Abstract

Quantum entanglement is a resource in quantum metrology that can be distributed to two conjugate physical quantities for the enhancement of their measurement sensitivity. This is demonstrated in the joint measurement of phase and amplitude modulation signals in quantum dense metrology schemes. We can also devote all the quantum resource to phase measurement only, leading to the optimum sensitivity enhancement. In this paper, we experimentally implement a dual-beam sensing scheme in an SU(1,1) interferometer for the optimum quantum enhancement of phase measurement sensitivity. We demonstrate a 3.9-dB improvement in signal-to-noise ratio over the optimum classical method, and this is 3-dB better than the traditional single-beam scheme. Furthermore, such as cheme also realizes a quantum optical tap of quantum entangled fields and has the full advantages of an SU(1,1) interferometer, such as detection loss tolerance, making it more suitable for practical applications in quantum metrology and quantum information.

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

Full Article  |  PDF Article
OSA Recommended Articles
Loss-tolerant quantum dense metrology with SU(1,1) interferometer

Yuhong Liu, Jiamin Li, Liang Cui, Nan Huo, Syed M. Assad, Xiaoying Li, and Z. Y. Ou
Opt. Express 26(21) 27705-27715 (2018)

Absolute sensitivity of phase measurement in an SU(1,1) type interferometer

Wei Du, Jun Jia, J. F. Chen, Z. Y. Ou, and Weiping Zhang
Opt. Lett. 43(5) 1051-1054 (2018)

Optimized phase sensing in a truncated SU(1,1) interferometer

Prasoon Gupta, Bonnie L. Schmittberger, Brian E. Anderson, Kevin M. Jones, and Paul D. Lett
Opt. Express 26(1) 391-401 (2018)

References

  • View by:
  • |
  • |
  • |

  1. A. A. Michelson and E. W. Morley, “On the relative motion of the earth and of the luminiferous ether,” Am. J. Sci. 34, 333 (1887).
    [Crossref]
  2. C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
    [Crossref]
  3. V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
    [Crossref] [PubMed]
  4. M. Xiao, L.-A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59, 278–281 (1987).
    [Crossref] [PubMed]
  5. P. Grangier, R. E. Slusher, B. Yurke, and A. Laporta, “Squeezed-light enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).
    [Crossref] [PubMed]
  6. S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A 61, 042302 (2000).
    [Crossref]
  7. Y. Ma, H. Miao, B. H. Pang, M. Evans, C. Zhao, J. Harms, R. Schnabel, and Y. Chen, “Proposal for gravitational-wave detection beyond the standard quantum limit through EPR entanglement,” Nat. Phys. 13, 776 (2017).
    [Crossref]
  8. B. Yurke, S. L. McCall, and J. R. Klauder, “SU(2) and SU(1,1) interferometers,” Phys. Rev. A 33, 4033–4054 (1986).
    [Crossref]
  9. W. N. Plick, J. P. Dowling, and G. S. Agarwal, “Coherent-light-boosted, sub-shot noise, quantum interferometry,” New J. Phys. 12, 083014 (2010).
    [Crossref]
  10. J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99, 011110 (2011).
    [Crossref]
  11. Z. Y. Ou, “Enhancement of the phase-measurement sensitivity beyond the standard quantum limit by a nonlinear interferometer,” Phys. Rev. A 85, 023815 (2012).
    [Crossref]
  12. A. M. Marino, N. V. Corzo Trejo, and P. D. Lett, “Effect of losses on the performance of an SU(1,1) interferometer,” Phys. Rev. A 86, 023844 (2012).
    [Crossref]
  13. F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
    [Crossref] [PubMed]
  14. B. E. Anderson, P. Gupta, B. L. Schmittberger, T. Horrom, C. Hermann-Avigliano, K. M. Jones, and P. D. Lett, “Phase sensing beyond the standard quantum limit with a variation on the SU(1,1) interferometer,” Optica 4, 752–756 (2017).
    [Crossref]
  15. M. Manceau, G. Leuchs, F. Khalili, and M. Chekhova, “Detection loss tolerant supersensitive phase measurement with an SU(1,1) interferometer,” Phys. Rev. Lett. 119, 223604 (2017).
    [Crossref] [PubMed]
  16. P. Gupta, B. L. Schmittberger, B. E. Anderson, K. M. Jones, and P. D. Lett, “Optimized phase sensing in a truncated SU(1,1) interferometer,” Opt. Express 26, 391–401 (2018).
    [Crossref] [PubMed]
  17. X. Ma, C. You, S. Adhikari, E. S. Matekole, R. T. Glasser, H. Lee, and J. P. Dowling, “Sub-shot-noise-limited phase estimation via SU(1,1) interferometer with thermal states,” Opt. Express 26, 18492–18504 (2018).
    [Crossref] [PubMed]
  18. S. Adhikari, N. Bhusal, C. You, H. Lee, and J. P. Dowling, “Phase estimation in an SU(1,1) interferometer with displaced squeezed states,” OSA Continuum 1, 438–450 (2018).
    [Crossref]
  19. D. Li, B. T. Gard, Y. Gao, C.-H. Yuan, W. Zhang, H. Lee, and J. P. Dowling, “Phase sensitivity at the Heisenberg limit in an SU(1,1) interferometer via parity detection,” Phys. Rev. A 94, 063840 (2016).
    [Crossref]
  20. D. Li, C.-H. Yuan, Z. Y. Ou, and W. Zhang, “The phase sensitivity of an SU(1,1) interferometer with homodyne detection,” New J. Phys. 16, 073020 (2014).
    [Crossref]
  21. X.-L. Hu, D. Li, L. Q. Chen, K. Zhang, W. Zhang, and C.-H. Yuan, “Phase estimation for an SU(1,1) interferometer in the presence of phase diffusion and photon losses,” Phys. Rev. A 98, 023803 (2018).
    [Crossref]
  22. J. Kong, Z. Y. Ou, and W. Zhang, “Phase-measurement sensitivity beyond the standard quantum limit in an interferometer consisting of a parametric amplifier and a beam splitter,” Phys. Rev. A 87, 023825 (2013).
    [Crossref]
  23. B. E. Anderson, B. L. Schmittberger, P. Gupta, K. M. Jones, and P. D. Lett, “Optimal phase measurements with bright- and vacuum-seeded SU(1,1) interferometers,” Phys. Rev. A 95, 063843 (2017).
    [Crossref]
  24. J. Li, Y. Liu, L. Cui, N. Huo, S. M. Assad, X. Li, and Z. Y. Ou, “Joint measurement of multiple noncommuting parameters,” Phys. Rev. A 97, 052127 (2018).
    [Crossref]
  25. X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright einstein-podolsky-rosen beam,” Phys. Rev. Lett. 88, 047904 (2002).
    [Crossref] [PubMed]
  26. S. Steinlechner, J. Bauchrowitz, M. Meinders, H. Müller-Ebhardt, K. Danzmann, and R. Schnabel, “Quantum-dense metrology,” Nat. Photonics 7, 626–630 (2013).
    [Crossref]
  27. Y. Liu, J. Li, L. Cui, N. Huo, S. M. Assad, X. Li, and Z. Y. Ou, “Loss-tolerant quantum dense metrology with SU(1,1) interferometer,” Opt. Express 26, 27705–27715 (2018).
    [Crossref] [PubMed]
  28. B. Abbott, R. Abbott, R. Adhikari, P. Ajith, B. Allen, G. Allen, R. Amin, S. Anderson, W. Anderson, M. Arain, and et al.., “Ligo: the laser interferometer gravitational-wave observatory,” Reports Prog. Phys. 72, 076901 (2009).
    [Crossref]
  29. R. L. Forward, “Wideband laser-interferometer graviational-radiation experiment,” Phys. Rev. D 17, 379–390 (1978).
    [Crossref]
  30. X. Guo, X. Li, N. Liu, and Z. Y. Ou, “Quantum information tapping using a fiber optical parametric amplifier with noise figure improved by correlated inputs,” Sci. Rep. 6, 30214 (2016).
    [Crossref] [PubMed]
  31. R. Tang, J. Lasri, P. S. Devgan, V. Grigoryan, P. Kumar, and M. Vasilyev, “Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input,” Opt. Express 13, 10483 (2005).
    [Crossref] [PubMed]
  32. B. Chen, C. Qiu, S. Chen, J. Guo, L. Chen, Z. Ou, and W. Zhang, “Atom-light hybrid interferometer,” Phys. Rev. Lett. 115, 043602 (2015).
    [Crossref] [PubMed]
  33. X. Guo, N. Liu, Y. Liu, X. Li, and Z. Y. Ou, “Generation of continuous variable quantum entanglement using a fiber optical parametric amplifier,” Opt. Lett. 41, 653 (2016).
    [Crossref] [PubMed]
  34. J. Li, Y. Liu, N. Huo, L. Cui, X. Li, and Z. Ou, “Loss-tolerant measurement of continuous-variable quantum entanglement with the aid of a high gain parametric amplifier,” arXiv 1808.10258 (2018).
  35. J. H. Shapiro, “Optical waveguide tap with infinitesimal insertion loss,” Opt. Lett. 5, 351–353 (1980).
    [Crossref] [PubMed]
  36. J.-A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267 (1993).
    [Crossref] [PubMed]
  37. D. K. Serkland and P. Kumar, “Tunable fiber-optic parametric oscillator,” Opt. Lett. 24, 92 (1999).
    [Crossref]
  38. X. Guo, X. Li, N. Liu, L. Yang, and Z. Y. Ou, “An all-fiber source of pulsed twin beams for quantum communication,” Appl. Phys. Lett. 101, 261111 (2012).
    [Crossref]

