Abstract

We experimentally validate the vibration suppression capabilities of a weak-value-like protocol. The phase-sensitive heterodyne technique exhibits advantageous characteristics of a weak measurement including anomalous amplification in sensitivity and technical noise suppression. It does not, however, leverage the entanglement between the system and meter to amplify the signal of interest, as is typical in a weak measurement. In this formalism, we demonstrate an amplification in sensitivity to the roll angle of over 700 times. High precision roll experiments anchor numerical simulations to show that the interferometer outperforms standard interferometry by a factor of 500 in terms of peak-to-peak noise amplitude. During the measurement of a rolling stage, technical noise - primarily in the form of vibrations - is substantially attenuated. This is the first demonstration of vibration suppression capabilities that are inherent to the light from a metrology instrument instead of achieved via mechanical damping. The emulation presented in this work also identifies an avenue to achieve anomalous amplification outside of the standard weak measurement protocol.

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

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References

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2017 (3)

J. Harris, R. W. Boyd, and J. S. Lundeen, “Weak value amplification can outperform conventional measurement in the presence of detector saturation,” Phys. Rev. Lett. 118, 070802 (2017).
[Crossref] [PubMed]

J. Martínez-Rincón, C. A. Mullarkey, G. I. Viza, W.-T. Liu, and J. C. Howell, “Ultrasensitive inverse weak-value tilt meter,” Opt. Lett. 42, 13 (2017).
[Crossref]

X. Qiu, L. Xie, X. Liu, L. Luo, Z. Li, Z. Zhang, and J. Du, “Precision phase estimation based on weak-value amplification,” Appl. Phys. Lett. 110, 071105 (2017).
[Crossref]

2016 (3)

J. P. Torres and L. J. Salazar-Serrano, “Weak value amplification: a view from quantum estimation theory that highlights what it is and what isn?t,” Sci. Reports 6, 19702 (2016).
[Crossref]

J. Martínez-Rincón, W.-T. Liu, G. I. Viza, and J. C. Howell, “Can anomalous amplification be attained without postselection?” Phys. Rev. Lett. 116, 100803 (2016).
[Crossref] [PubMed]

B. Abbott and et al., “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 061102 (2016).
[Crossref] [PubMed]

2015 (2)

G. I. Viza, J. Martínez-Rincón, G. B. Alves, A. N. Jordan, and J. C. Howell, “Experimentally quantifying the advantages of weak-value-based metrology,” Phys. Rev. A 92, 032127 (2015).
[Crossref]

S. R. Gillmer, X. Yu, C. Wang, and J. D. Ellis, “Robust high-dynamic-range optical roll sensing,” Opt. Lett. 40, 2497–2500 (2015).
[Crossref] [PubMed]

2014 (3)

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86, 307 (2014).
[Crossref]

A. N. Jordan, J. Martínez-Rincón, and J. C. Howell, “Technical advantages for weak-value amplification: when less is more,” Phys. Rev. X 4, 011031 (2014).

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

2013 (3)

W. Chen, S. Zhang, and X. Long, “Angle measurement with laser feedback instrument,” Opt. Express 21, 8044–8050 (2013).
[Crossref] [PubMed]

Y. Le, W. Hou, K. Hu, and K. Shi, “High-sensitivity roll-angle interferometer,” Opt. Lett. 38, 3600–3603 (2013).
[Crossref] [PubMed]

G. Wu, M. Takahashi, K. Arai, H. Inaba, and K. Minoshima, “Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs,” Sci. Reports 3, 1894 (2013).
[Crossref]

2012 (1)

J. Dressel and A. N. Jordan, “Significance of the imaginary part of the weak value,” Phys. Rev. A 85, 012107 (2012).
[Crossref]

2010 (3)

N. Brunner and C. Simon, “Measuring small longitudinal phase shifts: Weak measurements or standard interferometry?” Phys. Rev. Lett. 105, 010405 (2010).
[Crossref] [PubMed]

A. Mitra, B. Deutsch, F. Ignatovich, C. Dykes, and L. Novotny, “Nano-optofluidic detection of single viruses and nanoparticles,” ACS Nano 4, 3 (2010).
[Crossref]

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, “Precision frequency measurements with interferometric weak values,” Phys. Rev. A 82, 063822 (2010).
[Crossref]

