Abstract

Enzymes are essential to maintain organisms alive. Some of the reactions they catalyze are associated with a change in reagents chirality, hence their activity can be tracked by using optical means. However, illumination affects enzyme activity: the challenge is to operate at low-intensity regime avoiding loss in sensitivity. Here we apply quantum phase estimation to real-time measurement of invertase enzymatic activity. Control of the probe at the quantum level demonstrates the potential for reducing invasiveness with optimized sensitivity at once. This preliminary effort, bringing together methods of quantum physics and biology, constitutes an important step towards full development of quantum sensors for biological systems.

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

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References

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    [Crossref]

2019 (2)

V. Cimini, I. Gianani, L. Ruggiero, T. Gasperi, M. Sbroscia, E. Roccia, D. Tofani, F. Bruni, M. Ricci, and M. Barbieri, “Quantum sensors for dynamical tracking of chemical processes,” Phys. Rev. A 99(5), 053817 (2019).
[Crossref]

M. Oppermann, B. Bauer, T. Rossi, F. Zinna, J. Helbing, J. Lacour, and M. Chergui, “Ultrafast broadband circular dichroism in the deep ultraviolet,” Optica 6(1), 56–60 (2019).
[Crossref]

2018 (3)

2017 (1)

M. W. S. Slussarenko, H. Chrzanowski, L. Shalm, V. B. Verma, S.-W. Nam, and G. J. Pryde, “Unconditional violation of the shot-noise limit in photonic quantum metrology,” Nat. Photonics 11(11), 700–703 (2017).
[Crossref]

2016 (1)

N. Tischler, M. Krenn, R. Fickler, X. Vida, A. Zeilinger, and G. Molina-Terriza, “Quantum optical rotatory dispersion,” Sci. Adv. 2(10), e1601306 (2016).
[Crossref]

2015 (2)

A. Berni, T. Gehring, B. Nielsen, V. Handchen, M. Paris, and U. Andersen, “Ab initio quantum-enhanced optical phase estimation using real-time feedback control,” Nat. Photonics 9(9), 577–581 (2015).
[Crossref]

J. M. Choi, S. S. Han, and H. Kim, “Industrial applications of enzyme biocatalysis: Current status and future aspects,” Biotechnol. Adv. 33(7), 1443–1454 (2015).
[Crossref]

2014 (2)

C. E. Vollmer, C. Baune, A. Samblowski, T. Eberle, V. Händchen, J. Fiurášek, and R. Schnabel, “Quantum up-conversion of squeezed vacuum states from 1550 to 532 nm,” Phys. Rev. Lett. 112(7), 073602 (2014).
[Crossref]

Y. Israel, S. Rosen, and Y. Silberberg, “Supersensitive polarization microscopy using noon states of light,” Phys. Rev. Lett. 112(10), 103604 (2014).
[Crossref]

2013 (4)

F. Wolfgramm, C. Vitelli, F. Beduini, N. Godbout, and M. Mitchell, “Entanglement-enhanced probing of a delicate material system,” Nat. Photonics 7(1), 28–32 (2013).
[Crossref]

T. Ono, R. Okamoto, and S. Takeuchi, “An entanglement-enhanced microscope,” Nat. Commun. 4(1), 2426 (2013).
[Crossref]

V. D’Ambrosio, N. Spagnolo, L. D. Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4(1), 2432 (2013).
[Crossref]

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

2012 (3)

A. Crespi, M. Lobino, J. Matthews, A. Politi, C. Neal, R. Ramponi, R. Osellame, and J. O’BrienBrien, “Measuring protein concentration with entangled photons,” Appl. Phys. Lett. 100(23), 233704 (2012).
[Crossref]

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

A. B. Pena, B. Kemper, M. Woerdemann, A. Vollmer, S. Ketelhut, G. vonBally, and C. Denz, “Optical tweezers induced photodamage in living cells quantified with digital holographic phase microscopy,” Proc. SPIE 8427, 84270A (2012).
[Crossref]

2011 (4)

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

N. Thomas-Peter, B. Smith, A. Datta, L. Zhang, U. Dorner, and I. Walmsley, “Real-world quantum sensors: evaluating resources for precision measurement,” Phys. Rev. Lett. 107(11), 113603 (2011).
[Crossref]

J. Matthews, A. Politi, D. Bonneau, and J. O’Brien, “Heralding two-photon and four-photon path entanglement on a chip,” Phys. Rev. Lett. 107(16), 163602 (2011).
[Crossref]

G. 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(1), 43–47 (2011).
[Crossref]

2010 (1)

P. Carlton, J. Boulanger, C. Kervrann, J.-B. Sibarita, J. Salamero, S. Gordon-Messer, D. Bressan, J. Haber, S. Haase, L. Shao, L. Winoto, A. Matsuda, P. Kner, S. Uzawa, M. Gustafsson, Z. Kam, D. Agard, and J. Sedat, “Fast live simultaneous multiwavelength four-dimensional optical microscopy,” Proc. Natl. Acad. Sci. U. S. A. 107(37), 16016–16022 (2010).
[Crossref]