2018 (6)

2017 (4)

B. E. Anderson, B. L. Schmittberger, P. Gupta, K. M. Jones, and P. D. Lett, “Optimal phase measurements with bright- and vacuum-seeded SU(1,1) interferometers,” Phys. Rev. A 95, 063843 (2017).
[Crossref]

B. E. Anderson, P. Gupta, B. L. Schmittberger, T. Horrom, C. Hermann-Avigliano, K. M. Jones, and P. D. Lett, “Phase sensing beyond the standard quantum limit with a variation on the SU(1,1) interferometer,” Optica 4, 752–756 (2017).
[Crossref]

M. Manceau, G. Leuchs, F. Khalili, and M. Chekhova, “Detection loss tolerant supersensitive phase measurement with an SU(1,1) interferometer,” Phys. Rev. Lett. 119, 223604 (2017).
[Crossref] [PubMed]

Y. Ma, H. Miao, B. H. Pang, M. Evans, C. Zhao, J. Harms, R. Schnabel, and Y. Chen, “Proposal for gravitational-wave detection beyond the standard quantum limit through EPR entanglement,” Nat. Phys. 13, 776 (2017).
[Crossref]

2016 (3)

D. Li, B. T. Gard, Y. Gao, C.-H. Yuan, W. Zhang, H. Lee, and J. P. Dowling, “Phase sensitivity at the Heisenberg limit in an SU(1,1) interferometer via parity detection,” Phys. Rev. A 94, 063840 (2016).
[Crossref]

X. Guo, X. Li, N. Liu, and Z. Y. Ou, “Quantum information tapping using a fiber optical parametric amplifier with noise figure improved by correlated inputs,” Sci. Rep. 6, 30214 (2016).
[Crossref] [PubMed]

X. Guo, N. Liu, Y. Liu, X. Li, and Z. Y. Ou, “Generation of continuous variable quantum entanglement using a fiber optical parametric amplifier,” Opt. Lett. 41, 653 (2016).
[Crossref] [PubMed]

2015 (1)

B. Chen, C. Qiu, S. Chen, J. Guo, L. Chen, Z. Ou, and W. Zhang, “Atom-light hybrid interferometer,” Phys. Rev. Lett. 115, 043602 (2015).
[Crossref] [PubMed]

2014 (2)

D. Li, C.-H. Yuan, Z. Y. Ou, and W. Zhang, “The phase sensitivity of an SU(1,1) interferometer with homodyne detection,” New J. Phys. 16, 073020 (2014).
[Crossref]

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
[Crossref] [PubMed]

2013 (2)

J. Kong, Z. Y. Ou, and W. Zhang, “Phase-measurement sensitivity beyond the standard quantum limit in an interferometer consisting of a parametric amplifier and a beam splitter,” Phys. Rev. A 87, 023825 (2013).
[Crossref]

S. Steinlechner, J. Bauchrowitz, M. Meinders, H. Müller-Ebhardt, K. Danzmann, and R. Schnabel, “Quantum-dense metrology,” Nat. Photonics 7, 626–630 (2013).
[Crossref]

2012 (3)

Z. Y. Ou, “Enhancement of the phase-measurement sensitivity beyond the standard quantum limit by a nonlinear interferometer,” Phys. Rev. A 85, 023815 (2012).
[Crossref]

A. M. Marino, N. V. Corzo Trejo, and P. D. Lett, “Effect of losses on the performance of an SU(1,1) interferometer,” Phys. Rev. A 86, 023844 (2012).
[Crossref]

X. Guo, X. Li, N. Liu, L. Yang, and Z. Y. Ou, “An all-fiber source of pulsed twin beams for quantum communication,” Appl. Phys. Lett. 101, 261111 (2012).
[Crossref]

2011 (1)

J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99, 011110 (2011).
[Crossref]

2010 (1)

W. N. Plick, J. P. Dowling, and G. S. Agarwal, “Coherent-light-boosted, sub-shot noise, quantum interferometry,” New J. Phys. 12, 083014 (2010).
[Crossref]

2009 (1)

B. Abbott, R. Abbott, R. Adhikari, P. Ajith, B. Allen, G. Allen, R. Amin, S. Anderson, W. Anderson, M. Arain, and et al.., “Ligo: the laser interferometer gravitational-wave observatory,” Reports Prog. Phys. 72, 076901 (2009).
[Crossref]

2006 (1)

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
[Crossref] [PubMed]

2005 (1)

2002 (1)

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright einstein-podolsky-rosen beam,” Phys. Rev. Lett. 88, 047904 (2002).
[Crossref] [PubMed]

2000 (1)

S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A 61, 042302 (2000).
[Crossref]

1999 (1)

1993 (1)

J.-A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267 (1993).
[Crossref] [PubMed]

1987 (2)

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

P. Grangier, R. E. Slusher, B. Yurke, and A. Laporta, “Squeezed-light enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).
[Crossref] [PubMed]

1986 (1)

B. Yurke, S. L. McCall, and J. R. Klauder, “SU(2) and SU(1,1) interferometers,” Phys. Rev. A 33, 4033–4054 (1986).
[Crossref]

1981 (1)

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

1980 (1)

1978 (1)

R. L. Forward, “Wideband laser-interferometer graviational-radiation experiment,” Phys. Rev. D 17, 379–390 (1978).
[Crossref]

1887 (1)

A. A. Michelson and E. W. Morley, “On the relative motion of the earth and of the luminiferous ether,” Am. J. Sci. 34, 333 (1887).
[Crossref]

Abbott, B.