2009 (3)

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102, 173601 (2009).
[Crossref] [PubMed]

A. N. J. David, J. Starling, P. Ben Dixon, and J. C. Howell, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A 80, 041803 (2009).
[Crossref]

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the lisa gravitational reference sensor,” Class. Quantum Gravity 26, 8 (2009).
[Crossref]

2008 (1)

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319, 5864 (2008).
[Crossref]

2005 (1)

2004 (1)

C.-M. Wu and Y.-T. Chuang, “Roll angular displacement measurement system with microradian accuracy,” Sensors Actuators A: Phys. 116, 145–149 (2004).
[Crossref]

2003 (1)

Z. Liu, D. Lin, H. Jiang, and C. Yin, “Roll angle interferometer by means of waveplates,” Sensors Actuators A: Phys. 104, 127–131 (2003).
[Crossref]

2000 (1)

J. Lawall and E. Kessler, “Michelson interferometry with 10 pm accuracy,” Rev. Sci. Instruments 71, 7 (2000).
[Crossref]

1993 (1)

A. Stevenson, M. Gray, H.-A. Bachor, and D. McClelland, “Quantum-noise-limited interferometric phase measurements,” Appl. Opt. 32, 19 (1993).
[Crossref]

1988 (1)

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988).
[Crossref] [PubMed]

Abbott, B.

B. Abbott and et al., “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 061102 (2016).
[Crossref] [PubMed]

Aharonov, Y.

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988).
[Crossref] [PubMed]

Albert, D. Z.

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988).
[Crossref] [PubMed]

Alves, G. B.

G. I. Viza, J. Martínez-Rincón, G. B. Alves, A. N. Jordan, and J. C. Howell, “Experimentally quantifying the advantages of weak-value-based metrology,” Phys. Rev. A 92, 032127 (2015).
[Crossref]

Arai, K.

G. Wu, M. Takahashi, K. Arai, H. Inaba, and K. Minoshima, “Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs,” Sci. Reports 3, 1894 (2013).
[Crossref]

Bachor, H.-A.

A. Stevenson, M. Gray, H.-A. Bachor, and D. McClelland, “Quantum-noise-limited interferometric phase measurements,” Appl. Opt. 32, 19 (1993).
[Crossref]

Ben Dixon, P.

A. N. J. David, J. Starling, P. Ben Dixon, and J. C. Howell, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A 80, 041803 (2009).
[Crossref]

Boyd, R. W.

J. Harris, R. W. Boyd, and J. S. Lundeen, “Weak value amplification can outperform conventional measurement in the presence of detector saturation,” Phys. Rev. Lett. 118, 070802 (2017).
[Crossref] [PubMed]

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86, 307 (2014).
[Crossref]

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

Braxmaier, C.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the lisa gravitational reference sensor,” Class. Quantum Gravity 26, 8 (2009).
[Crossref]

Brunner, N.

N. Brunner and C. Simon, “Measuring small longitudinal phase shifts: Weak measurements or standard interferometry?” Phys. Rev. Lett. 105, 010405 (2010).
[Crossref] [PubMed]

Chen, W.

Chuang, Y.-T.

C.-M. Wu and Y.-T. Chuang, “Roll angular displacement measurement system with microradian accuracy,” Sensors Actuators A: Phys. 116, 145–149 (2004).
[Crossref]

David, A. N. J.

A. N. J. David, J. Starling, P. Ben Dixon, and J. C. Howell, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A 80, 041803 (2009).
[Crossref]

Deutsch, B.

A. Mitra, B. Deutsch, F. Ignatovich, C. Dykes, and L. Novotny, “Nano-optofluidic detection of single viruses and nanoparticles,” ACS Nano 4, 3 (2010).
[Crossref]

Dixon, P. B.

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, “Precision frequency measurements with interferometric weak values,” Phys. Rev. A 82, 063822 (2010).
[Crossref]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102, 173601 (2009).
[Crossref] [PubMed]

Dressel, J.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86, 307 (2014).
[Crossref]

J. Dressel and A. N. Jordan, “Significance of the imaginary part of the weak value,” Phys. Rev. A 85, 012107 (2012).
[Crossref]

Du, J.