2009 (1)

T. Harris and M. Keshwani, “Measurement of enzyme activity,” Methods Enzymol. 463, 57–71 (2009).
[Crossref]

2008 (1)

J. Dowling, “Quantum optical metrology - the lowdown on high-n00n states,” Contemp. Phys. 49(2), 125–143 (2008).
[Crossref]

2007 (3)

V. Vojisavljevic, E. Pirogova, and I. Cosic, “Influence of electromagnetic radiation on enzyme kinetics,” Conf Proc IEEE Eng Med Biol Soc. 2007, 5021–5024 (2007).
[Crossref]

T. Nagata, R. Okamoto, J. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four entangled photons,” Science 316(5825), 726–729 (2007).
[Crossref]

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98(22), 223601 (2007).
[Crossref]

2006 (1)

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96(1), 010401 (2006).
[Crossref]

2004 (2)

P. Walther, J. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De broglie wavelength of a non-local four-photon state,” Nature 429(6988), 158–161 (2004).
[Crossref]

M. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled stat,” Nature 429(6988), 161–164 (2004).
[Crossref]

1987 (1)

P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light–enhanced polarization interferometer,” Phys. Rev. Lett. 59(19), 2153–2156 (1987).
[Crossref]

1983 (1)

D. Combes and P. Monsan, “Sucrose hydrolysis by invertase. characterization of products and substrate inhibition,” Carbohydr. Res. 117, 215–228 (1983).
[Crossref]

1973 (1)

1921 (1)

J. Sumber, “Dinitrosalicylic acid: a reagent for the estimation of sugar in normal and diabetic urine,” J. Biol. Chem 47, 5–9 (1921).

Agard, D.

P. Carlton, J. Boulanger, C. Kervrann, J.-B. Sibarita, J. Salamero, S. Gordon-Messer, D. Bressan, J. Haber, S. Haase, L. Shao, L. Winoto, A. Matsuda, P. Kner, S. Uzawa, M. Gustafsson, Z. Kam, D. Agard, and J. Sedat, “Fast live simultaneous multiwavelength four-dimensional optical microscopy,” Proc. Natl. Acad. Sci. U. S. A. 107(37), 16016–16022 (2010).
[Crossref]

Amjadi, A.

H. Mirmiranpour, F. S. Nosrati, S. O. Sobhani, S. N. Takantape, and A. Amjadi, “Effect of low-level laser irradiation on the function of glycated catalase,” J. Lasers Med. Sci. 9(3), 212–218 (2018).
[Crossref]

Andersen, U.

A. Berni, T. Gehring, B. Nielsen, V. Handchen, M. Paris, and U. Andersen, “Ab initio quantum-enhanced optical phase estimation using real-time feedback control,” Nat. Photonics 9(9), 577–581 (2015).
[Crossref]

Aolita, L.

V. D’Ambrosio, N. Spagnolo, L. D. Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4(1), 2432 (2013).
[Crossref]

Arao, H.

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

Aspelmeyer, M.

P. Walther, J. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De broglie wavelength of a non-local four-photon state,” Nature 429(6988), 158–161 (2004).
[Crossref]

Bachor, H.

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

Barbieri, M.

V. Cimini, I. Gianani, L. Ruggiero, T. Gasperi, M. Sbroscia, E. Roccia, D. Tofani, F. Bruni, M. Ricci, and M. Barbieri, “Quantum sensors for dynamical tracking of chemical processes,” Phys. Rev. A 99(5), 053817 (2019).
[Crossref]

E. Roccia, V. Cimini, M. Sbroscia, I. Gianani, L. Ruggiero, L. Mancino, M. Genoni, M. Ricci, and M. Barbieri, “Multiparameter approach to quantum phase estimation with limited visibility,” Optica 5(10), 1171–1176 (2018).
[Crossref]

Bauer, B.

Baune, C.

C. E. Vollmer, C. Baune, A. Samblowski, T. Eberle, V. Händchen, J. Fiurášek, and R. Schnabel, “Quantum up-conversion of squeezed vacuum states from 1550 to 532 nm,” Phys. Rev. Lett. 112(7), 073602 (2014).
[Crossref]

Beduini, F.

F. Wolfgramm, C. Vitelli, F. Beduini, N. Godbout, and M. Mitchell, “Entanglement-enhanced probing of a delicate material system,” Nat. Photonics 7(1), 28–32 (2013).
[Crossref]

Berni, A.

A. Berni, T. Gehring, B. Nielsen, V. Handchen, M. Paris, and U. Andersen, “Ab initio quantum-enhanced optical phase estimation using real-time feedback control,” Nat. Photonics 9(9), 577–581 (2015).
[Crossref]

Berry, D.

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

Berry, D. W.

G. 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(1), 43–47 (2011).
[Crossref]

Bonneau, D.

J. Matthews, A. Politi, D. Bonneau, and J. O’Brien, “Heralding two-photon and four-photon path entanglement on a chip,” Phys. Rev. Lett. 107(16), 163602 (2011).
[Crossref]

Boulanger, J.