B. Abbott, R. Abbott, R. Adhikari, P. Ajith, B. Allen, G. Allen, R. Amin, S. Anderson, W. Anderson, M. Arain, and et al.., “Ligo: the laser interferometer gravitational-wave observatory,” Reports Prog. Phys. 72, 076901 (2009).
[Crossref]

Abbott, R.

B. Abbott, R. Abbott, R. Adhikari, P. Ajith, B. Allen, G. Allen, R. Amin, S. Anderson, W. Anderson, M. Arain, and et al.., “Ligo: the laser interferometer gravitational-wave observatory,” Reports Prog. Phys. 72, 076901 (2009).
[Crossref]

Abram, I.

J.-A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267 (1993).
[Crossref] [PubMed]

Adhikari, R.

B. Abbott, R. Abbott, R. Adhikari, P. Ajith, B. Allen, G. Allen, R. Amin, S. Anderson, W. Anderson, M. Arain, and et al.., “Ligo: the laser interferometer gravitational-wave observatory,” Reports Prog. Phys. 72, 076901 (2009).
[Crossref]

Adhikari, S.

Agarwal, G. S.

W. N. Plick, J. P. Dowling, and G. S. Agarwal, “Coherent-light-boosted, sub-shot noise, quantum interferometry,” New J. Phys. 12, 083014 (2010).
[Crossref]

Ajith, P.

B. Abbott, R. Abbott, R. Adhikari, P. Ajith, B. Allen, G. Allen, R. Amin, S. Anderson, W. Anderson, M. Arain, and et al.., “Ligo: the laser interferometer gravitational-wave observatory,” Reports Prog. Phys. 72, 076901 (2009).
[Crossref]

Allen, B.

B. Abbott, R. Abbott, R. Adhikari, P. Ajith, B. Allen, G. Allen, R. Amin, S. Anderson, W. Anderson, M. Arain, and et al.., “Ligo: the laser interferometer gravitational-wave observatory,” Reports Prog. Phys. 72, 076901 (2009).
[Crossref]

Allen, G.

B. Abbott, R. Abbott, R. Adhikari, P. Ajith, B. Allen, G. Allen, R. Amin, S. Anderson, W. Anderson, M. Arain, and et al.., “Ligo: the laser interferometer gravitational-wave observatory,” Reports Prog. Phys. 72, 076901 (2009).
[Crossref]

Amin, R.

B. Abbott, R. Abbott, R. Adhikari, P. Ajith, B. Allen, G. Allen, R. Amin, S. Anderson, W. Anderson, M. Arain, and et al.., “Ligo: the laser interferometer gravitational-wave observatory,” Reports Prog. Phys. 72, 076901 (2009).
[Crossref]

Anderson, B. E.

Anderson, S.

B. Abbott, R. Abbott, R. Adhikari, P. Ajith, B. Allen, G. Allen, R. Amin, S. Anderson, W. Anderson, M. Arain, and et al.., “Ligo: the laser interferometer gravitational-wave observatory,” Reports Prog. Phys. 72, 076901 (2009).
[Crossref]

Anderson, W.

B. Abbott, R. Abbott, R. Adhikari, P. Ajith, B. Allen, G. Allen, R. Amin, S. Anderson, W. Anderson, M. Arain, and et al.., “Ligo: the laser interferometer gravitational-wave observatory,” Reports Prog. Phys. 72, 076901 (2009).
[Crossref]

Arain, M.

B. Abbott, R. Abbott, R. Adhikari, P. Ajith, B. Allen, G. Allen, R. Amin, S. Anderson, W. Anderson, M. Arain, and et al.., “Ligo: the laser interferometer gravitational-wave observatory,” Reports Prog. Phys. 72, 076901 (2009).
[Crossref]

Assad, S. M.

J. Li, Y. Liu, L. Cui, N. Huo, S. M. Assad, X. Li, and Z. Y. Ou, “Joint measurement of multiple noncommuting parameters,” Phys. Rev. A 97, 052127 (2018).
[Crossref]

Y. Liu, J. Li, L. Cui, N. Huo, S. M. Assad, X. Li, and Z. Y. Ou, “Loss-tolerant quantum dense metrology with SU(1,1) interferometer,” Opt. Express 26, 27705–27715 (2018).
[Crossref] [PubMed]

Bauchrowitz, J.

S. Steinlechner, J. Bauchrowitz, M. Meinders, H. Müller-Ebhardt, K. Danzmann, and R. Schnabel, “Quantum-dense metrology,” Nat. Photonics 7, 626–630 (2013).
[Crossref]

Bhusal, N.

Braunstein, S. L.

S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A 61, 042302 (2000).
[Crossref]

Caves, C. M.

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

Chekhova, M.

M. Manceau, G. Leuchs, F. Khalili, and M. Chekhova, “Detection loss tolerant supersensitive phase measurement with an SU(1,1) interferometer,” Phys. Rev. Lett. 119, 223604 (2017).
[Crossref] [PubMed]

Chen, B.

B. Chen, C. Qiu, S. Chen, J. Guo, L. Chen, Z. Ou, and W. Zhang, “Atom-light hybrid interferometer,” Phys. Rev. Lett. 115, 043602 (2015).
[Crossref] [PubMed]

Chen, L.

B. Chen, C. Qiu, S. Chen, J. Guo, L. Chen, Z. Ou, and W. Zhang, “Atom-light hybrid interferometer,” Phys. Rev. Lett. 115, 043602 (2015).
[Crossref] [PubMed]

Chen, L. Q.

X.-L. Hu, D. Li, L. Q. Chen, K. Zhang, W. Zhang, and C.-H. Yuan, “Phase estimation for an SU(1,1) interferometer in the presence of phase diffusion and photon losses,” Phys. Rev. A 98, 023803 (2018).
[Crossref]

Chen, S.

B. Chen, C. Qiu, S. Chen, J. Guo, L. Chen, Z. Ou, and W. Zhang, “Atom-light hybrid interferometer,” Phys. Rev. Lett. 115, 043602 (2015).
[Crossref] [PubMed]

Chen, Y.

