Abstract

We experimentally demonstrate a fiber-based phase tracking system through an adaptive homodyne detection technique. In the experiment, we use a random phase signal as an example. The system works well when the random phase varies between −2.4 and + 2.4 radians. Such tracking range is much larger than previous work due to the improved performance of phase-locked loop. The minimum mean square error reaches theoretical value at a photon flux of ~106, which proves a quantum-limited fiber phase tracking. Such system has potential applications in high-precision real-time fiber sensing of temperature, strain, and so on.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Sensing and tracking enhanced by quantum squeezing

Chuan Xu, Lidan Zhang, Songtao Huang, Taxue Ma, Fang Liu, Hidehiro Yonezawa, Yong Zhang, and Min Xiao
Photon. Res. 7(6) A14-A26 (2019)

Phase sensing beyond the standard quantum limit with a variation on the SU(1,1) interferometer

Brian E. Anderson, Prasoon Gupta, Bonnie L. Schmittberger, Travis Horrom, Carla Hermann-Avigliano, Kevin M. Jones, and Paul D. Lett
Optica 4(7) 752-756 (2017)

Homodyne coherent optical receiver for intersatellite communication

Chaolei Yue, Jiawei Li, Jianfeng Sun, Ren Zhu, Xia Hou, Xiaoxi Zhang, Lei Liu, and Weibiao Chen
Appl. Opt. 57(27) 7915-7923 (2018)

References

  • View by:
  • |
  • |
  • |

  1. V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5(4), 222–229 (2011).
    [Crossref]
  2. N. P. Mauranyapin, L. S. Madsen, M. A. Taylor, M. Waleed, and W. P. Bowen, “Evanescent single-molecule biosensing with quantum-limited precision,” Nat. Photonics 11(8), 477–481 (2017).
    [Crossref]
  3. M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
    [Crossref]
  4. C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D Part. Fields 23(8), 1693–1708 (1981).
    [Crossref]
  5. M. Xiao, L. A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59(3), 278–281 (1987).
    [Crossref] [PubMed]
  6. C. Xia, D. Wang, Y. Wu, J. Guo, F. Liu, Y. Zhang, and M. Xiao, “Continuous-variable entanglement measurement using an unbalanced Mach-Zehnder interferometer,” Opt. Lett. 40(6), 1121–1124 (2015).
    [Crossref] [PubMed]
  7. F. Liu, Y. Zhou, J. Yu, J. Guo, Y. Wu, S. Xiao, D. Wei, Y. Zhang, X. Jia, and M. Xiao, “Squeezing-enhanced fiber Mach-Zehnder interferometer for low-frequency phase measurement,” Appl. Phys. Lett. 110(2), 021106 (2017).
    [Crossref]
  8. K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, “A quantum-enhanced prototype gravitational-wave detector,” Nat. Phys. 4(6), 472–476 (2008).
    [Crossref]
  9. K. Jacobs, Quantum measurement theory and its applications (Cambridge University, 2014).
  10. H.-A. Bachor and T. C. Ralph, A guide to experiments in quantum optics (Wiley, 2004).
  11. D. W. Berry and H. M. Wiseman, “Adaptive quantum measurements of a continuously varying phase,” Phys. Rev. A 65(4), 043803 (2002).
    [Crossref]
  12. M. Tsang, “Time-symmetric quantum theory of smoothing,” Phys. Rev. Lett. 102(25), 250403 (2009).
    [Crossref] [PubMed]
  13. T. A. Wheatley, D. W. Berry, H. Yonezawa, D. Nakane, H. Arao, D. T. Pope, T. C. Ralph, H. M. Wiseman, A. Furusawa, and E. H. Huntington, “Adaptive optical phase estimation using time-symmetric quantum smoothing,” Phys. Rev. Lett. 104(9), 093601 (2010).
    [Crossref] [PubMed]
  14. M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89(13), 133602 (2002).
    [Crossref] [PubMed]
  15. D. Pope, H. Wiseman, and N. Langford, “Adaptive phase estimation is more accurate than nonadaptive phase estimation for continuous beams of light,” Phys. Rev. A 70(4), 043812 (2004).
    [Crossref]
  16. J. Zhang, Y. Liu, R.-B. Wu, K. Jacobs, and F. Nori, “Quantum feedback: theory, experiments, and applications,” Phys. Rep. 679, 1–60 (2017).
    [Crossref]
  17. H. Yonezawa, D. Nakane, T. A. Wheatley, K. Iwasawa, S. Takeda, H. Arao, K. Ohki, K. Tsumura, D. W. Berry, T. C. Ralph, H. M. Wiseman, E. H. Huntington, and A. Furusawa, “Quantum-enhanced optical-phase tracking,” Science 337(6101), 1514–1517 (2012).
    [Crossref] [PubMed]
  18. K. Iwasawa, K. Makino, H. Yonezawa, M. Tsang, A. Davidovic, E. Huntington, and A. Furusawa, “Quantum-limited mirror-motion estimation,” Phys. Rev. Lett. 111(16), 163602 (2013).
    [Crossref] [PubMed]
  19. R. Jiménez-Martínez, J. Kołodyński, C. Troullinou, V. G. Lucivero, J. Kong, and M. W. Mitchell, “Signal tracking beyond the time resolution of an atomic sensor by Kalman filtering,” Phys. Rev. Lett. 120(4), 040503 (2018).
    [Crossref] [PubMed]
  20. J. L. Kou, M. Ding, J. Feng, Y. Q. Lu, F. Xu, and G. Brambilla, “Microfiber-based Bragg gratings for sensing applications: a review,” Sensors (Basel) 12(7), 8861–8876 (2012).
    [Crossref] [PubMed]
  21. J. Lou, Y. Wang, and L. Tong, “Microfiber optical sensors: a review,” Sensors (Basel) 14(4), 5823–5844 (2014).
    [Crossref] [PubMed]
  22. Y. Xu, P. Lu, L. Chen, and X. Bao, “Recent developments in micro-structured fiber optic sensors,” Fibers (Basel) 5(1), 3 (2017).
    [Crossref]
  23. B. Lee, “Review of the present status of optical fiber sensors,” Opt. Fiber Technol. 9(2), 57–79 (2003).
    [Crossref]
  24. L. Mescia and F. Prudenzano, “Advances on Optical Fiber Sensors,” Fibers (Basel) 2(1), 1–23 (2013).
    [Crossref]
  25. G. A. Cranch, P. J. Nash, and C. K. Kirkendall, “Large-scale remotely interrogated arrays of fiber-optic interferometric sensors for underwater acoustic applications,” IEEE Sens. J. 3(1), 19–30 (2003).
    [Crossref]
  26. J. E. Parsons, C. A. Cain, and J. B. Fowlkes, “Cost-effective assembly of a basic fiber-optic hydrophone for measurement of high-amplitude therapeutic ultrasound fields,” J. Acoust. Soc. Am. 119(3), 1432–1440 (2006).
    [Crossref] [PubMed]
  27. H. M. Wiseman and G. J. Milburn, Quantum measurement and control (Cambridge University, 2009).
  28. S. Stepanov, M. P. Sánchez, and E. H. Hernández, “Noise in adaptive interferometric fiber sensor based on population dynamic grating in erbium-doped fiber,” Appl. Opt. 55(26), 7324–7329 (2016).
    [Crossref] [PubMed]
  29. M. Tsang, J. H. Shapiro, and S. Lloyd, “Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous-time limit and state-variable approach to phase-locked loop design,” Phys. Rev. A 79(5), 053843 (2009).
    [Crossref]
  30. H. Wiseman and R. Killip, “Adaptive single-shot phase measurements: The full quantum theory,” Phys. Rev. A 57(3), 2169–2185 (1998).
    [Crossref]
  31. C. Gardiner, P. Zoller, and P. Zoller, Quantum noise: a handbook of Markovian and non-Markovian quantum stochastic methods with applications to quantum optics (Springer Science & Business Media, 2004).
  32. A. B. Baggeroer, State variables and communication theory (MIT, 1970).

