Weak interference in the high-signal regime

doi:10.1364/OE.20.018869

Weak interference in the high-signal regime

Juan P. Torres, Graciana Puentes, Nathaniel Hermosa, and Luis Jose Salazar-Serrano »View Author Affiliations

Optics Express, Vol. 20, Issue 17, pp. 18869-18875 (2012)
http://dx.doi.org/10.1364/OE.20.018869

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Abstract

Weak amplification is a signal enhancement technique which is used to measure tiny changes that otherwise cannot be determined because of technical limitations. It is based on: a) the existence of a weak interaction which couples a property of a system (the system) with a separate degree of freedom (the pointer), and b) the measurement of an anomalously large mean value of the pointer state (weak mean value), after appropriate pre-and post-selection of the state of the system. Unfortunately, the weak amplification process is generally accompanied by severe losses of the detected signal, which limits its applicability. However, we will show here that since weak amplification is essentially the result of an interference phenomena, it should be possible to use the degree of interference (weak interference) to get relevant information about the physical system under study in a more general scenario, where the signal is not severely depleted (high-signal regime).

OCIS Codes
(030.1670) Coherence and statistical optics : Coherent optical effects
(270.0270) Quantum optics : Quantum optics
(350.7420) Other areas of optics : Waves

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: May 1, 2012
Revised Manuscript: June 17, 2012
Manuscript Accepted: June 18, 2012
Published: August 2, 2012

Citation
Juan P. Torres, Graciana Puentes, Nathaniel Hermosa, and Luis Jose Salazar-Serrano, "Weak interference in the high-signal regime," Opt. Express 20, 18869-18875 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-17-18869

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References

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]
O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science319, 787–790 (2008). [CrossRef] [PubMed]
N. W. Ritchie, J. G. Story, and R. G. Hulet, “Realization of a measuremernt of a weak value,”Phys. Rev. Lett.66, 1107–1110 (1991). [CrossRef] [PubMed]
P. Ben 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]
D. J. Starling, P. Ben Dixon, A. N. Jordan, and J. C. Howell, “Precision frequency measurements with interferometric weak values,” Phys. Rev. A82, 063822 (2010). [CrossRef]
N. Brunner, A. Acin, D. Collins, N. Gisin, and V. Scarini, “Optical telecom networks as weak quantum measurements with postselection,” Phys. Rev. Lett.91, 180402 (2003). [CrossRef] [PubMed]
D. R. Solli, C. F. McCormick, R. Y. Chiao, S. Popescu, and J. H. Hickmann, “Fast light, slow light, and phase singularities: a connection to generalized weak values,” Phys. Rev. Lett.92, 043601 (2004). [CrossRef] [PubMed]
I. M. Duck, P. M. Stevenson, and E. C. G. Sudarhshan, “The sense in which a ’weak measurement’ of a spin-1/2 particles’s spin component yields a value of 100,” Phys. Rev. D40, 2112–2117 (1989). [CrossRef]
J. C. Howell, D. J. Starling, P. B. Dixon, K. P. Vudyasetu, and A. N. Jordan, “Interferometric weak value deflections: quantum and classical treatments,” Phys. Rev. A81, 033813 (2010). [CrossRef]
G. J. Pryde, J. L. O’Brien, A. G. White, T. C. Ralph, and H. M. Wiseman, “Measurement of quantum weak values of photon polarization,” Phys. Rev. Lett.94, 220405 (2005). [CrossRef] [PubMed]
M. E. Goggin, M. P. Almeida, M. Barbieri, B. P. Lanyon, J. L. O’Brien, A. G. White, and G. J. Pryde, “Violation of the Leggett-Garg inequality with weak measurements of photons,” Proc. Natl. Acad. Sci. U.S.A.108, 1256–1261 (2011). [CrossRef] [PubMed]
E. Wolf, J. T. Foley, and F. Gori, “Frequency shifts of frequency lines produced by scattering from spatially random media,” J. Opt. Soc. Am. A6, 1142–1149 (1989). [CrossRef]
C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science322, 1857–1861 (2008). [CrossRef] [PubMed]
B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. S. Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science330, 1368–1370 (2010). [CrossRef] [PubMed]
D. J. Starling, P. Ben Dixon, A. N. Jordan, and J. C. Howell, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A80, 041803 (2009). [CrossRef]
A. Nishizawa, K. Nakamura, and M. Fujimoto, “Weak-value amplification in a shot-noise-limited interferometer,” Phys. Rev. A85, 062108 (2012). [CrossRef]
J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett.80, 3217–3219 (1998). [CrossRef]
M. V. Vasnetsov, J. P. Torres, D. V. Petrov, and L. Torner, “Measurement of orbital angular momentum spectrum of a light beam,” Opt. Lett.28, 2285–2287 (2003). [CrossRef] [PubMed]