Y. Ma, H. Miao, B. H. Pang, M. Evans, C. Zhao, J. Harms, R. Schnabel, and Y. Chen, “Proposal for gravitational-wave detection beyond the standard quantum limit through EPR entanglement,” Nat. Phys. 13, 776 (2017).
[Crossref]

Corzo Trejo, N. V.

A. M. Marino, N. V. Corzo Trejo, and P. D. Lett, “Effect of losses on the performance of an SU(1,1) interferometer,” Phys. Rev. A 86, 023844 (2012).
[Crossref]

Cui, L.

J. Li, Y. Liu, L. Cui, N. Huo, S. M. Assad, X. Li, and Z. Y. Ou, “Joint measurement of multiple noncommuting parameters,” Phys. Rev. A 97, 052127 (2018).
[Crossref]

Y. Liu, J. Li, L. Cui, N. Huo, S. M. Assad, X. Li, and Z. Y. Ou, “Loss-tolerant quantum dense metrology with SU(1,1) interferometer,” Opt. Express 26, 27705–27715 (2018).
[Crossref] [PubMed]

J. Li, Y. Liu, N. Huo, L. Cui, X. Li, and Z. Ou, “Loss-tolerant measurement of continuous-variable quantum entanglement with the aid of a high gain parametric amplifier,” arXiv 1808.10258 (2018).

Danzmann, K.

S. Steinlechner, J. Bauchrowitz, M. Meinders, H. Müller-Ebhardt, K. Danzmann, and R. Schnabel, “Quantum-dense metrology,” Nat. Photonics 7, 626–630 (2013).
[Crossref]

Devgan, P. S.

Dowling, J. P.

X. Ma, C. You, S. Adhikari, E. S. Matekole, R. T. Glasser, H. Lee, and J. P. Dowling, “Sub-shot-noise-limited phase estimation via SU(1,1) interferometer with thermal states,” Opt. Express 26, 18492–18504 (2018).
[Crossref] [PubMed]

S. Adhikari, N. Bhusal, C. You, H. Lee, and J. P. Dowling, “Phase estimation in an SU(1,1) interferometer with displaced squeezed states,” OSA Continuum 1, 438–450 (2018).
[Crossref]

D. Li, B. T. Gard, Y. Gao, C.-H. Yuan, W. Zhang, H. Lee, and J. P. Dowling, “Phase sensitivity at the Heisenberg limit in an SU(1,1) interferometer via parity detection,” Phys. Rev. A 94, 063840 (2016).
[Crossref]

W. N. Plick, J. P. Dowling, and G. S. Agarwal, “Coherent-light-boosted, sub-shot noise, quantum interferometry,” New J. Phys. 12, 083014 (2010).
[Crossref]

Evans, M.

Y. Ma, H. Miao, B. H. Pang, M. Evans, C. Zhao, J. Harms, R. Schnabel, and Y. Chen, “Proposal for gravitational-wave detection beyond the standard quantum limit through EPR entanglement,” Nat. Phys. 13, 776 (2017).
[Crossref]

Fayolle, P.

J.-A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267 (1993).
[Crossref] [PubMed]

Forward, R. L.

R. L. Forward, “Wideband laser-interferometer graviational-radiation experiment,” Phys. Rev. D 17, 379–390 (1978).
[Crossref]

Gao, Y.

D. Li, B. T. Gard, Y. Gao, C.-H. Yuan, W. Zhang, H. Lee, and J. P. Dowling, “Phase sensitivity at the Heisenberg limit in an SU(1,1) interferometer via parity detection,” Phys. Rev. A 94, 063840 (2016).
[Crossref]

Gard, B. T.

D. Li, B. T. Gard, Y. Gao, C.-H. Yuan, W. Zhang, H. Lee, and J. P. Dowling, “Phase sensitivity at the Heisenberg limit in an SU(1,1) interferometer via parity detection,” Phys. Rev. A 94, 063840 (2016).
[Crossref]

Garreau, J.

J.-A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267 (1993).
[Crossref] [PubMed]

Giovannetti, V.

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
[Crossref] [PubMed]

Glasser, R. T.

Grangier, P.

J.-A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267 (1993).
[Crossref] [PubMed]

P. Grangier, R. E. Slusher, B. Yurke, and A. Laporta, “Squeezed-light enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).
[Crossref] [PubMed]

Grigoryan, V.

Guo, J.

B. Chen, C. Qiu, S. Chen, J. Guo, L. Chen, Z. Ou, and W. Zhang, “Atom-light hybrid interferometer,” Phys. Rev. Lett. 115, 043602 (2015).
[Crossref] [PubMed]

Guo, X.

X. Guo, X. Li, N. Liu, and Z. Y. Ou, “Quantum information tapping using a fiber optical parametric amplifier with noise figure improved by correlated inputs,” Sci. Rep. 6, 30214 (2016).
[Crossref] [PubMed]

X. Guo, N. Liu, Y. Liu, X. Li, and Z. Y. Ou, “Generation of continuous variable quantum entanglement using a fiber optical parametric amplifier,” Opt. Lett. 41, 653 (2016).
[Crossref] [PubMed]

X. Guo, X. Li, N. Liu, L. Yang, and Z. Y. Ou, “An all-fiber source of pulsed twin beams for quantum communication,” Appl. Phys. Lett. 101, 261111 (2012).
[Crossref]

Gupta, P.

Harms, J.

Y. Ma, H. Miao, B. H. Pang, M. Evans, C. Zhao, J. Harms, R. Schnabel, and Y. Chen, “Proposal for gravitational-wave detection beyond the standard quantum limit through EPR entanglement,” Nat. Phys. 13, 776 (2017).
[Crossref]

Hermann-Avigliano, C.

Horrom, T.

Hu, X.-L.

X.-L. Hu, D. Li, L. Q. Chen, K. Zhang, W. Zhang, and C.-H. Yuan, “Phase estimation for an SU(1,1) interferometer in the presence of phase diffusion and photon losses,” Phys. Rev. A 98, 023803 (2018).
[Crossref]

Hudelist, F.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
[Crossref] [PubMed]

Huo, N.

J. Li, Y. Liu, L. Cui, N. Huo, S. M. Assad, X. Li, and Z. Y. Ou, “Joint measurement of multiple noncommuting parameters,” Phys. Rev. A 97, 052127 (2018).
[Crossref]

Y. Liu, J. Li, L. Cui, N. Huo, S. M. Assad, X. Li, and Z. Y. Ou, “Loss-tolerant quantum dense metrology with SU(1,1) interferometer,” Opt. Express 26, 27705–27715 (2018).
[Crossref] [PubMed]

J. Li, Y. Liu, N. Huo, L. Cui, X. Li, and Z. Ou, “Loss-tolerant measurement of continuous-variable quantum entanglement with the aid of a high gain parametric amplifier,” arXiv 1808.10258 (2018).

Jing, J.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
[Crossref] [PubMed]

J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99, 011110 (2011).
[Crossref]

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright einstein-podolsky-rosen beam,” Phys. Rev. Lett. 88, 047904 (2002).
[Crossref] [PubMed]

Jones, K. M.

Khalili, F.

M. Manceau, G. Leuchs, F. Khalili, and M. Chekhova, “Detection loss tolerant supersensitive phase measurement with an SU(1,1) interferometer,” Phys. Rev. Lett. 119, 223604 (2017).
[Crossref] [PubMed]

Kimble, H. J.