X. Qiu, L. Xie, X. Liu, L. Luo, Z. Li, Z. Zhang, and J. Du, “Precision phase estimation based on weak-value amplification,” Appl. Phys. Lett. 110, 071105 (2017).
[Crossref]

Dykes, C.

A. Mitra, B. Deutsch, F. Ignatovich, C. Dykes, and L. Novotny, “Nano-optofluidic detection of single viruses and nanoparticles,” ACS Nano 4, 3 (2010).
[Crossref]

Ellis, J. D.

Gillmer, S. R.

Gohlke, M.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the lisa gravitational reference sensor,” Class. Quantum Gravity 26, 8 (2009).
[Crossref]

Gray, M.

A. Stevenson, M. Gray, H.-A. Bachor, and D. McClelland, “Quantum-noise-limited interferometric phase measurements,” Appl. Opt. 32, 19 (1993).
[Crossref]

Harris, J.

J. Harris, R. W. Boyd, and J. S. Lundeen, “Weak value amplification can outperform conventional measurement in the presence of detector saturation,” Phys. Rev. Lett. 118, 070802 (2017).
[Crossref] [PubMed]

Hosten, O.

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319, 5864 (2008).
[Crossref]

Hou, W.

Howell, J. C.

J. Martínez-Rincón, C. A. Mullarkey, G. I. Viza, W.-T. Liu, and J. C. Howell, “Ultrasensitive inverse weak-value tilt meter,” Opt. Lett. 42, 13 (2017).
[Crossref]

J. Martínez-Rincón, W.-T. Liu, G. I. Viza, and J. C. Howell, “Can anomalous amplification be attained without postselection?” Phys. Rev. Lett. 116, 100803 (2016).
[Crossref] [PubMed]

G. I. Viza, J. Martínez-Rincón, G. B. Alves, A. N. Jordan, and J. C. Howell, “Experimentally quantifying the advantages of weak-value-based metrology,” Phys. Rev. A 92, 032127 (2015).
[Crossref]

A. N. Jordan, J. Martínez-Rincón, and J. C. Howell, “Technical advantages for weak-value amplification: when less is more,” Phys. Rev. X 4, 011031 (2014).

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, “Precision frequency measurements with interferometric weak values,” Phys. Rev. A 82, 063822 (2010).
[Crossref]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102, 173601 (2009).
[Crossref] [PubMed]

A. N. J. David, J. Starling, P. Ben Dixon, and J. C. Howell, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A 80, 041803 (2009).
[Crossref]

Hu, K.

Hu, M.-J.

M.-J. Hu and Y.-S. Zhang, “Gravitational wave detection via weak measurements amplification,” arXiv (2017).

Ignatovich, F.

A. Mitra, B. Deutsch, F. Ignatovich, C. Dykes, and L. Novotny, “Nano-optofluidic detection of single viruses and nanoparticles,” ACS Nano 4, 3 (2010).
[Crossref]

Inaba, H.

G. Wu, M. Takahashi, K. Arai, H. Inaba, and K. Minoshima, “Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs,” Sci. Reports 3, 1894 (2013).
[Crossref]

Jiang, H.

Z. Liu, D. Lin, H. Jiang, and C. Yin, “Roll angle interferometer by means of waveplates,” Sensors Actuators A: Phys. 104, 127–131 (2003).
[Crossref]

Jin, G.

Johann, U.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the lisa gravitational reference sensor,” Class. Quantum Gravity 26, 8 (2009).
[Crossref]

Jordan, A. N.

G. I. Viza, J. Martínez-Rincón, G. B. Alves, A. N. Jordan, and J. C. Howell, “Experimentally quantifying the advantages of weak-value-based metrology,” Phys. Rev. A 92, 032127 (2015).
[Crossref]

A. N. Jordan, J. Martínez-Rincón, and J. C. Howell, “Technical advantages for weak-value amplification: when less is more,” Phys. Rev. X 4, 011031 (2014).

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86, 307 (2014).
[Crossref]

J. Dressel and A. N. Jordan, “Significance of the imaginary part of the weak value,” Phys. Rev. A 85, 012107 (2012).
[Crossref]

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, “Precision frequency measurements with interferometric weak values,” Phys. Rev. A 82, 063822 (2010).
[Crossref]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102, 173601 (2009).
[Crossref] [PubMed]

Kessler, E.

