Abstract

We demonstrate experimentally a nonunity gain quantum nondemolition measurement based on a simple homodyne measurement and recreation strategy. Although the output state is an amplified version of the input state, the device meets standard criteria for QND measurements: the transfer coefficient was measured to 1.78, and the conditional variance was measured to 0.66.

© 2006 Optical Society of America

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  1. V. B. Braginsky, Y. I. Vorontsov, and F. Y. Khalili, Zh. Eksp. Teor. Fiz. 73, 1340 (1977) V. B. Braginsky, Y. I. Vorontsov, and F. Y. Khalili,[Sov. Phys. JETP 46, 705 (1977)].
  2. V. B. Braginsky, Y. I. Vorontsov, and K. S. Thorne, Science 209, 547 (1980).
    [CrossRef] [PubMed]
  3. P. Grangier, J. A. Levenson, and J.-P. Poizat, Nature 396, 537 (1998).
    [CrossRef]
  4. F. König, B. Buchler, T. Rechtenwald, G. Leuchs, and S. Sizmann, Phys. Rev. A 66, 043810 (2002).
    [CrossRef]
  5. J.-Ph. Poizat and P. Grangier, Phys. Rev. Lett. 70, 271 (1993).
    [CrossRef] [PubMed]
  6. S. F. Pereria, Z. Y. Ou, and H. J. Kimble, Phys. Rev. Lett. 72, 214 (1994).
    [CrossRef]
  7. R. Bruckmeier, K. Schneider, S. Schiller, and J. Mlynek, Phys. Rev. Lett. 78, 1243 (1997).
    [CrossRef]
  8. B. Buchler, P. K. Lam, and T. C. Ralph, Phys. Rev. A 60, 4943 (1999).
    [CrossRef]
  9. M. J. Holland, M. J. Collett, D. F. Walls, and M. D. Levenson, Phys. Rev. Lett. 42, 2995 (1990).
  10. J.-Ph. Poizat, J.-F. Roch, and P. Grangier, Ann. Phys. (Paris) 19, 265 (1994).
    [CrossRef]
  11. J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, and P. Grangier, Phys. Rev. Lett. 70, 267 (1993).
    [CrossRef] [PubMed]
  12. B. Buchler, P. K. Lam, H.-A. Bachor, U. L. Andersen, and T. C. Ralph, Phys. Rev. A 65, 011803 (2001).
    [CrossRef]
  13. E. Goobar, A. Karlsson, and G. Björk, Phys. Rev. Lett. 71, 2002 (1993).
    [CrossRef] [PubMed]
  14. J.-F. Roch, J.-Ph. Poizat, and P. Grangier, Phys. Rev. Lett. 71, 2006 (1993).
    [CrossRef] [PubMed]
  15. S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 2446 (1998).
    [CrossRef]

2002 (1)

F. König, B. Buchler, T. Rechtenwald, G. Leuchs, and S. Sizmann, Phys. Rev. A 66, 043810 (2002).
[CrossRef]

2001 (1)

B. Buchler, P. K. Lam, H.-A. Bachor, U. L. Andersen, and T. C. Ralph, Phys. Rev. A 65, 011803 (2001).
[CrossRef]

1999 (1)

B. Buchler, P. K. Lam, and T. C. Ralph, Phys. Rev. A 60, 4943 (1999).
[CrossRef]

1998 (2)

P. Grangier, J. A. Levenson, and J.-P. Poizat, Nature 396, 537 (1998).
[CrossRef]

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

1997 (1)

R. Bruckmeier, K. Schneider, S. Schiller, and J. Mlynek, Phys. Rev. Lett. 78, 1243 (1997).
[CrossRef]

1994 (2)

J.-Ph. Poizat, J.-F. Roch, and P. Grangier, Ann. Phys. (Paris) 19, 265 (1994).
[CrossRef]

S. F. Pereria, Z. Y. Ou, and H. J. Kimble, Phys. Rev. Lett. 72, 214 (1994).
[CrossRef]

1993 (4)

J.-Ph. Poizat and P. Grangier, Phys. Rev. Lett. 70, 271 (1993).
[CrossRef] [PubMed]

J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, and P. Grangier, Phys. Rev. Lett. 70, 267 (1993).
[CrossRef] [PubMed]