P. Carlton, J. Boulanger, C. Kervrann, J.-B. Sibarita, J. Salamero, S. Gordon-Messer, D. Bressan, J. Haber, S. Haase, L. Shao, L. Winoto, A. Matsuda, P. Kner, S. Uzawa, M. Gustafsson, Z. Kam, D. Agard, and J. Sedat, “Fast live simultaneous multiwavelength four-dimensional optical microscopy,” Proc. Natl. Acad. Sci. U. S. A. 107(37), 16016–16022 (2010).
[Crossref]

Bowen, W.

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

Bressan, D.

P. Carlton, J. Boulanger, C. Kervrann, J.-B. Sibarita, J. Salamero, S. Gordon-Messer, D. Bressan, J. Haber, S. Haase, L. Shao, L. Winoto, A. Matsuda, P. Kner, S. Uzawa, M. Gustafsson, Z. Kam, D. Agard, and J. Sedat, “Fast live simultaneous multiwavelength four-dimensional optical microscopy,” Proc. Natl. Acad. Sci. U. S. A. 107(37), 16016–16022 (2010).
[Crossref]

Bruni, F.

V. Cimini, I. Gianani, L. Ruggiero, T. Gasperi, M. Sbroscia, E. Roccia, D. Tofani, F. Bruni, M. Ricci, and M. Barbieri, “Quantum sensors for dynamical tracking of chemical processes,” Phys. Rev. A 99(5), 053817 (2019).
[Crossref]

Carlton, P.

P. Carlton, J. Boulanger, C. Kervrann, J.-B. Sibarita, J. Salamero, S. Gordon-Messer, D. Bressan, J. Haber, S. Haase, L. Shao, L. Winoto, A. Matsuda, P. Kner, S. Uzawa, M. Gustafsson, Z. Kam, D. Agard, and J. Sedat, “Fast live simultaneous multiwavelength four-dimensional optical microscopy,” Proc. Natl. Acad. Sci. U. S. A. 107(37), 16016–16022 (2010).
[Crossref]

Chen, Y.

Chergui, M.

Choi, J. M.

J. M. Choi, S. S. Han, and H. Kim, “Industrial applications of enzyme biocatalysis: Current status and future aspects,” Biotechnol. Adv. 33(7), 1443–1454 (2015).
[Crossref]

Chrzanowski, H.

M. W. S. Slussarenko, H. Chrzanowski, L. Shalm, V. B. Verma, S.-W. Nam, and G. J. Pryde, “Unconditional violation of the shot-noise limit in photonic quantum metrology,” Nat. Photonics 11(11), 700–703 (2017).
[Crossref]

Cimini, V.

V. Cimini, I. Gianani, L. Ruggiero, T. Gasperi, M. Sbroscia, E. Roccia, D. Tofani, F. Bruni, M. Ricci, and M. Barbieri, “Quantum sensors for dynamical tracking of chemical processes,” Phys. Rev. A 99(5), 053817 (2019).
[Crossref]

E. Roccia, V. Cimini, M. Sbroscia, I. Gianani, L. Ruggiero, L. Mancino, M. Genoni, M. Ricci, and M. Barbieri, “Multiparameter approach to quantum phase estimation with limited visibility,” Optica 5(10), 1171–1176 (2018).
[Crossref]

Combes, D.

D. Combes and P. Monsan, “Sucrose hydrolysis by invertase. characterization of products and substrate inhibition,” Carbohydr. Res. 117, 215–228 (1983).
[Crossref]

Cooper, G. M.

G. M. Cooper, The Cell: A Molecular Approach (Sinauer Associates, 2000).

Cosic, I.

V. Vojisavljevic, E. Pirogova, and I. Cosic, “Influence of electromagnetic radiation on enzyme kinetics,” Conf Proc IEEE Eng Med Biol Soc. 2007, 5021–5024 (2007).
[Crossref]

Crespi, A.

A. Crespi, M. Lobino, J. Matthews, A. Politi, C. Neal, R. Ramponi, R. Osellame, and J. O’BrienBrien, “Measuring protein concentration with entangled photons,” Appl. Phys. Lett. 100(23), 233704 (2012).
[Crossref]

D’Ambrosio, V.

V. D’Ambrosio, N. Spagnolo, L. D. Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4(1), 2432 (2013).
[Crossref]

Daria, V.

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

Datta, A.

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[Crossref]

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Rockstuhl, C.

Rosen, S.

Y. Israel, S. Rosen, and Y. Silberberg, “Supersensitive polarization microscopy using noon states of light,” Phys. Rev. Lett. 112(10), 103604 (2014).
[Crossref]

Rossi, T.

Ruggiero, L.