J. Lawall and E. Kessler, “Michelson interferometry with 10 pm accuracy,” Rev. Sci. Instruments 71, 7 (2000).
[Crossref]

Kwiat, P.

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319, 5864 (2008).
[Crossref]

Lawall, J.

J. Lawall and E. Kessler, “Michelson interferometry with 10 pm accuracy,” Rev. Sci. Instruments 71, 7 (2000).
[Crossref]

Le, Y.

Li, S.

Li, Z.

X. Qiu, L. Xie, X. Liu, L. Luo, Z. Li, Z. Zhang, and J. Du, “Precision phase estimation based on weak-value amplification,” Appl. Phys. Lett. 110, 071105 (2017).
[Crossref]

Lin, D.

Z. Liu, D. Lin, H. Jiang, and C. Yin, “Roll angle interferometer by means of waveplates,” Sensors Actuators A: Phys. 104, 127–131 (2003).
[Crossref]

Liu, W.-T.

J. Martínez-Rincón, C. A. Mullarkey, G. I. Viza, W.-T. Liu, and J. C. Howell, “Ultrasensitive inverse weak-value tilt meter,” Opt. Lett. 42, 13 (2017).
[Crossref]

J. Martínez-Rincón, W.-T. Liu, G. I. Viza, and J. C. Howell, “Can anomalous amplification be attained without postselection?” Phys. Rev. Lett. 116, 100803 (2016).
[Crossref] [PubMed]

Liu, X.

X. Qiu, L. Xie, X. Liu, L. Luo, Z. Li, Z. Zhang, and J. Du, “Precision phase estimation based on weak-value amplification,” Appl. Phys. Lett. 110, 071105 (2017).
[Crossref]

Liu, Z.

Z. Liu, D. Lin, H. Jiang, and C. Yin, “Roll angle interferometer by means of waveplates,” Sensors Actuators A: Phys. 104, 127–131 (2003).
[Crossref]

Long, X.

Lundeen, J. S.

J. Harris, R. W. Boyd, and J. S. Lundeen, “Weak value amplification can outperform conventional measurement in the presence of detector saturation,” Phys. Rev. Lett. 118, 070802 (2017).
[Crossref] [PubMed]

Luo, L.

X. Qiu, L. Xie, X. Liu, L. Luo, Z. Li, Z. Zhang, and J. Du, “Precision phase estimation based on weak-value amplification,” Appl. Phys. Lett. 110, 071105 (2017).
[Crossref]

Magaa-Loaiza, O. S.

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

Malik, M.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86, 307 (2014).
[Crossref]

Martínez-Rincón, J.

J. Martínez-Rincón, C. A. Mullarkey, G. I. Viza, W.-T. Liu, and J. C. Howell, “Ultrasensitive inverse weak-value tilt meter,” Opt. Lett. 42, 13 (2017).
[Crossref]

J. Martínez-Rincón, W.-T. Liu, G. I. Viza, and J. C. Howell, “Can anomalous amplification be attained without postselection?” Phys. Rev. Lett. 116, 100803 (2016).
[Crossref] [PubMed]

G. I. Viza, J. Martínez-Rincón, G. B. Alves, A. N. Jordan, and J. C. Howell, “Experimentally quantifying the advantages of weak-value-based metrology,” Phys. Rev. A 92, 032127 (2015).
[Crossref]

A. N. Jordan, J. Martínez-Rincón, and J. C. Howell, “Technical advantages for weak-value amplification: when less is more,” Phys. Rev. X 4, 011031 (2014).

J. Martínez-Rincón, “Weak-values metrological techniques for parameter estimation,” Ph.D. thesis (2017).

McClelland, D.

A. Stevenson, M. Gray, H.-A. Bachor, and D. McClelland, “Quantum-noise-limited interferometric phase measurements,” Appl. Opt. 32, 19 (1993).
[Crossref]

Miatto, F. M.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86, 307 (2014).
[Crossref]

Minoshima, K.

G. Wu, M. Takahashi, K. Arai, H. Inaba, and K. Minoshima, “Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs,” Sci. Reports 3, 1894 (2013).
[Crossref]

Mirhosseini, M.

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

Mitra, A.