E. Goobar, A. Karlsson, and G. Björk, Phys. Rev. Lett. 71, 2002 (1993).
[CrossRef] [PubMed]

J.-F. Roch, J.-Ph. Poizat, and P. Grangier, Phys. Rev. Lett. 71, 2006 (1993).
[CrossRef] [PubMed]

1990 (1)

M. J. Holland, M. J. Collett, D. F. Walls, and M. D. Levenson, Phys. Rev. Lett. 42, 2995 (1990).

1980 (1)

V. B. Braginsky, Y. I. Vorontsov, and K. S. Thorne, Science 209, 547 (1980).
[CrossRef] [PubMed]

1977 (1)

V. B. Braginsky, Y. I. Vorontsov, and F. Y. Khalili, Zh. Eksp. Teor. Fiz. 73, 1340 (1977) V. B. Braginsky, Y. I. Vorontsov, and F. Y. Khalili,[Sov. Phys. JETP 46, 705 (1977)].

Abram, I.

J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, and P. Grangier, Phys. Rev. Lett. 70, 267 (1993).
[CrossRef] [PubMed]

Andersen, U. L.

B. Buchler, P. K. Lam, H.-A. Bachor, U. L. Andersen, and T. C. Ralph, Phys. Rev. A 65, 011803 (2001).
[CrossRef]

Bachor, H.-A.

B. Buchler, P. K. Lam, H.-A. Bachor, U. L. Andersen, and T. C. Ralph, Phys. Rev. A 65, 011803 (2001).
[CrossRef]

Björk, G.

E. Goobar, A. Karlsson, and G. Björk, Phys. Rev. Lett. 71, 2002 (1993).
[CrossRef] [PubMed]

Braginsky, V. B.

V. B. Braginsky, Y. I. Vorontsov, and K. S. Thorne, Science 209, 547 (1980).
[CrossRef] [PubMed]

V. B. Braginsky, Y. I. Vorontsov, and F. Y. Khalili, Zh. Eksp. Teor. Fiz. 73, 1340 (1977) V. B. Braginsky, Y. I. Vorontsov, and F. Y. Khalili,[Sov. Phys. JETP 46, 705 (1977)].

Bruckmeier, R.

R. Bruckmeier, K. Schneider, S. Schiller, and J. Mlynek, Phys. Rev. Lett. 78, 1243 (1997).
[CrossRef]

Buchler, B.

F. König, B. Buchler, T. Rechtenwald, G. Leuchs, and S. Sizmann, Phys. Rev. A 66, 043810 (2002).
[CrossRef]

B. Buchler, P. K. Lam, H.-A. Bachor, U. L. Andersen, and T. C. Ralph, Phys. Rev. A 65, 011803 (2001).
[CrossRef]

B. Buchler, P. K. Lam, and T. C. Ralph, Phys. Rev. A 60, 4943 (1999).
[CrossRef]

Collett, M. J.

M. J. Holland, M. J. Collett, D. F. Walls, and M. D. Levenson, Phys. Rev. Lett. 42, 2995 (1990).

Fayolle, P.

J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, and P. Grangier, Phys. Rev. Lett. 70, 267 (1993).
[CrossRef] [PubMed]

Ficker, J.

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

Garreau, J. C.

J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, and P. Grangier, Phys. Rev. Lett. 70, 267 (1993).
[CrossRef] [PubMed]

Goobar, E.

E. Goobar, A. Karlsson, and G. Björk, Phys. Rev. Lett. 71, 2002 (1993).
[CrossRef] [PubMed]

Grangier, P.

P. Grangier, J. A. Levenson, and J.-P. Poizat, Nature 396, 537 (1998).
[CrossRef]

J.-Ph. Poizat, J.-F. Roch, and P. Grangier, Ann. Phys. (Paris) 19, 265 (1994).
[CrossRef]

J.-F. Roch, J.-Ph. Poizat, and P. Grangier, Phys. Rev. Lett. 71, 2006 (1993).
[CrossRef] [PubMed]

J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, and P. Grangier, Phys. Rev. Lett. 70, 267 (1993).
[CrossRef] [PubMed]

J.-Ph. Poizat and P. Grangier, Phys. Rev. Lett. 70, 271 (1993).
[CrossRef] [PubMed]

Holland, M. J.