S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A 61, 042302 (2000).
[Crossref]

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

Klauder, J. R.

B. Yurke, S. L. McCall, and J. R. Klauder, “SU(2) and SU(1,1) interferometers,” Phys. Rev. A 33, 4033–4054 (1986).
[Crossref]

Kong, J.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
[Crossref] [PubMed]

J. Kong, Z. Y. Ou, and W. Zhang, “Phase-measurement sensitivity beyond the standard quantum limit in an interferometer consisting of a parametric amplifier and a beam splitter,” Phys. Rev. A 87, 023825 (2013).
[Crossref]

Kumar, P.

Laporta, A.

P. Grangier, R. E. Slusher, B. Yurke, and A. Laporta, “Squeezed-light enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).
[Crossref] [PubMed]

Lasri, J.

Lee, H.

Lett, P. D.

P. Gupta, B. L. Schmittberger, B. E. Anderson, K. M. Jones, and P. D. Lett, “Optimized phase sensing in a truncated SU(1,1) interferometer,” Opt. Express 26, 391–401 (2018).
[Crossref] [PubMed]

B. E. Anderson, B. L. Schmittberger, P. Gupta, K. M. Jones, and P. D. Lett, “Optimal phase measurements with bright- and vacuum-seeded SU(1,1) interferometers,” Phys. Rev. A 95, 063843 (2017).
[Crossref]

B. E. Anderson, P. Gupta, B. L. Schmittberger, T. Horrom, C. Hermann-Avigliano, K. M. Jones, and P. D. Lett, “Phase sensing beyond the standard quantum limit with a variation on the SU(1,1) interferometer,” Optica 4, 752–756 (2017).
[Crossref]

A. M. Marino, N. V. Corzo Trejo, and P. D. Lett, “Effect of losses on the performance of an SU(1,1) interferometer,” Phys. Rev. A 86, 023844 (2012).
[Crossref]

Leuchs, G.

M. Manceau, G. Leuchs, F. Khalili, and M. Chekhova, “Detection loss tolerant supersensitive phase measurement with an SU(1,1) interferometer,” Phys. Rev. Lett. 119, 223604 (2017).
[Crossref] [PubMed]

Levenson, J.-A.

J.-A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267 (1993).
[Crossref] [PubMed]

Li, D.

X.-L. Hu, D. Li, L. Q. Chen, K. Zhang, W. Zhang, and C.-H. Yuan, “Phase estimation for an SU(1,1) interferometer in the presence of phase diffusion and photon losses,” Phys. Rev. A 98, 023803 (2018).
[Crossref]

D. Li, B. T. Gard, Y. Gao, C.-H. Yuan, W. Zhang, H. Lee, and J. P. Dowling, “Phase sensitivity at the Heisenberg limit in an SU(1,1) interferometer via parity detection,” Phys. Rev. A 94, 063840 (2016).
[Crossref]

D. Li, C.-H. Yuan, Z. Y. Ou, and W. Zhang, “The phase sensitivity of an SU(1,1) interferometer with homodyne detection,” New J. Phys. 16, 073020 (2014).
[Crossref]

Li, J.

J. Li, Y. Liu, L. Cui, N. Huo, S. M. Assad, X. Li, and Z. Y. Ou, “Joint measurement of multiple noncommuting parameters,” Phys. Rev. A 97, 052127 (2018).
[Crossref]

Y. Liu, J. Li, L. Cui, N. Huo, S. M. Assad, X. Li, and Z. Y. Ou, “Loss-tolerant quantum dense metrology with SU(1,1) interferometer,” Opt. Express 26, 27705–27715 (2018).
[Crossref] [PubMed]

J. Li, Y. Liu, N. Huo, L. Cui, X. Li, and Z. Ou, “Loss-tolerant measurement of continuous-variable quantum entanglement with the aid of a high gain parametric amplifier,” arXiv 1808.10258 (2018).

Li, X.

J. Li, Y. Liu, L. Cui, N. Huo, S. M. Assad, X. Li, and Z. Y. Ou, “Joint measurement of multiple noncommuting parameters,” Phys. Rev. A 97, 052127 (2018).
[Crossref]

Y. Liu, J. Li, L. Cui, N. Huo, S. M. Assad, X. Li, and Z. Y. Ou, “Loss-tolerant quantum dense metrology with SU(1,1) interferometer,” Opt. Express 26, 27705–27715 (2018).
[Crossref] [PubMed]

X. Guo, N. Liu, Y. Liu, X. Li, and Z. Y. Ou, “Generation of continuous variable quantum entanglement using a fiber optical parametric amplifier,” Opt. Lett. 41, 653 (2016).
[Crossref] [PubMed]

X. Guo, X. Li, N. Liu, and Z. Y. Ou, “Quantum information tapping using a fiber optical parametric amplifier with noise figure improved by correlated inputs,” Sci. Rep. 6, 30214 (2016).
[Crossref] [PubMed]

X. Guo, X. Li, N. Liu, L. Yang, and Z. Y. Ou, “An all-fiber source of pulsed twin beams for quantum communication,” Appl. Phys. Lett. 101, 261111 (2012).
[Crossref]

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright einstein-podolsky-rosen beam,” Phys. Rev. Lett. 88, 047904 (2002).
[Crossref] [PubMed]

J. Li, Y. Liu, N. Huo, L. Cui, X. Li, and Z. Ou, “Loss-tolerant measurement of continuous-variable quantum entanglement with the aid of a high gain parametric amplifier,” arXiv 1808.10258 (2018).

Liu, C.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
[Crossref] [PubMed]

J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99, 011110 (2011).
[Crossref]

Liu, N.

X. Guo, N. Liu, Y. Liu, X. Li, and Z. Y. Ou, “Generation of continuous variable quantum entanglement using a fiber optical parametric amplifier,” Opt. Lett. 41, 653 (2016).
[Crossref] [PubMed]

X. Guo, X. Li, N. Liu, and Z. Y. Ou, “Quantum information tapping using a fiber optical parametric amplifier with noise figure improved by correlated inputs,” Sci. Rep. 6, 30214 (2016).
[Crossref] [PubMed]

X. Guo, X. Li, N. Liu, L. Yang, and Z. Y. Ou, “An all-fiber source of pulsed twin beams for quantum communication,” Appl. Phys. Lett. 101, 261111 (2012).
[Crossref]

Liu, Y.

J. Li, Y. Liu, L. Cui, N. Huo, S. M. Assad, X. Li, and Z. Y. Ou, “Joint measurement of multiple noncommuting parameters,” Phys. Rev. A 97, 052127 (2018).
[Crossref]

Y. Liu, J. Li, L. Cui, N. Huo, S. M. Assad, X. Li, and Z. Y. Ou, “Loss-tolerant quantum dense metrology with SU(1,1) interferometer,” Opt. Express 26, 27705–27715 (2018).
[Crossref] [PubMed]

X. Guo, N. Liu, Y. Liu, X. Li, and Z. Y. Ou, “Generation of continuous variable quantum entanglement using a fiber optical parametric amplifier,” Opt. Lett. 41, 653 (2016).
[Crossref] [PubMed]

J. Li, Y. Liu, N. Huo, L. Cui, X. Li, and Z. Ou, “Loss-tolerant measurement of continuous-variable quantum entanglement with the aid of a high gain parametric amplifier,” arXiv 1808.10258 (2018).

