Abstract

Photon-number squeezing and correlations enable measurement of absorption with an accuracy exceeding that of the shot-noise limit. However, sub-shot noise imaging and sensing based on these methods require high detection efficiency, which can be a serious obstacle if measurements are carried out in “difficult” spectral ranges. We show that this problem can be overcome through the phase-sensitive amplification before detection. Here we propose an experimental scheme of sub-shot-noise imaging with tolerance to detection losses.

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

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References

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  44. T. S. Iskhakov, V. C. Usenko, U. L. Andersen, R. Filip, M. V. Chekhova, and G. Leuchs, “Heralded source of bright multi-mode mesoscopic sub-poissonian light,” Opt. Lett. 41(10), 2149–2152 (2016).
    [Crossref] [PubMed]

2018 (2)

E. Losero, I. Ruo-Berchera, A. Meda, A. Avella, and M. Genovese, “Unbiased estimation of an optical loss at the ultimate quantum limit with twin-beams,” Sci. Rep. 8(1), 7431 (2018).
[Crossref] [PubMed]

E. Knyazev, K.Yu. Spasibko, F. Ya. Khalili, and M. Chekhova, “Quantum tomography enhanced through parametric amplification,” New J. Phys. 20(1), 013005 (2018).
[Crossref]

2017 (6)

R. Whittaker, C. Erven, A. Neville, M. Berry, J. L. O’Brien, H. Cable, and J. C. F. Matthews, “Absorption spectroscopy at the ultimate quantum limit from single-photon states,” New J. Phys. 19(2), 023013 (2017).
[Crossref]

P.-A. Moreau, J. Sabines-Chesterking, R. Whittaker, S. K. Joshi, P. M. Birchall, A. McMillan, J. G. Rarity, and J. C. F. Matthews, “Demonstrating an absolute quantum advantage in direct absorption measurement,” Sci. Rep. 7, 6256 (2017).
[Crossref] [PubMed]

N. Samantaray, I. Ruo-Berchera, A. Meda, and M. Genovese, “Realization of the first sub-shot-noise wide field microscope,” Light: Sci. Appl. 6, e17005 (2017).
[Crossref]

M. Manceau, F. Ya. Khalili, and M. Chekhova, “Improving the phase super-sensitivity of squeezing-assisted interferometers by squeeze factor unbalancing,” New J. Phys. 19(1), 013014 (2017).
[Crossref]

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

O. Hosten, R. Krishnakumar, N. J. Engelsen, and M. A. Kasevich, “Quantum phase magnification,” Science 352(6293), 1552–1555 (2017).
[Crossref]

2016 (3)

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

H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
[Crossref]

T. S. Iskhakov, V. C. Usenko, U. L. Andersen, R. Filip, M. V. Chekhova, and G. Leuchs, “Heralded source of bright multi-mode mesoscopic sub-poissonian light,” Opt. Lett. 41(10), 2149–2152 (2016).
[Crossref] [PubMed]

2015 (1)

S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, “Microwave quantum illumination,” Phys. Rev. Lett. 114, 080503 (2015).
[Crossref] [PubMed]

2014 (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]

2013 (3)

E. D. Lopaeva, I. Ruo-Berchera, I. P. Degiovanni, S. Olivares, G. Brida, and M. Genovese, “Experimental realization of quantum illumination,” Phys. Rev. Lett. 110, 153603 (2013).
[Crossref] [PubMed]

J. Hodgkinson and R. P. Tatam, “Optical gas sensing: a review,” Meas. Sci. Technol. 24(1), 012004 (2013).
[Crossref]

J. Kong, J. Jing, H. Wang, F. Hudelist, C. Liu, and W. Zhang, “Experimental investigation of the visibility dependence in a nonlinear interferometer using parametric amplifiers,” Appl. Phys. Lett. 102, 011130 (2013).
[Crossref]

2012 (1)

A. M. Marino, N. V. C. Trejo, and P. D. Lett, “Effect of losses on the performance of an su(1,1) interferometer,” Phys. Rev. A 86, 023844 (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 (2)

I. N. Agafonov, M. V. Chekhova, and G. Leuchs, “Two-color bright squeezed vacuum,” Phys. Rev. A 82, 011801 (2010).
[Crossref]

G. Brida, M. Genovese, and I. Ruo-Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227 (2010).
[Crossref]

2009 (2)

G. Adesso, F. Dell’Anno, S. De Siena, F. Illuminati, and L. A. M. Souza, “Optimal estimation of losses at the ultimate quantum limit with non-Gaussian states,” Phys. Rev. A 79, 040305 (2009).
[Crossref]

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. Ruo-Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[Crossref] [PubMed]

2008 (3)

S. Lloyd, “Enhanced sensitivity of photodetection via quantum illumination,” Science 321(5895), 1463–1465 (2008).
[Crossref] [PubMed]

S.-H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, “Quantum illumination with Gaussian states,” Phys. Rev. Lett. 101, 253601 (2008).
[Crossref] [PubMed]

E. Brambilla, L. Caspani, O. Jedrkiewicz, L. A. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A 77, 053807 (2008).
[Crossref]

2007 (1)

A. Monras and M. G. A. Paris, “Optimal quantum estimation of loss in bosonic channels,” Phys. Rev. Lett. 98, 160401 (2007).
[Crossref] [PubMed]

2004 (2)

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93243601 (2004).
[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: Beating the standard quantum limit,” Science 306, 1330–1336 (2004).
[Crossref] [PubMed]

2000 (1)

S. Kasapi, S. Lathi, and Y. Yamamoto, “Sub-shot-noise frequency-modulation spectroscopy by use of amplitude-squeezed light from semiconductor lasers,” J. Opt. Soc. Am. B 17(2), 275–279 (2000).
[Crossref]

1999 (1)

S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless optical amplification of images,” Phys. Rev. Lett. 83, 1938–1941 (1999).
[Crossref]

1997 (1)

P. H. Souto Ribeiro, C. Schwob, A. Maître, and C. Fabre, “Sub-shot-noise high-sensitivity spectroscopy with optical parametric oscillator twin beams,” Opt. Lett. 22(24), 1893–1895 (1997).
[Crossref]

1996 (1)

V. B. Braginsky and F. Ya. Khalili, “Quantum nondemolition measurements: the route from toys to tools,” Rev. Mod. Phys. 68, 1–11 (1996).
[Crossref]

1993 (1)

U. Leonhardt and H. Paul, “Realistic optical homodyne measurements and quasiprobability distributions,” Phys. Rev. A 48, 4598–4604 (1993).
[Crossref] [PubMed]

1992 (1)

E. S. Polzik, J. Carri, and H. J. Kimble, “Spectroscopy with squeezed light,” Phys. Rev. Lett. 68, 3020–3023 (1992).
[Crossref] [PubMed]

1991 (1)

P. R. Tapster, S. F. Seward, and J. G. Rarity, “Sub-shot-noise measurement of modulated absorption using parametric down-conversion,” Phys. Rev. A 44, 3266–3269 (1991).
[Crossref] [PubMed]

1988 (1)

M. Xiao, L.-A. Wu, and H. J. Kimble, “Detection of amplitude modulation with squeezed light for sensitivity beyond the shot-noise limit,” Opt. Lett. 13(6), 476–478 (1988).
[Crossref] [PubMed]

1986 (2)

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

E. Jakeman and J. G. Rarity, “The use of pair production processes to reduce quantum noise in transmission measurements,” Opt. Comm. 59(3), 219–223 (1986).
[Crossref]

1981 (1)

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

Adesso, G.

