worek, “2-Wavelength Interferometric Technique for Measuring the Refractive Index Of Salt-Water Solutions,” Appl. Opt. 32(21), 3992–4002 (1993).
    [Crossref] [PubMed]
  23. X. D. Qiu, L. G. Xie, X. Liu, L. Luo, Z. X. Li, Z. Y. Zhang, and J. L. Du, “Precision phase estimation based on weak-value amplification,” Appl. Phys. Lett. 110(7), 071105 (2017).
    [Crossref]

2017 (2)

D. Li, Q. He, Y. He, M. Xin, Y. Zhang, and Z. Shen, “Molecular imprinting sensor based on quantum weak measurement,” Biosens. Bioelectron. 94, 328–334 (2017).
[Crossref] [PubMed]

X. D. Qiu, L. G. Xie, X. Liu, L. Luo, Z. X. Li, Z. Y. Zhang, and J. L. Du, “Precision phase estimation based on weak-value amplification,” Appl. Phys. Lett. 110(7), 071105 (2017).
[Crossref]

2016 (2)

2015 (2)

2014 (4)

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86(1), 307–316 (2014).
[Crossref]

T. Denkmayr, H. Geppert, S. Sponar, H. Lemmel, A. Matzkin, J. Tollaksen, and Y. Hasegawa, “Observation of a quantum Cheshire Cat in a matter-wave interferometer experiment,” Nat. Commun. 5(1), 4492 (2014).
[Crossref] [PubMed]

L. J. Salazar-Serrano, D. Janner, N. Brunner, V. Pruneri, and J. P. Torres, “Measurement of sub-pulse-width temporal delays via spectral interference induced by weak value amplification,” Phys. Rev. A 89(1), 012126 (2014).
[Crossref]

B. D. L. Bernardo, S. Azevedo, and A. Rosas, “Ultrasmall polarization rotation measurements via weak value amplification,” Phys. Lett. A 378(30-31), 2029–2033 (2014).
[Crossref]

2013 (3)

2011 (1)

C. F. Li, J. S. Tang, Y. L. Li, and G. C. Guo, “Experimentally witnessing the initial correlation between an open quantum system and its environment,” Phys. Rev. A 83(6), 064102 (2011).
[Crossref]

2010 (1)

N. Brunner and C. Simon, “Measuring Small Longitudinal Phase Shifts: Weak Measurements or Standard Interferometry?” Phys. Rev. Lett. 105(1), 010405 (2010).
[Crossref] [PubMed]

2009 (1)

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, “Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification,” Phys. Rev. Lett. 102(17), 173601 (2009).
[Crossref] [PubMed]

2008 (1)

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref] [PubMed]

1993 (2)

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71(5), 708–711 (1993).
[Crossref] [PubMed]

W. Lu and W. M. Worek, “2-Wavelength Interferometric Technique for Measuring the Refractive Index Of Salt-Water Solutions,” Appl. Opt. 32(21), 3992–4002 (1993).
[Crossref] [PubMed]

1991 (1)

N. W. M. Ritchie, J. G. Story, and R. G. Hulet, “Realization Of a Measurement Of a “Weak Value”,” Phys. Rev. Lett. 66(9), 1107–1110 (1991).
[Crossref] [PubMed]

1990 (1)

Y. Aharonov and L. Vaidman, “Properties Of a Quantum System during the Time Interval Between 2 Measurements,” Phys. Rev. A 41(1), 11–20 (1990).
[Crossref] [PubMed]

1988 (2)

P. D. Hale and G. W. Day, “Stability Of Birefringent Linear Retarders (Waveplates),” Appl. Opt. 27(24), 5146–5153 (1988).
[Crossref] [PubMed]

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] [PubMed]

Aharonov, Y.

Y. Aharonov and L. Vaidman, “Properties Of a Quantum System during the Time Interval Between 2 Measurements,” Phys. Rev. A 41(1), 11–20 (1990).
[Crossref] [PubMed]

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] [PubMed]

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] [PubMed]

Amaya, W.

Azevedo, S.

B. D. L. Bernardo, S. Azevedo, and A. Rosas, “Ultrasmall polarization rotation measurements via weak value amplification,” Phys. Lett. A 378(30-31), 2029–2033 (2014).
[Crossref]

Barrera, D.