Lloyd, S.

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
[Crossref] [PubMed]

Ma, X.

Ma, Y.

Y. Ma, H. Miao, B. H. Pang, M. Evans, C. Zhao, J. Harms, R. Schnabel, and Y. Chen, “Proposal for gravitational-wave detection beyond the standard quantum limit through EPR entanglement,” Nat. Phys. 13, 776 (2017).
[Crossref]

Maccone, L.

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
[Crossref] [PubMed]

Manceau, M.

M. Manceau, G. Leuchs, F. Khalili, and M. Chekhova, “Detection loss tolerant supersensitive phase measurement with an SU(1,1) interferometer,” Phys. Rev. Lett. 119, 223604 (2017).
[Crossref] [PubMed]

Marino, A. M.

A. M. Marino, N. V. Corzo Trejo, and P. D. Lett, “Effect of losses on the performance of an SU(1,1) interferometer,” Phys. Rev. A 86, 023844 (2012).
[Crossref]

Matekole, E. S.

McCall, S. L.

B. Yurke, S. L. McCall, and J. R. Klauder, “SU(2) and SU(1,1) interferometers,” Phys. Rev. A 33, 4033–4054 (1986).
[Crossref]

Meinders, M.

S. Steinlechner, J. Bauchrowitz, M. Meinders, H. Müller-Ebhardt, K. Danzmann, and R. Schnabel, “Quantum-dense metrology,” Nat. Photonics 7, 626–630 (2013).
[Crossref]

Miao, H.

Y. Ma, H. Miao, B. H. Pang, M. Evans, C. Zhao, J. Harms, R. Schnabel, and Y. Chen, “Proposal for gravitational-wave detection beyond the standard quantum limit through EPR entanglement,” Nat. Phys. 13, 776 (2017).
[Crossref]

Michelson, A. A.

A. A. Michelson and E. W. Morley, “On the relative motion of the earth and of the luminiferous ether,” Am. J. Sci. 34, 333 (1887).
[Crossref]

Morley, E. W.

A. A. Michelson and E. W. Morley, “On the relative motion of the earth and of the luminiferous ether,” Am. J. Sci. 34, 333 (1887).
[Crossref]

Müller-Ebhardt, H.

S. Steinlechner, J. Bauchrowitz, M. Meinders, H. Müller-Ebhardt, K. Danzmann, and R. Schnabel, “Quantum-dense metrology,” Nat. Photonics 7, 626–630 (2013).
[Crossref]

Ou, Z.

B. Chen, C. Qiu, S. Chen, J. Guo, L. Chen, Z. Ou, and W. Zhang, “Atom-light hybrid interferometer,” Phys. Rev. Lett. 115, 043602 (2015).
[Crossref] [PubMed]

J. Li, Y. Liu, N. Huo, L. Cui, X. Li, and Z. Ou, “Loss-tolerant measurement of continuous-variable quantum entanglement with the aid of a high gain parametric amplifier,” arXiv 1808.10258 (2018).

Ou, Z. Y.

J. Li, Y. Liu, L. Cui, N. Huo, S. M. Assad, X. Li, and Z. Y. Ou, “Joint measurement of multiple noncommuting parameters,” Phys. Rev. A 97, 052127 (2018).
[Crossref]

Y. Liu, J. Li, L. Cui, N. Huo, S. M. Assad, X. Li, and Z. Y. Ou, “Loss-tolerant quantum dense metrology with SU(1,1) interferometer,” Opt. Express 26, 27705–27715 (2018).
[Crossref] [PubMed]

X. Guo, N. Liu, Y. Liu, X. Li, and Z. Y. Ou, “Generation of continuous variable quantum entanglement using a fiber optical parametric amplifier,” Opt. Lett. 41, 653 (2016).
[Crossref] [PubMed]

X. Guo, X. Li, N. Liu, and Z. Y. Ou, “Quantum information tapping using a fiber optical parametric amplifier with noise figure improved by correlated inputs,” Sci. Rep. 6, 30214 (2016).
[Crossref] [PubMed]

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
[Crossref] [PubMed]

D. Li, C.-H. Yuan, Z. Y. Ou, and W. Zhang, “The phase sensitivity of an SU(1,1) interferometer with homodyne detection,” New J. Phys. 16, 073020 (2014).
[Crossref]

J. Kong, Z. Y. Ou, and W. Zhang, “Phase-measurement sensitivity beyond the standard quantum limit in an interferometer consisting of a parametric amplifier and a beam splitter,” Phys. Rev. A 87, 023825 (2013).
[Crossref]

Z. Y. Ou, “Enhancement of the phase-measurement sensitivity beyond the standard quantum limit by a nonlinear interferometer,” Phys. Rev. A 85, 023815 (2012).
[Crossref]

X. Guo, X. Li, N. Liu, L. Yang, and Z. Y. Ou, “An all-fiber source of pulsed twin beams for quantum communication,” Appl. Phys. Lett. 101, 261111 (2012).
[Crossref]

J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99, 011110 (2011).
[Crossref]

Pan, Q.

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright einstein-podolsky-rosen beam,” Phys. Rev. Lett. 88, 047904 (2002).
[Crossref] [PubMed]

Pang, B. H.

Y. Ma, H. Miao, B. H. Pang, M. Evans, C. Zhao, J. Harms, R. Schnabel, and Y. Chen, “Proposal for gravitational-wave detection beyond the standard quantum limit through EPR entanglement,” Nat. Phys. 13, 776 (2017).
[Crossref]

Peng, K.

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright einstein-podolsky-rosen beam,” Phys. Rev. Lett. 88, 047904 (2002).
[Crossref] [PubMed]

Plick, W. N.

W. N. Plick, J. P. Dowling, and G. S. Agarwal, “Coherent-light-boosted, sub-shot noise, quantum interferometry,” New J. Phys. 12, 083014 (2010).
[Crossref]

Qiu, C.

B. Chen, C. Qiu, S. Chen, J. Guo, L. Chen, Z. Ou, and W. Zhang, “Atom-light hybrid interferometer,” Phys. Rev. Lett. 115, 043602 (2015).
[Crossref] [PubMed]

Rivera, T.

J.-A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267 (1993).
[Crossref] [PubMed]

Schmittberger, B. L.

Schnabel, R.

Y. Ma, H. Miao, B. H. Pang, M. Evans, C. Zhao, J. Harms, R. Schnabel, and Y. Chen, “Proposal for gravitational-wave detection beyond the standard quantum limit through EPR entanglement,” Nat. Phys. 13, 776 (2017).
[Crossref]

S. Steinlechner, J. Bauchrowitz, M. Meinders, H. Müller-Ebhardt, K. Danzmann, and R. Schnabel, “Quantum-dense metrology,” Nat. Photonics 7, 626–630 (2013).
[Crossref]

Serkland, D. K.