G. Adesso, F. Dell’Anno, S. De Siena, F. Illuminati, and L. A. M. Souza, “Optimal estimation of losses at the ultimate quantum limit with non-Gaussian states,” Phys. Rev. A 79, 040305 (2009).
[Crossref]

Agafonov, I. N.

I. N. Agafonov, M. V. Chekhova, and G. Leuchs, “Two-color bright squeezed vacuum,” Phys. Rev. A 82, 011801 (2010).
[Crossref]

Andersen, U. L.

T. S. Iskhakov, V. C. Usenko, U. L. Andersen, R. Filip, M. V. Chekhova, and G. Leuchs, “Heralded source of bright multi-mode mesoscopic sub-poissonian light,” Opt. Lett. 41(10), 2149–2152 (2016).
[Crossref] [PubMed]

Avella, A.

E. Losero, I. Ruo-Berchera, A. Meda, A. Avella, and M. Genovese, “Unbiased estimation of an optical loss at the ultimate quantum limit with twin-beams,” Sci. Rep. 8(1), 7431 (2018).
[Crossref] [PubMed]

Bache, M.

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93243601 (2004).
[Crossref]

Barzanjeh, S.

S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, “Microwave quantum illumination,” Phys. Rev. Lett. 114, 080503 (2015).
[Crossref] [PubMed]

Berry, M.

R. Whittaker, C. Erven, A. Neville, M. Berry, J. L. O’Brien, H. Cable, and J. C. F. Matthews, “Absorption spectroscopy at the ultimate quantum limit from single-photon states,” New J. Phys. 19(2), 023013 (2017).
[Crossref]

Birchall, P. M.

P.-A. Moreau, J. Sabines-Chesterking, R. Whittaker, S. K. Joshi, P. M. Birchall, A. McMillan, J. G. Rarity, and J. C. F. Matthews, “Demonstrating an absolute quantum advantage in direct absorption measurement,” Sci. Rep. 7, 6256 (2017).
[Crossref] [PubMed]

Braginsky, V. B.

V. B. Braginsky and F. Ya. Khalili, “Quantum nondemolition measurements: the route from toys to tools,” Rev. Mod. Phys. 68, 1–11 (1996).
[Crossref]

Brambilla, E.

E. Brambilla, L. Caspani, O. Jedrkiewicz, L. A. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A 77, 053807 (2008).
[Crossref]

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93243601 (2004).
[Crossref]

Brida, G.

E. D. Lopaeva, I. Ruo-Berchera, I. P. Degiovanni, S. Olivares, G. Brida, and M. Genovese, “Experimental realization of quantum illumination,” Phys. Rev. Lett. 110, 153603 (2013).
[Crossref] [PubMed]

G. Brida, M. Genovese, and I. Ruo-Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227 (2010).
[Crossref]

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. Ruo-Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[Crossref] [PubMed]

Cable, H.

R. Whittaker, C. Erven, A. Neville, M. Berry, J. L. O’Brien, H. Cable, and J. C. F. Matthews, “Absorption spectroscopy at the ultimate quantum limit from single-photon states,” New J. Phys. 19(2), 023013 (2017).
[Crossref]

Carri, J.

E. S. Polzik, J. Carri, and H. J. Kimble, “Spectroscopy with squeezed light,” Phys. Rev. Lett. 68, 3020–3023 (1992).
[Crossref] [PubMed]

Caspani, L.

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. Ruo-Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[Crossref] [PubMed]

E. Brambilla, L. Caspani, O. Jedrkiewicz, L. A. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A 77, 053807 (2008).
[Crossref]

Caves, C. M.

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

Chekhova, M.

E. Knyazev, K.Yu. Spasibko, F. Ya. Khalili, and M. Chekhova, “Quantum tomography enhanced through parametric amplification,” New J. Phys. 20(1), 013005 (2018).
[Crossref]

M. Manceau, F. Ya. Khalili, and M. Chekhova, “Improving the phase super-sensitivity of squeezing-assisted interferometers by squeeze factor unbalancing,” New J. Phys. 19(1), 013014 (2017).
[Crossref]

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

Chekhova, M. V.

T. S. Iskhakov, V. C. Usenko, U. L. Andersen, R. Filip, M. V. Chekhova, and G. Leuchs, “Heralded source of bright multi-mode mesoscopic sub-poissonian light,” Opt. Lett. 41(10), 2149–2152 (2016).
[Crossref] [PubMed]

I. N. Agafonov, M. V. Chekhova, and G. Leuchs, “Two-color bright squeezed vacuum,” Phys. Rev. A 82, 011801 (2010).
[Crossref]

Choi, S.-K.

S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless optical amplification of images,” Phys. Rev. Lett. 83, 1938–1941 (1999).
[Crossref]

Danzmann, K.

H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
[Crossref]

De Siena, S.

G. Adesso, F. Dell’Anno, S. De Siena, F. Illuminati, and L. A. M. Souza, “Optimal estimation of losses at the ultimate quantum limit with non-Gaussian states,” Phys. Rev. A 79, 040305 (2009).
[Crossref]

Degiovanni, I. P.

E. D. Lopaeva, I. Ruo-Berchera, I. P. Degiovanni, S. Olivares, G. Brida, and M. Genovese, “Experimental realization of quantum illumination,” Phys. Rev. Lett. 110, 153603 (2013).
[Crossref] [PubMed]

Dell’Anno, F.

G. Adesso, F. Dell’Anno, S. De Siena, F. Illuminati, and L. A. M. Souza, “Optimal estimation of losses at the ultimate quantum limit with non-Gaussian states,” Phys. Rev. A 79, 040305 (2009).
[Crossref]

Demkowicz-Dobrzanski, R.

R. Demkowicz-Dobrzanski, M. Jarzyna, and J. Kolodynski, Progress in Optics (Elsevier, 2015), Chap. 4.

Di Trapani, P.

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93243601 (2004).
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V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, 1999).
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Engelsen, N. J.

O. Hosten, R. Krishnakumar, N. J. Engelsen, and M. A. Kasevich, “Quantum phase magnification,” Science 352(6293), 1552–1555 (2017).
[Crossref]

Erkmen, B. I.

S.-H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, “Quantum illumination with Gaussian states,” Phys. Rev. Lett. 101, 253601 (2008).
[Crossref] [PubMed]

Erven, C.

R. Whittaker, C. Erven, A. Neville, M. Berry, J. L. O’Brien, H. Cable, and J. C. F. Matthews, “Absorption spectroscopy at the ultimate quantum limit from single-photon states,” New J. Phys. 19(2), 023013 (2017).
[Crossref]

Fabre, C.