V. Cimini, I. Gianani, L. Ruggiero, T. Gasperi, M. Sbroscia, E. Roccia, D. Tofani, F. Bruni, M. Ricci, and M. Barbieri, “Quantum sensors for dynamical tracking of chemical processes,” Phys. Rev. A 99(5), 053817 (2019).
[Crossref]

E. Roccia, V. Cimini, M. Sbroscia, I. Gianani, L. Ruggiero, L. Mancino, M. Genoni, M. Ricci, and M. Barbieri, “Multiparameter approach to quantum phase estimation with limited visibility,” Optica 5(10), 1171–1176 (2018).
[Crossref]

Salamero, J.

P. Carlton, J. Boulanger, C. Kervrann, J.-B. Sibarita, J. Salamero, S. Gordon-Messer, D. Bressan, J. Haber, S. Haase, L. Shao, L. Winoto, A. Matsuda, P. Kner, S. Uzawa, M. Gustafsson, Z. Kam, D. Agard, and J. Sedat, “Fast live simultaneous multiwavelength four-dimensional optical microscopy,” Proc. Natl. Acad. Sci. U. S. A. 107(37), 16016–16022 (2010).
[Crossref]

Samblowski, A.

C. E. Vollmer, C. Baune, A. Samblowski, T. Eberle, V. Händchen, J. Fiurášek, and R. Schnabel, “Quantum up-conversion of squeezed vacuum states from 1550 to 532 nm,” Phys. Rev. Lett. 112(7), 073602 (2014).
[Crossref]

Sasaki, K.

T. Nagata, R. Okamoto, J. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four entangled photons,” Science 316(5825), 726–729 (2007).
[Crossref]

Sbroscia, M.

V. Cimini, I. Gianani, L. Ruggiero, T. Gasperi, M. Sbroscia, E. Roccia, D. Tofani, F. Bruni, M. Ricci, and M. Barbieri, “Quantum sensors for dynamical tracking of chemical processes,” Phys. Rev. A 99(5), 053817 (2019).
[Crossref]

E. Roccia, V. Cimini, M. Sbroscia, I. Gianani, L. Ruggiero, L. Mancino, M. Genoni, M. Ricci, and M. Barbieri, “Multiparameter approach to quantum phase estimation with limited visibility,” Optica 5(10), 1171–1176 (2018).
[Crossref]

Schnabel, R.

C. E. Vollmer, C. Baune, A. Samblowski, T. Eberle, V. Händchen, J. Fiurášek, and R. Schnabel, “Quantum up-conversion of squeezed vacuum states from 1550 to 532 nm,” Phys. Rev. Lett. 112(7), 073602 (2014).
[Crossref]

Sciarrino, F.

V. D’Ambrosio, N. Spagnolo, L. D. Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4(1), 2432 (2013).
[Crossref]

Sedat, J.

P. Carlton, J. Boulanger, C. Kervrann, J.-B. Sibarita, J. Salamero, S. Gordon-Messer, D. Bressan, J. Haber, S. Haase, L. Shao, L. Winoto, A. Matsuda, P. Kner, S. Uzawa, M. Gustafsson, Z. Kam, D. Agard, and J. Sedat, “Fast live simultaneous multiwavelength four-dimensional optical microscopy,” Proc. Natl. Acad. Sci. U. S. A. 107(37), 16016–16022 (2010).
[Crossref]

Shalm, L.

M. W. S. Slussarenko, H. Chrzanowski, L. Shalm, V. B. Verma, S.-W. Nam, and G. J. Pryde, “Unconditional violation of the shot-noise limit in photonic quantum metrology,” Nat. Photonics 11(11), 700–703 (2017).
[Crossref]

Shao, L.

P. Carlton, J. Boulanger, C. Kervrann, J.-B. Sibarita, J. Salamero, S. Gordon-Messer, D. Bressan, J. Haber, S. Haase, L. Shao, L. Winoto, A. Matsuda, P. Kner, S. Uzawa, M. Gustafsson, Z. Kam, D. Agard, and J. Sedat, “Fast live simultaneous multiwavelength four-dimensional optical microscopy,” Proc. Natl. Acad. Sci. U. S. A. 107(37), 16016–16022 (2010).
[Crossref]

Sibarita, J.-B.

P. Carlton, J. Boulanger, C. Kervrann, J.-B. Sibarita, J. Salamero, S. Gordon-Messer, D. Bressan, J. Haber, S. Haase, L. Shao, L. Winoto, A. Matsuda, P. Kner, S. Uzawa, M. Gustafsson, Z. Kam, D. Agard, and J. Sedat, “Fast live simultaneous multiwavelength four-dimensional optical microscopy,” Proc. Natl. Acad. Sci. U. S. A. 107(37), 16016–16022 (2010).
[Crossref]

Silberberg, Y.

Y. Israel, S. Rosen, and Y. Silberberg, “Supersensitive polarization microscopy using noon states of light,” Phys. Rev. Lett. 112(10), 103604 (2014).
[Crossref]

Slusher, R. E.

P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light–enhanced polarization interferometer,” Phys. Rev. Lett. 59(19), 2153–2156 (1987).
[Crossref]

Slussarenko, M. W. S.