A. Mitra, B. Deutsch, F. Ignatovich, C. Dykes, and L. Novotny, “Nano-optofluidic detection of single viruses and nanoparticles,” ACS Nano 4, 3 (2010).
[Crossref]

Mullarkey, C. A.

Novotny, L.

A. Mitra, B. Deutsch, F. Ignatovich, C. Dykes, and L. Novotny, “Nano-optofluidic detection of single viruses and nanoparticles,” ACS Nano 4, 3 (2010).
[Crossref]

Peters, A.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the lisa gravitational reference sensor,” Class. Quantum Gravity 26, 8 (2009).
[Crossref]

Qiu, X.

X. Qiu, L. Xie, X. Liu, L. Luo, Z. Li, Z. Zhang, and J. Du, “Precision phase estimation based on weak-value amplification,” Appl. Phys. Lett. 110, 071105 (2017).
[Crossref]

Rodenburg, B.

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

Salazar-Serrano, L. J.

J. P. Torres and L. J. Salazar-Serrano, “Weak value amplification: a view from quantum estimation theory that highlights what it is and what isn?t,” Sci. Reports 6, 19702 (2016).
[Crossref]

Schuldt, T.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the lisa gravitational reference sensor,” Class. Quantum Gravity 26, 8 (2009).
[Crossref]

Shi, K.

Simon, C.

N. Brunner and C. Simon, “Measuring small longitudinal phase shifts: Weak measurements or standard interferometry?” Phys. Rev. Lett. 105, 010405 (2010).
[Crossref] [PubMed]

Slocum, A. H.

A. H. Slocum, Precision Machine Design (Society of Manufacturing Engineers, 1992).

Starling, D. J.

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, “Precision frequency measurements with interferometric weak values,” Phys. Rev. A 82, 063822 (2010).
[Crossref]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102, 173601 (2009).
[Crossref] [PubMed]

Starling, J.

A. N. J. David, J. Starling, P. Ben Dixon, and J. C. Howell, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A 80, 041803 (2009).
[Crossref]

Stevenson, A.

A. Stevenson, M. Gray, H.-A. Bachor, and D. McClelland, “Quantum-noise-limited interferometric phase measurements,” Appl. Opt. 32, 19 (1993).
[Crossref]

Takahashi, M.

G. Wu, M. Takahashi, K. Arai, H. Inaba, and K. Minoshima, “Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs,” Sci. Reports 3, 1894 (2013).
[Crossref]

Torres, J. P.

J. P. Torres and L. J. Salazar-Serrano, “Weak value amplification: a view from quantum estimation theory that highlights what it is and what isn?t,” Sci. Reports 6, 19702 (2016).
[Crossref]

Vaidman, L.

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988).
[Crossref] [PubMed]

Viza, G. I.

J. Martínez-Rincón, C. A. Mullarkey, G. I. Viza, W.-T. Liu, and J. C. Howell, “Ultrasensitive inverse weak-value tilt meter,” Opt. Lett. 42, 13 (2017).
[Crossref]

J. Martínez-Rincón, W.-T. Liu, G. I. Viza, and J. C. Howell, “Can anomalous amplification be attained without postselection?” Phys. Rev. Lett. 116, 100803 (2016).
[Crossref] [PubMed]

G. I. Viza, J. Martínez-Rincón, G. B. Alves, A. N. Jordan, and J. C. Howell, “Experimentally quantifying the advantages of weak-value-based metrology,” Phys. Rev. A 92, 032127 (2015).
[Crossref]

Wang, C.

Weise, D.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the lisa gravitational reference sensor,” Class. Quantum Gravity 26, 8 (2009).
[Crossref]

Wu, C.-M.

C.-M. Wu and Y.-T. Chuang, “Roll angular displacement measurement system with microradian accuracy,” Sensors Actuators A: Phys. 116, 145–149 (2004).
[Crossref]

Wu, G.

G. Wu, M. Takahashi, K. Arai, H. Inaba, and K. Minoshima, “Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs,” Sci. Reports 3, 1894 (2013).
[Crossref]

Xie, L.

X. Qiu, L. Xie, X. Liu, L. Luo, Z. Li, Z. Zhang, and J. Du, “Precision phase estimation based on weak-value amplification,” Appl. Phys. Lett. 110, 071105 (2017).
[Crossref]

Yang, C.