P. H. Souto Ribeiro, C. Schwob, A. Maître, and C. Fabre, “Sub-shot-noise high-sensitivity spectroscopy with optical parametric oscillator twin beams,” Opt. Lett. 22(24), 1893–1895 (1997).
[Crossref]

Filip, R.

T. S. Iskhakov, V. C. Usenko, U. L. Andersen, R. Filip, M. V. Chekhova, and G. Leuchs, “Heralded source of bright multi-mode mesoscopic sub-poissonian light,” Opt. Lett. 41(10), 2149–2152 (2016).
[Crossref] [PubMed]

Gatti, A.

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. Ruo-Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[Crossref] [PubMed]

E. Brambilla, L. Caspani, O. Jedrkiewicz, L. A. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A 77, 053807 (2008).
[Crossref]

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93243601 (2004).
[Crossref]

Genovese, M.

E. Losero, I. Ruo-Berchera, A. Meda, A. Avella, and M. Genovese, “Unbiased estimation of an optical loss at the ultimate quantum limit with twin-beams,” Sci. Rep. 8(1), 7431 (2018).
[Crossref] [PubMed]

N. Samantaray, I. Ruo-Berchera, A. Meda, and M. Genovese, “Realization of the first sub-shot-noise wide field microscope,” Light: Sci. Appl. 6, e17005 (2017).
[Crossref]

E. D. Lopaeva, I. Ruo-Berchera, I. P. Degiovanni, S. Olivares, G. Brida, and M. Genovese, “Experimental realization of quantum illumination,” Phys. Rev. Lett. 110, 153603 (2013).
[Crossref] [PubMed]

G. Brida, M. Genovese, and I. Ruo-Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227 (2010).
[Crossref]

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. Ruo-Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[Crossref] [PubMed]

Giovannetti, V.

S.-H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, “Quantum illumination with Gaussian states,” Phys. Rev. Lett. 101, 253601 (2008).
[Crossref] [PubMed]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: Beating the standard quantum limit,” Science 306, 1330–1336 (2004).
[Crossref] [PubMed]

Guha, S.

S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, “Microwave quantum illumination,” Phys. Rev. Lett. 114, 080503 (2015).
[Crossref] [PubMed]

S.-H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, “Quantum illumination with Gaussian states,” Phys. Rev. Lett. 101, 253601 (2008).
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V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, 1999).
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O. Hosten, R. Krishnakumar, N. J. Engelsen, and M. A. Kasevich, “Quantum phase magnification,” Science 352(6293), 1552–1555 (2017).
[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]

J. Kong, J. Jing, H. Wang, F. Hudelist, C. Liu, and W. Zhang, “Experimental investigation of the visibility dependence in a nonlinear interferometer using parametric amplifiers,” Appl. Phys. Lett. 102, 011130 (2013).
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G. Adesso, F. Dell’Anno, S. De Siena, F. Illuminati, and L. A. M. Souza, “Optimal estimation of losses at the ultimate quantum limit with non-Gaussian states,” Phys. Rev. A 79, 040305 (2009).
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T. S. Iskhakov, V. C. Usenko, U. L. Andersen, R. Filip, M. V. Chekhova, and G. Leuchs, “Heralded source of bright multi-mode mesoscopic sub-poissonian light,” Opt. Lett. 41(10), 2149–2152 (2016).
[Crossref] [PubMed]

Jakeman, E.

E. Jakeman and J. G. Rarity, “The use of pair production processes to reduce quantum noise in transmission measurements,” Opt. Comm. 59(3), 219–223 (1986).
[Crossref]

Jarzyna, M.

R. Demkowicz-Dobrzanski, M. Jarzyna, and J. Kolodynski, Progress in Optics (Elsevier, 2015), Chap. 4.

Jedrkiewicz, O.

E. Brambilla, L. Caspani, O. Jedrkiewicz, L. A. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A 77, 053807 (2008).
[Crossref]

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93243601 (2004).
[Crossref]

Jiang, Y.-K.

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93243601 (2004).
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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).
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J. Kong, J. Jing, H. Wang, F. Hudelist, C. Liu, and W. Zhang, “Experimental investigation of the visibility dependence in a nonlinear interferometer using parametric amplifiers,” Appl. Phys. Lett. 102, 011130 (2013).
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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).
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P.-A. Moreau, J. Sabines-Chesterking, R. Whittaker, S. K. Joshi, P. M. Birchall, A. McMillan, J. G. Rarity, and J. C. F. Matthews, “Demonstrating an absolute quantum advantage in direct absorption measurement,” Sci. Rep. 7, 6256 (2017).
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S. Kasapi, S. Lathi, and Y. Yamamoto, “Sub-shot-noise frequency-modulation spectroscopy by use of amplitude-squeezed light from semiconductor lasers,” J. Opt. Soc. Am. B 17(2), 275–279 (2000).
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O. Hosten, R. Krishnakumar, N. J. Engelsen, and M. A. Kasevich, “Quantum phase magnification,” Science 352(6293), 1552–1555 (2017).
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M. Manceau, G. Leuchs, F. Ya. Khalili, and M. Chekhova, “Detection loss tolerant supersensitive phase measurement with an SU(1,1) interferometer,” Phys. Rev. Lett. 119, 223604 (2017).
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M. Manceau, F. Ya. Khalili, and M. Chekhova, “Improving the phase super-sensitivity of squeezing-assisted interferometers by squeeze factor unbalancing,” New J. Phys. 19(1), 013014 (2017).
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E. Knyazev, K.Yu. Spasibko, F. Ya. Khalili, and M. Chekhova, “Quantum tomography enhanced through parametric amplification,” New J. Phys. 20(1), 013005 (2018).
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R. Demkowicz-Dobrzanski, M. Jarzyna, and J. Kolodynski, Progress in Optics (Elsevier, 2015), Chap. 4.

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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).
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J. Kong, J. Jing, H. Wang, F. Hudelist, C. Liu, and W. Zhang, “Experimental investigation of the visibility dependence in a nonlinear interferometer using parametric amplifiers,” Appl. Phys. Lett. 102, 011130 (2013).
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O. Hosten, R. Krishnakumar, N. J. Engelsen, and M. A. Kasevich, “Quantum phase magnification,” Science 352(6293), 1552–1555 (2017).
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S. Kasapi, S. Lathi, and Y. Yamamoto, “Sub-shot-noise frequency-modulation spectroscopy by use of amplitude-squeezed light from semiconductor lasers,” J. Opt. Soc. Am. B 17(2), 275–279 (2000).
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U. Leonhardt and H. Paul, “Realistic optical homodyne measurements and quasiprobability distributions,” Phys. Rev. A 48, 4598–4604 (1993).
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A. M. Marino, N. V. C. 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. Ya. Khalili, and M. Chekhova, “Detection loss tolerant supersensitive phase measurement with an SU(1,1) interferometer,” Phys. Rev. Lett. 119, 223604 (2017).
[Crossref] [PubMed]

T. S. Iskhakov, V. C. Usenko, U. L. Andersen, R. Filip, M. V. Chekhova, and G. Leuchs, “Heralded source of bright multi-mode mesoscopic sub-poissonian light,” Opt. Lett. 41(10), 2149–2152 (2016).
[Crossref] [PubMed]

I. N. Agafonov, M. V. Chekhova, and G. Leuchs, “Two-color bright squeezed vacuum,” Phys. Rev. A 82, 011801 (2010).
[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] [PubMed]

J. Kong, J. Jing, H. Wang, F. Hudelist, C. Liu, and W. Zhang, “Experimental investigation of the visibility dependence in a nonlinear interferometer using parametric amplifiers,” Appl. Phys. Lett. 102, 011130 (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]

Lloyd, S.