M. W. S. Slussarenko, H. Chrzanowski, L. Shalm, V. B. Verma, S.-W. Nam, and G. J. Pryde, “Unconditional violation of the shot-noise limit in photonic quantum metrology,” Nat. Photonics 11(11), 700–703 (2017).
[Crossref]

Slussarenko, S.

V. D’Ambrosio, N. Spagnolo, L. D. Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4(1), 2432 (2013).
[Crossref]

Smith, B.

N. Thomas-Peter, B. Smith, A. Datta, L. Zhang, U. Dorner, and I. Walmsley, “Real-world quantum sensors: evaluating resources for precision measurement,” Phys. Rev. Lett. 107(11), 113603 (2011).
[Crossref]

Sobhani, S. O.

H. Mirmiranpour, F. S. Nosrati, S. O. Sobhani, S. N. Takantape, and A. Amjadi, “Effect of low-level laser irradiation on the function of glycated catalase,” J. Lasers Med. Sci. 9(3), 212–218 (2018).
[Crossref]

Spagnolo, N.

V. D’Ambrosio, N. Spagnolo, L. D. Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4(1), 2432 (2013).
[Crossref]

Steinberg, A. M.

M. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled stat,” Nature 429(6988), 161–164 (2004).
[Crossref]

Sumber, J.

J. Sumber, “Dinitrosalicylic acid: a reagent for the estimation of sugar in normal and diabetic urine,” J. Biol. Chem 47, 5–9 (1921).

Takantape, S. N.

H. Mirmiranpour, F. S. Nosrati, S. O. Sobhani, S. N. Takantape, and A. Amjadi, “Effect of low-level laser irradiation on the function of glycated catalase,” J. Lasers Med. Sci. 9(3), 212–218 (2018).
[Crossref]

Takeda, S.

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

Takeuchi, S.

T. Ono, R. Okamoto, and S. Takeuchi, “An entanglement-enhanced microscope,” Nat. Commun. 4(1), 2426 (2013).
[Crossref]

T. Nagata, R. Okamoto, J. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four entangled photons,” Science 316(5825), 726–729 (2007).
[Crossref]

Tame, M.

Taylor, M.

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

Thomas-Peter, N.

N. Thomas-Peter, B. Smith, A. Datta, L. Zhang, U. Dorner, and I. Walmsley, “Real-world quantum sensors: evaluating resources for precision measurement,” Phys. Rev. Lett. 107(11), 113603 (2011).
[Crossref]

Tischler, N.

N. Tischler, M. Krenn, R. Fickler, X. Vida, A. Zeilinger, and G. Molina-Terriza, “Quantum optical rotatory dispersion,” Sci. Adv. 2(10), e1601306 (2016).
[Crossref]

Tofani, D.

V. Cimini, I. Gianani, L. Ruggiero, T. Gasperi, M. Sbroscia, E. Roccia, D. Tofani, F. Bruni, M. Ricci, and M. Barbieri, “Quantum sensors for dynamical tracking of chemical processes,” Phys. Rev. A 99(5), 053817 (2019).
[Crossref]

Tsumura, K.

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

Ursin, R.

P. Walther, J. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De broglie wavelength of a non-local four-photon state,” Nature 429(6988), 158–161 (2004).
[Crossref]

Uzawa, S.

P. Carlton, J. Boulanger, C. Kervrann, J.-B. Sibarita, J. Salamero, S. Gordon-Messer, D. Bressan, J. Haber, S. Haase, L. Shao, L. Winoto, A. Matsuda, P. Kner, S. Uzawa, M. Gustafsson, Z. Kam, D. Agard, and J. Sedat, “Fast live simultaneous multiwavelength four-dimensional optical microscopy,” Proc. Natl. Acad. Sci. U. S. A. 107(37), 16016–16022 (2010).
[Crossref]

Verma, V. B.

M. W. S. Slussarenko, H. Chrzanowski, L. Shalm, V. B. Verma, S.-W. Nam, and G. J. Pryde, “Unconditional violation of the shot-noise limit in photonic quantum metrology,” Nat. Photonics 11(11), 700–703 (2017).
[Crossref]

Vida, X.

N. Tischler, M. Krenn, R. Fickler, X. Vida, A. Zeilinger, and G. Molina-Terriza, “Quantum optical rotatory dispersion,” Sci. Adv. 2(10), e1601306 (2016).
[Crossref]

Vitelli, C.

F. Wolfgramm, C. Vitelli, F. Beduini, N. Godbout, and M. Mitchell, “Entanglement-enhanced probing of a delicate material system,” Nat. Photonics 7(1), 28–32 (2013).
[Crossref]

Vojisavljevic, V.

V. Vojisavljevic, E. Pirogova, and I. Cosic, “Influence of electromagnetic radiation on enzyme kinetics,” Conf Proc IEEE Eng Med Biol Soc. 2007, 5021–5024 (2007).
[Crossref]

Vollmer, A.