Yin, C.

Z. Liu, D. Lin, H. Jiang, and C. Yin, “Roll angle interferometer by means of waveplates,” Sensors Actuators A: Phys. 104, 127–131 (2003).
[Crossref]

Yu, X.

Zhang, E.

Zhang, S.

Zhang, Y.-S.

M.-J. Hu and Y.-S. Zhang, “Gravitational wave detection via weak measurements amplification,” arXiv (2017).

Zhang, Z.

X. Qiu, L. Xie, X. Liu, L. Luo, Z. Li, Z. Zhang, and J. Du, “Precision phase estimation based on weak-value amplification,” Appl. Phys. Lett. 110, 071105 (2017).
[Crossref]

ACS Nano (1)

A. Mitra, B. Deutsch, F. Ignatovich, C. Dykes, and L. Novotny, “Nano-optofluidic detection of single viruses and nanoparticles,” ACS Nano 4, 3 (2010).
[Crossref]

Appl. Opt. (1)

A. Stevenson, M. Gray, H.-A. Bachor, and D. McClelland, “Quantum-noise-limited interferometric phase measurements,” Appl. Opt. 32, 19 (1993).
[Crossref]

Appl. Phys. Lett. (1)

X. Qiu, L. Xie, X. Liu, L. Luo, Z. Li, Z. Zhang, and J. Du, “Precision phase estimation based on weak-value amplification,” Appl. Phys. Lett. 110, 071105 (2017).
[Crossref]

Class. Quantum Gravity (1)

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the lisa gravitational reference sensor,” Class. Quantum Gravity 26, 8 (2009).
[Crossref]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (4)

A. N. J. David, J. Starling, P. Ben Dixon, and J. C. Howell, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A 80, 041803 (2009).
[Crossref]

G. I. Viza, J. Martínez-Rincón, G. B. Alves, A. N. Jordan, and J. C. Howell, “Experimentally quantifying the advantages of weak-value-based metrology,” Phys. Rev. A 92, 032127 (2015).
[Crossref]

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, “Precision frequency measurements with interferometric weak values,” Phys. Rev. A 82, 063822 (2010).
[Crossref]

J. Dressel and A. N. Jordan, “Significance of the imaginary part of the weak value,” Phys. Rev. A 85, 012107 (2012).
[Crossref]

Phys. Rev. Lett. (7)

B. Abbott and et al., “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 061102 (2016).
[Crossref] [PubMed]

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

N. Brunner and C. Simon, “Measuring small longitudinal phase shifts: Weak measurements or standard interferometry?” Phys. Rev. Lett. 105, 010405 (2010).
[Crossref] [PubMed]

J. Martínez-Rincón, W.-T. Liu, G. I. Viza, and J. C. Howell, “Can anomalous amplification be attained without postselection?” Phys. Rev. Lett. 116, 100803 (2016).
[Crossref] [PubMed]

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988).
[Crossref] [PubMed]

J. Harris, R. W. Boyd, and J. S. Lundeen, “Weak value amplification can outperform conventional measurement in the presence of detector saturation,” Phys. Rev. Lett. 118, 070802 (2017).
[Crossref] [PubMed]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102, 173601 (2009).
[Crossref] [PubMed]

Phys. Rev. X (1)

A. N. Jordan, J. Martínez-Rincón, and J. C. Howell, “Technical advantages for weak-value amplification: when less is more,” Phys. Rev. X 4, 011031 (2014).

Rev. Mod. Phys. (1)

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86, 307 (2014).
[Crossref]

Rev. Sci. Instruments (1)

J. Lawall and E. Kessler, “Michelson interferometry with 10 pm accuracy,” Rev. Sci. Instruments 71, 7 (2000).
[Crossref]

Sci. Reports (2)

G. Wu, M. Takahashi, K. Arai, H. Inaba, and K. Minoshima, “Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs,” Sci. Reports 3, 1894 (2013).
[Crossref]

J. P. Torres and L. J. Salazar-Serrano, “Weak value amplification: a view from quantum estimation theory that highlights what it is and what isn?t,” Sci. Reports 6, 19702 (2016).
[Crossref]

Science (1)

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319, 5864 (2008).
[Crossref]

Sensors Actuators A: Phys. (2)

