Abstract

In this paper, we propose a protocol for the estimation of angular displacement based upon orbital angular momentum and an SU(1,1)-SU(2) hybrid interferometer. This interferometer consists of an optical parametric amplifier, a beam splitter, and reflection mirrors; the balanced homodyne detection is used as the detection strategy. The results indicate that super-resolution and super-sensitivity can be achieved with an ideal scenario. Additionally, we study the effect of photon loss on resolution and sensitivity, and the robustness of our protocol is also discussed. Finally, the advantage of our protocol compared with an SU(1,1) protocol is demonstrated, and the merits of orbital angular momentum-enhanced protocol are summarized.

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

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References

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  1. V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
    [Crossref]
  2. J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
    [Crossref]
  3. L. Cen, Z. Zhang, J. Zhang, S. Li, Y. Sun, L. Yan, Y. Zhao, and F. Wang, “State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting,” Phys. Rev. A 96, 053846 (2017).
    [Crossref]
  4. O. S. Magaña Loaiza, M. Mirhosseini, B. Rodenburg, and R. W. Boyd, “Amplification of angular rotations using weak measurements,” Phys. Rev. Lett. 112, 200401 (2014).
    [Crossref]
  5. J. Zhang, Z. Zhang, L. Cen, M. Yu, S. Li, F. Wang, and Y. Zhao, “Effects of imperfect elements on resolution and sensitivity of quantum metrology using two-mode squeezed vacuum state,” Opt. Express 25, 24907–24916 (2017).
    [Crossref] [PubMed]
  6. A. K. Jha, G. S. Agarwal, and R. W. Boyd, “Supersensitive measurement of angular displacements using entangled photons,” Phys. Rev. A 83, 053829 (2011).
    [Crossref]
  7. J. Liu, W. Liu, S. Li, D. Wei, H. Gao, and F. Li, “Enhancement of the angular rotation measurement sensitivity based on SU(2) and SU(1, 1) interferometers,” Photonics Res. 5, 617–622 (2017).
    [Crossref]
  8. W. Zhang, Q. Qi, J. Zhou, and L. Chen, “Mimicking faraday rotation to sort the orbital angular momentum of light,” Phys. Rev. Lett. 112, 153601 (2014).
    [Crossref] [PubMed]
  9. F. Wolfgramm, C. Vitelli, F. A. Beduini, N. Godbout, and M. W. Mitchell, “Entanglement-enhanced probing of a delicate material system,” Nat. Photon. 7, 28–32 (2012).
    [Crossref]
  10. R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
    [Crossref]
  11. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
    [Crossref] [PubMed]
  12. B. M. Escher, R. L. D. M. Filho, and L. Davidovich, “General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology,” Nat. Phys. 7, 406–411 (2011).
    [Crossref]
  13. M. D. Lang and C. M. Caves, “Optimal quantum-enhanced interferometry using a laser power source,” Phys. Rev. Lett. 111, 173601 (2013).
    [Crossref] [PubMed]
  14. 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]
  15. 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]
  16. 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]
  17. M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
    [Crossref]
  18. 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]
  19. C. Sparaciari, S. Olivares, and M. G. A. Paris, “Gaussian-state interferometry with passive and active elements,” Phys. Rev. A 93, 023810 (2016).
    [Crossref]
  20. W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys. 12, 113025 (2010).
    [Crossref]
  21. J. P. Dowling, “Quantum optical metrology-the lowdown on high-N00N states,” Contemp. Phys 49, 125–143 (2008).
    [Crossref]
  22. 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]
  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. D. Li, C.-H. Yuan, Z. Y. Ou, and W. Zhang, “The phase sensitivity of an SU(1,1) interferometer with coherent and squeezed-vacuum light,” New J. Phys. 16, 073020 (2014).
    [Crossref]

2018 (2)

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]

L. Cen, Z. Zhang, J. Zhang, S. Li, Y. Sun, L. Yan, Y. Zhao, and F. Wang, “State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting,” Phys. Rev. A 96, 053846 (2017).
[Crossref]

