Abstract

An SU(1,1) interferometer, which replaces the beam splitters in a Mach–Zehnder interferometer with nonlinear interactions, offers the potential of achieving improved phase sensitivity in applications with low optical powers. We present a novel variation on the SU(1,1) interferometer in which the second nonlinear interaction is replaced with balanced homodyne detection. We show theoretically that this “truncated SU(1,1) interferometer” can achieve the same potential phase sensitivity as the conventional SU(1,1) interferometer. We build an experimental realization of this device using seeded four-wave mixing in Rb85 vapor as the nonlinear interaction, thus employing a bright two-mode squeezed state as the phase-sensing quantum state inside the interferometer. Measurements as a function of operating point show that even with 35% loss, this device can surpass the standard quantum limit by 4 dB. This device is simpler to build and operate than the conventional SU(1,1) interferometer, and also eliminates some sources of loss, thus making it useful for applications in precision metrology.

© 2017 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  4. D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
    [Crossref]
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  6. M. Xiao, L.-A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59, 278–281 (1987).
    [Crossref]
  7. P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light—enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).
    [Crossref]
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    [Crossref]
  9. M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett. 71, 1355–1358 (1993).
    [Crossref]
  10. G. Y. Xiang, B. L. Higgins, D. W. Berry, H. M. Wiseman, and G. J. Pryde, “Entanglement-enhanced measurement of a completely unknown optical phase,” Nat. Photonics 5, 43–47 (2010).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  22. H. Bachor and T. Ralph, A Guide to Experiments in Quantum Optics (Wiley, 2004).
  23. C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
    [Crossref]
  24. 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,” arXiv:1704.04261 (2017), accepted for publication in Phys. Rev. A.
  25. L. Pezzé, A. Smerzi, G. Khoury, J. F. Hodelin, and D. Bouwmeester, “Phase detection at the quantum limit with multiphoton Mach–Zehnder interferometry,” Phys. Rev. Lett. 99, 223602 (2007).
    [Crossref]

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 (2)

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]

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]

2013 (1)

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 (5)

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]

A. Crespi, M. Lobino, J. C. F. Matthews, A. Politi, C. R. Neal, R. Ramponi, R. Osellame, and J. L. O’Brien, “Measuring protein concentration with entangled photons,” Appl. Phys. Lett. 100, 233704 (2012).
[Crossref]

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, 1514–1517 (2012).
[Crossref]

M. Jarzyna and R. Demkowicz-Dobrzański, “Quantum interferometry with and without an external phase reference,” Phys. Rev. A 85, 011801 (2012).
[Crossref]

2011 (1)

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

2010 (3)

C. Gross, T. Zibold, E. Nicklas, J. Estève, and M. K. Oberthaler, “Nonlinear atom interferometer surpasses classical precision limit,” Nature 464, 1165–1169 (2010).
[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]

G. Y. Xiang, B. L. Higgins, D. W. Berry, H. M. Wiseman, and G. J. Pryde, “Entanglement-enhanced measurement of a completely unknown optical phase,” Nat. Photonics 5, 43–47 (2010).
[Crossref]

2009 (1)

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102, 040403 (2009).
[Crossref]

2008 (1)

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
[Crossref]

2007 (1)

L. Pezzé, A. Smerzi, G. Khoury, J. F. Hodelin, and D. Bouwmeester, “Phase detection at the quantum limit with multiphoton Mach–Zehnder interferometry,” Phys. Rev. Lett. 99, 223602 (2007).
[Crossref]

2004 (1)

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429, 161–164 (2004).
[Crossref]

2002 (1)

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[Crossref]

1993 (1)

M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett. 71, 1355–1358 (1993).
[Crossref]

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]

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

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]

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]

Anderson, B. E.

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,” arXiv:1704.04261 (2017), accepted for publication in Phys. Rev. A.

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, 1514–1517 (2012).
[Crossref]

Bachor, H.

H. Bachor and T. Ralph, A Guide to Experiments in Quantum Optics (Wiley, 2004).

Banaszek, K.