2018 (1)

R. Jiménez-Martínez, J. Kołodyński, C. Troullinou, V. G. Lucivero, J. Kong, and M. W. Mitchell, “Signal tracking beyond the time resolution of an atomic sensor by Kalman filtering,” Phys. Rev. Lett. 120(4), 040503 (2018).
[Crossref] [PubMed]

2017 (4)

Y. Xu, P. Lu, L. Chen, and X. Bao, “Recent developments in micro-structured fiber optic sensors,” Fibers (Basel) 5(1), 3 (2017).
[Crossref]

F. Liu, Y. Zhou, J. Yu, J. Guo, Y. Wu, S. Xiao, D. Wei, Y. Zhang, X. Jia, and M. Xiao, “Squeezing-enhanced fiber Mach-Zehnder interferometer for low-frequency phase measurement,” Appl. Phys. Lett. 110(2), 021106 (2017).
[Crossref]

J. Zhang, Y. Liu, R.-B. Wu, K. Jacobs, and F. Nori, “Quantum feedback: theory, experiments, and applications,” Phys. Rep. 679, 1–60 (2017).
[Crossref]

N. P. Mauranyapin, L. S. Madsen, M. A. Taylor, M. Waleed, and W. P. Bowen, “Evanescent single-molecule biosensing with quantum-limited precision,” Nat. Photonics 11(8), 477–481 (2017).
[Crossref]

2016 (1)

2015 (1)

2014 (1)

J. Lou, Y. Wang, and L. Tong, “Microfiber optical sensors: a review,” Sensors (Basel) 14(4), 5823–5844 (2014).
[Crossref] [PubMed]

2013 (3)

K. Iwasawa, K. Makino, H. Yonezawa, M. Tsang, A. Davidovic, E. Huntington, and A. Furusawa, “Quantum-limited mirror-motion estimation,” Phys. Rev. Lett. 111(16), 163602 (2013).
[Crossref] [PubMed]

L. Mescia and F. Prudenzano, “Advances on Optical Fiber Sensors,” Fibers (Basel) 2(1), 1–23 (2013).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

2012 (2)

J. L. Kou, M. Ding, J. Feng, Y. Q. Lu, F. Xu, and G. Brambilla, “Microfiber-based Bragg gratings for sensing applications: a review,” Sensors (Basel) 12(7), 8861–8876 (2012).
[Crossref] [PubMed]

H. Yonezawa, D. Nakane, T. A. Wheatley, K. Iwasawa, S. Takeda, H. Arao, K. Ohki, K. Tsumura, D. W. Berry, T. C. Ralph, H. M. Wiseman, E. H. Huntington, and A. Furusawa, “Quantum-enhanced optical-phase tracking,” Science 337(6101), 1514–1517 (2012).
[Crossref] [PubMed]

2011 (1)

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5(4), 222–229 (2011).
[Crossref]

2010 (1)

T. A. Wheatley, D. W. Berry, H. Yonezawa, D. Nakane, H. Arao, D. T. Pope, T. C. Ralph, H. M. Wiseman, A. Furusawa, and E. H. Huntington, “Adaptive optical phase estimation using time-symmetric quantum smoothing,” Phys. Rev. Lett. 104(9), 093601 (2010).
[Crossref] [PubMed]

2009 (2)

M. Tsang, “Time-symmetric quantum theory of smoothing,” Phys. Rev. Lett. 102(25), 250403 (2009).
[Crossref] [PubMed]

M. Tsang, J. H. Shapiro, and S. Lloyd, “Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous-time limit and state-variable approach to phase-locked loop design,” Phys. Rev. A 79(5), 053843 (2009).
[Crossref]

2008 (1)

K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, “A quantum-enhanced prototype gravitational-wave detector,” Nat. Phys. 4(6), 472–476 (2008).
[Crossref]

2006 (1)

J. E. Parsons, C. A. Cain, and J. B. Fowlkes, “Cost-effective assembly of a basic fiber-optic hydrophone for measurement of high-amplitude therapeutic ultrasound fields,” J. Acoust. Soc. Am. 119(3), 1432–1440 (2006).
[Crossref] [PubMed]

2004 (1)

D. Pope, H. Wiseman, and N. Langford, “Adaptive phase estimation is more accurate than nonadaptive phase estimation for continuous beams of light,” Phys. Rev. A 70(4), 043812 (2004).
[Crossref]

2003 (2)

G. A. Cranch, P. J. Nash, and C. K. Kirkendall, “Large-scale remotely interrogated arrays of fiber-optic interferometric sensors for underwater acoustic applications,” IEEE Sens. J. 3(1), 19–30 (2003).
[Crossref]

B. Lee, “Review of the present status of optical fiber sensors,” Opt. Fiber Technol. 9(2), 57–79 (2003).
[Crossref]

2002 (2)

D. W. Berry and H. M. Wiseman, “Adaptive quantum measurements of a continuously varying phase,” Phys. Rev. A 65(4), 043803 (2002).
[Crossref]

M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89(13), 133602 (2002).
[Crossref] [PubMed]

1998 (1)

H. Wiseman and R. Killip, “Adaptive single-shot phase measurements: The full quantum theory,” Phys. Rev. A 57(3), 2169–2185 (1998).
[Crossref]

1987 (1)

M. Xiao, L. A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59(3), 278–281 (1987).
[Crossref] [PubMed]

1981 (1)

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D Part. Fields 23(8), 1693–1708 (1981).
[Crossref]

Adhikari, R.

K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, “A quantum-enhanced prototype gravitational-wave detector,” Nat. Phys. 4(6), 472–476 (2008).
[Crossref]

Arao, H.