S.-H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, “Quantum illumination with Gaussian states,” Phys. Rev. Lett. 101, 253601 (2008).
[Crossref] [PubMed]

S. Lloyd, “Enhanced sensitivity of photodetection via quantum illumination,” Science 321(5895), 1463–1465 (2008).
[Crossref] [PubMed]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: Beating the standard quantum limit,” Science 306, 1330–1336 (2004).
[Crossref] [PubMed]

Lopaeva, E. D.

E. D. Lopaeva, I. Ruo-Berchera, I. P. Degiovanni, S. Olivares, G. Brida, and M. Genovese, “Experimental realization of quantum illumination,” Phys. Rev. Lett. 110, 153603 (2013).
[Crossref] [PubMed]

Losero, E.

E. Losero, I. Ruo-Berchera, A. Meda, A. Avella, and M. Genovese, “Unbiased estimation of an optical loss at the ultimate quantum limit with twin-beams,” Sci. Rep. 8(1), 7431 (2018).
[Crossref] [PubMed]

Lugiato, L. A.

E. Brambilla, L. Caspani, O. Jedrkiewicz, L. A. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A 77, 053807 (2008).
[Crossref]

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93243601 (2004).
[Crossref]

Maccone, L.

S.-H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, “Quantum illumination with Gaussian states,” Phys. Rev. Lett. 101, 253601 (2008).
[Crossref] [PubMed]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: Beating the standard quantum limit,” Science 306, 1330–1336 (2004).
[Crossref] [PubMed]

Maître, A.

P. H. Souto Ribeiro, C. Schwob, A. Maître, and C. Fabre, “Sub-shot-noise high-sensitivity spectroscopy with optical parametric oscillator twin beams,” Opt. Lett. 22(24), 1893–1895 (1997).
[Crossref]

Manceau, M.

M. Manceau, F. Ya. Khalili, and M. Chekhova, “Improving the phase super-sensitivity of squeezing-assisted interferometers by squeeze factor unbalancing,” New J. Phys. 19(1), 013014 (2017).
[Crossref]

M. Manceau, G. Leuchs, F. Ya. 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. C. Trejo, and P. D. Lett, “Effect of losses on the performance of an su(1,1) interferometer,” Phys. Rev. A 86, 023844 (2012).
[Crossref]

Matthews, J. C. F.

R. Whittaker, C. Erven, A. Neville, M. Berry, J. L. O’Brien, H. Cable, and J. C. F. Matthews, “Absorption spectroscopy at the ultimate quantum limit from single-photon states,” New J. Phys. 19(2), 023013 (2017).
[Crossref]

P.-A. Moreau, J. Sabines-Chesterking, R. Whittaker, S. K. Joshi, P. M. Birchall, A. McMillan, J. G. Rarity, and J. C. F. Matthews, “Demonstrating an absolute quantum advantage in direct absorption measurement,” Sci. Rep. 7, 6256 (2017).
[Crossref] [PubMed]

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]

McMillan, A.

P.-A. Moreau, J. Sabines-Chesterking, R. Whittaker, S. K. Joshi, P. M. Birchall, A. McMillan, J. G. Rarity, and J. C. F. Matthews, “Demonstrating an absolute quantum advantage in direct absorption measurement,” Sci. Rep. 7, 6256 (2017).
[Crossref] [PubMed]

Meda, A.

E. Losero, I. Ruo-Berchera, A. Meda, A. Avella, and M. Genovese, “Unbiased estimation of an optical loss at the ultimate quantum limit with twin-beams,” Sci. Rep. 8(1), 7431 (2018).
[Crossref] [PubMed]

N. Samantaray, I. Ruo-Berchera, A. Meda, and M. Genovese, “Realization of the first sub-shot-noise wide field microscope,” Light: Sci. Appl. 6, e17005 (2017).
[Crossref]

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. Ruo-Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[Crossref] [PubMed]

Mehmet, M.

H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
[Crossref]

Monras, A.

A. Monras and M. G. A. Paris, “Optimal quantum estimation of loss in bosonic channels,” Phys. Rev. Lett. 98, 160401 (2007).
[Crossref] [PubMed]

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P.-A. Moreau, J. Sabines-Chesterking, R. Whittaker, S. K. Joshi, P. M. Birchall, A. McMillan, J. G. Rarity, and J. C. F. Matthews, “Demonstrating an absolute quantum advantage in direct absorption measurement,” Sci. Rep. 7, 6256 (2017).
[Crossref] [PubMed]

Neville, A.

R. Whittaker, C. Erven, A. Neville, M. Berry, J. L. O’Brien, H. Cable, and J. C. F. Matthews, “Absorption spectroscopy at the ultimate quantum limit from single-photon states,” New J. Phys. 19(2), 023013 (2017).
[Crossref]

Nikogosyan, D. N.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, 1999).
[Crossref]

O’Brien, J. L.

R. Whittaker, C. Erven, A. Neville, M. Berry, J. L. O’Brien, H. Cable, and J. C. F. Matthews, “Absorption spectroscopy at the ultimate quantum limit from single-photon states,” New J. Phys. 19(2), 023013 (2017).
[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]

E. D. Lopaeva, I. Ruo-Berchera, I. P. Degiovanni, S. Olivares, G. Brida, and M. Genovese, “Experimental realization of quantum illumination,” Phys. Rev. Lett. 110, 153603 (2013).
[Crossref] [PubMed]

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] [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]

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]

A. Monras and M. G. A. Paris, “Optimal quantum estimation of loss in bosonic channels,” Phys. Rev. Lett. 98, 160401 (2007).
[Crossref] [PubMed]

Paul, H.

U. Leonhardt and H. Paul, “Realistic optical homodyne measurements and quasiprobability distributions,” Phys. Rev. A 48, 4598–4604 (1993).
[Crossref] [PubMed]

Pirandola, S.

S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, “Microwave quantum illumination,” Phys. Rev. Lett. 114, 080503 (2015).
[Crossref] [PubMed]

S.-H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, “Quantum illumination with Gaussian states,” Phys. Rev. Lett. 101, 253601 (2008).
[Crossref] [PubMed]

Polzik, E. S.

E. S. Polzik, J. Carri, and H. J. Kimble, “Spectroscopy with squeezed light,” Phys. Rev. Lett. 68, 3020–3023 (1992).
[Crossref] [PubMed]

Rarity, J. G.