Acin, A.
Aharonov, Y.
Albert, D. Z.
Allen, L.
Almeida, M. P.
Barbieri, M.
Ben Dixon, P.
Brunner, N.
Chiao, R. Y.
Collins, D.
Courtial, J.
Dholakia, K.
Dixon, P. B.
Duck, I. M.
Foley, J. T.
Freudiger, C. W.
Fujimoto, M.
Gisin, N.
Goggin, M. E.
Gori, F.
He, C.
Hickmann, J. H.
Holtom, G. R.
Hosten, O.
Howell, J. C.
Hulet, R. G.
Jordan, A. N.
Kang, J. X.
Kwiat, P.
Lanyon, B. P.
Lu, S.
McCormick, C. F.
Min, W.
Nakamura, K.
Nishizawa, A.
O’Brien, J. L.
Padgett, M. J.
Petrov, D. V.
Popescu, S.
Pryde, G. J.
Ralph, T. C.
Reichman, J.
Ritchie, N. W.
Robertson, D. A.
Saar, B. G.
Scarini, V.
Solli, D. R.
Stanley, C. M.
Starling, D. J.
Stevenson, P. M.
Story, J. G.
Sudarhshan, E. C. G.
Torner, L.
Torres, J. P.
Tsai, J. C.
Vaidman, L.
Vasnetsov, M. V.
Vudyasetu, K. P.
White, A. G.
Wiseman, H. M.
Wolf, E.
Xie, X. S.

J. Opt. Soc. Am. A

E. Wolf, J. T. Foley, and F. Gori, “Frequency shifts of frequency lines produced by scattering from spatially random media,” J. Opt. Soc. Am. A6, 1142–1149 (1989). [CrossRef]

Opt. Lett.

M. V. Vasnetsov, J. P. Torres, D. V. Petrov, and L. Torner, “Measurement of orbital angular momentum spectrum of a light beam,” Opt. Lett.28, 2285–2287 (2003). [CrossRef] [PubMed]

Phys. Rev. A

D. J. Starling, P. Ben Dixon, A. N. Jordan, and J. C. Howell, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A80, 041803 (2009). [CrossRef]
A. Nishizawa, K. Nakamura, and M. Fujimoto, “Weak-value amplification in a shot-noise-limited interferometer,” Phys. Rev. A85, 062108 (2012). [CrossRef]
D. J. Starling, P. Ben Dixon, A. N. Jordan, and J. C. Howell, “Precision frequency measurements with interferometric weak values,” Phys. Rev. A82, 063822 (2010). [CrossRef]
J. C. Howell, D. J. Starling, P. B. Dixon, K. P. Vudyasetu, and A. N. Jordan, “Interferometric weak value deflections: quantum and classical treatments,” Phys. Rev. A81, 033813 (2010). [CrossRef]

Phys. Rev. D

I. M. Duck, P. M. Stevenson, and E. C. G. Sudarhshan, “The sense in which a ’weak measurement’ of a spin-1/2 particles’s spin component yields a value of 100,” Phys. Rev. D40, 2112–2117 (1989). [CrossRef]

Phys. Rev. Lett.

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett.80, 3217–3219 (1998). [CrossRef]
G. J. Pryde, J. L. O’Brien, A. G. White, T. C. Ralph, and H. M. Wiseman, “Measurement of quantum weak values of photon polarization,” Phys. Rev. Lett.94, 220405 (2005). [CrossRef] [PubMed]
N. Brunner, A. Acin, D. Collins, N. Gisin, and V. Scarini, “Optical telecom networks as weak quantum measurements with postselection,” Phys. Rev. Lett.91, 180402 (2003). [CrossRef] [PubMed]
D. R. Solli, C. F. McCormick, R. Y. Chiao, S. Popescu, and J. H. Hickmann, “Fast light, slow light, and phase singularities: a connection to generalized weak values,” Phys. Rev. Lett.92, 043601 (2004). [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]
N. W. Ritchie, J. G. Story, and R. G. Hulet, “Realization of a measuremernt of a weak value,”Phys. Rev. Lett.66, 1107–1110 (1991). [CrossRef] [PubMed]
P. Ben 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]

Proc. Natl. Acad. Sci. U.S.A.