H. Yonezawa, D. Nakane, T. A. Wheatley, K. Iwasawa, S. Takeda, H. Arao, K. Ohki, K. Tsumura, D. W. Berry, T. C. Ralph, H. M. Wiseman, E. H. Huntington, and A. Furusawa, “Quantum-enhanced optical-phase tracking,” Science 337(6101), 1514–1517 (2012).
[Crossref] [PubMed]

T. A. Wheatley, D. W. Berry, H. Yonezawa, D. Nakane, H. Arao, D. T. Pope, T. C. Ralph, H. M. Wiseman, A. Furusawa, and E. H. Huntington, “Adaptive optical phase estimation using time-symmetric quantum smoothing,” Phys. Rev. Lett. 104(9), 093601 (2010).
[Crossref] [PubMed]

Armen, M. A.

M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89(13), 133602 (2002).
[Crossref] [PubMed]

Au, J. K.

M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89(13), 133602 (2002).
[Crossref] [PubMed]

Bachor, H.-A.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

Bao, X.

Y. Xu, P. Lu, L. Chen, and X. Bao, “Recent developments in micro-structured fiber optic sensors,” Fibers (Basel) 5(1), 3 (2017).
[Crossref]

Berry, D. W.

H. Yonezawa, D. Nakane, T. A. Wheatley, K. Iwasawa, S. Takeda, H. Arao, K. Ohki, K. Tsumura, D. W. Berry, T. C. Ralph, H. M. Wiseman, E. H. Huntington, and A. Furusawa, “Quantum-enhanced optical-phase tracking,” Science 337(6101), 1514–1517 (2012).
[Crossref] [PubMed]

T. A. Wheatley, D. W. Berry, H. Yonezawa, D. Nakane, H. Arao, D. T. Pope, T. C. Ralph, H. M. Wiseman, A. Furusawa, and E. H. Huntington, “Adaptive optical phase estimation using time-symmetric quantum smoothing,” Phys. Rev. Lett. 104(9), 093601 (2010).
[Crossref] [PubMed]

D. W. Berry and H. M. Wiseman, “Adaptive quantum measurements of a continuously varying phase,” Phys. Rev. A 65(4), 043803 (2002).
[Crossref]

Bowen, W. P.

N. P. Mauranyapin, L. S. Madsen, M. A. Taylor, M. Waleed, and W. P. Bowen, “Evanescent single-molecule biosensing with quantum-limited precision,” Nat. Photonics 11(8), 477–481 (2017).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

Brambilla, G.

J. L. Kou, M. Ding, J. Feng, Y. Q. Lu, F. Xu, and G. Brambilla, “Microfiber-based Bragg gratings for sensing applications: a review,” Sensors (Basel) 12(7), 8861–8876 (2012).
[Crossref] [PubMed]

Cain, C. A.

J. E. Parsons, C. A. Cain, and J. B. Fowlkes, “Cost-effective assembly of a basic fiber-optic hydrophone for measurement of high-amplitude therapeutic ultrasound fields,” J. Acoust. Soc. Am. 119(3), 1432–1440 (2006).
[Crossref] [PubMed]

Caves, C. M.

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D Part. Fields 23(8), 1693–1708 (1981).
[Crossref]

Chen, L.

Y. Xu, P. Lu, L. Chen, and X. Bao, “Recent developments in micro-structured fiber optic sensors,” Fibers (Basel) 5(1), 3 (2017).
[Crossref]

Cranch, G. A.

G. A. Cranch, P. J. Nash, and C. K. Kirkendall, “Large-scale remotely interrogated arrays of fiber-optic interferometric sensors for underwater acoustic applications,” IEEE Sens. J. 3(1), 19–30 (2003).
[Crossref]

Daria, V.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

Davidovic, A.

K. Iwasawa, K. Makino, H. Yonezawa, M. Tsang, A. Davidovic, E. Huntington, and A. Furusawa, “Quantum-limited mirror-motion estimation,” Phys. Rev. Lett. 111(16), 163602 (2013).
[Crossref] [PubMed]

Ding, M.

J. L. Kou, M. Ding, J. Feng, Y. Q. Lu, F. Xu, and G. Brambilla, “Microfiber-based Bragg gratings for sensing applications: a review,” Sensors (Basel) 12(7), 8861–8876 (2012).
[Crossref] [PubMed]

Doherty, A. C.

M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89(13), 133602 (2002).
[Crossref] [PubMed]

Feng, J.

J. L. Kou, M. Ding, J. Feng, Y. Q. Lu, F. Xu, and G. Brambilla, “Microfiber-based Bragg gratings for sensing applications: a review,” Sensors (Basel) 12(7), 8861–8876 (2012).
[Crossref] [PubMed]

Fowlkes, J. B.

J. E. Parsons, C. A. Cain, and J. B. Fowlkes, “Cost-effective assembly of a basic fiber-optic hydrophone for measurement of high-amplitude therapeutic ultrasound fields,” J. Acoust. Soc. Am. 119(3), 1432–1440 (2006).
[Crossref] [PubMed]

Furusawa, A.

K. Iwasawa, K. Makino, H. Yonezawa, M. Tsang, A. Davidovic, E. Huntington, and A. Furusawa, “Quantum-limited mirror-motion estimation,” Phys. Rev. Lett. 111(16), 163602 (2013).
[Crossref] [PubMed]

H. Yonezawa, D. Nakane, T. A. Wheatley, K. Iwasawa, S. Takeda, H. Arao, K. Ohki, K. Tsumura, D. W. Berry, T. C. Ralph, H. M. Wiseman, E. H. Huntington, and A. Furusawa, “Quantum-enhanced optical-phase tracking,” Science 337(6101), 1514–1517 (2012).
[Crossref] [PubMed]

T. A. Wheatley, D. W. Berry, H. Yonezawa, D. Nakane, H. Arao, D. T. Pope, T. C. Ralph, H. M. Wiseman, A. Furusawa, and E. H. Huntington, “Adaptive optical phase estimation using time-symmetric quantum smoothing,” Phys. Rev. Lett. 104(9), 093601 (2010).
[Crossref] [PubMed]

Giovannetti, V.

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5(4), 222–229 (2011).
[Crossref]

Goda, K.

K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, “A quantum-enhanced prototype gravitational-wave detector,” Nat. Phys. 4(6), 472–476 (2008).
[Crossref]

Guo, J.

F. Liu, Y. Zhou, J. Yu, J. Guo, Y. Wu, S. Xiao, D. Wei, Y. Zhang, X. Jia, and M. Xiao, “Squeezing-enhanced fiber Mach-Zehnder interferometer for low-frequency phase measurement,” Appl. Phys. Lett. 110(2), 021106 (2017).
[Crossref]

C. Xia, D. Wang, Y. Wu, J. Guo, F. Liu, Y. Zhang, and M. Xiao, “Continuous-variable entanglement measurement using an unbalanced Mach-Zehnder interferometer,” Opt. Lett. 40(6), 1121–1124 (2015).
[Crossref] [PubMed]

Hage, B.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

Hernández, E. H.