J. Liu, W. Liu, S. Li, D. Wei, H. Gao, and F. Li, “Enhancement of the angular rotation measurement sensitivity based on SU(2) and SU(1, 1) interferometers,” Photonics Res. 5, 617–622 (2017).
[Crossref]

J. Zhang, Z. Zhang, L. Cen, M. Yu, S. Li, F. Wang, and Y. Zhao, “Effects of imperfect elements on resolution and sensitivity of quantum metrology using two-mode squeezed vacuum state,” Opt. Express 25, 24907–24916 (2017).
[Crossref] [PubMed]

2016 (1)

C. Sparaciari, S. Olivares, and M. G. A. Paris, “Gaussian-state interferometry with passive and active elements,” Phys. Rev. A 93, 023810 (2016).
[Crossref]

2014 (3)

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

W. Zhang, Q. Qi, J. Zhou, and L. Chen, “Mimicking faraday rotation to sort the orbital angular momentum of light,” Phys. Rev. Lett. 112, 153601 (2014).
[Crossref] [PubMed]

O. S. Magaña Loaiza, M. Mirhosseini, B. Rodenburg, and R. W. Boyd, “Amplification of angular rotations using weak measurements,” Phys. Rev. Lett. 112, 200401 (2014).
[Crossref]

2013 (3)

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
[Crossref]

M. D. Lang and C. M. Caves, “Optimal quantum-enhanced interferometry using a laser power source,” Phys. Rev. Lett. 111, 173601 (2013).
[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]

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]

F. Wolfgramm, C. Vitelli, F. A. Beduini, N. Godbout, and M. W. Mitchell, “Entanglement-enhanced probing of a delicate material system,” Nat. Photon. 7, 28–32 (2012).
[Crossref]

2011 (3)

M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
[Crossref]

A. K. Jha, G. S. Agarwal, and R. W. Boyd, “Supersensitive measurement of angular displacements using entangled photons,” Phys. Rev. A 83, 053829 (2011).
[Crossref]

B. M. Escher, R. L. D. M. Filho, and L. Davidovich, “General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology,” Nat. Phys. 7, 406–411 (2011).
[Crossref]

2010 (1)

W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys. 12, 113025 (2010).
[Crossref]

2008 (1)

J. P. Dowling, “Quantum optical metrology-the lowdown on high-N00N states,” Contemp. Phys 49, 125–143 (2008).
[Crossref]

1998 (1)

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[Crossref]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref] [PubMed]

1936 (1)

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
[Crossref]

Adhikari, S.

Agarwal, G. S.

A. K. Jha, G. S. Agarwal, and R. W. Boyd, “Supersensitive measurement of angular displacements using entangled photons,” Phys. Rev. A 83, 053829 (2011).
[Crossref]

W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys. 12, 113025 (2010).
[Crossref]

Allen, L.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref] [PubMed]

Anderson, B. E.

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]

Anisimov, P. M.

W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys. 12, 113025 (2010).
[Crossref]

Aolita, L.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
[Crossref]

Beduini, F. A.

F. Wolfgramm, C. Vitelli, F. A. Beduini, N. Godbout, and M. W. Mitchell, “Entanglement-enhanced probing of a delicate material system,” Nat. Photon. 7, 28–32 (2012).
[Crossref]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref] [PubMed]

Beth, R. A.

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
[Crossref]

Boyd, R. W.

O. S. Magaña Loaiza, M. Mirhosseini, B. Rodenburg, and R. W. Boyd, “Amplification of angular rotations using weak measurements,” Phys. Rev. Lett. 112, 200401 (2014).
[Crossref]

A. K. Jha, G. S. Agarwal, and R. W. Boyd, “Supersensitive measurement of angular displacements using entangled photons,” Phys. Rev. A 83, 053829 (2011).
[Crossref]

Caves, C. M.

M. D. Lang and C. M. Caves, “Optimal quantum-enhanced interferometry using a laser power source,” Phys. Rev. Lett. 111, 173601 (2013).
[Crossref] [PubMed]

Cen, L.