A. B. Pena, B. Kemper, M. Woerdemann, A. Vollmer, S. Ketelhut, G. vonBally, and C. Denz, “Optical tweezers induced photodamage in living cells quantified with digital holographic phase microscopy,” Proc. SPIE 8427, 84270A (2012).
[Crossref]

Vollmer, C. E.

C. E. Vollmer, C. Baune, A. Samblowski, T. Eberle, V. Händchen, J. Fiurášek, and R. Schnabel, “Quantum up-conversion of squeezed vacuum states from 1550 to 532 nm,” Phys. Rev. Lett. 112(7), 073602 (2014).
[Crossref]

vonBally, G.

A. B. Pena, B. Kemper, M. Woerdemann, A. Vollmer, S. Ketelhut, G. vonBally, and C. Denz, “Optical tweezers induced photodamage in living cells quantified with digital holographic phase microscopy,” Proc. SPIE 8427, 84270A (2012).
[Crossref]

Walborn, S. P.

V. D’Ambrosio, N. Spagnolo, L. D. Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4(1), 2432 (2013).
[Crossref]

Walmsley, I.

N. Thomas-Peter, B. Smith, A. Datta, L. Zhang, U. Dorner, and I. Walmsley, “Real-world quantum sensors: evaluating resources for precision measurement,” Phys. Rev. Lett. 107(11), 113603 (2011).
[Crossref]

Walther, P.

P. Walther, J. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De broglie wavelength of a non-local four-photon state,” Nature 429(6988), 158–161 (2004).
[Crossref]

Wheatley, T.

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

White, A. G.

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98(22), 223601 (2007).
[Crossref]

Winoto, L.

P. Carlton, J. Boulanger, C. Kervrann, J.-B. Sibarita, J. Salamero, S. Gordon-Messer, D. Bressan, J. Haber, S. Haase, L. Shao, L. Winoto, A. Matsuda, P. Kner, S. Uzawa, M. Gustafsson, Z. Kam, D. Agard, and J. Sedat, “Fast live simultaneous multiwavelength four-dimensional optical microscopy,” Proc. Natl. Acad. Sci. U. S. A. 107(37), 16016–16022 (2010).
[Crossref]

Wiseman, H.

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

Wiseman, H. M.

G. 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(1), 43–47 (2011).
[Crossref]

Woerdemann, M.

A. B. Pena, B. Kemper, M. Woerdemann, A. Vollmer, S. Ketelhut, G. vonBally, and C. Denz, “Optical tweezers induced photodamage in living cells quantified with digital holographic phase microscopy,” Proc. SPIE 8427, 84270A (2012).
[Crossref]

Wolfgramm, F.

F. Wolfgramm, C. Vitelli, F. Beduini, N. Godbout, and M. Mitchell, “Entanglement-enhanced probing of a delicate material system,” Nat. Photonics 7(1), 28–32 (2013).
[Crossref]

Wu, Y.-K.

Xiang, G.

G. 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(1), 43–47 (2011).
[Crossref]

Yonezawa, H.

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

Yurke, B.

P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light–enhanced polarization interferometer,” Phys. Rev. Lett. 59(19), 2153–2156 (1987).
[Crossref]

Zeilinger, A.

N. Tischler, M. Krenn, R. Fickler, X. Vida, A. Zeilinger, and G. Molina-Terriza, “Quantum optical rotatory dispersion,” Sci. Adv. 2(10), e1601306 (2016).
[Crossref]

P. Walther, J. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De broglie wavelength of a non-local four-photon state,” Nature 429(6988), 158–161 (2004).
[Crossref]

Zhang, L.

N. Thomas-Peter, B. Smith, A. Datta, L. Zhang, U. Dorner, and I. Walmsley, “Real-world quantum sensors: evaluating resources for precision measurement,” Phys. Rev. Lett. 107(11), 113603 (2011).
[Crossref]

Zinna, F.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. Crespi, M. Lobino, J. Matthews, A. Politi, C. Neal, R. Ramponi, R. Osellame, and J. O’BrienBrien, “Measuring protein concentration with entangled photons,” Appl. Phys. Lett. 100(23), 233704 (2012).
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Biotechnol. Adv. (1)

J. M. Choi, S. S. Han, and H. Kim, “Industrial applications of enzyme biocatalysis: Current status and future aspects,” Biotechnol. Adv. 33(7), 1443–1454 (2015).
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Carbohydr. Res. (1)

D. Combes and P. Monsan, “Sucrose hydrolysis by invertase. characterization of products and substrate inhibition,” Carbohydr. Res. 117, 215–228 (1983).
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V. Vojisavljevic, E. Pirogova, and I. Cosic, “Influence of electromagnetic radiation on enzyme kinetics,” Conf Proc IEEE Eng Med Biol Soc. 2007, 5021–5024 (2007).
[Crossref]

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J. Dowling, “Quantum optical metrology - the lowdown on high-n00n states,” Contemp. Phys. 49(2), 125–143 (2008).
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J. Biol. Chem (1)

J. Sumber, “Dinitrosalicylic acid: a reagent for the estimation of sugar in normal and diabetic urine,” J. Biol. Chem 47, 5–9 (1921).

