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).

© 2012 OSA

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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]

2012

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

2011

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]

2010

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]

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, “Precision frequency measurements with interferometric weak values,” Phys. Rev. A82, 063822 (2010).
[CrossRef]

2009

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, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A80, 041803 (2009).
[CrossRef]

2008

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]

2005

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]

2004

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]

2003

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]

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]

1998

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]

1991

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]

1989

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]

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]

1988

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]

Acin, A.

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]

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]

Allen, L.

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]

Almeida, M. P.

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]

Barbieri, M.

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]

Ben Dixon, P.

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]

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, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A80, 041803 (2009).
[CrossRef]

Brunner, N.

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]

Chiao, R. Y.

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]

Collins, D.

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]

Courtial, J.

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]

Dholakia, K.

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]

Dixon, P. B.

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]

Duck, I. M.

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]

Foley, J. T.

Freudiger, C. W.

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]

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]

Fujimoto, M.

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

Gisin, N.

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]

Goggin, M. E.

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]

Gori, F.

He, C.

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]

Hickmann, J. H.

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]

Holtom, G. R.

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]

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]

Hosten, O.

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

Howell, J. C.

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]

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, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A80, 041803 (2009).
[CrossRef]

Hulet, R. G.

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]

Jordan, A. N.

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]

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, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A80, 041803 (2009).
[CrossRef]

Kang, J. X.

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]

Kwiat, P.

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

Lanyon, B. P.

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]

Lu, S.

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]

McCormick, C. F.

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]

Min, W.

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]

Nakamura, K.

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

Nishizawa, A.

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

O’Brien, J. L.

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]

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]

Padgett, M. J.

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]

Petrov, D. V.

Popescu, S.

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]

Pryde, G. J.

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]

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]

Ralph, T. C.

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]

Reichman, J.

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]

Ritchie, N. W.

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]

Robertson, D. A.

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]

Saar, B. G.

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]

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]

Scarini, V.

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]

Solli, D. R.

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]

Stanley, C. M.

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]

Starling, D. J.

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]

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]

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, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A80, 041803 (2009).
[CrossRef]

Stevenson, P. M.

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]

Story, J. G.

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]

Sudarhshan, E. C. G.

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]

Torner, L.

Torres, J. P.

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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).
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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]

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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]

Wolf, E.

Xie, X. S.

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]

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]

J. Opt. Soc. Am. A

Opt. Lett.

Phys. Rev. A

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[CrossRef]

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[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).
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Phys. Rev. Lett.

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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).
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[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]

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[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

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[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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Figures (4)

Fig. 1
Fig. 1

Weak amplification of the displacement Δ as a function of the output polarization of the system (angle α). The phase difference is θ = 0.01°. We consider displacements Δ = Δ1 = −Δ2 = 10 nm, and the beam waist is w0 = 10μm.

Fig. 2
Fig. 2

Signal loss as a function of the angle α of the polarization of the output state. The phase difference is θ = 0.01°, Δ1 = −Δ2 = 10 nm and w0 = 10μm.

Fig. 3
Fig. 3

Signal loss as a function of the angle θ. The beam waist is w0 = 10μm. Red solid line: α = 45°; Blue dashed line: α = 0°; Black dotted line: α = −30°; Green dotted dashed line: α = −45°.

Fig. 4
Fig. 4

Fractional loss ΔP/P as a function of the spatial shift Δ. α = 45° and w0 = 10μm. Red solid line: θ = 0°; Blue dashed line: θ = 0.1°; Black dotted line: θ = 0.2°; Green dot-dashed line: θ = 0.3°.

Equations (11)

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A w = Ψ out | A | Ψ in Ψ out | Ψ in ~ 1 ε .
| in = | Ψ in d x Φ ( x ) | x .
| out = d x { Φ ( x Δ 1 ) | H + Φ ( x Δ 2 ) exp ( i φ ) | V } | x ,
I ( x ) = | cos α Φ ( x Δ 1 ) + sin α Φ ( x Δ 2 ) exp ( i θ ) | 2 ,
x = Δ + 2 + Δ 2 cos 2 α 1 + γ sin 2 α cos θ ,
γ = exp [ ( Δ 1 Δ 2 ) 2 4 w 0 2 ] ,
𝒜 = cos 2 α 1 + γ sin 2 α cos θ .
P out P in = 1 2 [ 1 + γ cos θ sin 2 α ] ,
Δ P P in = 1 2 [ γ cos θ sin 2 α 1 ] .
| in = 1 n i = 1 n | u i d x Φ ( x ) | x ,
| out = m d ω Φ ( ω + 2 m Ω ) | m | ω

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