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102, 040403 (2009).
[Crossref]

Ben-Kish, A.

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[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, 1514–1517 (2012).
[Crossref]

G. Y. Xiang, B. L. Higgins, D. W. Berry, H. M. Wiseman, and G. J. Pryde, “Entanglement-enhanced measurement of a completely unknown optical phase,” Nat. Photonics 5, 43–47 (2010).
[Crossref]

Bouwmeester, D.

L. Pezzé, A. Smerzi, G. Khoury, J. F. Hodelin, and D. Bouwmeester, “Phase detection at the quantum limit with multiphoton Mach–Zehnder interferometry,” Phys. Rev. Lett. 99, 223602 (2007).
[Crossref]

Boyer, V.

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
[Crossref]

Britton, J.

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[Crossref]

Burnett, K.

M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett. 71, 1355–1358 (1993).
[Crossref]

Caves, C. M.

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

Crespi, A.

A. Crespi, M. Lobino, J. C. F. Matthews, A. Politi, C. R. Neal, R. Ramponi, R. Osellame, and J. L. O’Brien, “Measuring protein concentration with entangled photons,” Appl. Phys. Lett. 100, 233704 (2012).
[Crossref]

DeMarco, B.

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[Crossref]

Demkowicz-Dobrzanski, R.

M. Jarzyna and R. Demkowicz-Dobrzański, “Quantum interferometry with and without an external phase reference,” Phys. Rev. A 85, 011801 (2012).
[Crossref]

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102, 040403 (2009).
[Crossref]

Dorner, U.

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102, 040403 (2009).
[Crossref]

Dowling, J. P.

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]

Estève, J.

C. Gross, T. Zibold, E. Nicklas, J. Estève, and M. K. Oberthaler, “Nonlinear atom interferometer surpasses classical precision limit,” Nature 464, 1165–1169 (2010).
[Crossref]

Furusawa, 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, 1514–1517 (2012).
[Crossref]

Giovannetti, V.

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

Grangier, P.

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

Gross, C.

C. Gross, T. Zibold, E. Nicklas, J. Estève, and M. K. Oberthaler, “Nonlinear atom interferometer surpasses classical precision limit,” Nature 464, 1165–1169 (2010).
[Crossref]

Gupta, P.

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,” arXiv:1704.04261 (2017), accepted for publication in Phys. Rev. A.

Higgins, B. L.

G. Y. Xiang, B. L. Higgins, D. W. Berry, H. M. Wiseman, and G. J. Pryde, “Entanglement-enhanced measurement of a completely unknown optical phase,” Nat. Photonics 5, 43–47 (2010).
[Crossref]

Hodelin, J. F.

L. Pezzé, A. Smerzi, G. Khoury, J. F. Hodelin, and D. Bouwmeester, “Phase detection at the quantum limit with multiphoton Mach–Zehnder interferometry,” Phys. Rev. Lett. 99, 223602 (2007).
[Crossref]

Holland, M. J.

M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett. 71, 1355–1358 (1993).
[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]

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, 1514–1517 (2012).
[Crossref]

Itano, W. M.

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[Crossref]

Iwasawa, 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, 1514–1517 (2012).
[Crossref]

Jarzyna, M.

M. Jarzyna and R. Demkowicz-Dobrzański, “Quantum interferometry with and without an external phase reference,” Phys. Rev. A 85, 011801 (2012).
[Crossref]

Jelenkovic, B.

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[Crossref]

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]

Jones, K. M.

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,” arXiv:1704.04261 (2017), accepted for publication in Phys. Rev. A.

Khoury, G.

L. Pezzé, A. Smerzi, G. Khoury, J. F. Hodelin, and D. Bouwmeester, “Phase detection at the quantum limit with multiphoton Mach–Zehnder interferometry,” Phys. Rev. Lett. 99, 223602 (2007).
[Crossref]

Kimble, H. J.

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

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]

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]

Langer, C.

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[Crossref]

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]

Leibfried, D.

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[Crossref]

Lett, P. D.