Shapiro, J. H.

Slusher, R. E.

P. Grangier, R. E. Slusher, B. Yurke, and A. Laporta, “Squeezed-light enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).
[Crossref] [PubMed]

Steinlechner, S.

S. Steinlechner, J. Bauchrowitz, M. Meinders, H. Müller-Ebhardt, K. Danzmann, and R. Schnabel, “Quantum-dense metrology,” Nat. Photonics 7, 626–630 (2013).
[Crossref]

Tang, R.

Vasilyev, M.

Wu, L.-A.

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

Xiao, M.

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

Xie, C.

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright einstein-podolsky-rosen beam,” Phys. Rev. Lett. 88, 047904 (2002).
[Crossref] [PubMed]

Yang, L.

X. Guo, X. Li, N. Liu, L. Yang, and Z. Y. Ou, “An all-fiber source of pulsed twin beams for quantum communication,” Appl. Phys. Lett. 101, 261111 (2012).
[Crossref]

You, C.

Yuan, C.-H.

X.-L. Hu, D. Li, L. Q. Chen, K. Zhang, W. Zhang, and C.-H. Yuan, “Phase estimation for an SU(1,1) interferometer in the presence of phase diffusion and photon losses,” Phys. Rev. A 98, 023803 (2018).
[Crossref]

D. Li, B. T. Gard, Y. Gao, C.-H. Yuan, W. Zhang, H. Lee, and J. P. Dowling, “Phase sensitivity at the Heisenberg limit in an SU(1,1) interferometer via parity detection,” Phys. Rev. A 94, 063840 (2016).
[Crossref]

D. Li, C.-H. Yuan, Z. Y. Ou, and W. Zhang, “The phase sensitivity of an SU(1,1) interferometer with homodyne detection,” New J. Phys. 16, 073020 (2014).
[Crossref]

Yurke, B.

P. Grangier, R. E. Slusher, B. Yurke, and A. Laporta, “Squeezed-light enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).
[Crossref] [PubMed]

B. Yurke, S. L. McCall, and J. R. Klauder, “SU(2) and SU(1,1) interferometers,” Phys. Rev. A 33, 4033–4054 (1986).
[Crossref]

Zhang, J.

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright einstein-podolsky-rosen beam,” Phys. Rev. Lett. 88, 047904 (2002).
[Crossref] [PubMed]

Zhang, K.

X.-L. Hu, D. Li, L. Q. Chen, K. Zhang, W. Zhang, and C.-H. Yuan, “Phase estimation for an SU(1,1) interferometer in the presence of phase diffusion and photon losses,” Phys. Rev. A 98, 023803 (2018).
[Crossref]

Zhang, W.

X.-L. Hu, D. Li, L. Q. Chen, K. Zhang, W. Zhang, and C.-H. Yuan, “Phase estimation for an SU(1,1) interferometer in the presence of phase diffusion and photon losses,” Phys. Rev. A 98, 023803 (2018).
[Crossref]

D. Li, B. T. Gard, Y. Gao, C.-H. Yuan, W. Zhang, H. Lee, and J. P. Dowling, “Phase sensitivity at the Heisenberg limit in an SU(1,1) interferometer via parity detection,” Phys. Rev. A 94, 063840 (2016).
[Crossref]

B. Chen, C. Qiu, S. Chen, J. Guo, L. Chen, Z. Ou, and W. Zhang, “Atom-light hybrid interferometer,” Phys. Rev. Lett. 115, 043602 (2015).
[Crossref] [PubMed]

D. Li, C.-H. Yuan, Z. Y. Ou, and W. Zhang, “The phase sensitivity of an SU(1,1) interferometer with homodyne detection,” New J. Phys. 16, 073020 (2014).
[Crossref]

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
[Crossref] [PubMed]

J. Kong, Z. Y. Ou, and W. Zhang, “Phase-measurement sensitivity beyond the standard quantum limit in an interferometer consisting of a parametric amplifier and a beam splitter,” Phys. Rev. A 87, 023825 (2013).
[Crossref]

J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99, 011110 (2011).
[Crossref]

Zhao, C.

Y. Ma, H. Miao, B. H. Pang, M. Evans, C. Zhao, J. Harms, R. Schnabel, and Y. Chen, “Proposal for gravitational-wave detection beyond the standard quantum limit through EPR entanglement,” Nat. Phys. 13, 776 (2017).
[Crossref]

Zhou, Z.

J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99, 011110 (2011).
[Crossref]

Am. J. Sci. (1)

A. A. Michelson and E. W. Morley, “On the relative motion of the earth and of the luminiferous ether,” Am. J. Sci. 34, 333 (1887).
[Crossref]

Appl. Phys. Lett. (2)

J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99, 011110 (2011).
[Crossref]

X. Guo, X. Li, N. Liu, L. Yang, and Z. Y. Ou, “An all-fiber source of pulsed twin beams for quantum communication,” Appl. Phys. Lett. 101, 261111 (2012).
[Crossref]

Nat. Commun. (1)

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
[Crossref] [PubMed]

Nat. Photonics (1)

S. Steinlechner, J. Bauchrowitz, M. Meinders, H. Müller-Ebhardt, K. Danzmann, and R. Schnabel, “Quantum-dense metrology,” Nat. Photonics 7, 626–630 (2013).
[Crossref]

Nat. Phys. (1)

Y. Ma, H. Miao, B. H. Pang, M. Evans, C. Zhao, J. Harms, R. Schnabel, and Y. Chen, “Proposal for gravitational-wave detection beyond the standard quantum limit through EPR entanglement,” Nat. Phys. 13, 776 (2017).
[Crossref]

New J. Phys. (2)

W. N. Plick, J. P. Dowling, and G. S. Agarwal, “Coherent-light-boosted, sub-shot noise, quantum interferometry,” New J. Phys. 12, 083014 (2010).
[Crossref]

D. Li, C.-H. Yuan, Z. Y. Ou, and W. Zhang, “The phase sensitivity of an SU(1,1) interferometer with homodyne detection,” New J. Phys. 16, 073020 (2014).
[Crossref]

Opt. Express (4)

Opt. Lett. (3)

Optica (1)

OSA Continuum (1)

Phys. Rev. A (9)

X.-L. Hu, D. Li, L. Q. Chen, K. Zhang, W. Zhang, and C.-H. Yuan, “Phase estimation for an SU(1,1) interferometer in the presence of phase diffusion and photon losses,” Phys. Rev. A 98, 023803 (2018).
[Crossref]

J. Kong, Z. Y. Ou, and W. Zhang, “Phase-measurement sensitivity beyond the standard quantum limit in an interferometer consisting of a parametric amplifier and a beam splitter,” Phys. Rev. A 87, 023825 (2013).
[Crossref]

B. E. Anderson, B. L. Schmittberger, P. Gupta, K. M. Jones, and P. D. Lett, “Optimal phase measurements with bright- and vacuum-seeded SU(1,1) interferometers,” Phys. Rev. A 95, 063843 (2017).
[Crossref]

J. Li, Y. Liu, L. Cui, N. Huo, S. M. Assad, X. Li, and Z. Y. Ou, “Joint measurement of multiple noncommuting parameters,” Phys. Rev. A 97, 052127 (2018).
[Crossref]