M. J. Holland, M. J. Collett, D. F. Walls, and M. D. Levenson, Phys. Rev. Lett. 42, 2995 (1990).

Karlsson, A.

E. Goobar, A. Karlsson, and G. Björk, Phys. Rev. Lett. 71, 2002 (1993).
[CrossRef] [PubMed]

Khalili, F. Y.

V. B. Braginsky, Y. I. Vorontsov, and F. Y. Khalili, Zh. Eksp. Teor. Fiz. 73, 1340 (1977) V. B. Braginsky, Y. I. Vorontsov, and F. Y. Khalili,[Sov. Phys. JETP 46, 705 (1977)].

Kimble, H. J.

S. F. Pereria, Z. Y. Ou, and H. J. Kimble, Phys. Rev. Lett. 72, 214 (1994).
[CrossRef]

König, F.

F. König, B. Buchler, T. Rechtenwald, G. Leuchs, and S. Sizmann, Phys. Rev. A 66, 043810 (2002).
[CrossRef]

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

Lam, P. K.

B. Buchler, P. K. Lam, H.-A. Bachor, U. L. Andersen, and T. C. Ralph, Phys. Rev. A 65, 011803 (2001).
[CrossRef]

B. Buchler, P. K. Lam, and T. C. Ralph, Phys. Rev. A 60, 4943 (1999).
[CrossRef]

Leuchs, G.

F. König, B. Buchler, T. Rechtenwald, G. Leuchs, and S. Sizmann, Phys. Rev. A 66, 043810 (2002).
[CrossRef]

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

Levenson, J. A.

P. Grangier, J. A. Levenson, and J.-P. Poizat, Nature 396, 537 (1998).
[CrossRef]

J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, and P. Grangier, Phys. Rev. Lett. 70, 267 (1993).
[CrossRef] [PubMed]

Levenson, M. D.

M. J. Holland, M. J. Collett, D. F. Walls, and M. D. Levenson, Phys. Rev. Lett. 42, 2995 (1990).

Mlynek, J.

R. Bruckmeier, K. Schneider, S. Schiller, and J. Mlynek, Phys. Rev. Lett. 78, 1243 (1997).
[CrossRef]

Ou, Z. Y.

S. F. Pereria, Z. Y. Ou, and H. J. Kimble, Phys. Rev. Lett. 72, 214 (1994).
[CrossRef]

Pereria, S. F.

S. F. Pereria, Z. Y. Ou, and H. J. Kimble, Phys. Rev. Lett. 72, 214 (1994).
[CrossRef]

Poizat, J.-P.

P. Grangier, J. A. Levenson, and J.-P. Poizat, Nature 396, 537 (1998).
[CrossRef]

Poizat, J.-Ph.

J.-Ph. Poizat, J.-F. Roch, and P. Grangier, Ann. Phys. (Paris) 19, 265 (1994).
[CrossRef]

J.-F. Roch, J.-Ph. Poizat, and P. Grangier, Phys. Rev. Lett. 71, 2006 (1993).
[CrossRef] [PubMed]

J.-Ph. Poizat and P. Grangier, Phys. Rev. Lett. 70, 271 (1993).
[CrossRef] [PubMed]

Ralph, T. C.

B. Buchler, P. K. Lam, H.-A. Bachor, U. L. Andersen, and T. C. Ralph, Phys. Rev. A 65, 011803 (2001).
[CrossRef]

B. Buchler, P. K. Lam, and T. C. Ralph, Phys. Rev. A 60, 4943 (1999).
[CrossRef]

Rechtenwald, T.

F. König, B. Buchler, T. Rechtenwald, G. Leuchs, and S. Sizmann, Phys. Rev. A 66, 043810 (2002).
[CrossRef]

Rivera, T.

J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, and P. Grangier, Phys. Rev. Lett. 70, 267 (1993).
[CrossRef] [PubMed]

Roch, J.-F.

J.-Ph. Poizat, J.-F. Roch, and P. Grangier, Ann. Phys. (Paris) 19, 265 (1994).
[CrossRef]

J.-F. Roch, J.-Ph. Poizat, and P. Grangier, Phys. Rev. Lett. 71, 2006 (1993).
[CrossRef] [PubMed]

Schiller, S.