Huntington, E.

K. Iwasawa, K. Makino, H. Yonezawa, M. Tsang, A. Davidovic, E. Huntington, and A. Furusawa, “Quantum-limited mirror-motion estimation,” Phys. Rev. Lett. 111(16), 163602 (2013).
[Crossref] [PubMed]

Huntington, E. H.

H. Yonezawa, D. Nakane, T. A. Wheatley, K. Iwasawa, S. Takeda, H. Arao, K. Ohki, K. Tsumura, D. W. Berry, T. C. Ralph, H. M. Wiseman, E. H. Huntington, and A. Furusawa, “Quantum-enhanced optical-phase tracking,” Science 337(6101), 1514–1517 (2012).
[Crossref] [PubMed]

T. A. Wheatley, D. W. Berry, H. Yonezawa, D. Nakane, H. Arao, D. T. Pope, T. C. Ralph, H. M. Wiseman, A. Furusawa, and E. H. Huntington, “Adaptive optical phase estimation using time-symmetric quantum smoothing,” Phys. Rev. Lett. 104(9), 093601 (2010).
[Crossref] [PubMed]

Iwasawa, K.

K. Iwasawa, K. Makino, H. Yonezawa, M. Tsang, A. Davidovic, E. Huntington, and A. Furusawa, “Quantum-limited mirror-motion estimation,” Phys. Rev. Lett. 111(16), 163602 (2013).
[Crossref] [PubMed]

H. Yonezawa, D. Nakane, T. A. Wheatley, K. Iwasawa, S. Takeda, H. Arao, K. Ohki, K. Tsumura, D. W. Berry, T. C. Ralph, H. M. Wiseman, E. H. Huntington, and A. Furusawa, “Quantum-enhanced optical-phase tracking,” Science 337(6101), 1514–1517 (2012).
[Crossref] [PubMed]

Jacobs, K.

J. Zhang, Y. Liu, R.-B. Wu, K. Jacobs, and F. Nori, “Quantum feedback: theory, experiments, and applications,” Phys. Rep. 679, 1–60 (2017).
[Crossref]

Janousek, J.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

Jia, X.

F. Liu, Y. Zhou, J. Yu, J. Guo, Y. Wu, S. Xiao, D. Wei, Y. Zhang, X. Jia, and M. Xiao, “Squeezing-enhanced fiber Mach-Zehnder interferometer for low-frequency phase measurement,” Appl. Phys. Lett. 110(2), 021106 (2017).
[Crossref]

Jiménez-Martínez, R.

R. Jiménez-Martínez, J. Kołodyński, C. Troullinou, V. G. Lucivero, J. Kong, and M. W. Mitchell, “Signal tracking beyond the time resolution of an atomic sensor by Kalman filtering,” Phys. Rev. Lett. 120(4), 040503 (2018).
[Crossref] [PubMed]

Killip, R.

H. Wiseman and R. Killip, “Adaptive single-shot phase measurements: The full quantum theory,” Phys. Rev. A 57(3), 2169–2185 (1998).
[Crossref]

Kimble, H. J.

M. Xiao, L. A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59(3), 278–281 (1987).
[Crossref] [PubMed]

Kirkendall, C. K.

G. A. Cranch, P. J. Nash, and C. K. Kirkendall, “Large-scale remotely interrogated arrays of fiber-optic interferometric sensors for underwater acoustic applications,” IEEE Sens. J. 3(1), 19–30 (2003).
[Crossref]

Knittel, J.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

Kolodynski, J.

R. Jiménez-Martínez, J. Kołodyński, C. Troullinou, V. G. Lucivero, J. Kong, and M. W. Mitchell, “Signal tracking beyond the time resolution of an atomic sensor by Kalman filtering,” Phys. Rev. Lett. 120(4), 040503 (2018).
[Crossref] [PubMed]

Kong, J.

R. Jiménez-Martínez, J. Kołodyński, C. Troullinou, V. G. Lucivero, J. Kong, and M. W. Mitchell, “Signal tracking beyond the time resolution of an atomic sensor by Kalman filtering,” Phys. Rev. Lett. 120(4), 040503 (2018).
[Crossref] [PubMed]

Kou, J. L.

J. L. Kou, M. Ding, J. Feng, Y. Q. Lu, F. Xu, and G. Brambilla, “Microfiber-based Bragg gratings for sensing applications: a review,” Sensors (Basel) 12(7), 8861–8876 (2012).
[Crossref] [PubMed]

Langford, N.

D. Pope, H. Wiseman, and N. Langford, “Adaptive phase estimation is more accurate than nonadaptive phase estimation for continuous beams of light,” Phys. Rev. A 70(4), 043812 (2004).
[Crossref]

Lee, B.

B. Lee, “Review of the present status of optical fiber sensors,” Opt. Fiber Technol. 9(2), 57–79 (2003).
[Crossref]

Liu, F.

F. Liu, Y. Zhou, J. Yu, J. Guo, Y. Wu, S. Xiao, D. Wei, Y. Zhang, X. Jia, and M. Xiao, “Squeezing-enhanced fiber Mach-Zehnder interferometer for low-frequency phase measurement,” Appl. Phys. Lett. 110(2), 021106 (2017).
[Crossref]

C. Xia, D. Wang, Y. Wu, J. Guo, F. Liu, Y. Zhang, and M. Xiao, “Continuous-variable entanglement measurement using an unbalanced Mach-Zehnder interferometer,” Opt. Lett. 40(6), 1121–1124 (2015).
[Crossref] [PubMed]

Liu, Y.

J. Zhang, Y. Liu, R.-B. Wu, K. Jacobs, and F. Nori, “Quantum feedback: theory, experiments, and applications,” Phys. Rep. 679, 1–60 (2017).
[Crossref]

Lloyd, S.

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5(4), 222–229 (2011).
[Crossref]

M. Tsang, J. H. Shapiro, and S. Lloyd, “Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous-time limit and state-variable approach to phase-locked loop design,” Phys. Rev. A 79(5), 053843 (2009).
[Crossref]

Lou, J.

J. Lou, Y. Wang, and L. Tong, “Microfiber optical sensors: a review,” Sensors (Basel) 14(4), 5823–5844 (2014).
[Crossref] [PubMed]

Lu, P.

Y. Xu, P. Lu, L. Chen, and X. Bao, “Recent developments in micro-structured fiber optic sensors,” Fibers (Basel) 5(1), 3 (2017).
[Crossref]

Lu, Y. Q.