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]

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
[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,” arXiv:1704.04261 (2017), accepted for publication in Phys. Rev. A.

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]

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]

Lloyd, S.

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

Lobino, M.

A. Crespi, M. Lobino, J. C. F. Matthews, A. Politi, C. R. Neal, R. Ramponi, R. Osellame, and J. L. O’Brien, “Measuring protein concentration with entangled photons,” Appl. Phys. Lett. 100, 233704 (2012).
[Crossref]

Lundeen, J. S.

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102, 040403 (2009).
[Crossref]

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429, 161–164 (2004).
[Crossref]

Maccone, L.

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

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
[Crossref]

Matthews, J. C. F.

A. Crespi, M. Lobino, J. C. F. Matthews, A. Politi, C. R. Neal, R. Ramponi, R. Osellame, and J. L. O’Brien, “Measuring protein concentration with entangled photons,” Appl. Phys. Lett. 100, 233704 (2012).
[Crossref]

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]

McCormick, C. F.

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
[Crossref]

Meyer, V.

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[Crossref]

Mitchell, M. W.

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429, 161–164 (2004).
[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, 1514–1517 (2012).
[Crossref]

Neal, C. R.

A. Crespi, M. Lobino, J. C. F. Matthews, A. Politi, C. R. Neal, R. Ramponi, R. Osellame, and J. L. O’Brien, “Measuring protein concentration with entangled photons,” Appl. Phys. Lett. 100, 233704 (2012).
[Crossref]

Nicklas, E.

C. Gross, T. Zibold, E. Nicklas, J. Estève, and M. K. Oberthaler, “Nonlinear atom interferometer surpasses classical precision limit,” Nature 464, 1165–1169 (2010).
[Crossref]

O’Brien, J. L.

A. Crespi, M. Lobino, J. C. F. Matthews, A. Politi, C. R. Neal, R. Ramponi, R. Osellame, and J. L. O’Brien, “Measuring protein concentration with entangled photons,” Appl. Phys. Lett. 100, 233704 (2012).
[Crossref]

Oberthaler, M. K.

C. Gross, T. Zibold, E. Nicklas, J. Estève, and M. K. Oberthaler, “Nonlinear atom interferometer surpasses classical precision limit,” Nature 464, 1165–1169 (2010).
[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, 1514–1517 (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]

Osellame, R.

A. Crespi, M. Lobino, J. C. F. Matthews, A. Politi, C. R. Neal, R. Ramponi, R. Osellame, and J. L. O’Brien, “Measuring protein concentration with entangled photons,” Appl. Phys. Lett. 100, 233704 (2012).
[Crossref]

Ou, Z. Y.

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]

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]

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]

Pezzé, L.

L. Pezzé, A. Smerzi, G. Khoury, J. F. Hodelin, and D. Bouwmeester, “Phase detection at the quantum limit with multiphoton Mach–Zehnder interferometry,” Phys. Rev. Lett. 99, 223602 (2007).
[Crossref]

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]

Politi, A.

A. Crespi, M. Lobino, J. C. F. Matthews, A. Politi, C. R. Neal, R. Ramponi, R. Osellame, and J. L. O’Brien, “Measuring protein concentration with entangled photons,” Appl. Phys. Lett. 100, 233704 (2012).
[Crossref]

Pryde, G. J.

G. Y. Xiang, B. L. Higgins, D. W. Berry, H. M. Wiseman, and G. J. Pryde, “Entanglement-enhanced measurement of a completely unknown optical phase,” Nat. Photonics 5, 43–47 (2010).
[Crossref]

Ralph, T.

H. Bachor and T. Ralph, A Guide to Experiments in Quantum Optics (Wiley, 2004).

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, 1514–1517 (2012).
[Crossref]

Ramponi, R.

A. Crespi, M. Lobino, J. C. F. Matthews, A. Politi, C. R. Neal, R. Ramponi, R. Osellame, and J. L. O’Brien, “Measuring protein concentration with entangled photons,” Appl. Phys. Lett. 100, 233704 (2012).
[Crossref]

Rosenband, T.