Bernardo, B. D. L.

B. D. L. Bernardo, S. Azevedo, and A. Rosas, “Ultrasmall polarization rotation measurements via weak value amplification,” Phys. Lett. A 378(30-31), 2029–2033 (2014).
[Crossref]

Boyd, R. W.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86(1), 307–316 (2014).
[Crossref]

Brun, T. A.

S. Pang and T. A. Brun, “Improving the precision of weak measurements by postselection measurement,” Phys. Rev. Lett. 115(12), 120401 (2015).
[Crossref] [PubMed]

Brunner, N.

L. J. Salazar-Serrano, D. Janner, N. Brunner, V. Pruneri, and J. P. Torres, “Measurement of sub-pulse-width temporal delays via spectral interference induced by weak value amplification,” Phys. Rev. A 89(1), 012126 (2014).
[Crossref]

N. Brunner and C. Simon, “Measuring Small Longitudinal Phase Shifts: Weak Measurements or Standard Interferometry?” Phys. Rev. Lett. 105(1), 010405 (2010).
[Crossref] [PubMed]

Capmany, J.

Chen, Z.

Chiao, R. Y.

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71(5), 708–711 (1993).
[Crossref] [PubMed]

Day, G. W.

Dayan, B.

Denkmayr, T.

T. Denkmayr, H. Geppert, S. Sponar, H. Lemmel, A. Matzkin, J. Tollaksen, and Y. Hasegawa, “Observation of a quantum Cheshire Cat in a matter-wave interferometer experiment,” Nat. Commun. 5(1), 4492 (2014).
[Crossref] [PubMed]

Dixon, P. B.

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, “Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification,” Phys. Rev. Lett. 102(17), 173601 (2009).
[Crossref] [PubMed]

Dressel, J.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86(1), 307–316 (2014).
[Crossref]

Du, J. L.

X. D. Qiu, L. G. Xie, X. Liu, L. Luo, Z. X. Li, Z. Y. Zhang, and J. L. Du, “Precision phase estimation based on weak-value amplification,” Appl. Phys. Lett. 110(7), 071105 (2017).
[Crossref]

Frostig, H.

Geppert, H.

T. Denkmayr, H. Geppert, S. Sponar, H. Lemmel, A. Matzkin, J. Tollaksen, and Y. Hasegawa, “Observation of a quantum Cheshire Cat in a matter-wave interferometer experiment,” Nat. Commun. 5(1), 4492 (2014).
[Crossref] [PubMed]

Guo, G. C.

X. Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C. F. Li, and G. C. Guo, “Phase Estimation With Weak Measurement Using a White Light Source,” Phys. Rev. Lett. 111(3), 033604 (2013).
[Crossref] [PubMed]

C. F. Li, J. S. Tang, Y. L. Li, and G. C. Guo, “Experimentally witnessing the initial correlation between an open quantum system and its environment,” Phys. Rev. A 83(6), 064102 (2011).
[Crossref]

Hale, P. D.

Hasegawa, Y.

T. Denkmayr, H. Geppert, S. Sponar, H. Lemmel, A. Matzkin, J. Tollaksen, and Y. Hasegawa, “Observation of a quantum Cheshire Cat in a matter-wave interferometer experiment,” Nat. Commun. 5(1), 4492 (2014).
[Crossref] [PubMed]

He, Q.

D. Li, Q. He, Y. He, M. Xin, Y. Zhang, and Z. Shen, “Molecular imprinting sensor based on quantum weak measurement,” Biosens. Bioelectron. 94, 328–334 (2017).
[Crossref] [PubMed]

Y. Zhang, D. Li, Y. He, Z. Shen, and Q. He, “Optical weak measurement system with common path implementation for label-free biomolecule sensing,” Opt. Lett. 41(22), 5409–5412 (2016).
[Crossref] [PubMed]

He, Y.

Hosten, O.

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref] [PubMed]

Howell, J. C.

G. I. Viza, J. Martínez-Rincón, G. A. Howland, H. Frostig, I. Shomroni, B. Dayan, and J. C. Howell, “Weak-values technique for velocity measurements,” Opt. Lett. 38(16), 2949–2952 (2013).
[Crossref] [PubMed]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, “Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification,” Phys. Rev. Lett. 102(17), 173601 (2009).
[Crossref] [PubMed]

Howland, G. A.