P.-A. Moreau, J. Sabines-Chesterking, R. Whittaker, S. K. Joshi, P. M. Birchall, A. McMillan, J. G. Rarity, and J. C. F. Matthews, “Demonstrating an absolute quantum advantage in direct absorption measurement,” Sci. Rep. 7, 6256 (2017).
[Crossref] [PubMed]

P. R. Tapster, S. F. Seward, and J. G. Rarity, “Sub-shot-noise measurement of modulated absorption using parametric down-conversion,” Phys. Rev. A 44, 3266–3269 (1991).
[Crossref] [PubMed]

E. Jakeman and J. G. Rarity, “The use of pair production processes to reduce quantum noise in transmission measurements,” Opt. Comm. 59(3), 219–223 (1986).
[Crossref]

Ruo-Berchera, I.

E. Losero, I. Ruo-Berchera, A. Meda, A. Avella, and M. Genovese, “Unbiased estimation of an optical loss at the ultimate quantum limit with twin-beams,” Sci. Rep. 8(1), 7431 (2018).
[Crossref] [PubMed]

N. Samantaray, I. Ruo-Berchera, A. Meda, and M. Genovese, “Realization of the first sub-shot-noise wide field microscope,” Light: Sci. Appl. 6, e17005 (2017).
[Crossref]

E. D. Lopaeva, I. Ruo-Berchera, I. P. Degiovanni, S. Olivares, G. Brida, and M. Genovese, “Experimental realization of quantum illumination,” Phys. Rev. Lett. 110, 153603 (2013).
[Crossref] [PubMed]

G. Brida, M. Genovese, and I. Ruo-Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227 (2010).
[Crossref]

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. Ruo-Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[Crossref] [PubMed]

Sabines-Chesterking, J.

P.-A. Moreau, J. Sabines-Chesterking, R. Whittaker, S. K. Joshi, P. M. Birchall, A. McMillan, J. G. Rarity, and J. C. F. Matthews, “Demonstrating an absolute quantum advantage in direct absorption measurement,” Sci. Rep. 7, 6256 (2017).
[Crossref] [PubMed]

Samantaray, N.

N. Samantaray, I. Ruo-Berchera, A. Meda, and M. Genovese, “Realization of the first sub-shot-noise wide field microscope,” Light: Sci. Appl. 6, e17005 (2017).
[Crossref]

Schnabel, R.

H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
[Crossref]

Schwob, C.

P. H. Souto Ribeiro, C. Schwob, A. Maître, and C. Fabre, “Sub-shot-noise high-sensitivity spectroscopy with optical parametric oscillator twin beams,” Opt. Lett. 22(24), 1893–1895 (1997).
[Crossref]

Seward, S. F.

P. R. Tapster, S. F. Seward, and J. G. Rarity, “Sub-shot-noise measurement of modulated absorption using parametric down-conversion,” Phys. Rev. A 44, 3266–3269 (1991).
[Crossref] [PubMed]

Shapiro, J. H.

S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, “Microwave quantum illumination,” Phys. Rev. Lett. 114, 080503 (2015).
[Crossref] [PubMed]

S.-H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, “Quantum illumination with Gaussian states,” Phys. Rev. Lett. 101, 253601 (2008).
[Crossref] [PubMed]

Souto Ribeiro, P. H.

P. H. Souto Ribeiro, C. Schwob, A. Maître, and C. Fabre, “Sub-shot-noise high-sensitivity spectroscopy with optical parametric oscillator twin beams,” Opt. Lett. 22(24), 1893–1895 (1997).
[Crossref]

Souza, L. A. M.

G. Adesso, F. Dell’Anno, S. De Siena, F. Illuminati, and L. A. M. Souza, “Optimal estimation of losses at the ultimate quantum limit with non-Gaussian states,” Phys. Rev. A 79, 040305 (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]

Spasibko, K.Yu.

E. Knyazev, K.Yu. Spasibko, F. Ya. Khalili, and M. Chekhova, “Quantum tomography enhanced through parametric amplification,” New J. Phys. 20(1), 013005 (2018).
[Crossref]

Tan, S.-H.

S.-H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, “Quantum illumination with Gaussian states,” Phys. Rev. Lett. 101, 253601 (2008).
[Crossref] [PubMed]

Tapster, P. R.

P. R. Tapster, S. F. Seward, and J. G. Rarity, “Sub-shot-noise measurement of modulated absorption using parametric down-conversion,” Phys. Rev. A 44, 3266–3269 (1991).
[Crossref] [PubMed]

Tatam, R. P.

J. Hodgkinson and R. P. Tatam, “Optical gas sensing: a review,” Meas. Sci. Technol. 24(1), 012004 (2013).
[Crossref]

Trejo, N. V. C.

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

Usenko, V. C.

T. S. Iskhakov, V. C. Usenko, U. L. Andersen, R. Filip, M. V. Chekhova, and G. Leuchs, “Heralded source of bright multi-mode mesoscopic sub-poissonian light,” Opt. Lett. 41(10), 2149–2152 (2016).
[Crossref] [PubMed]

Vahlbruch, H.

H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
[Crossref]

Vasilyev, M.

S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless optical amplification of images,” Phys. Rev. Lett. 83, 1938–1941 (1999).
[Crossref]

Vitali, D.

S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, “Microwave quantum illumination,” Phys. Rev. Lett. 114, 080503 (2015).
[Crossref] [PubMed]

Wang, H.

J. Kong, J. Jing, H. Wang, F. Hudelist, C. Liu, and W. Zhang, “Experimental investigation of the visibility dependence in a nonlinear interferometer using parametric amplifiers,” Appl. Phys. Lett. 102, 011130 (2013).
[Crossref]

Weedbrook, C.

S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, “Microwave quantum illumination,” Phys. Rev. Lett. 114, 080503 (2015).
[Crossref] [PubMed]

Whittaker, R.

R. Whittaker, C. Erven, A. Neville, M. Berry, J. L. O’Brien, H. Cable, and J. C. F. Matthews, “Absorption spectroscopy at the ultimate quantum limit from single-photon states,” New J. Phys. 19(2), 023013 (2017).
[Crossref]

P.-A. Moreau, J. Sabines-Chesterking, R. Whittaker, S. K. Joshi, P. M. Birchall, A. McMillan, J. G. Rarity, and J. C. F. Matthews, “Demonstrating an absolute quantum advantage in direct absorption measurement,” Sci. Rep. 7, 6256 (2017).
[Crossref] [PubMed]

Wu, L.-A.

M. Xiao, L.-A. Wu, and H. J. Kimble, “Detection of amplitude modulation with squeezed light for sensitivity beyond the shot-noise limit,” Opt. Lett. 13(6), 476–478 (1988).
[Crossref] [PubMed]

Xiao, M.

M. Xiao, L.-A. Wu, and H. J. Kimble, “Detection of amplitude modulation with squeezed light for sensitivity beyond the shot-noise limit,” Opt. Lett. 13(6), 476–478 (1988).
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Yamamoto, Y.