J. Zhang, Z. Zhang, L. Cen, M. Yu, S. Li, F. Wang, and Y. Zhao, “Effects of imperfect elements on resolution and sensitivity of quantum metrology using two-mode squeezed vacuum state,” Opt. Express 25, 24907–24916 (2017).
[Crossref] [PubMed]

L. Cen, Z. Zhang, J. Zhang, S. Li, Y. Sun, L. Yan, Y. Zhao, and F. Wang, “State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting,” Phys. Rev. A 96, 053846 (2017).
[Crossref]

Chen, L.

W. Zhang, Q. Qi, J. Zhou, and L. Chen, “Mimicking faraday rotation to sort the orbital angular momentum of light,” Phys. Rev. Lett. 112, 153601 (2014).
[Crossref] [PubMed]

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]

Courtial, J.

M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
[Crossref]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[Crossref]

D’ambrosio, V.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
[Crossref]

Davidovich, L.

B. M. Escher, R. L. D. M. Filho, and L. Davidovich, “General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology,” Nat. Phys. 7, 406–411 (2011).
[Crossref]

Del Re, L.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
[Crossref]

Dholakia, K.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[Crossref]

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]

W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys. 12, 113025 (2010).
[Crossref]

J. P. Dowling, “Quantum optical metrology-the lowdown on high-N00N states,” Contemp. Phys 49, 125–143 (2008).
[Crossref]

Dudley, A.

M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
[Crossref]

Escher, B. M.

B. M. Escher, R. L. D. M. Filho, and L. Davidovich, “General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology,” Nat. Phys. 7, 406–411 (2011).
[Crossref]

Filho, R. L. D. M.

B. M. Escher, R. L. D. M. Filho, and L. Davidovich, “General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology,” Nat. Phys. 7, 406–411 (2011).
[Crossref]

Forbes, A.

M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
[Crossref]

Gao, H.

J. Liu, W. Liu, S. Li, D. Wei, H. Gao, and F. Li, “Enhancement of the angular rotation measurement sensitivity based on SU(2) and SU(1, 1) interferometers,” Photonics Res. 5, 617–622 (2017).
[Crossref]

Glasser, R. T.

Godbout, N.

F. Wolfgramm, C. Vitelli, F. A. Beduini, N. Godbout, and M. W. Mitchell, “Entanglement-enhanced probing of a delicate material system,” Nat. Photon. 7, 28–32 (2012).
[Crossref]

Gupta, P.

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]

Jha, A. K.

A. K. Jha, G. S. Agarwal, and R. W. Boyd, “Supersensitive measurement of angular displacements using entangled photons,” Phys. Rev. A 83, 053829 (2011).
[Crossref]

Jones, K. M.

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]

Kong, J.

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]

Kwek, L. C.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
[Crossref]

Lang, M. D.

M. D. Lang and C. M. Caves, “Optimal quantum-enhanced interferometry using a laser power source,” Phys. Rev. Lett. 111, 173601 (2013).
[Crossref] [PubMed]

Lavery, M. P. J.

M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
[Crossref]

Lee, H.

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]

W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys. 12, 113025 (2010).
[Crossref]

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]

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]

Li, D.

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

Li, F.

J. Liu, W. Liu, S. Li, D. Wei, H. Gao, and F. Li, “Enhancement of the angular rotation measurement sensitivity based on SU(2) and SU(1, 1) interferometers,” Photonics Res. 5, 617–622 (2017).
[Crossref]

Li, S.

J. Liu, W. Liu, S. Li, D. Wei, H. Gao, and F. Li, “Enhancement of the angular rotation measurement sensitivity based on SU(2) and SU(1, 1) interferometers,” Photonics Res. 5, 617–622 (2017).
[Crossref]

J. Zhang, Z. Zhang, L. Cen, M. Yu, S. Li, F. Wang, and Y. Zhao, “Effects of imperfect elements on resolution and sensitivity of quantum metrology using two-mode squeezed vacuum state,” Opt. Express 25, 24907–24916 (2017).
[Crossref] [PubMed]

L. Cen, Z. Zhang, J. Zhang, S. Li, Y. Sun, L. Yan, Y. Zhao, and F. Wang, “State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting,” Phys. Rev. A 96, 053846 (2017).
[Crossref]

Li, Y.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
[Crossref]

Liu, J.