J. Lasers Med. Sci. (1)

H. Mirmiranpour, F. S. Nosrati, S. O. Sobhani, S. N. Takantape, and A. Amjadi, “Effect of low-level laser irradiation on the function of glycated catalase,” J. Lasers Med. Sci. 9(3), 212–218 (2018).
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T. Harris and M. Keshwani, “Measurement of enzyme activity,” Methods Enzymol. 463, 57–71 (2009).
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Nat. Commun. (2)

T. Ono, R. Okamoto, and S. Takeuchi, “An entanglement-enhanced microscope,” Nat. Commun. 4(1), 2426 (2013).
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V. D’Ambrosio, N. Spagnolo, L. D. Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4(1), 2432 (2013).
[Crossref]

Nat. Photonics (6)

M. W. S. Slussarenko, H. Chrzanowski, L. Shalm, V. B. Verma, S.-W. Nam, and G. J. Pryde, “Unconditional violation of the shot-noise limit in photonic quantum metrology,” Nat. Photonics 11(11), 700–703 (2017).
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A. Berni, T. Gehring, B. Nielsen, V. Handchen, M. Paris, and U. Andersen, “Ab initio quantum-enhanced optical phase estimation using real-time feedback control,” Nat. Photonics 9(9), 577–581 (2015).
[Crossref]

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

G. 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(1), 43–47 (2011).
[Crossref]

F. Wolfgramm, C. Vitelli, F. Beduini, N. Godbout, and M. Mitchell, “Entanglement-enhanced probing of a delicate material system,” Nat. Photonics 7(1), 28–32 (2013).
[Crossref]

Nature (2)

P. Walther, J. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De broglie wavelength of a non-local four-photon state,” Nature 429(6988), 158–161 (2004).
[Crossref]

M. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled stat,” Nature 429(6988), 161–164 (2004).
[Crossref]

Optica (3)

Phys. Rev. A (1)

V. Cimini, I. Gianani, L. Ruggiero, T. Gasperi, M. Sbroscia, E. Roccia, D. Tofani, F. Bruni, M. Ricci, and M. Barbieri, “Quantum sensors for dynamical tracking of chemical processes,” Phys. Rev. A 99(5), 053817 (2019).
[Crossref]

Phys. Rev. Lett. (7)

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98(22), 223601 (2007).
[Crossref]

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[Crossref]

C. E. Vollmer, C. Baune, A. Samblowski, T. Eberle, V. Händchen, J. Fiurášek, and R. Schnabel, “Quantum up-conversion of squeezed vacuum states from 1550 to 532 nm,” Phys. Rev. Lett. 112(7), 073602 (2014).
[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96(1), 010401 (2006).
[Crossref]

N. Thomas-Peter, B. Smith, A. Datta, L. Zhang, U. Dorner, and I. Walmsley, “Real-world quantum sensors: evaluating resources for precision measurement,” Phys. Rev. Lett. 107(11), 113603 (2011).
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Proc. Natl. Acad. Sci. U. S. A. (1)

P. Carlton, J. Boulanger, C. Kervrann, J.-B. Sibarita, J. Salamero, S. Gordon-Messer, D. Bressan, J. Haber, S. Haase, L. Shao, L. Winoto, A. Matsuda, P. Kner, S. Uzawa, M. Gustafsson, Z. Kam, D. Agard, and J. Sedat, “Fast live simultaneous multiwavelength four-dimensional optical microscopy,” Proc. Natl. Acad. Sci. U. S. A. 107(37), 16016–16022 (2010).
[Crossref]

Proc. SPIE (1)

A. B. Pena, B. Kemper, M. Woerdemann, A. Vollmer, S. Ketelhut, G. vonBally, and C. Denz, “Optical tweezers induced photodamage in living cells quantified with digital holographic phase microscopy,” Proc. SPIE 8427, 84270A (2012).
[Crossref]

Sci. Adv. (1)

N. Tischler, M. Krenn, R. Fickler, X. Vida, A. Zeilinger, and G. Molina-Terriza, “Quantum optical rotatory dispersion,” Sci. Adv. 2(10), e1601306 (2016).
[Crossref]

Science (2)

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

T. Nagata, R. Okamoto, J. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four entangled photons,” Science 316(5825), 726–729 (2007).
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Other (1)

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Figures (7)