S. Kasapi, S. Lathi, and Y. Yamamoto, “Sub-shot-noise frequency-modulation spectroscopy by use of amplitude-squeezed light from semiconductor lasers,” J. Opt. Soc. Am. B 17(2), 275–279 (2000).
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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] [PubMed]

J. Kong, J. Jing, H. Wang, F. Hudelist, C. Liu, and W. Zhang, “Experimental investigation of the visibility dependence in a nonlinear interferometer using parametric amplifiers,” Appl. Phys. Lett. 102, 011130 (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]

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]

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]

J. Kong, J. Jing, H. Wang, F. Hudelist, C. Liu, and W. Zhang, “Experimental investigation of the visibility dependence in a nonlinear interferometer using parametric amplifiers,” Appl. Phys. Lett. 102, 011130 (2013).
[Crossref]

J. Opt. Soc. Am. B (1)

S. Kasapi, S. Lathi, and Y. Yamamoto, “Sub-shot-noise frequency-modulation spectroscopy by use of amplitude-squeezed light from semiconductor lasers,” J. Opt. Soc. Am. B 17(2), 275–279 (2000).
[Crossref]

Light: Sci. Appl. (1)

N. Samantaray, I. Ruo-Berchera, A. Meda, and M. Genovese, “Realization of the first sub-shot-noise wide field microscope,” Light: Sci. Appl. 6, e17005 (2017).
[Crossref]

Meas. Sci. Technol. (1)

J. Hodgkinson and R. P. Tatam, “Optical gas sensing: a review,” Meas. Sci. Technol. 24(1), 012004 (2013).
[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)

G. Brida, M. Genovese, and I. Ruo-Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227 (2010).
[Crossref]

New J. Phys. (3)

R. Whittaker, C. Erven, A. Neville, M. Berry, J. L. O’Brien, H. Cable, and J. C. F. Matthews, “Absorption spectroscopy at the ultimate quantum limit from single-photon states,” New J. Phys. 19(2), 023013 (2017).
[Crossref]

E. Knyazev, K.Yu. Spasibko, F. Ya. Khalili, and M. Chekhova, “Quantum tomography enhanced through parametric amplification,” New J. Phys. 20(1), 013005 (2018).
[Crossref]

M. Manceau, F. Ya. Khalili, and M. Chekhova, “Improving the phase super-sensitivity of squeezing-assisted interferometers by squeeze factor unbalancing,” New J. Phys. 19(1), 013014 (2017).
[Crossref]

Opt. Comm. (1)

E. Jakeman and J. G. Rarity, “The use of pair production processes to reduce quantum noise in transmission measurements,” Opt. Comm. 59(3), 219–223 (1986).
[Crossref]

Opt. Lett. (3)

P. H. Souto Ribeiro, C. Schwob, A. Maître, and C. Fabre, “Sub-shot-noise high-sensitivity spectroscopy with optical parametric oscillator twin beams,” Opt. Lett. 22(24), 1893–1895 (1997).
[Crossref]

M. Xiao, L.-A. Wu, and H. J. Kimble, “Detection of amplitude modulation with squeezed light for sensitivity beyond the shot-noise limit,” Opt. Lett. 13(6), 476–478 (1988).
[Crossref] [PubMed]

T. S. Iskhakov, V. C. Usenko, U. L. Andersen, R. Filip, M. V. Chekhova, and G. Leuchs, “Heralded source of bright multi-mode mesoscopic sub-poissonian light,” Opt. Lett. 41(10), 2149–2152 (2016).
[Crossref] [PubMed]

Phys. Rev. A (8)

U. Leonhardt and H. Paul, “Realistic optical homodyne measurements and quasiprobability distributions,” Phys. Rev. A 48, 4598–4604 (1993).
[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]

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

E. Brambilla, L. Caspani, O. Jedrkiewicz, L. A. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A 77, 053807 (2008).
[Crossref]

I. N. Agafonov, M. V. Chekhova, and G. Leuchs, “Two-color bright squeezed vacuum,” Phys. Rev. A 82, 011801 (2010).
[Crossref]

P. R. Tapster, S. F. Seward, and J. G. Rarity, “Sub-shot-noise measurement of modulated absorption using parametric down-conversion,” Phys. Rev. A 44, 3266–3269 (1991).
[Crossref] [PubMed]

G. Adesso, F. Dell’Anno, S. De Siena, F. Illuminati, and L. A. M. Souza, “Optimal estimation of losses at the ultimate quantum limit with non-Gaussian states,” Phys. Rev. A 79, 040305 (2009).
[Crossref]

Phys. Rev. D (1)

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
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Phys. Rev. Lett. (10)

E. S. Polzik, J. Carri, and H. J. Kimble, “Spectroscopy with squeezed light,” Phys. Rev. Lett. 68, 3020–3023 (1992).
[Crossref] [PubMed]

S.-H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, “Quantum illumination with Gaussian states,” Phys. Rev. Lett. 101, 253601 (2008).
[Crossref] [PubMed]

E. D. Lopaeva, I. Ruo-Berchera, I. P. Degiovanni, S. Olivares, G. Brida, and M. Genovese, “Experimental realization of quantum illumination,” Phys. Rev. Lett. 110, 153603 (2013).
[Crossref] [PubMed]

S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, “Microwave quantum illumination,” Phys. Rev. Lett. 114, 080503 (2015).
[Crossref] [PubMed]

S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless optical amplification of images,” Phys. Rev. Lett. 83, 1938–1941 (1999).
[Crossref]

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

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93243601 (2004).
[Crossref]

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. Ruo-Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[Crossref] [PubMed]

A. Monras and M. G. A. Paris, “Optimal quantum estimation of loss in bosonic channels,” Phys. Rev. Lett. 98, 160401 (2007).
[Crossref] [PubMed]

H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
[Crossref]

Rev. Mod. Phys. (1)

V. B. Braginsky and F. Ya. Khalili, “Quantum nondemolition measurements: the route from toys to tools,” Rev. Mod. Phys. 68, 1–11 (1996).
[Crossref]

Sci. Rep. (2)

P.-A. Moreau, J. Sabines-Chesterking, R. Whittaker, S. K. Joshi, P. M. Birchall, A. McMillan, J. G. Rarity, and J. C. F. Matthews, “Demonstrating an absolute quantum advantage in direct absorption measurement,” Sci. Rep. 7, 6256 (2017).
[Crossref] [PubMed]

E. Losero, I. Ruo-Berchera, A. Meda, A. Avella, and M. Genovese, “Unbiased estimation of an optical loss at the ultimate quantum limit with twin-beams,” Sci. Rep. 8(1), 7431 (2018).
[Crossref] [PubMed]

Science (3)

S. Lloyd, “Enhanced sensitivity of photodetection via quantum illumination,” Science 321(5895), 1463–1465 (2008).
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V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: Beating the standard quantum limit,” Science 306, 1330–1336 (2004).
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O. Hosten, R. Krishnakumar, N. J. Engelsen, and M. A. Kasevich, “Quantum phase magnification,” Science 352(6293), 1552–1555 (2017).
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Newlight Photonics Inc., “Thin BBO crystal for ultrafast lasers,” http://newlightphotonics.com/v1/ultrathin-bbo-crystals.html .

