Abstract

We present an “interferometric quasi-autocollimator” that employs weak value amplification to measure angular deflections of a target mirror. The device has been designed to be insensitive to all translations of the target. We present a conceptual explanation of the amplification effect used by the device. An implementation of the device demonstrates sensitivities better than 10 picoradians per root hertz between 10 and 200Hz.

© 2011 Optical Society of America

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  1. Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
    [CrossRef] [PubMed]
  2. N. W. M. Ritchie, J. G. Story, and R. G. Hulet, Phys. Rev. Lett. 66, 1107 (1991).
    [CrossRef] [PubMed]
  3. O. Hosten and P. Kwiat, Science 319, 787 (2008).
    [CrossRef] [PubMed]
  4. Y. Aharonov, S. Popescu, and J. Tollaksen, Phys. Today 63, 27 (2010).
    [CrossRef]
  5. P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, Phys. Rev. Lett. 102, 173601 (2009).
    [CrossRef] [PubMed]
  6. D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, Phys. Rev. A 80, 041803 (2009).
    [CrossRef]
  7. S. Schlamminger, K.-Y. Choi, T. A. Wagner, J. H. Gundlach, and E. G. Adelberger, Phys. Rev. Lett. 100, 041101 (2008).
    [CrossRef] [PubMed]
  8. G. L. Smith, C. D. Hoyle, J. H. Gundlach, E. G. Adelberger, B. R. Heckel, and H. E. Swanson, Phys. Rev. D 61, 022001 (1999).
    [CrossRef]
  9. C. A. J. Putman, B. G. de Grooth, N. F. van Hulst, and J. Greve, J. Appl. Phys. 72, 6 (1992).
    [CrossRef]
  10. J. C. Howell, D. J. Starling, P. B. Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
    [CrossRef]

2010

Y. Aharonov, S. Popescu, and J. Tollaksen, Phys. Today 63, 27 (2010).
[CrossRef]

J. C. Howell, D. J. Starling, P. B. Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
[CrossRef]

2009

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef] [PubMed]

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, Phys. Rev. A 80, 041803 (2009).
[CrossRef]

2008

S. Schlamminger, K.-Y. Choi, T. A. Wagner, J. H. Gundlach, and E. G. Adelberger, Phys. Rev. Lett. 100, 041101 (2008).
[CrossRef] [PubMed]

O. Hosten and P. Kwiat, Science 319, 787 (2008).
[CrossRef] [PubMed]

1999

G. L. Smith, C. D. Hoyle, J. H. Gundlach, E. G. Adelberger, B. R. Heckel, and H. E. Swanson, Phys. Rev. D 61, 022001 (1999).
[CrossRef]

1992

C. A. J. Putman, B. G. de Grooth, N. F. van Hulst, and J. Greve, J. Appl. Phys. 72, 6 (1992).
[CrossRef]

1991

N. W. M. Ritchie, J. G. Story, and R. G. Hulet, Phys. Rev. Lett. 66, 1107 (1991).
[CrossRef] [PubMed]

1988

Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
[CrossRef] [PubMed]

Adelberger, E. G.

S. Schlamminger, K.-Y. Choi, T. A. Wagner, J. H. Gundlach, and E. G. Adelberger, Phys. Rev. Lett. 100, 041101 (2008).
[CrossRef] [PubMed]

G. L. Smith, C. D. Hoyle, J. H. Gundlach, E. G. Adelberger, B. R. Heckel, and H. E. Swanson, Phys. Rev. D 61, 022001 (1999).
[CrossRef]

Aharonov, Y.

Y. Aharonov, S. Popescu, and J. Tollaksen, Phys. Today 63, 27 (2010).
[CrossRef]

Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
[CrossRef] [PubMed]

Albert, D. Z.

Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
[CrossRef] [PubMed]

Choi, K.-Y.

S. Schlamminger, K.-Y. Choi, T. A. Wagner, J. H. Gundlach, and E. G. Adelberger, Phys. Rev. Lett. 100, 041101 (2008).
[CrossRef] [PubMed]

de Grooth, B. G.

C. A. J. Putman, B. G. de Grooth, N. F. van Hulst, and J. Greve, J. Appl. Phys. 72, 6 (1992).
[CrossRef]

Dixon, P. B.

J. C. Howell, D. J. Starling, P. B. Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
[CrossRef]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef] [PubMed]

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, Phys. Rev. A 80, 041803 (2009).
[CrossRef]

Greve, J.

C. A. J. Putman, B. G. de Grooth, N. F. van Hulst, and J. Greve, J. Appl. Phys. 72, 6 (1992).
[CrossRef]

Gundlach, J. H.

S. Schlamminger, K.-Y. Choi, T. A. Wagner, J. H. Gundlach, and E. G. Adelberger, Phys. Rev. Lett. 100, 041101 (2008).
[CrossRef] [PubMed]

G. L. Smith, C. D. Hoyle, J. H. Gundlach, E. G. Adelberger, B. R. Heckel, and H. E. Swanson, Phys. Rev. D 61, 022001 (1999).
[CrossRef]

Heckel, B. R.

G. L. Smith, C. D. Hoyle, J. H. Gundlach, E. G. Adelberger, B. R. Heckel, and H. E. Swanson, Phys. Rev. D 61, 022001 (1999).
[CrossRef]

Hosten, O.

O. Hosten and P. Kwiat, Science 319, 787 (2008).
[CrossRef] [PubMed]

Howell, J. C.

J. C. Howell, D. J. Starling, P. B. Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
[CrossRef]

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, Phys. Rev. A 80, 041803 (2009).
[CrossRef]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef] [PubMed]

Hoyle, C. D.