J. Liu, W. Liu, S. Li, D. Wei, H. Gao, and F. Li, “Enhancement of the angular rotation measurement sensitivity based on SU(2) and SU(1, 1) interferometers,” Photonics Res. 5, 617–622 (2017).
[Crossref]

Liu, W.

J. Liu, W. Liu, S. Li, D. Wei, H. Gao, and F. Li, “Enhancement of the angular rotation measurement sensitivity based on SU(2) and SU(1, 1) interferometers,” Photonics Res. 5, 617–622 (2017).
[Crossref]

Ma, X.

Magaña Loaiza, O. S.

O. S. Magaña Loaiza, M. Mirhosseini, B. Rodenburg, and R. W. Boyd, “Amplification of angular rotations using weak measurements,” Phys. Rev. Lett. 112, 200401 (2014).
[Crossref]

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]

Marrucci, L.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
[Crossref]

Matekole, E. S.

Mirhosseini, M.

O. S. Magaña Loaiza, M. Mirhosseini, B. Rodenburg, and R. W. Boyd, “Amplification of angular rotations using weak measurements,” Phys. Rev. Lett. 112, 200401 (2014).
[Crossref]

Mitchell, M. W.

F. Wolfgramm, C. Vitelli, F. A. Beduini, N. Godbout, and M. W. Mitchell, “Entanglement-enhanced probing of a delicate material system,” Nat. Photon. 7, 28–32 (2012).
[Crossref]

Olivares, S.

C. Sparaciari, S. Olivares, and M. G. A. Paris, “Gaussian-state interferometry with passive and active elements,” Phys. Rev. A 93, 023810 (2016).
[Crossref]

Ou, Z. Y.

D. Li, C.-H. Yuan, Z. Y. Ou, and W. Zhang, “The phase sensitivity of an SU(1,1) interferometer with coherent and squeezed-vacuum light,” 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]

Padgett, M. J.

M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
[Crossref]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[Crossref]

Paris, M. G. A.

C. Sparaciari, S. Olivares, and M. G. A. Paris, “Gaussian-state interferometry with passive and active elements,” Phys. Rev. A 93, 023810 (2016).
[Crossref]

Plick, W. N.

W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys. 12, 113025 (2010).
[Crossref]

Qi, Q.

W. Zhang, Q. Qi, J. Zhou, and L. Chen, “Mimicking faraday rotation to sort the orbital angular momentum of light,” Phys. Rev. Lett. 112, 153601 (2014).
[Crossref] [PubMed]

Robertson, D. A.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[Crossref]

Rodenburg, B.

O. S. Magaña Loaiza, M. Mirhosseini, B. Rodenburg, and R. W. Boyd, “Amplification of angular rotations using weak measurements,” Phys. Rev. Lett. 112, 200401 (2014).
[Crossref]

Schmittberger, B. L.

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]

Sciarrino, F.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
[Crossref]

Slussarenko, S.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
[Crossref]

Spagnolo, N.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
[Crossref]

Sparaciari, C.

C. Sparaciari, S. Olivares, and M. G. A. Paris, “Gaussian-state interferometry with passive and active elements,” Phys. Rev. A 93, 023810 (2016).
[Crossref]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref] [PubMed]

Sun, Y.

L. Cen, Z. Zhang, J. Zhang, S. Li, Y. Sun, L. Yan, Y. Zhao, and F. Wang, “State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting,” Phys. Rev. A 96, 053846 (2017).
[Crossref]

Vitelli, C.

F. Wolfgramm, C. Vitelli, F. A. Beduini, N. Godbout, and M. W. Mitchell, “Entanglement-enhanced probing of a delicate material system,” Nat. Photon. 7, 28–32 (2012).
[Crossref]

Walborn, S. P.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
[Crossref]

Wang, F.