M. E. Goggin, M. P. Almeida, M. Barbieri, B. P. Lanyon, J. L. O’Brien, A. G. White, and G. J. Pryde, “Violation of the Leggett-Garg inequality with weak measurements of photons,” Proc. Natl. Acad. Sci. U.S.A.108, 1256–1261 (2011). [CrossRef] [PubMed]

Science

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science319, 787–790 (2008). [CrossRef] [PubMed]
C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science322, 1857–1861 (2008). [CrossRef] [PubMed]
B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. S. Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science330, 1368–1370 (2010). [CrossRef] [PubMed]

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[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]

[2] O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science319, 787–790 (2008). [CrossRef] [PubMed]

[3] N. W. Ritchie, J. G. Story, and R. G. Hulet, “Realization of a measuremernt of a weak value,”Phys. Rev. Lett.66, 1107–1110 (1991). [CrossRef] [PubMed]

[4] P. Ben 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]

[5] D. J. Starling, P. Ben Dixon, A. N. Jordan, and J. C. Howell, “Precision frequency measurements with interferometric weak values,” Phys. Rev. A82, 063822 (2010). [CrossRef]

[6] N. Brunner, A. Acin, D. Collins, N. Gisin, and V. Scarini, “Optical telecom networks as weak quantum measurements with postselection,” Phys. Rev. Lett.91, 180402 (2003). [CrossRef] [PubMed]

[7] D. R. Solli, C. F. McCormick, R. Y. Chiao, S. Popescu, and J. H. Hickmann, “Fast light, slow light, and phase singularities: a connection to generalized weak values,” Phys. Rev. Lett.92, 043601 (2004). [CrossRef] [PubMed]

[8] I. M. Duck, P. M. Stevenson, and E. C. G. Sudarhshan, “The sense in which a ’weak measurement’ of a spin-1/2 particles’s spin component yields a value of 100,” Phys. Rev. D40, 2112–2117 (1989). [CrossRef]

[9] J. C. Howell, D. J. Starling, P. B. Dixon, K. P. Vudyasetu, and A. N. Jordan, “Interferometric weak value deflections: quantum and classical treatments,” Phys. Rev. A81, 033813 (2010). [CrossRef]

[10] G. J. Pryde, J. L. O’Brien, A. G. White, T. C. Ralph, and H. M. Wiseman, “Measurement of quantum weak values of photon polarization,” Phys. Rev. Lett.94, 220405 (2005). [CrossRef] [PubMed]

[11] M. E. Goggin, M. P. Almeida, M. Barbieri, B. P. Lanyon, J. L. O’Brien, A. G. White, and G. J. Pryde, “Violation of the Leggett-Garg inequality with weak measurements of photons,” Proc. Natl. Acad. Sci. U.S.A.108, 1256–1261 (2011). [CrossRef] [PubMed]

[12] E. Wolf, J. T. Foley, and F. Gori, “Frequency shifts of frequency lines produced by scattering from spatially random media,” J. Opt. Soc. Am. A6, 1142–1149 (1989). [CrossRef]

[13] C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science322, 1857–1861 (2008). [CrossRef] [PubMed]

[14] B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. S. Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science330, 1368–1370 (2010). [CrossRef] [PubMed]

[15] D. J. Starling, P. Ben Dixon, A. N. Jordan, and J. C. Howell, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A80, 041803 (2009). [CrossRef]

[16] A. Nishizawa, K. Nakamura, and M. Fujimoto, “Weak-value amplification in a shot-noise-limited interferometer,” Phys. Rev. A85, 062108 (2012). [CrossRef]

[17] J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett.80, 3217–3219 (1998). [CrossRef]

[18] M. V. Vasnetsov, J. P. Torres, D. V. Petrov, and L. Torner, “Measurement of orbital angular momentum spectrum of a light beam,” Opt. Lett.28, 2285–2287 (2003). [CrossRef] [PubMed]

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Weak interference in the high-signal regime

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Abstract

References

J. Opt. Soc. Am. A

Opt. Lett.

Phys. Rev. A

Phys. Rev. D

Phys. Rev. Lett.

Proc. Natl. Acad. Sci. U.S.A.

Science

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