G. L. Smith, C. D. Hoyle, J. H. Gundlach, E. G. Adelberger, B. R. Heckel, and H. E. Swanson, Phys. Rev. D 61, 022001 (1999).
[CrossRef]

Hulet, R. G.

N. W. M. Ritchie, J. G. Story, and R. G. Hulet, Phys. Rev. Lett. 66, 1107 (1991).
[CrossRef] [PubMed]

Jordan, A. N.

J. C. Howell, D. J. Starling, P. B. Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
[CrossRef]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef] [PubMed]

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, Phys. Rev. A 80, 041803 (2009).
[CrossRef]

Kwiat, P.

O. Hosten and P. Kwiat, Science 319, 787 (2008).
[CrossRef] [PubMed]

Popescu, S.

Y. Aharonov, S. Popescu, and J. Tollaksen, Phys. Today 63, 27 (2010).
[CrossRef]

Putman, C. A. J.

C. A. J. Putman, B. G. de Grooth, N. F. van Hulst, and J. Greve, J. Appl. Phys. 72, 6 (1992).
[CrossRef]

Ritchie, N. W. M.

N. W. M. Ritchie, J. G. Story, and R. G. Hulet, Phys. Rev. Lett. 66, 1107 (1991).
[CrossRef] [PubMed]

Schlamminger, S.

S. Schlamminger, K.-Y. Choi, T. A. Wagner, J. H. Gundlach, and E. G. Adelberger, Phys. Rev. Lett. 100, 041101 (2008).
[CrossRef] [PubMed]

Smith, G. L.

G. L. Smith, C. D. Hoyle, J. H. Gundlach, E. G. Adelberger, B. R. Heckel, and H. E. Swanson, Phys. Rev. D 61, 022001 (1999).
[CrossRef]

Starling, D. J.

J. C. Howell, D. J. Starling, P. B. Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
[CrossRef]

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, Phys. Rev. A 80, 041803 (2009).
[CrossRef]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef] [PubMed]

Story, J. G.

N. W. M. Ritchie, J. G. Story, and R. G. Hulet, Phys. Rev. Lett. 66, 1107 (1991).
[CrossRef] [PubMed]

Swanson, H. E.

G. L. Smith, C. D. Hoyle, J. H. Gundlach, E. G. Adelberger, B. R. Heckel, and H. E. Swanson, Phys. Rev. D 61, 022001 (1999).
[CrossRef]

Tollaksen, J.

Y. Aharonov, S. Popescu, and J. Tollaksen, Phys. Today 63, 27 (2010).
[CrossRef]

Vaidman, L.

Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
[CrossRef] [PubMed]

van Hulst, N. F.

C. A. J. Putman, B. G. de Grooth, N. F. van Hulst, and J. Greve, J. Appl. Phys. 72, 6 (1992).
[CrossRef]

Vudyasetu, P. K.

J. C. Howell, D. J. Starling, P. B. Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
[CrossRef]

Wagner, T. A.

S. Schlamminger, K.-Y. Choi, T. A. Wagner, J. H. Gundlach, and E. G. Adelberger, Phys. Rev. Lett. 100, 041101 (2008).
[CrossRef] [PubMed]

J. Appl. Phys.

C. A. J. Putman, B. G. de Grooth, N. F. van Hulst, and J. Greve, J. Appl. Phys. 72, 6 (1992).
[CrossRef]

Phys. Rev. A

J. C. Howell, D. J. Starling, P. B. Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
[CrossRef]

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, Phys. Rev. A 80, 041803 (2009).
[CrossRef]

Phys. Rev. D

G. L. Smith, C. D. Hoyle, J. H. Gundlach, E. G. Adelberger, B. R. Heckel, and H. E. Swanson, Phys. Rev. D 61, 022001 (1999).
[CrossRef]

Phys. Rev. Lett.

S. Schlamminger, K.-Y. Choi, T. A. Wagner, J. H. Gundlach, and E. G. Adelberger, Phys. Rev. Lett. 100, 041101 (2008).
[CrossRef] [PubMed]

Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
[CrossRef] [PubMed]

N. W. M. Ritchie, J. G. Story, and R. G. Hulet, Phys. Rev. Lett. 66, 1107 (1991).
[CrossRef] [PubMed]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef] [PubMed]

Phys. Today

Y. Aharonov, S. Popescu, and J. Tollaksen, Phys. Today 63, 27 (2010).
[CrossRef]

Science

O. Hosten and P. Kwiat, Science 319, 787 (2008).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic diagram of the Rochester design. A phase offset between the two optical paths is created either by the insertion of a Soleil–Babinet compensator or an out-of-plane deflection of one of the mirrors. (b) Schematic diagram of the iQuAC. The beam polarization is used to separate the two paths after reflection from the target. In both setups, an in-plane angular deflection of the target mirror results in a proportional displacement of the beam spot on the position- sensitive photodetector (PSD).

Fig. 2
Fig. 2

(a) An example of the fringe pattern which would result from a spatially uniform source being directed into the iQuAC. The central minimum is shifted due to a phase offset between the two paths. (b) The portion of the previous plot denoted by the black box, with an example Gaussian profile (red, solid). The result of multiplying the Gaussian with the fringe pattern appears as a shifted Gaussian profile (green, dashed). The first Gaussian profile has been scaled for clarity.

Fig. 3
Fig. 3

A plot of the noise floor of an implemented iQuAC setup. A 620 prad calibration signal is visible at 2 Hz . A weak value amplification factor of 60, as compared to a simple beam-deflection measurement, was measured for this dataset.

Equations (1)

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( a + b x ) exp [ x 2 / ( 2 σ 2 ) ] a exp [ ( x b σ 2 / a ) 2 2 σ 2 ] .

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