R. Demkowicz-Dobrzanski, M. Jarzyna, and J. Kolodynski, Progress in Optics (Elsevier, 2015), Chap. 4.

M. I. Kolobov, Quantum Imaging (Springer, 2007).
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 Schemes of quantum imaging and sensing. (a) Classical differential scheme. The object with absorption �� is placed into one of the outputs of a 50% beamsplitter, and the absorption is retrieved through intensity subtraction measurement. (b) Conventional scheme of sub-shot-noise quantum imaging. The object is placed into one of the twin beams, emerging from a NOPA with the parametric gain r. Two photodetectors with equal quantum efficiencies η measure the numbers of photons in signal and idler beams, and the difference is calculated. (c) An alternative scheme, where only one beam is squeezed by a DOPA before probing the object, the other (much stronger) one being coherent. In schemes (b) and (c), additional DOPAs with gain R (shown by dashed lines) can be placed into both arms (b) or into the signal arm (c) to overcome the detrimental effect of the detection loss.
Fig. 2
Fig. 2 The quantum advantage Q of the ‘twin beams’ scheme, see Eqs. (17) and (59), for the case of no parametric amplification (R = 0) as a function of detection efficiency ηd for p 2 = 0(black, maximum efficiency), 10−5 (red), 10−4 (green), 10−3 (blue), and 10−2 (magenta). The object absorption is �� = 10−5 and the mean photon number is N = 107.
Fig. 3
Fig. 3 The quantum advantage Q of the ‘twin beams’ scheme in the presence of additional parametric amplification, see Eqs. (17) and (59), as a function of the gain R for different values of the detection efficiency: η = 0.99 (red), 0.9 (green), 0.5 (blue), and 0.1 (magenta). The mean photon number is N = 107 and the absorption is �� = 10−5.
Fig. 4
Fig. 4 The quantum advantage Q of the “squeezed coherent” scheme, see Eqs. (17) and (69), for the case of no parametric amplification (R = 0) as a function of detection efficiency ηd for p 2 = 0(black), 10−3 (blue), and 10−2 (magenta). The object absorption is �� = 10−5 and the mean photon number is N = 107.
Fig. 5
Fig. 5 The quantum advantage Q (top) and the corresponding numerically optimized squeeze factor r (bottom) for the “squeezed coherent” scheme, see Eqs. (17) and (69), as a function of the gain R for different values of the detection efficiency: η = 0.99 (red), 0.9 (green), 0.5 (blue), and 0.1 (magenta). The straight black line in the bottom plot shows the asymptotic (35). The mean photon number is N = 107 and the absorption is �� = 10−5.
Fig. 6
Fig. 6 Scheme of a possible experiment. NOPA1 generates beams in modes â1 and â2, and a weakly absorbing object is placed into mode â1. After the beam in mode â2 acquires a π/2 phase shift, both beams are overlapped on a 50% beamsplitter to form modes a ^ ± = ( a ^ 1 ± i a ^ 2 ) / 2 at the output. These two modes are amplified by NOPA2, which is equivalent to the phase-sensitive amplification of modes â1 and â2. In the end, photon numbers in modes â1 and â2 should be measured, which requires overlapping the modes on another 50% beamsplitter.
Fig. 7
Fig. 7 Polarization implementation of the experiment on sub-shot-noise imaging.
Fig. 8
Fig. 8 Measurement of absorption using twin-beams scheme with amplification before detection. The object under study is placed into the first beam, and both beams are simultaneously amplified before the direct detection. The state preparation loss is modeled by means of two identical beamsplitters with power transmissivity ηp, and the detection loss, by a similar beamsplitter ηd. The pump of the non-linear crystals is not depicted.
Fig. 9
Fig. 9 Measurement of absorption using a squeezed coherent state and amplification before detection. Since the reference beam is considered to have a very large amplitude in order to suppress the shot-noise in the corresponding channel, one can take into account only the noise of the signal channel. Here α is rescaled, see Eq. (63).

Equations (87)