Hulet, R. G.

N. W. M. Ritchie, J. G. Story, and R. G. Hulet, “Realization Of a Measurement Of a “Weak Value”,” Phys. Rev. Lett. 66(9), 1107–1110 (1991).
[Crossref] [PubMed]

Janner, D.

L. J. Salazar-Serrano, D. Janner, N. Brunner, V. Pruneri, and J. P. Torres, “Measurement of sub-pulse-width temporal delays via spectral interference induced by weak value amplification,” Phys. Rev. A 89(1), 012126 (2014).
[Crossref]

Jayaswal, G.

Jordan, A. N.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86(1), 307–316 (2014).
[Crossref]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, “Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification,” Phys. Rev. Lett. 102(17), 173601 (2009).
[Crossref] [PubMed]

Kedem, Y.

X. Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C. F. Li, and G. C. Guo, “Phase Estimation With Weak Measurement Using a White Light Source,” Phys. Rev. Lett. 111(3), 033604 (2013).
[Crossref] [PubMed]

Kwiat, P.

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref] [PubMed]

Kwiat, P. G.

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71(5), 708–711 (1993).
[Crossref] [PubMed]

Lemmel, H.

T. Denkmayr, H. Geppert, S. Sponar, H. Lemmel, A. Matzkin, J. Tollaksen, and Y. Hasegawa, “Observation of a quantum Cheshire Cat in a matter-wave interferometer experiment,” Nat. Commun. 5(1), 4492 (2014).
[Crossref] [PubMed]

Li, C. F.

X. Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C. F. Li, and G. C. Guo, “Phase Estimation With Weak Measurement Using a White Light Source,” Phys. Rev. Lett. 111(3), 033604 (2013).
[Crossref] [PubMed]

C. F. Li, J. S. Tang, Y. L. Li, and G. C. Guo, “Experimentally witnessing the initial correlation between an open quantum system and its environment,” Phys. Rev. A 83(6), 064102 (2011).
[Crossref]

Li, D.

Li, Y. L.

C. F. Li, J. S. Tang, Y. L. Li, and G. C. Guo, “Experimentally witnessing the initial correlation between an open quantum system and its environment,” Phys. Rev. A 83(6), 064102 (2011).
[Crossref]

Li, Z. X.

X. D. Qiu, L. G. Xie, X. Liu, L. Luo, Z. X. Li, Z. Y. Zhang, and J. L. Du, “Precision phase estimation based on weak-value amplification,” Appl. Phys. Lett. 110(7), 071105 (2017).
[Crossref]

Liu, X.

X. D. Qiu, L. G. Xie, X. Liu, L. Luo, Z. X. Li, Z. Y. Zhang, and J. L. Du, “Precision phase estimation based on weak-value amplification,” Appl. Phys. Lett. 110(7), 071105 (2017).
[Crossref]

Lu, W.

Luo, L.

X. D. Qiu, L. G. Xie, X. Liu, L. Luo, Z. X. Li, Z. Y. Zhang, and J. L. Du, “Precision phase estimation based on weak-value amplification,” Appl. Phys. Lett. 110(7), 071105 (2017).
[Crossref]

Ma, H.

Malik, M.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86(1), 307–316 (2014).
[Crossref]

Martínez-Rincón, J.

Matzkin, A.

T. Denkmayr, H. Geppert, S. Sponar, H. Lemmel, A. Matzkin, J. Tollaksen, and Y. Hasegawa, “Observation of a quantum Cheshire Cat in a matter-wave interferometer experiment,” Nat. Commun. 5(1), 4492 (2014).
[Crossref] [PubMed]

Merano, M.

Miatto, F. M.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86(1), 307–316 (2014).
[Crossref]

Mistura, G.

Pang, S.

S. Pang and T. A. Brun, “Improving the precision of weak measurements by postselection measurement,” Phys. Rev. Lett. 115(12), 120401 (2015).
[Crossref] [PubMed]

Pruneri, V.