L. Cen, Z. Zhang, J. Zhang, S. Li, Y. Sun, L. Yan, Y. Zhao, and F. Wang, “State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting,” Phys. Rev. A 96, 053846 (2017).
[Crossref]

J. Zhang, Z. Zhang, L. Cen, M. Yu, S. Li, F. Wang, and Y. Zhao, “Effects of imperfect elements on resolution and sensitivity of quantum metrology using two-mode squeezed vacuum state,” Opt. Express 25, 24907–24916 (2017).
[Crossref] [PubMed]

Wei, D.

J. Liu, W. Liu, S. Li, D. Wei, H. Gao, and F. Li, “Enhancement of the angular rotation measurement sensitivity based on SU(2) and SU(1, 1) interferometers,” Photonics Res. 5, 617–622 (2017).
[Crossref]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref] [PubMed]

Wolfgramm, F.

F. Wolfgramm, C. Vitelli, F. A. Beduini, N. Godbout, and M. W. Mitchell, “Entanglement-enhanced probing of a delicate material system,” Nat. Photon. 7, 28–32 (2012).
[Crossref]

Yan, L.

L. Cen, Z. Zhang, J. Zhang, S. Li, Y. Sun, L. Yan, Y. Zhao, and F. Wang, “State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting,” Phys. Rev. A 96, 053846 (2017).
[Crossref]

You, C.

Yu, M.

Yuan, C.-H.

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

Zhang, J.

J. Zhang, Z. Zhang, L. Cen, M. Yu, S. Li, F. Wang, and Y. Zhao, “Effects of imperfect elements on resolution and sensitivity of quantum metrology using two-mode squeezed vacuum state,” Opt. Express 25, 24907–24916 (2017).
[Crossref] [PubMed]

L. Cen, Z. Zhang, J. Zhang, S. Li, Y. Sun, L. Yan, Y. Zhao, and F. Wang, “State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting,” Phys. Rev. A 96, 053846 (2017).
[Crossref]

Zhang, W.

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

W. Zhang, Q. Qi, J. Zhou, and L. Chen, “Mimicking faraday rotation to sort the orbital angular momentum of light,” Phys. Rev. Lett. 112, 153601 (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]

Zhang, Z.

J. Zhang, Z. Zhang, L. Cen, M. Yu, S. Li, F. Wang, and Y. Zhao, “Effects of imperfect elements on resolution and sensitivity of quantum metrology using two-mode squeezed vacuum state,” Opt. Express 25, 24907–24916 (2017).
[Crossref] [PubMed]

L. Cen, Z. Zhang, J. Zhang, S. Li, Y. Sun, L. Yan, Y. Zhao, and F. Wang, “State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting,” Phys. Rev. A 96, 053846 (2017).
[Crossref]

Zhao, Y.

L. Cen, Z. Zhang, J. Zhang, S. Li, Y. Sun, L. Yan, Y. Zhao, and F. Wang, “State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting,” Phys. Rev. A 96, 053846 (2017).
[Crossref]

J. Zhang, Z. Zhang, L. Cen, M. Yu, S. Li, F. Wang, and Y. Zhao, “Effects of imperfect elements on resolution and sensitivity of quantum metrology using two-mode squeezed vacuum state,” Opt. Express 25, 24907–24916 (2017).
[Crossref] [PubMed]

Zhou, J.

W. Zhang, Q. Qi, J. Zhou, and L. Chen, “Mimicking faraday rotation to sort the orbital angular momentum of light,” Phys. Rev. Lett. 112, 153601 (2014).
[Crossref] [PubMed]

Contemp. Phys (1)

J. P. Dowling, “Quantum optical metrology-the lowdown on high-N00N states,” Contemp. Phys 49, 125–143 (2008).
[Crossref]

Nat. Commun. (1)

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
[Crossref]

Nat. Photon. (1)

F. Wolfgramm, C. Vitelli, F. A. Beduini, N. Godbout, and M. W. Mitchell, “Entanglement-enhanced probing of a delicate material system,” Nat. Photon. 7, 28–32 (2012).
[Crossref]