Fig. 1.
Fig. 1. Schematic rendition of the inhibitory effect of light on invertase (PDB: 4EQV) activity. Sucrose (light blue) is hydrolyzed to d-glucose and d-fructose (dark blue), while an optical measurement is carried out in either the low photon number (A) or intense laser regime (C). As the reaction is tracked, low illumination levels have a reduced impact on the enzymatic activity (B), while intense light could altered it, due to thermal and/or electrical processes (D). However, limiting the intensity of light to which the sample is exposed would result in loss of precision. This can be recovered by engineering the quantum state of the probing light.
Fig. 2.
Fig. 2. Schematics of the experiment and its working principles. (A) Experimental apparatus used for the phase tracking with quantum light. Two photons produced via spontaneous parametric down conversion with orthogonal polarizations are sent on a polarizing beam splitter (PBS) in order to produce a N00N state - a quantum superposition in which both photons are in either left-circular or right-circular polarization at once (panel B). As the probe interacts with the sugar solution an optical phase $2\phi$ between the two components of the N00N state is introduced. When reverting to the linear polarizations, the phase shift corresponds to a rotation by an angle $\phi /2$ on both photons (panel C). Finally, polarization is analyzed by means of a half wave plate (HWP) and a second PBS, and the photons are detected with avalanche photodiodes, registering coincidence events. A calibration of the measurement apparatus is reported in panel D for no sample ($\phi =0$). Oscillations in the coincidences (blue dots) occur at twice the frequency than a standard probe would deliver (red curve). This grants an improvement in its metrological features, as detailed in Section 2.
Fig. 3.
Fig. 3. Test of the adaptive measurement. The left column shows the measurement of a known phase obtained with a HWP inserted in place of the sample (upper panels) performed using the settings with $\theta _0=\pi /32$, while the right column shows the same measurement adapting the setting at each phase value; the prediction is obtained by a fitting of the previous values. After three points the error drops to its minimum (center panels), which is then tracked through all the remaining phases. The visibility is also shown (lower panels).
Fig. 4.
Fig. 4. Experimental setup: photon pairs are generated by spontaneous parametric down conversion (SPDC) source: a 3-mm $\beta$-Barium-Borate (BBO) nonlinear crystal is pumped with a CW laser at 100 mW at 405 nm (model Coherent OBIS). The laser beam is vertically polarized. The crystal is cut for a Type-I degenerate emission, so the generated photon-pairs are emitted at 810 nm and are horizontally polarized. To ensure photon indistinguishability, the photons are selected through interference filters with a bandwidth of 7.5 nm and single mode fibers. The two photons are then prepared into a N00N state in the circular polarization by means of half wave plates (HWPs) and a polarizing beam splitter (PBS): the polarization of the signal photon remains unaltered (horizontal polarization) while a HWP at 45$^\circ$ rotates the idler photon polarization to vertical. The detection stage consists in a HWP and a second PBS, which are used to select different polarizations by rotating the HWP. Photon counting is performed via single-mode-fiber-coupled avalanche photodiodes (APD) on each of the two output arms of the PBS. Coincidence counts between the two detectors are recorded. The electric signals converted by the APDs are then carried to the Field Programmable Gate Array (FPGA) board which delivers the coincidences counts, with the coincidence window fixed at 2 ns. Typical count rates are around 2000 coincidences/s.
Fig. 5.
Fig. 5. Experimental results of optical tracking and DNS assays. (A) Tracking of invertase activity using N00N states, for two different enzyme concentrations: 10 mg/ml (blue dots) and 20 mg/ml (orange squares). The concentration of sucrose corresponding to each phase measurement is also shown on the right axis. The sampling interval is 37 s. (B) Errors obtained with the adaptive measurement strategy for the two concentrations (color scheme as panel A). The light green line corresponds to the optimal lower bound achievable with 2-photon N00N states, while the dark green line is the bound related to a classical probe with the same average intensity. (C) Tracking with the DNS assay for two different invertase concentrations: 10 mg/ml (blue dots) and 20 mg/ml (orange squares). The dashed linens have been added as a guide to track the dynamics of the sugar concentration
Fig. 6.
Fig. 6. Visibility measurements. The figures report the visibility values obtained for the 10 mg/ml (blue) and 20 mg/ml (orange) invertase multiparameter tracking. The measurements show that the visibility does vary in the time scale of the reaction process, hence demonstrating the need for the multiparameter approach to obtain an unbiased estimation of the optical activity in time.
Fig. 7.
Fig. 7. Tracking invertase activity after exposure to laser light. (A) Products concentration measured with the DNS assay for samples of sucrose solution catalyzed by 10 mg/ml invertase undergone different illumination conditions. White: control sample; red: 1 h illumination with a 2.6 mW 800 nm CW laser; blue: 1 h illumination with 200 mW 405 nm CW laser. (B) Tracking with DNS assay performed on 0.8 M sucrose solutions mixed with 10 mg/ml invertase solutions undergone different illumination times. White: control sample (not illuminated); cyan: invertase illuminated for 10 min; light blue: invertase illuminated for 30 mins; dark blue: invertase illuminated for 60 min.

Equations (4)

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| ψ = a ^ H a ^ V | 0 = 1 2 ( ( a ^ R ) 2 ( a ^ L ) 2 ) | 0 = 1 2 ( | 2 R 0 L | 0 R 2 L ) ,
p ( θ ; ϕ , V ) = 1 4 ( 1 + V cos ( 8 θ 2 ϕ ) ) .
C s ( t ) = C s ( t 0 ) ϕ ( t ) ϕ ( t ) ϕ ( t 0 ) ϕ ( t ) ,
V > 1 η N ,