J. L. Kou, M. Ding, J. Feng, Y. Q. Lu, F. Xu, and G. Brambilla, “Microfiber-based Bragg gratings for sensing applications: a review,” Sensors (Basel) 12(7), 8861–8876 (2012).
[Crossref] [PubMed]

Lucivero, V. G.

R. Jiménez-Martínez, J. Kołodyński, C. Troullinou, V. G. Lucivero, J. Kong, and M. W. Mitchell, “Signal tracking beyond the time resolution of an atomic sensor by Kalman filtering,” Phys. Rev. Lett. 120(4), 040503 (2018).
[Crossref] [PubMed]

Mabuchi, H.

M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89(13), 133602 (2002).
[Crossref] [PubMed]

Maccone, L.

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5(4), 222–229 (2011).
[Crossref]

Madsen, L. S.

N. P. Mauranyapin, L. S. Madsen, M. A. Taylor, M. Waleed, and W. P. Bowen, “Evanescent single-molecule biosensing with quantum-limited precision,” Nat. Photonics 11(8), 477–481 (2017).
[Crossref]

Makino, K.

K. Iwasawa, K. Makino, H. Yonezawa, M. Tsang, A. Davidovic, E. Huntington, and A. Furusawa, “Quantum-limited mirror-motion estimation,” Phys. Rev. Lett. 111(16), 163602 (2013).
[Crossref] [PubMed]

Mauranyapin, N. P.

N. P. Mauranyapin, L. S. Madsen, M. A. Taylor, M. Waleed, and W. P. Bowen, “Evanescent single-molecule biosensing with quantum-limited precision,” Nat. Photonics 11(8), 477–481 (2017).
[Crossref]

Mavalvala, N.

K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, “A quantum-enhanced prototype gravitational-wave detector,” Nat. Phys. 4(6), 472–476 (2008).
[Crossref]

McKenzie, K.

K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, “A quantum-enhanced prototype gravitational-wave detector,” Nat. Phys. 4(6), 472–476 (2008).
[Crossref]

Mescia, L.

L. Mescia and F. Prudenzano, “Advances on Optical Fiber Sensors,” Fibers (Basel) 2(1), 1–23 (2013).
[Crossref]

Mikhailov, E. E.

K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, “A quantum-enhanced prototype gravitational-wave detector,” Nat. Phys. 4(6), 472–476 (2008).
[Crossref]

Mitchell, M. W.

R. Jiménez-Martínez, J. Kołodyński, C. Troullinou, V. G. Lucivero, J. Kong, and M. W. Mitchell, “Signal tracking beyond the time resolution of an atomic sensor by Kalman filtering,” Phys. Rev. Lett. 120(4), 040503 (2018).
[Crossref] [PubMed]

Miyakawa, O.

K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, “A quantum-enhanced prototype gravitational-wave detector,” Nat. Phys. 4(6), 472–476 (2008).
[Crossref]

Nakane, D.

H. Yonezawa, D. Nakane, T. A. Wheatley, K. Iwasawa, S. Takeda, H. Arao, K. Ohki, K. Tsumura, D. W. Berry, T. C. Ralph, H. M. Wiseman, E. H. Huntington, and A. Furusawa, “Quantum-enhanced optical-phase tracking,” Science 337(6101), 1514–1517 (2012).
[Crossref] [PubMed]

T. A. Wheatley, D. W. Berry, H. Yonezawa, D. Nakane, H. Arao, D. T. Pope, T. C. Ralph, H. M. Wiseman, A. Furusawa, and E. H. Huntington, “Adaptive optical phase estimation using time-symmetric quantum smoothing,” Phys. Rev. Lett. 104(9), 093601 (2010).
[Crossref] [PubMed]

Nash, P. J.

G. A. Cranch, P. J. Nash, and C. K. Kirkendall, “Large-scale remotely interrogated arrays of fiber-optic interferometric sensors for underwater acoustic applications,” IEEE Sens. J. 3(1), 19–30 (2003).
[Crossref]

Nori, F.

J. Zhang, Y. Liu, R.-B. Wu, K. Jacobs, and F. Nori, “Quantum feedback: theory, experiments, and applications,” Phys. Rep. 679, 1–60 (2017).
[Crossref]

Ohki, K.

H. Yonezawa, D. Nakane, T. A. Wheatley, K. Iwasawa, S. Takeda, H. Arao, K. Ohki, K. Tsumura, D. W. Berry, T. C. Ralph, H. M. Wiseman, E. H. Huntington, and A. Furusawa, “Quantum-enhanced optical-phase tracking,” Science 337(6101), 1514–1517 (2012).
[Crossref] [PubMed]

Parsons, J. E.

J. E. Parsons, C. A. Cain, and J. B. Fowlkes, “Cost-effective assembly of a basic fiber-optic hydrophone for measurement of high-amplitude therapeutic ultrasound fields,” J. Acoust. Soc. Am. 119(3), 1432–1440 (2006).
[Crossref] [PubMed]

Pope, D.

D. Pope, H. Wiseman, and N. Langford, “Adaptive phase estimation is more accurate than nonadaptive phase estimation for continuous beams of light,” Phys. Rev. A 70(4), 043812 (2004).
[Crossref]

Pope, D. T.

T. A. Wheatley, D. W. Berry, H. Yonezawa, D. Nakane, H. Arao, D. T. Pope, T. C. Ralph, H. M. Wiseman, A. Furusawa, and E. H. Huntington, “Adaptive optical phase estimation using time-symmetric quantum smoothing,” Phys. Rev. Lett. 104(9), 093601 (2010).
[Crossref] [PubMed]

Prudenzano, F.

L. Mescia and F. Prudenzano, “Advances on Optical Fiber Sensors,” Fibers (Basel) 2(1), 1–23 (2013).
[Crossref]

Ralph, T. C.

H. Yonezawa, D. Nakane, T. A. Wheatley, K. Iwasawa, S. Takeda, H. Arao, K. Ohki, K. Tsumura, D. W. Berry, T. C. Ralph, H. M. Wiseman, E. H. Huntington, and A. Furusawa, “Quantum-enhanced optical-phase tracking,” Science 337(6101), 1514–1517 (2012).
[Crossref] [PubMed]

T. A. Wheatley, D. W. Berry, H. Yonezawa, D. Nakane, H. Arao, D. T. Pope, T. C. Ralph, H. M. Wiseman, A. Furusawa, and E. H. Huntington, “Adaptive optical phase estimation using time-symmetric quantum smoothing,” Phys. Rev. Lett. 104(9), 093601 (2010).
[Crossref] [PubMed]

Sánchez, M. P.

Saraf, S.

K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, “A quantum-enhanced prototype gravitational-wave detector,” Nat. Phys. 4(6), 472–476 (2008).
[Crossref]

Shapiro, J. H.

M. Tsang, J. H. Shapiro, and S. Lloyd, “Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous-time limit and state-variable approach to phase-locked loop design,” Phys. Rev. A 79(5), 053843 (2009).
[Crossref]

Stepanov, S.