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[Crossref]

Rowe, M.

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[Crossref]

Schmittberger, B. L.

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,” arXiv:1704.04261 (2017), accepted for publication in Phys. Rev. A.

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]

Smerzi, A.

L. Pezzé, A. Smerzi, G. Khoury, J. F. Hodelin, and D. Bouwmeester, “Phase detection at the quantum limit with multiphoton Mach–Zehnder interferometry,” Phys. Rev. Lett. 99, 223602 (2007).
[Crossref]

Smith, B. J.

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102, 040403 (2009).
[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]

Steinberg, A. M.

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429, 161–164 (2004).
[Crossref]

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, 1514–1517 (2012).
[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, 1514–1517 (2012).
[Crossref]

Walmsley, I. A.

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102, 040403 (2009).
[Crossref]

Wasilewski, W.

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102, 040403 (2009).
[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, 1514–1517 (2012).
[Crossref]

Wineland, D. J.

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[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, 1514–1517 (2012).
[Crossref]

G. Y. Xiang, B. L. Higgins, D. W. Berry, H. M. Wiseman, and G. J. Pryde, “Entanglement-enhanced measurement of a completely unknown optical phase,” Nat. Photonics 5, 43–47 (2010).
[Crossref]

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]

Xiang, G. Y.

G. Y. Xiang, B. L. Higgins, D. W. Berry, H. M. Wiseman, and G. J. Pryde, “Entanglement-enhanced measurement of a completely unknown optical phase,” Nat. Photonics 5, 43–47 (2010).
[Crossref]

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]

Yonezawa, 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, 1514–1517 (2012).
[Crossref]

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]

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]

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, W.

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]

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]

Zibold, T.

C. Gross, T. Zibold, E. Nicklas, J. Estève, and M. K. Oberthaler, “Nonlinear atom interferometer surpasses classical precision limit,” Nature 464, 1165–1169 (2010).
[Crossref]

Appl. Phys. Lett. (1)

A. Crespi, M. Lobino, J. C. F. Matthews, A. Politi, C. R. Neal, R. Ramponi, R. Osellame, and J. L. O’Brien, “Measuring protein concentration with entangled photons,” Appl. Phys. Lett. 100, 233704 (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]

Nat. Photonics (2)

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

G. Y. Xiang, B. L. Higgins, D. W. Berry, H. M. Wiseman, and G. J. Pryde, “Entanglement-enhanced measurement of a completely unknown optical phase,” Nat. Photonics 5, 43–47 (2010).
[Crossref]

Nature (2)

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429, 161–164 (2004).
[Crossref]

C. Gross, T. Zibold, E. Nicklas, J. Estève, and M. K. Oberthaler, “Nonlinear atom interferometer surpasses classical precision limit,” Nature 464, 1165–1169 (2010).
[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 coherent and squeezed-vacuum light,” New J. Phys. 16, 073020 (2014).
[Crossref]

Phys. Rev. A (7)

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

M. Jarzyna and R. Demkowicz-Dobrzański, “Quantum interferometry with and without an external phase reference,” Phys. Rev. A 85, 011801 (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]

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

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
[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]

Phys. Rev. D (1)

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

Phys. Rev. Lett. (6)

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[Crossref]

M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett. 71, 1355–1358 (1993).
[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]

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

L. Pezzé, A. Smerzi, G. Khoury, J. F. Hodelin, and D. Bouwmeester, “Phase detection at the quantum limit with multiphoton Mach–Zehnder interferometry,” Phys. Rev. Lett. 99, 223602 (2007).
[Crossref]

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102, 040403 (2009).
[Crossref]

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, 1514–1517 (2012).
[Crossref]

Other (2)

H. Bachor and T. Ralph, A Guide to Experiments in Quantum Optics (Wiley, 2004).

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,” arXiv:1704.04261 (2017), accepted for publication in Phys. Rev. A.

Supplementary Material (1)

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» Supplement 1: PDF (865 KB)      Supplement 1

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Figures (4)

Fig. 1.
Fig. 1.