L. J. Salazar-Serrano, D. Barrera, W. Amaya, S. Sales, V. Pruneri, J. Capmany, and J. P. Torres, “Enhancement of the sensitivity of a temperature sensor based on fiber Bragg gratings via weak value amplification,” Opt. Lett. 40(17), 3962–3965 (2015).
[Crossref] [PubMed]

L. J. Salazar-Serrano, D. Janner, N. Brunner, V. Pruneri, and J. P. Torres, “Measurement of sub-pulse-width temporal delays via spectral interference induced by weak value amplification,” Phys. Rev. A 89(1), 012126 (2014).
[Crossref]

Qiu, X. D.

X. D. Qiu, L. G. Xie, X. Liu, L. Luo, Z. X. Li, Z. Y. Zhang, and J. L. Du, “Precision phase estimation based on weak-value amplification,” Appl. Phys. Lett. 110(7), 071105 (2017).
[Crossref]

Ritchie, N. W. M.

N. W. M. Ritchie, J. G. Story, and R. G. Hulet, “Realization Of a Measurement Of a “Weak Value”,” Phys. Rev. Lett. 66(9), 1107–1110 (1991).
[Crossref] [PubMed]

Rosas, A.

B. D. L. Bernardo, S. Azevedo, and A. Rosas, “Ultrasmall polarization rotation measurements via weak value amplification,” Phys. Lett. A 378(30-31), 2029–2033 (2014).
[Crossref]

Salazar-Serrano, L. J.

L. J. Salazar-Serrano, D. Barrera, W. Amaya, S. Sales, V. Pruneri, J. Capmany, and J. P. Torres, “Enhancement of the sensitivity of a temperature sensor based on fiber Bragg gratings via weak value amplification,” Opt. Lett. 40(17), 3962–3965 (2015).
[Crossref] [PubMed]

L. J. Salazar-Serrano, D. Janner, N. Brunner, V. Pruneri, and J. P. Torres, “Measurement of sub-pulse-width temporal delays via spectral interference induced by weak value amplification,” Phys. Rev. A 89(1), 012126 (2014).
[Crossref]

Sales, S.

Shen, Z.

Shomroni, I.

Simon, C.

N. Brunner and C. Simon, “Measuring Small Longitudinal Phase Shifts: Weak Measurements or Standard Interferometry?” Phys. Rev. Lett. 105(1), 010405 (2010).
[Crossref] [PubMed]

Sponar, S.

T. Denkmayr, H. Geppert, S. Sponar, H. Lemmel, A. Matzkin, J. Tollaksen, and Y. Hasegawa, “Observation of a quantum Cheshire Cat in a matter-wave interferometer experiment,” Nat. Commun. 5(1), 4492 (2014).
[Crossref] [PubMed]

Starling, D. J.

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, “Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification,” Phys. Rev. Lett. 102(17), 173601 (2009).
[Crossref] [PubMed]

Steinberg, A. M.

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71(5), 708–711 (1993).
[Crossref] [PubMed]

Story, J. G.

N. W. M. Ritchie, J. G. Story, and R. G. Hulet, “Realization Of a Measurement Of a “Weak Value”,” Phys. Rev. Lett. 66(9), 1107–1110 (1991).
[Crossref] [PubMed]

Sun, K.

X. Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C. F. Li, and G. C. Guo, “Phase Estimation With Weak Measurement Using a White Light Source,” Phys. Rev. Lett. 111(3), 033604 (2013).
[Crossref] [PubMed]

Tang, J. S.

C. F. Li, J. S. Tang, Y. L. Li, and G. C. Guo, “Experimentally witnessing the initial correlation between an open quantum system and its environment,” Phys. Rev. A 83(6), 064102 (2011).
[Crossref]

Tollaksen, J.

T. Denkmayr, H. Geppert, S. Sponar, H. Lemmel, A. Matzkin, J. Tollaksen, and Y. Hasegawa, “Observation of a quantum Cheshire Cat in a matter-wave interferometer experiment,” Nat. Commun. 5(1), 4492 (2014).
[Crossref] [PubMed]

Torres, J. P.