D. Li, B. T. Gard, Y. Gao, C.-H. Yuan, W. Zhang, H. Lee, and J. P. Dowling, “Phase sensitivity at the Heisenberg limit in an SU(1,1) interferometer via parity detection,” Phys. Rev. A 94, 063840 (2016).
[Crossref]

Z. Y. Ou, “Enhancement of the phase-measurement sensitivity beyond the standard quantum limit by a nonlinear interferometer,” Phys. Rev. A 85, 023815 (2012).
[Crossref]

A. M. Marino, N. V. Corzo Trejo, and P. D. Lett, “Effect of losses on the performance of an SU(1,1) interferometer,” Phys. Rev. A 86, 023844 (2012).
[Crossref]

S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A 61, 042302 (2000).
[Crossref]

B. Yurke, S. L. McCall, and J. R. Klauder, “SU(2) and SU(1,1) interferometers,” Phys. Rev. A 33, 4033–4054 (1986).
[Crossref]

Phys. Rev. D (2)

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

R. L. Forward, “Wideband laser-interferometer graviational-radiation experiment,” Phys. Rev. D 17, 379–390 (1978).
[Crossref]

Phys. Rev. Lett. (7)

M. Manceau, G. Leuchs, F. Khalili, and M. Chekhova, “Detection loss tolerant supersensitive phase measurement with an SU(1,1) interferometer,” Phys. Rev. Lett. 119, 223604 (2017).
[Crossref] [PubMed]

B. Chen, C. Qiu, S. Chen, J. Guo, L. Chen, Z. Ou, and W. Zhang, “Atom-light hybrid interferometer,” Phys. Rev. Lett. 115, 043602 (2015).
[Crossref] [PubMed]

J.-A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267 (1993).
[Crossref] [PubMed]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
[Crossref] [PubMed]

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

P. Grangier, R. E. Slusher, B. Yurke, and A. Laporta, “Squeezed-light enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).
[Crossref] [PubMed]

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright einstein-podolsky-rosen beam,” Phys. Rev. Lett. 88, 047904 (2002).
[Crossref] [PubMed]

Reports Prog. Phys. (1)

B. Abbott, R. Abbott, R. Adhikari, P. Ajith, B. Allen, G. Allen, R. Amin, S. Anderson, W. Anderson, M. Arain, and et al.., “Ligo: the laser interferometer gravitational-wave observatory,” Reports Prog. Phys. 72, 076901 (2009).
[Crossref]

Sci. Rep. (1)

X. Guo, X. Li, N. Liu, and Z. Y. Ou, “Quantum information tapping using a fiber optical parametric amplifier with noise figure improved by correlated inputs,” Sci. Rep. 6, 30214 (2016).
[Crossref] [PubMed]

Other (1)

J. Li, Y. Liu, N. Huo, L. Cui, X. Li, and Z. Ou, “Loss-tolerant measurement of continuous-variable quantum entanglement with the aid of a high gain parametric amplifier,” arXiv 1808.10258 (2018).

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 Typical phase measurement by homodyne detection with (a) classical coherent state and (b) coherent squeezed state. OPA, optical parametric amplifier; PM, phase modulator; HD, homodyne detection; Ips, phase sensing field intensity; BS, beam splitter with transmission efficiency of 1 - η is used to model non-ideal detection efficiency.
Fig. 2
Fig. 2 Phase measurement schemes with entangled source generated from an optical parametric amplifier (OPA1). (a), single-beam sensing SU(1,1) interferometer; (b), dual-beam sensing SU(1,1) interferometer; (c), direct joint measurement scheme. PM, phase modulator; HD1-2, homodyne detection; Ips, phase sensing field intensity. BS, beam splitter with transmission efficiency of 1 − η is used to model non-ideal detection efficiency; ki, electronic variable gain; JM, joint measurement.
Fig. 3
Fig. 3 Experiment setup. OPA1-2, optical parametric amplifiers; P1-2, pump for OPA1-2; F1-3, band-reflection filter centering at 1550 nm; DSF1-2. dispersion shifted fiber; PM, phase modulator; CWDM, coarse wavelength division multiplexer; HD1-2, homodyne detectors; LOs(LOi), local oscillator for signal (idler) field; PZT1-3, piezo-electric transducer; ki, electronic variable gain; JM, joint measurement.
Fig. 4
Fig. 4 The spectrums from HD1, HD2 and joint measurement (JM) for the measurement of a phase modulation signal at 1.56 MHz. The noise levels are all normalized to the shot noise level of HD1 at 0 dB. (a) Direct measurement by HD1 with a coherent probe beam when P1 = P2 = 0; (b): Measurement from SUI when P1 = 2mW and P2 = 4mW; (c): Measurement with entangled probe beams (truncated SUI scheme) when P1=2mW and P2=0. The black line in JM of (c) is the shot noise level SNRsi of the joint quantity Δ i = i s + k i i i (ki = 1), which is exactly 3 dB above the shot noise level at 0 dB for individual HD1.

Equations (14)

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

S N R H D = 4 | α | 2 δ 2 = 4 I p s δ 2 ,
S N R S Q = 4 | α | 2 δ 2 / S = 4 I p s δ 2 ( G + g ) 2
1 / S 1 = 1 / [ S + η / ( 1 η ) ]
S N R S U I = 2 I p s δ 2 ( G 1 + g 1 ) 2 .
ϕ S U I = ϕ s + ϕ i 2 ϕ p
S N R H D 1 = 4 ( G 1 G 2 + g 1 g 2 ) 2 | α | 2 δ 2 ( G 2 G 1 g 2 g 1 ) 2 + ( G 2 g 1 g 2 G 1 ) 2 S N R H D 2 = 4 ( G 1 g 2 + g 1 G 2 ) 2 | α | 2 δ 2 ( G 2 G 1 g 2 g 1 ) 2 + ( G 2 g 1 g 2 G 1 ) 2
S N R H D 1 ( o p ) = S N R H D 2 ( o p ) = 2 ( G 1 + g 1 ) 4 I p s δ 2 / ( G 1 2 + g 1 2 ) 4 ( G 1 + g 1 ) 2 I p s δ 2  for  g 1 1
Y ^ J M = Y ^ H D 1 + k i Y ^ H D 2
1 / S 3 1 / [ S + η / 2 G 2 2 ( 1 η ) ]
1 / S 3 1 / [ S + η / 4 G 2 2 ( 1 η ) ]
S N R i n = 4 I p s δ 2 ( G 1 + g 1 ) 2 ,
T H D 1 , H D 2 S N R H D 1 , H D 2 ( o p ) S N R i n = ( G 1 + g 1 ) 2 2 ( G 1 2 + g 1 2 ) 1  for  g 1 1 ,
S N R H D 2 ( o p ) ( A M ) = 2 I p s ϵ 2 / ( G 1 2 + g 1 2 ) .
S N R H D 1 ( o p ) ( P M ) + S N R H D 1 ( o p ) ( A M ) = 4 ( G 1 + g 1 ) 2 I p s δ 2 .

Metrics