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Δ 𝒜 CR = { n = 0 1 W ( n / 𝒜 ) [ W ( n / 𝒜 ) 𝒜 ] 2 } 1 / 2 .
𝒯 = 1 𝒜
1 𝒜 η = η 𝒯 ,
η = η p η d
Δ 𝒜 CR = { n = 0 1 W ( n / 𝒜 η ) [ W ( n / 𝒜 η ) 𝒜 ] 2 } 1 / 2 .
Δ 𝒜 CR = 1 η { n = 0 1 W ( n / 𝒜 η ) [ W ( n / 𝒜 η ) 𝒜 η ] 2 } 1 / 2 .
W ( n / 𝒜 ) = e ( 1 𝒜 η ) N 0 [ ( 1 𝒜 η ) N 0 ] n n ! .
Δ 𝒜 CRcoh = 𝒯 η d N ,
N = η p N 0
𝒜 1 , 1 η p , d 1 .
Δ 𝒜 CRcoh = 1 N .
W ( n / 𝒜 ) = N 0 ! n ! ( N 0 n ) ! 𝒜 η N 0 n ( 1 𝒜 η ) n ,
Δ 𝒜 CRFock = [ 𝒜 + ( 1 η ) 𝒯 ] 𝒯 η d N .
Δ 𝒜 CRFock = 𝒜 + 2 N ,
2 = p 2 + d 2
p , d 2 = 1 η p , d η p , d .
Q = Δ 𝒜 CRcoh Δ 𝒜 .
Q = 1 𝒜 + 2 .
𝒜 ˜ = n d 1 n d 2 G ,
G = n d 1 𝒜
N 1 .
e 2 R 1 .
( Δ 𝒜 ) 2 = 𝒜 2 + 𝒜 + 2 2 N .
( Δ 𝒜 ) 2 = 2 [ 𝒜 2 + 𝒜 + 2 ( p 2 + d 2 e 2 R ) N ] + 1 N 2 .
𝒜 ˜ = n d 1 k n d 2 G ,
( Δ 𝒜 ) 2 = 𝒜 + 2 2 N , Q = 1 𝒜 + 2 2 ,
( Δ 𝒜 ) 2 = 2 [ 𝒜 + 2 ( p 2 + d 2 e 2 R ) N ] + 1 N 2 , Q = 1 2 [ 𝒜 + 2 ( p 2 + d 2 e 2 R ) ] + 1 / N .
Q 1 2 .
Q = 1 2 ( 𝒜 + 2 p 2 ) + 1 / N ,
e 2 r 1 ,
( Δ 𝒜 ) 2 = e 2 | r | + 𝒜 + 2 N + e 4 | r | 8 N 2
Q = 1 e 2 | r | + 𝒜 + 2 + e 4 | r | 8 N .
e 2 | r | = ( 4 N ) 1 / 3 ,
( Δ 𝒜 ) 2 = 𝒜 + 2 N + 3 2 5 / 3 N 4 / 3 ,
Q = 1 𝒜 + 2 + 3 2 5 / 3 N 1 / 3 .
( Δ 𝒜 ) 2 = e 2 | r | + 𝒜 + p 2 + d 2 e 2 R N e 2 | r | 4 + e 4 | r | 8 R 8 ( N e 2 | r | 4 ) 2 .
e 2 | r | 4 N ,
( Δ 𝒜 ) 2 = e 2 | r | + 𝒜 + p 2 + d 2 e 2 R N + e 4 | r | 8 R 8 N 2 .
e 2 | r | = ( 4 N ) 1 / 3 e 8 R / 3 ,
( Δ 𝒜 ) 2 = 𝒜 + p 2 + d 2 e 2 R N + 3 e 8 R / 3 2 5 / 3 N 4 / 3 ,
Q = 1 𝒜 + p 2 + d 2 e 2 R + 3 e 8 R / 3 2 5 / 3 N 1 / 3 .
e 4 R 4 N .
H ^ = i γ a ^ 1 a ^ 2 + h . c . ,
H ^ = i Γ [ ( a ^ 1 ) 2 + ( a ^ 2 ) 2 ] + h . c . ,
H ^ = i Γ a ^ + a ^ + h . c . ,
a ^ ± = a ^ 1 ± i a ^ 2 2 .
d ^ 1 , 2 = η d c ^ 1 , 2 + 1 η d u ^ 1 , 2 = η d ( c ^ 1 , 2 + d u ^ 1 , 2 ) ,
n ^ d 1 , 2 = η d n ^ c 1 , 2 ,
( δ n ^ d 1 , 2 ) 2 = η d 2 [ ( δ n ^ c 1 , 2 ) 2 + d 2 n ^ c 1 , 2 ] ,
δ n ^ d 1 δ n ^ d 2 = η d 2 δ n ^ c 1 δ n ^ c 2 ,
n ^ c 1 , 2 = c ^ 1 , 2 c ^ 1 , 2 ,
n ^ d 1 , 2 = d ^ 1 , 2 d ^ 1 , 2 ,
δ n ^ c 1 , 2 = n ^ c 1 , 2 n ^ c 1 , 2 ,
δ n ^ d 1 , 2 = n ^ d 1 , 2 n ^ d 1 , 2 .
a ^ 1 , 2 = η p ( z ^ 1 , 2 cosh r + z ^ 2 , 1 sinh r ) + 1 η p v ^ 1 p , 2 p ,
b ^ 1 = 𝒯 a ^ 1 + 𝒜 v ^ obj = 𝒯 p ( z ^ 1 cosh r + z ^ 2 sinh r ) + 𝒜 p v ^ 1 ,
b ^ 2 = a ^ 2 = η p ( z ^ 2 cosh r + z ^ 1 sinh r ) + 1 η p v ^ 2 ,
𝒯 = 1 𝒜 ,
𝒯 p = η p 𝒯 , 𝒜 p = 1 η p 𝒯 ,
v ^ 1 = ( 1 η p ) 𝒯 v ^ 1 p + 𝒜 v ^ obj 𝒜 p ,
v ^ 2 = v ^ 2 p ,
c ^ 1 = b ^ 1 cosh R + b ^ 1 sinh R = 𝒯 p ( C ^ 1 + S ^ 1 ) + 𝒜 p ( v ^ 1 cosh R + v ^ 1 sinh R ) ,
c ^ 2 = b ^ 2 cosh R + b ^ 2 sinh R = η p ( C ^ 2 + S ^ 2 ) + 1 η p ( v ^ 2 cosh R + v ^ 2 sinh R ) ,
C ^ 1 , 2 = z ^ 1 , 2 cosh r cosh R + z ^ 2 , 1 sinh r sinh R ,
S ^ 1 , 2 = z ^ 1 , 2 cosh r sinh R + z ^ 2 , 1 sinh r cosh R .
n ^ c 1 = ( 𝒯 N + 1 2 ) cosh 2 R 1 2 ,
n ^ c 2 = ( N + 1 2 ) cosh 2 R 1 2 ,
( δ n ^ c 1 ) 2 = ( 𝒯 N + 1 2 ) 2 cosh 4 R 1 4 ,
( δ n ^ c 2 ) 2 = ( N + 1 2 ) 2 cosh 4 R 1 4 ,
δ n ^ c 1 δ n ^ c 2 = 𝒯 N ( N + η p ) cosh 4 R ,
N = η p sinh 2 r
( Δ 𝒜 ) 2 = ( δ n ^ d 1 δ n ^ d 2 ) 2 G 2 = 1 ( G / η d ) 2 [ ( δ n ^ c 1 ) 2 + ( δ n ^ c 2 ) 2 2 δ n ^ c 1 δ n ^ c 2 + 2 ( n ^ c 1 + n ^ c 2 ) ] .
G = n ^ d 1 𝒜 = η d N cosh 2 R
( Δ 𝒜 ) 2 = ( δ n ^ d 1 k δ n ^ d 2 ) 2 G 2 = ( δ n ^ d 1 ) 2 2 k δ n ^ d 1 δ n ^ d 2 + k 2 ( δ n ^ d 2 ) 2 G 2 .
k = δ n ^ d 1 δ n ^ d 2 ( δ n ^ d 2 ) 2 ,
( Δ 𝒜 ) 2 = 1 G 2 [ ( δ n ^ d 1 ) 2 δ n ^ d 1 δ n ^ d 2 2 ( δ n ^ d 2 ) 2 ] = 1 ( G / η d ) 2 [ ( δ n ^ c 1 ) 2 + 2 n c 1 δ n ^ c 1 δ n ^ c 2 2 ( δ n ^ c 2 ) 2 + 2 n c 1 ] .
( Δ 𝒜 ) 2 = 2 { 𝒜 2 + 1 N [ 𝒜 + 2 ( 1 η p ) 𝒯 + 2 ( 1 + 𝒯 ) e 2 R ] } + 1 N 2 ,
( Δ 𝒜 ) 2 = 2 𝒯 N [ 𝒜 + 2 ( 1 η p ) 𝒯 + 2 ( 1 + 𝒯 ) e 2 R ] + 1 N 2 [ 1 + 𝒯 2 2 + 2 𝒯 ( 1 𝒯 η p 2 ) ] .
a ^ = α + η p ( z ^ cosh r + z ^ sinh r ) + 1 η p v ^ p ,
α = N η p sinh 2 r
b ^ = 𝒯 a ^ + 𝒜 v ^ obj = 𝒯 α + 𝒯 p ( z ^ cosh r + z ^ sinh r ) + 𝒜 p v ^ ,
v ^ = ( 1 η p ) 𝒯 v ^ p + 𝒜 v ^ obj 𝒜 p
c ^ = b ^ cosh R + b ^ sinh R = 𝒯 α e R + 𝒯 p [ z ^ cosh ( r + R ) + z ^ sinh ( r + R ) ] + 𝒜 p ( v ^ cosh R + v ^ sinh R ) .
n ^ c = 𝒯 α 2 e 2 R + 𝒯 p sinh 2 ( r + R ) + 𝒜 p sinh 2 R ,
( δ n ^ c ) 2 = 𝒯 𝒯 p α 2 e 2 r + 4 R + 𝒯 p 2 2 sinh 2 2 ( r + R ) + 𝒯 𝒜 p α 2 e 4 R + 𝒯 p 𝒜 p sinh 2 ( r + 2 R ) + 𝒜 p 2 2 sinh 2 2 R .
( Δ 𝒜 ) 2 = ( δ n ^ d ) 2 G 2 = ( δ n ^ c ) 2 + 2 n ^ c ( G / η d ) 2 ,
G = n ^ d 𝒜 = η d [ α 2 e 2 R η p sinh 2 ( r + R ) + η p sinh 2 R ]

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