Stockton, J. K.

M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89(13), 133602 (2002).
[Crossref] [PubMed]

Takeda, S.

H. Yonezawa, D. Nakane, T. A. Wheatley, K. Iwasawa, S. Takeda, H. Arao, K. Ohki, K. Tsumura, D. W. Berry, T. C. Ralph, H. M. Wiseman, E. H. Huntington, and A. Furusawa, “Quantum-enhanced optical-phase tracking,” Science 337(6101), 1514–1517 (2012).
[Crossref] [PubMed]

Taylor, M. A.

N. P. Mauranyapin, L. S. Madsen, M. A. Taylor, M. Waleed, and W. P. Bowen, “Evanescent single-molecule biosensing with quantum-limited precision,” Nat. Photonics 11(8), 477–481 (2017).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

Tong, L.

J. Lou, Y. Wang, and L. Tong, “Microfiber optical sensors: a review,” Sensors (Basel) 14(4), 5823–5844 (2014).
[Crossref] [PubMed]

Troullinou, C.

R. Jiménez-Martínez, J. Kołodyński, C. Troullinou, V. G. Lucivero, J. Kong, and M. W. Mitchell, “Signal tracking beyond the time resolution of an atomic sensor by Kalman filtering,” Phys. Rev. Lett. 120(4), 040503 (2018).
[Crossref] [PubMed]

Tsang, M.

K. Iwasawa, K. Makino, H. Yonezawa, M. Tsang, A. Davidovic, E. Huntington, and A. Furusawa, “Quantum-limited mirror-motion estimation,” Phys. Rev. Lett. 111(16), 163602 (2013).
[Crossref] [PubMed]

M. Tsang, “Time-symmetric quantum theory of smoothing,” Phys. Rev. Lett. 102(25), 250403 (2009).
[Crossref] [PubMed]

M. Tsang, J. H. Shapiro, and S. Lloyd, “Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous-time limit and state-variable approach to phase-locked loop design,” Phys. Rev. A 79(5), 053843 (2009).
[Crossref]

Tsumura, K.

H. Yonezawa, D. Nakane, T. A. Wheatley, K. Iwasawa, S. Takeda, H. Arao, K. Ohki, K. Tsumura, D. W. Berry, T. C. Ralph, H. M. Wiseman, E. H. Huntington, and A. Furusawa, “Quantum-enhanced optical-phase tracking,” Science 337(6101), 1514–1517 (2012).
[Crossref] [PubMed]

Vass, S.

K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, “A quantum-enhanced prototype gravitational-wave detector,” Nat. Phys. 4(6), 472–476 (2008).
[Crossref]

Waleed, M.

N. P. Mauranyapin, L. S. Madsen, M. A. Taylor, M. Waleed, and W. P. Bowen, “Evanescent single-molecule biosensing with quantum-limited precision,” Nat. Photonics 11(8), 477–481 (2017).
[Crossref]

Wang, D.

Wang, Y.

J. Lou, Y. Wang, and L. Tong, “Microfiber optical sensors: a review,” Sensors (Basel) 14(4), 5823–5844 (2014).
[Crossref] [PubMed]

Ward, R.

K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, “A quantum-enhanced prototype gravitational-wave detector,” Nat. Phys. 4(6), 472–476 (2008).
[Crossref]

Wei, D.

F. Liu, Y. Zhou, J. Yu, J. Guo, Y. Wu, S. Xiao, D. Wei, Y. Zhang, X. Jia, and M. Xiao, “Squeezing-enhanced fiber Mach-Zehnder interferometer for low-frequency phase measurement,” Appl. Phys. Lett. 110(2), 021106 (2017).
[Crossref]

Weinstein, A. J.

K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, “A quantum-enhanced prototype gravitational-wave detector,” Nat. Phys. 4(6), 472–476 (2008).
[Crossref]

Wheatley, T. A.

H. Yonezawa, D. Nakane, T. A. Wheatley, K. Iwasawa, S. Takeda, H. Arao, K. Ohki, K. Tsumura, D. W. Berry, T. C. Ralph, H. M. Wiseman, E. H. Huntington, and A. Furusawa, “Quantum-enhanced optical-phase tracking,” Science 337(6101), 1514–1517 (2012).
[Crossref] [PubMed]

T. A. Wheatley, D. W. Berry, H. Yonezawa, D. Nakane, H. Arao, D. T. Pope, T. C. Ralph, H. M. Wiseman, A. Furusawa, and E. H. Huntington, “Adaptive optical phase estimation using time-symmetric quantum smoothing,” Phys. Rev. Lett. 104(9), 093601 (2010).
[Crossref] [PubMed]

Wiseman, H.

D. Pope, H. Wiseman, and N. Langford, “Adaptive phase estimation is more accurate than nonadaptive phase estimation for continuous beams of light,” Phys. Rev. A 70(4), 043812 (2004).
[Crossref]

H. Wiseman and R. Killip, “Adaptive single-shot phase measurements: The full quantum theory,” Phys. Rev. A 57(3), 2169–2185 (1998).
[Crossref]

Wiseman, H. M.

H. Yonezawa, D. Nakane, T. A. Wheatley, K. Iwasawa, S. Takeda, H. Arao, K. Ohki, K. Tsumura, D. W. Berry, T. C. Ralph, H. M. Wiseman, E. H. Huntington, and A. Furusawa, “Quantum-enhanced optical-phase tracking,” Science 337(6101), 1514–1517 (2012).
[Crossref] [PubMed]

T. A. Wheatley, D. W. Berry, H. Yonezawa, D. Nakane, H. Arao, D. T. Pope, T. C. Ralph, H. M. Wiseman, A. Furusawa, and E. H. Huntington, “Adaptive optical phase estimation using time-symmetric quantum smoothing,” Phys. Rev. Lett. 104(9), 093601 (2010).
[Crossref] [PubMed]

D. W. Berry and H. M. Wiseman, “Adaptive quantum measurements of a continuously varying phase,” Phys. Rev. A 65(4), 043803 (2002).
[Crossref]

Wu, L. A.

M. Xiao, L. A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59(3), 278–281 (1987).
[Crossref] [PubMed]

Wu, R.-B.

J. Zhang, Y. Liu, R.-B. Wu, K. Jacobs, and F. Nori, “Quantum feedback: theory, experiments, and applications,” Phys. Rep. 679, 1–60 (2017).
[Crossref]

Wu, Y.