Nat. Phys. (1)

B. M. Escher, R. L. D. M. Filho, and L. Davidovich, “General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology,” Nat. Phys. 7, 406–411 (2011).
[Crossref]

New J. Phys. (3)

M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
[Crossref]

W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys. 12, 113025 (2010).
[Crossref]

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

Opt. Express (3)

Photonics Res. (1)

J. Liu, W. Liu, S. Li, D. Wei, H. Gao, and F. Li, “Enhancement of the angular rotation measurement sensitivity based on SU(2) and SU(1, 1) interferometers,” Photonics Res. 5, 617–622 (2017).
[Crossref]

Phys. Rev. (1)

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
[Crossref]

Phys. Rev. A (8)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref] [PubMed]

C. Sparaciari, S. Olivares, and M. G. A. Paris, “Gaussian-state interferometry with passive and active elements,” Phys. Rev. A 93, 023810 (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]

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]

A. K. Jha, G. S. Agarwal, and R. W. Boyd, “Supersensitive measurement of angular displacements using entangled photons,” Phys. Rev. A 83, 053829 (2011).
[Crossref]

L. Cen, Z. Zhang, J. Zhang, S. Li, Y. Sun, L. Yan, Y. Zhao, and F. Wang, “State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting,” Phys. Rev. A 96, 053846 (2017).
[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]

Phys. Rev. Lett. (4)

O. S. Magaña Loaiza, M. Mirhosseini, B. Rodenburg, and R. W. Boyd, “Amplification of angular rotations using weak measurements,” Phys. Rev. Lett. 112, 200401 (2014).
[Crossref]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[Crossref]

W. Zhang, Q. Qi, J. Zhou, and L. Chen, “Mimicking faraday rotation to sort the orbital angular momentum of light,” Phys. Rev. Lett. 112, 153601 (2014).
[Crossref] [PubMed]

M. D. Lang and C. M. Caves, “Optimal quantum-enhanced interferometry using a laser power source,” Phys. Rev. Lett. 111, 173601 (2013).
[Crossref] [PubMed]

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Figures (8)

Fig. 1
Fig. 1 A schematic diagram of the OAM-enhanced angular displacement estimation protocol. The input coherent state and pump light enter a hybrid interferometer. Two sets of spiral phase plates (SPPs) and Dove prisms (DPs) modulate the OAM and introduce angular displacement, respectively, and the output signal is detected by two detectors. The other abbreviations are defined as follows: OPA-optical parametric amplifier, RM-reflection mirror, BS-beam splitter, D-detector.
Fig. 2
Fig. 2 Output signal with balanced homodyne detection as a function of angular displacement φ (radians) and phase angle θ (radians) in the case of g = 1, = 3, and |α|2 = 10.
Fig. 3
Fig. 3 Sensitivity with balanced homodyne detection as a function of angular displacement φ (radians) in the case of g = 2, = 1 and |α|2 = 100. Y and X are the optimal sensitivity and the value of angular displacement φ corresponding to the optimal sensitivity, respectively. The sensitivity sits at its minimum Δφ = 0.001275 when φ = π/2.
Fig. 4
Fig. 4 Sensitivity with balanced homodyne detection as a function of angular displacement φ (radians) and phase angle θ (radians) in the case of g = 1, = 3, and |α|2 = 10. The color bar on the right indicates the corresponding value of the sensitivity.
Fig. 5
Fig. 5 Optimal sensitivity with balanced homodyne detection (BHD) as a function of squeezing factor in the case of = 1 and different values of |α|2. The arrow shows the intersection points of sensitivities and QCRBs.
Fig. 6
Fig. 6 A simplified model for photon loss. Two virtual BSs are used to simulate photon loss. A and B are the operators for two vacuums.
Fig. 7
Fig. 7 Sensitivity with balanced homodyne detection (BHD) as a function of angular displacement φ (radians) in the case of g = 2, = 1, |α|2 = 100 and 38% loss in transmission process.
Fig. 8
Fig. 8 Maximum allowable loss with balanced homodyne detection as a function of squeezing factor in the case of l = 1 and different mean photon numbers of coherent state. The arrow shows the maxima of allowable loss curves.