L. J. Salazar-Serrano, D. Barrera, W. Amaya, S. Sales, V. Pruneri, J. Capmany, and J. P. Torres, “Enhancement of the sensitivity of a temperature sensor based on fiber Bragg gratings via weak value amplification,” Opt. Lett. 40(17), 3962–3965 (2015).
[Crossref] [PubMed]

L. J. Salazar-Serrano, D. Janner, N. Brunner, V. Pruneri, and J. P. Torres, “Measurement of sub-pulse-width temporal delays via spectral interference induced by weak value amplification,” Phys. Rev. A 89(1), 012126 (2014).
[Crossref]

Vaidman, L.

X. Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C. F. Li, and G. C. Guo, “Phase Estimation With Weak Measurement Using a White Light Source,” Phys. Rev. Lett. 111(3), 033604 (2013).
[Crossref] [PubMed]

Y. Aharonov and L. Vaidman, “Properties Of a Quantum System during the Time Interval Between 2 Measurements,” Phys. Rev. A 41(1), 11–20 (1990).
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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] [PubMed]

Viza, G. I.

Worek, W. M.

Xie, L. G.

X. D. Qiu, L. G. Xie, X. Liu, L. Luo, Z. X. Li, Z. Y. Zhang, and J. L. Du, “Precision phase estimation based on weak-value amplification,” Appl. Phys. Lett. 110(7), 071105 (2017).
[Crossref]

Xin, M.

D. Li, Q. He, Y. He, M. Xin, Y. Zhang, and Z. Shen, “Molecular imprinting sensor based on quantum weak measurement,” Biosens. Bioelectron. 94, 328–334 (2017).
[Crossref] [PubMed]

Xu, X. Y.

X. Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C. F. Li, and G. C. Guo, “Phase Estimation With Weak Measurement Using a White Light Source,” Phys. Rev. Lett. 111(3), 033604 (2013).
[Crossref] [PubMed]

Zhang, Y.

Zhang, Z. Y.

X. D. Qiu, L. G. Xie, X. Liu, L. Luo, Z. X. Li, Z. Y. Zhang, and J. L. Du, “Precision phase estimation based on weak-value amplification,” Appl. Phys. Lett. 110(7), 071105 (2017).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

X. D. Qiu, L. G. Xie, X. Liu, L. Luo, Z. X. Li, Z. Y. Zhang, and J. L. Du, “Precision phase estimation based on weak-value amplification,” Appl. Phys. Lett. 110(7), 071105 (2017).
[Crossref]

Biosens. Bioelectron. (1)

D. Li, Q. He, Y. He, M. Xin, Y. Zhang, and Z. Shen, “Molecular imprinting sensor based on quantum weak measurement,” Biosens. Bioelectron. 94, 328–334 (2017).
[Crossref] [PubMed]

Nat. Commun. (1)

T. Denkmayr, H. Geppert, S. Sponar, H. Lemmel, A. Matzkin, J. Tollaksen, and Y. Hasegawa, “Observation of a quantum Cheshire Cat in a matter-wave interferometer experiment,” Nat. Commun. 5(1), 4492 (2014).
[Crossref] [PubMed]

Opt. Lett. (4)

Phys. Lett. A (1)

B. D. L. Bernardo, S. Azevedo, and A. Rosas, “Ultrasmall polarization rotation measurements via weak value amplification,” Phys. Lett. A 378(30-31), 2029–2033 (2014).
[Crossref]

Phys. Rev. A (3)

C. F. Li, J. S. Tang, Y. L. Li, and G. C. Guo, “Experimentally witnessing the initial correlation between an open quantum system and its environment,” Phys. Rev. A 83(6), 064102 (2011).
[Crossref]

Y. Aharonov and L. Vaidman, “Properties Of a Quantum System during the Time Interval Between 2 Measurements,” Phys. Rev. A 41(1), 11–20 (1990).
[Crossref] [PubMed]

L. J. Salazar-Serrano, D. Janner, N. Brunner, V. Pruneri, and J. P. Torres, “Measurement of sub-pulse-width temporal delays via spectral interference induced by weak value amplification,” Phys. Rev. A 89(1), 012126 (2014).
[Crossref]

Phys. Rev. Lett. (7)

X. Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C. F. Li, and G. C. Guo, “Phase Estimation With Weak Measurement Using a White Light Source,” Phys. Rev. Lett. 111(3), 033604 (2013).
[Crossref] [PubMed]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, “Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification,” Phys. Rev. Lett. 102(17), 173601 (2009).
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S. Pang and T. A. Brun, “Improving the precision of weak measurements by postselection measurement,” Phys. Rev. Lett. 115(12), 120401 (2015).
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A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71(5), 708–711 (1993).
[Crossref] [PubMed]