F. Liu, Y. Zhou, J. Yu, J. Guo, Y. Wu, S. Xiao, D. Wei, Y. Zhang, X. Jia, and M. Xiao, “Squeezing-enhanced fiber Mach-Zehnder interferometer for low-frequency phase measurement,” Appl. Phys. Lett. 110(2), 021106 (2017).
[Crossref]

C. Xia, D. Wang, Y. Wu, J. Guo, F. Liu, Y. Zhang, and M. Xiao, “Continuous-variable entanglement measurement using an unbalanced Mach-Zehnder interferometer,” Opt. Lett. 40(6), 1121–1124 (2015).
[Crossref] [PubMed]

Xia, C.

Xiao, M.

F. Liu, Y. Zhou, J. Yu, J. Guo, Y. Wu, S. Xiao, D. Wei, Y. Zhang, X. Jia, and M. Xiao, “Squeezing-enhanced fiber Mach-Zehnder interferometer for low-frequency phase measurement,” Appl. Phys. Lett. 110(2), 021106 (2017).
[Crossref]

C. Xia, D. Wang, Y. Wu, J. Guo, F. Liu, Y. Zhang, and M. Xiao, “Continuous-variable entanglement measurement using an unbalanced Mach-Zehnder interferometer,” Opt. Lett. 40(6), 1121–1124 (2015).
[Crossref] [PubMed]

M. Xiao, L. A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59(3), 278–281 (1987).
[Crossref] [PubMed]

Xiao, S.

F. Liu, Y. Zhou, J. Yu, J. Guo, Y. Wu, S. Xiao, D. Wei, Y. Zhang, X. Jia, and M. Xiao, “Squeezing-enhanced fiber Mach-Zehnder interferometer for low-frequency phase measurement,” Appl. Phys. Lett. 110(2), 021106 (2017).
[Crossref]

Xu, F.

J. L. Kou, M. Ding, J. Feng, Y. Q. Lu, F. Xu, and G. Brambilla, “Microfiber-based Bragg gratings for sensing applications: a review,” Sensors (Basel) 12(7), 8861–8876 (2012).
[Crossref] [PubMed]

Xu, Y.

Y. Xu, P. Lu, L. Chen, and X. Bao, “Recent developments in micro-structured fiber optic sensors,” Fibers (Basel) 5(1), 3 (2017).
[Crossref]

Yonezawa, H.

K. Iwasawa, K. Makino, H. Yonezawa, M. Tsang, A. Davidovic, E. Huntington, and A. Furusawa, “Quantum-limited mirror-motion estimation,” Phys. Rev. Lett. 111(16), 163602 (2013).
[Crossref] [PubMed]

H. Yonezawa, D. Nakane, T. A. Wheatley, K. Iwasawa, S. Takeda, H. Arao, K. Ohki, K. Tsumura, D. W. Berry, T. C. Ralph, H. M. Wiseman, E. H. Huntington, and A. Furusawa, “Quantum-enhanced optical-phase tracking,” Science 337(6101), 1514–1517 (2012).
[Crossref] [PubMed]

T. A. Wheatley, D. W. Berry, H. Yonezawa, D. Nakane, H. Arao, D. T. Pope, T. C. Ralph, H. M. Wiseman, A. Furusawa, and E. H. Huntington, “Adaptive optical phase estimation using time-symmetric quantum smoothing,” Phys. Rev. Lett. 104(9), 093601 (2010).
[Crossref] [PubMed]

Yu, J.

F. Liu, Y. Zhou, J. Yu, J. Guo, Y. Wu, S. Xiao, D. Wei, Y. Zhang, X. Jia, and M. Xiao, “Squeezing-enhanced fiber Mach-Zehnder interferometer for low-frequency phase measurement,” Appl. Phys. Lett. 110(2), 021106 (2017).
[Crossref]

Zhang, J.

J. Zhang, Y. Liu, R.-B. Wu, K. Jacobs, and F. Nori, “Quantum feedback: theory, experiments, and applications,” Phys. Rep. 679, 1–60 (2017).
[Crossref]

Zhang, Y.

F. Liu, Y. Zhou, J. Yu, J. Guo, Y. Wu, S. Xiao, D. Wei, Y. Zhang, X. Jia, and M. Xiao, “Squeezing-enhanced fiber Mach-Zehnder interferometer for low-frequency phase measurement,” Appl. Phys. Lett. 110(2), 021106 (2017).
[Crossref]

C. Xia, D. Wang, Y. Wu, J. Guo, F. Liu, Y. Zhang, and M. Xiao, “Continuous-variable entanglement measurement using an unbalanced Mach-Zehnder interferometer,” Opt. Lett. 40(6), 1121–1124 (2015).
[Crossref] [PubMed]

Zhou, Y.

F. Liu, Y. Zhou, J. Yu, J. Guo, Y. Wu, S. Xiao, D. Wei, Y. Zhang, X. Jia, and M. Xiao, “Squeezing-enhanced fiber Mach-Zehnder interferometer for low-frequency phase measurement,” Appl. Phys. Lett. 110(2), 021106 (2017).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

F. Liu, Y. Zhou, J. Yu, J. Guo, Y. Wu, S. Xiao, D. Wei, Y. Zhang, X. Jia, and M. Xiao, “Squeezing-enhanced fiber Mach-Zehnder interferometer for low-frequency phase measurement,” Appl. Phys. Lett. 110(2), 021106 (2017).
[Crossref]

Fibers (Basel) (2)

Y. Xu, P. Lu, L. Chen, and X. Bao, “Recent developments in micro-structured fiber optic sensors,” Fibers (Basel) 5(1), 3 (2017).
[Crossref]

L. Mescia and F. Prudenzano, “Advances on Optical Fiber Sensors,” Fibers (Basel) 2(1), 1–23 (2013).
[Crossref]

IEEE Sens. J. (1)

G. A. Cranch, P. J. Nash, and C. K. Kirkendall, “Large-scale remotely interrogated arrays of fiber-optic interferometric sensors for underwater acoustic applications,” IEEE Sens. J. 3(1), 19–30 (2003).
[Crossref]

J. Acoust. Soc. Am. (1)

J. E. Parsons, C. A. Cain, and J. B. Fowlkes, “Cost-effective assembly of a basic fiber-optic hydrophone for measurement of high-amplitude therapeutic ultrasound fields,” J. Acoust. Soc. Am. 119(3), 1432–1440 (2006).
[Crossref] [PubMed]

Nat. Photonics (3)

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5(4), 222–229 (2011).
[Crossref]

N. P. Mauranyapin, L. S. Madsen, M. A. Taylor, M. Waleed, and W. P. Bowen, “Evanescent single-molecule biosensing with quantum-limited precision,” Nat. Photonics 11(8), 477–481 (2017).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

Nat. Phys. (1)

K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, “A quantum-enhanced prototype gravitational-wave detector,” Nat. Phys. 4(6), 472–476 (2008).
[Crossref]

Opt. Fiber Technol. (1)

B. Lee, “Review of the present status of optical fiber sensors,” Opt. Fiber Technol. 9(2), 57–79 (2003).
[Crossref]

Opt. Lett. (1)