Equations (29)

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

N = A ^ A ^ + B ^ B ^ = cosh ( 2 g ) | α | 2 + 2 sinh 2 g .
A ^ = a ^ cosh g + b ^ sinh g ,
B ^ = b ^ cosh g + a ^ sinh g ,
Δ φ SNL = 1 2 cosh ( 2 g ) | α | 2 + 2 sinh 2 g ,
Δ φ HL = 1 2 [ cosh ( 2 g ) | α | 2 + 2 sinh 2 g ] .
Δ φ Q = 1 2 sinh 2 ( 2 g ) + | α | 2 [ 1 + 2 cosh ( 2 g ) + cosh ( 4 g ) ] .
X ^ A = a ^ out + a ^ out ,
P ^ A = i ( a ^ out a ^ out ) .
X ^ A = 2 | α | [ cos ( θ + 2 φ ) cosh g + cos θ sinh g ] ,
a ^ out = 1 2 [ ( e i 2 φ a ^ + b ^ ) ν + ( a ^ + e i 2 φ b ^ ) μ ] ,
a ^ out = 1 2 [ ( e i 2 φ a ^ + b ^ ) ν + ( a ^ + e i 2 φ b ^ ) μ ] .
V = X A max X A min | X A max | + | X A min | ,
X ^ A 2 = cos ( 2 θ + 4 φ ) cosh 2 g | α | 2 + cos ( 2 θ ) sinh 2 g | α | 2 + cos ( 2 θ + 2 φ ) sinh ( 2 g ) | α | 2 + [ cosh ( 2 g ) + cos ( 2 φ ) sinh ( 2 g ) ] ( | α | 2 + 1 ) .
Δ X ^ A = X ^ A 2 X ^ A 2 = cosh ( 2 g ) + sinh ( 2 g ) cos ( 2 φ ) .
Δ φ = Δ X ^ A | X ^ A / φ | = cosh ( 2 g ) + sinh ( 2 g ) cos ( 2 φ ) 2 2 cosh g | α | sin ( θ + 2 φ ) .
θ + 2 φ = k π + π / 2
X ^ A L = T X ^ A ,
X ^ A 2 L = T X ^ A 2 + ( 1 T ) .
Δ φ L = T [ cosh ( 2 g ) + sinh ( 2 g ) cos ( 2 φ ) 1 ] + 1 2 2 T cosh g | α sin ( θ + 2 φ ) | .
Δ φ min 1 4 cosh g cosh ( 2 g ) | α |
U OPA = ( cosh g 0 sinh g 0 0 cosh g 0 sinh g sinh g 0 cosh g 0 0 sinh g 0 cosh g ) ,
U AD = ( cos ( 2 φ ) sin ( 2 φ ) 0 0 sin ( 2 φ ) cos ( 2 φ ) 0 0 0 0 1 0 0 0 0 1 ) ,
U BS = 1 2 ( 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 ) .
U ˜ OPA = U OPA I ( 4 ) ,
U ˜ AD = U AD I ( 4 ) ,
U ˜ VBS = ( T I ( 4 ) 1 T I ( 4 ) 1 T I ( 4 ) T I ( 4 ) ) 8 × 8 ,
U ˜ BS = U BS I ( 4 ) .
Δ φ min Δ φ Q = cosh ( 2 g ) sinh ( 2 g ) 2 cosh g 1 + 2 cosh ( 2 g ) + cosh ( 4 g ) = cosh ( 2 g ) sinh ( 2 g ) cosh g cosh ( g ) [ 1 + cosh ( 2 g ) ] 1 + cosh ( 2 g ) 2 cosh g = 1
Δ φ min = cosh ( 2 g ) sinh ( 2 g ) 2 2 cosh g | α | = 1 2 2 e 2 g cosh g | α | 1 4 cosh g cosh ( 2 g ) | α | .

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