C.-M. Wu and Y.-T. Chuang, “Roll angular displacement measurement system with microradian accuracy,” Sensors Actuators A: Phys. 116, 145–149 (2004).
[Crossref]

Z. Liu, D. Lin, H. Jiang, and C. Yin, “Roll angle interferometer by means of waveplates,” Sensors Actuators A: Phys. 104, 127–131 (2003).
[Crossref]

Other (4)

J. D. Ellis, Field Guide to Displacement Measuring Interferometry (SPIE, 2014).
[Crossref]

M.-J. Hu and Y.-S. Zhang, “Gravitational wave detection via weak measurements amplification,” arXiv (2017).

J. Martínez-Rincón, “Weak-values metrological techniques for parameter estimation,” Ph.D. thesis (2017).

A. H. Slocum, Precision Machine Design (Society of Manufacturing Engineers, 1992).

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Figures (5)

Fig. 1
Fig. 1 Full schematic of the measurement setup used for interferometric roll sensing; BS, beamsplitter, AOM, acousto-optic modulator, HWP, halfwave plate, PBS, polarizing beamsplitter, pol., polarizer, PDr and PDm, reference and measurement photodetectors, QWP, quarterwave plate. A Renishaw interferometer measures pitch for calibration from an orthogonal measurement position.
Fig. 2
Fig. 2 Simulations of the weak-value-emulated amplification in the heterodyne roll interferometer. (a) The phase sensitivity between pre- and post-selection as a function of QWP angle, θ, and HWP ‘roll’ angle, α. (b) The AC amplitude of the interferometer drops to near zero when the phase sensitivity is amplified. (c) The derivative of phase as a function of roll angle showing that the phase sensitivity is amplified by over 700 times. The QWP angle of 0.160° is experimentally validated later in Fig. 3. (d) Amplification manifests mainly in the imaginary part of the complex phasor signal.
Fig. 3
Fig. 3 The effects of increased phase sensitivity in the interferometer in the (a) time domain and (b) frequency domain. As the fast axis of the QWP, θ, approaches the fast axis of the HWP, α, technical noise - mainly in the form of vibrations - is suppressed.
Fig. 4
Fig. 4 Statistical limitations of shot noise and detector noise as outlined in Eqs. (7)(8). In the absence of all forms of technical noise, our setup is fundamentally limited by detector noise due to the discarding of photons during post-selection.
Fig. 5
Fig. 5 Experimental peak-to-peak noise results with vibration content as shown in Fig. 3. The numerical simulation assumes white noise with the same nominal amplitude as the raw phase signals recorded in this paper followed by post-processing from Eq. (6) - the theoretical line.

Equations (8)

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

P = [ 1 0 0 0 ] , H ( α ) = [ cos ( 2 α ) sin ( 2 α ) sin ( 2 α ) cos ( 2 α ) ] , Q = [ 1 0 0 i ] R ( θ ) = [ cos ( θ ) sin ( θ ) sin ( θ ) cos ( θ ) ] , and E 0 = [ A 1 e i ω 1 t A 2 e i ω 2 t ] ,
E s = PH ( α ) R ( θ ) QR ( θ ) E 0 ,
E s = [ A 1 e i ω 1 t { i sin ( θ ) [ sin ( 2 α + θ ) ] + cos ( θ ) [ cos ( 2 α + θ ) ] } + A 2 e i ω 2 t { i cos ( θ ) [ sin ( 2 α + θ ) ] sin ( θ ) [ cos ( 2 α + θ ) ] } ] [ 1 0 ] .
I = | E s | 2 = C 1 2 A 1 2 + C 2 2 A 2 2 + 2 C 1 C 2 A 1 A 2 cos [ ( ω 1 ω 2 ) t + ϕ m ] .
tan ( ϕ m ) = tan ( 4 α + 2 θ ) sin ( 2 θ ) , C 1 = 1 2 2 + cos [ 4 α ] + cos [ 4 ( α + θ ) ] , and C 2 = 1 2 2 cos [ 4 α ] cos [ 4 ( α + θ ) ] .
α = θ 2 1 4 arctan [ tan ( ϕ m ) sin ( 2 θ ) ]
ϕ s = 1 λ 2 hc λ B η P ,
ϕ d = NEP B P ,

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