Phys. Rep. (1)

J. Zhang, Y. Liu, R.-B. Wu, K. Jacobs, and F. Nori, “Quantum feedback: theory, experiments, and applications,” Phys. Rep. 679, 1–60 (2017).
[Crossref]

Phys. Rev. A (4)

D. W. Berry and H. M. Wiseman, “Adaptive quantum measurements of a continuously varying phase,” Phys. Rev. A 65(4), 043803 (2002).
[Crossref]

D. Pope, H. Wiseman, and N. Langford, “Adaptive phase estimation is more accurate than nonadaptive phase estimation for continuous beams of light,” Phys. Rev. A 70(4), 043812 (2004).
[Crossref]

M. Tsang, J. H. Shapiro, and S. Lloyd, “Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous-time limit and state-variable approach to phase-locked loop design,” Phys. Rev. A 79(5), 053843 (2009).
[Crossref]

H. Wiseman and R. Killip, “Adaptive single-shot phase measurements: The full quantum theory,” Phys. Rev. A 57(3), 2169–2185 (1998).
[Crossref]

Phys. Rev. D Part. Fields (1)

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D Part. Fields 23(8), 1693–1708 (1981).
[Crossref]

Phys. Rev. Lett. (6)

M. Xiao, L. A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59(3), 278–281 (1987).
[Crossref] [PubMed]

M. Tsang, “Time-symmetric quantum theory of smoothing,” Phys. Rev. Lett. 102(25), 250403 (2009).
[Crossref] [PubMed]

T. A. Wheatley, D. W. Berry, H. Yonezawa, D. Nakane, H. Arao, D. T. Pope, T. C. Ralph, H. M. Wiseman, A. Furusawa, and E. H. Huntington, “Adaptive optical phase estimation using time-symmetric quantum smoothing,” Phys. Rev. Lett. 104(9), 093601 (2010).
[Crossref] [PubMed]

M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89(13), 133602 (2002).
[Crossref] [PubMed]

K. Iwasawa, K. Makino, H. Yonezawa, M. Tsang, A. Davidovic, E. Huntington, and A. Furusawa, “Quantum-limited mirror-motion estimation,” Phys. Rev. Lett. 111(16), 163602 (2013).
[Crossref] [PubMed]

R. Jiménez-Martínez, J. Kołodyński, C. Troullinou, V. G. Lucivero, J. Kong, and M. W. Mitchell, “Signal tracking beyond the time resolution of an atomic sensor by Kalman filtering,” Phys. Rev. Lett. 120(4), 040503 (2018).
[Crossref] [PubMed]

Science (1)

H. Yonezawa, D. Nakane, T. A. Wheatley, K. Iwasawa, S. Takeda, H. Arao, K. Ohki, K. Tsumura, D. W. Berry, T. C. Ralph, H. M. Wiseman, E. H. Huntington, and A. Furusawa, “Quantum-enhanced optical-phase tracking,” Science 337(6101), 1514–1517 (2012).
[Crossref] [PubMed]

Sensors (Basel) (2)

J. L. Kou, M. Ding, J. Feng, Y. Q. Lu, F. Xu, and G. Brambilla, “Microfiber-based Bragg gratings for sensing applications: a review,” Sensors (Basel) 12(7), 8861–8876 (2012).
[Crossref] [PubMed]

J. Lou, Y. Wang, and L. Tong, “Microfiber optical sensors: a review,” Sensors (Basel) 14(4), 5823–5844 (2014).
[Crossref] [PubMed]

Other (5)

K. Jacobs, Quantum measurement theory and its applications (Cambridge University, 2014).

H.-A. Bachor and T. C. Ralph, A guide to experiments in quantum optics (Wiley, 2004).

H. M. Wiseman and G. J. Milburn, Quantum measurement and control (Cambridge University, 2009).

C. Gardiner, P. Zoller, and P. Zoller, Quantum noise: a handbook of Markovian and non-Markovian quantum stochastic methods with applications to quantum optics (Springer Science & Business Media, 2004).

A. B. Baggeroer, State variables and communication theory (MIT, 1970).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1 Diagram of a homodyne phase-locked loop that implements the Kalman filtering estimation. The signal beam is combined with the local oscillator at a 50/50 beam splitter (BS) and then are detected by two photodetectors (PD). The outputs from the photodetectors are subtracted. The obtained current I is processed by a integrator( t ds ) with a Kalman gain (Γ), which determines an optimal phase estimate. The phase modulator (PM) is adjusted accordingly for the next estimate.
Fig. 2
Fig. 2 Experimental configuration for adaptive homodyne measurements. The red and black lines denote optical and electrical paths, respectively. The green and blue lines denote the locking loop 1 (LL1) and locking loop 2 (LL2), respectively. FC: fiber coupler; BS: beam splitter; EOM: electro-optical modulator; PZT: piezoelectric transducer; PD: photodiode; RF: rf synthesizer; LPF: low pass filter; KF: Kalman filter; PID: PID servo; P: Proportion controller; HA: high-voltage amplifier; LA: Lock-in amplifier.
Fig. 3
Fig. 3 Time domain results of fiber-based phase tracking. The blue curve is the input OU random signal with a bandwidth of 1 kHz and the red curve is the estimation result in our fiber homodyne system.
Fig. 4
Fig. 4 Dependence of MSE σ2 on |α|2. The black spots are the measured MSE. The red and blue spots are the simulated MSEs based on adaptive homodyne and heterodyne theories, respectively. In the calibration of the amplitude |α|2 for coherent beam, we has considered the imperfect efficiency of the system. The spots for adaptive homodyne and heterodyne theories are calculated including the experimental imperfections. If considering an ideal system without losses, the theoretical MSE can be further reduced as shown by the red and blue lines.

Equations (11)

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

a=[α( e i(ω+Ω)t + e i(ωΩ)t )+δα] e iΦ(t)
L=(l e iωt +δl) e i Φ LO (t)
I(t)=2| α |sin[ Φ(t) Φ f ' (t) ]+dW(t)/dt
[ Φ(t) Φ f ' (t) ] 2 <<1
I(t)2| α |( Φ(t) Φ f ' (t) )+dW(t)/dt
dΦ(t)=λΦ(t)dt+ κ dV(t)
d Φ ' (t)=λ Φ ' (t)dt+ΓI(t)dt
dΣ(t)=2λΣ(t)dt4 | α | 2 ( Σ(t) ) 2 dt+κdt
Φ f ' (t)= Γ opt t e λ(ts) I(s) 2| α | ds
σ adap 2 = [ Φ(t) Φ f ' (t) ] 2 = -λ+ λ 2 +4κ | α | 2 4 | α | 2
σ hetero 2 = [ Φ(t) Φ est ' (t) ] 2 = -λ+ λ 2 +4κ | α | 2 2 2 | α | 2

Metrics