Overview of the SU(1,1)-type phase-measurement device: a coherent state and a vacuum state are mixed with a pump beam in a nonlinear optical medium (NLO) to produce a two-mode quantum state. A phase shift ϕ is applied to the seeded arm. The detection scheme is referenced to the input phase ϕ0. (a) The full SU(1,1) interferometer recombines the two-mode squeezed state with a pump beam, phase-shifted by π/2, in a second nonlinear process, and then detects the output modes using (i) two homodyne detectors (HDs), (ii) one HD on the unseeded mode, (iii) direct intensity detection of only the unseeded mode, or (iv) direct detection in both modes. (b) The truncated SU(1,1) interferometer consists of the first nonlinear interaction, followed by two homodyne detectors (scheme v) that directly collect the two-mode quantum state.

Fig. 2.
Fig. 2.

Theoretical prediction for the variance of the phase estimation Δ2ϕ times |α|2, in the case of no loss, as a function of gain, calculated from Eq. (1) with SNR=1 [24]. The black, solid curve (i, v) defines the optimal phase sensitivities for the full and truncated SU(1,1) interferometers using both HDs (schemes i and v). This curve is also equivalent to |α|2/FC for each detection scheme. The red (short-dashed) and black (long-dashed) curves are the phase sensitivities for the full SU(1,1) interferometer using just a conjugate detector (HD or intensity, schemes ii and iii), and for both intensity detectors (scheme iv), respectively. The gray circles are |α|2/FQ, and represent the fundamental phase sensitivity of the two-mode squeezed state.

Fig. 3.
Fig. 3.

(a) The experimental setup consists of a strong pump beam (power 400  mW, 1/e2 beam waist 0.7 mm) and orthogonally polarized weak probe beam (power 100  nW, 1/e2 beam waist 0.4 mm) propagating at a small angle (4  mrad) through a warm rubidium vapor (temperature 105 °C). After the cell, the pump beam is blocked using a Glan–Taylor polarizer, and the probe and conjugate beams propagate to separate balanced HDs. The local oscillators for each HD are generated using a similar 4WM setup, resulting in local oscillator powers of 1  mW. The sum of the AC photocurrents is sent to the spectrum analyzer. (b) We pump the D1 5S1/25P1/2 transition in Rb85. Here, Δ700  MHz, and νHF=3.03  GHz is the hyperfine splitting between the F=2 and F=3 ground state sublevels. The 4WM generates a conjugate field (blue) that is 6.06 GHz higher in frequency than the applied probe field (red). (c) The probe HD setup consists of a local oscillator (LO) propagating through an electro-optic modulator (EOM) and reflecting off a piezo-electric-transducer-mounted mirror (PZT). The LO mixes with the probe beam on a 50/50 beam splitter, and each output is sent to a subtracting detector. The conjugate HD setup does not contain an EOM.

Fig. 4.
Fig. 4.

(a) An example SNR measurement (resolution bandwidth 30 kHz) using two-mode squeezed beams (blue, solid) and coherent beams (red, dashed), with identical optical power in the phase-sensing (probe) beam path. (b) The SNRI as a function of ϕp. The inset shows the region where we observe an improvement beyond the SQL. The red curve is from Eq. (3) with best-fit parameters η=0.65 and intrinsic gain G=3.3. The black, dashed curve shows the potential improvement (SNRIFC) that could be obtained by additional signal processing as derived from the classical Fisher information in Eq. (5) using those fit parameters. The uncertainties are statistical, one standard deviation for 10 measurements.

Equations (6)

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

SNR=[(ϕX)Δϕ]2Δ2X,
X=Xp(ϕp)+Xc(ϕc),
Δ2ϕtSUI=2η+(12η)sech2(r)2ηsin(ϕp)tanh(r)2η|α|2sin2(ϕp),
FQ=2cosh2(r)[(1+2|α|2)cosh(2r)1].
FC=(ϕX)2+2(ϕΔX)2Δ2X.
SNRI=10log10Δ2ϕtSUIΔ2ϕcoh,