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] [PubMed]

N. W. M. Ritchie, J. G. Story, and R. G. Hulet, “Realization Of a Measurement Of a “Weak Value”,” Phys. Rev. Lett. 66(9), 1107–1110 (1991).
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N. Brunner and C. Simon, “Measuring Small Longitudinal Phase Shifts: Weak Measurements or Standard Interferometry?” Phys. Rev. Lett. 105(1), 010405 (2010).
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Rev. Mod. Phys. (1)

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86(1), 307–316 (2014).
[Crossref]

Science (1)

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 The schematic diagram of the weak measurement system.
Fig. 2
Fig. 2 Figure (a) shows the simulation curves and experimental results of the weak measurement operating area obtained by adjusting the SBC under the condition that the front and rear selection states are parallel to each other, and denoted as A and C, respectively. The theoretical curves and experimental data of the pink and black dashed boxes in the upper part of figure (a) are shown in the lower left and right figures respectively. Figure (b) shows the simulation curve and experimental results of the weak measurement working area obtained by adjusting the SBC under the condition that the front and rear selection states are perpendicular to each other, and denoted as B and D, respectively. The theoretical curves and experimental data of the pink and black dashed boxes in the upper part of figure (b) are shown in the lower left and right figures respectively.
Fig. 3
Fig. 3 The bimodal spectra of different concentrations of sodium chloride solution at four operating areas A, B, C, and D.
Fig. 4
Fig. 4 Intensity integration contrast of 0.9% sodium chloride solution at four-working areas A, B, C, D (The error bar indicates the standard deviation for three measurements).
Fig. 5
Fig. 5 Figures (a), (b), (c), and (d) show the results of the sodium chloride solution at four operating areas A, B, C, and D, respectively, and a linear plot. In each figure, the left picture shows the experimental results of the central wavelength shift of NaCl, 0.45%, 0.9%, 1.35%, and 1.80% of five concentration gradient sodium chloride solutions; the right picture shows the linearly-fitted spectral shift of each operating area (The error bar (red) indicates the standard deviation for three measurements).

Tables (1)

Tables Icon

Table 1 Advantages and disadvantages of each working areas

Equations (11)

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H=g(t)PA
Δ=2 tan 1 n 2 sin 2 θ nsinθtanθ
δ(λ)=± π( n e n o )h χ 2 λ
A ω ψ post | A ^ | ψ pre ψ post | ψ pre = sinαsinβcosαcosβ e i( δ 0 +ε(λ)Δ) sinαsinβ+cosαcosβ e i( δ 0 +ε(λ)Δ) = 1+γ e i( δ 0 +ε(λ)Δ) 1γ e i( δ 0 +ε(λ)Δ)
Im( A ω )= 2γsin( δ 0 +ε(λ)Δ) 1+ γ 2 2γcos( δ 0 +ε(λ)Δ)
Im( A ω )= 2γsin( δ 0 Δ) 1+ γ 2 2γcos( δ 0 Δ)
δλ= 2πk (Δλ) 2 λ 0 Im( A ω )= 4πk (Δλ) 2 γsin( δ 0 Δ) λ 0 (1+ γ 2 2γcos( δ 0 Δ))
Δλmax{ λ 0 | sinαsinβ | 1n n δ 0 +ε(λ)Δ | 1+ γ 2 2γsin( δ 0 +ε(λ)Δ) | | 1+ γ 2 + (1) n1 2γcos( δ 0 +ε(λ)Δ) | 1 n }
| ψ post | e iHdt | ψ pre | | ψ post | ψ pre | 2 e i2kP ψ post | A ^ | ψ pre ψ post | ψ pre e P 2 4Δ P 2
ϕ 0 (λ)= | ψ post | ψ pre | 2 e (λ λ 0 δλ) 2 4Δ λ 2
ϕ 0 2 (λ)= | sinαsinβcosαcosβ e i( δ 0 +ε(λ)Δ) | 2 e (λ λ 0 δλ) 2 2Δ λ 2

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