R. Bruckmeier, K. Schneider, S. Schiller, and J. Mlynek, Phys. Rev. Lett. 78, 1243 (1997).
[CrossRef]

Schmitt, S.

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

Schneider, K.

R. Bruckmeier, K. Schneider, S. Schiller, and J. Mlynek, Phys. Rev. Lett. 78, 1243 (1997).
[CrossRef]

Sizmann, A.

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

Sizmann, S.

F. König, B. Buchler, T. Rechtenwald, G. Leuchs, and S. Sizmann, Phys. Rev. A 66, 043810 (2002).
[CrossRef]

Thorne, K. S.

V. B. Braginsky, Y. I. Vorontsov, and K. S. Thorne, Science 209, 547 (1980).
[CrossRef] [PubMed]

Vorontsov, Y. I.

V. B. Braginsky, Y. I. Vorontsov, and K. S. Thorne, Science 209, 547 (1980).
[CrossRef] [PubMed]

V. B. Braginsky, Y. I. Vorontsov, and F. Y. Khalili, Zh. Eksp. Teor. Fiz. 73, 1340 (1977) V. B. Braginsky, Y. I. Vorontsov, and F. Y. Khalili,[Sov. Phys. JETP 46, 705 (1977)].

Walls, D. F.

M. J. Holland, M. J. Collett, D. F. Walls, and M. D. Levenson, Phys. Rev. Lett. 42, 2995 (1990).

Wolff, M.

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

Ann. Phys. (Paris) (1)

J.-Ph. Poizat, J.-F. Roch, and P. Grangier, Ann. Phys. (Paris) 19, 265 (1994).
[CrossRef]

Nature (1)

P. Grangier, J. A. Levenson, and J.-P. Poizat, Nature 396, 537 (1998).
[CrossRef]

Phys. Rev. A (3)

F. König, B. Buchler, T. Rechtenwald, G. Leuchs, and S. Sizmann, Phys. Rev. A 66, 043810 (2002).
[CrossRef]

B. Buchler, P. K. Lam, and T. C. Ralph, Phys. Rev. A 60, 4943 (1999).
[CrossRef]

B. Buchler, P. K. Lam, H.-A. Bachor, U. L. Andersen, and T. C. Ralph, Phys. Rev. A 65, 011803 (2001).
[CrossRef]

Phys. Rev. Lett. (8)

E. Goobar, A. Karlsson, and G. Björk, Phys. Rev. Lett. 71, 2002 (1993).
[CrossRef] [PubMed]

J.-F. Roch, J.-Ph. Poizat, and P. Grangier, Phys. Rev. Lett. 71, 2006 (1993).
[CrossRef] [PubMed]

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, and P. Grangier, Phys. Rev. Lett. 70, 267 (1993).
[CrossRef] [PubMed]

M. J. Holland, M. J. Collett, D. F. Walls, and M. D. Levenson, Phys. Rev. Lett. 42, 2995 (1990).

J.-Ph. Poizat and P. Grangier, Phys. Rev. Lett. 70, 271 (1993).
[CrossRef] [PubMed]

S. F. Pereria, Z. Y. Ou, and H. J. Kimble, Phys. Rev. Lett. 72, 214 (1994).
[CrossRef]

R. Bruckmeier, K. Schneider, S. Schiller, and J. Mlynek, Phys. Rev. Lett. 78, 1243 (1997).
[CrossRef]

Science (1)

V. B. Braginsky, Y. I. Vorontsov, and K. S. Thorne, Science 209, 547 (1980).
[CrossRef] [PubMed]

Zh. Eksp. Teor. Fiz. (1)

V. B. Braginsky, Y. I. Vorontsov, and F. Y. Khalili, Zh. Eksp. Teor. Fiz. 73, 1340 (1977) V. B. Braginsky, Y. I. Vorontsov, and F. Y. Khalili,[Sov. Phys. JETP 46, 705 (1977)].

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Figures (4)

Fig. 1
Fig. 1

Schematic of the experimental setup.

Fig. 2
Fig. 2

Signal transfer coefficient as a function of the noise gain. The solid curve represents the theoretical prediction, according to Eq. (3). Inset, spectral densities of the signal output for various gains. All traces are normalized to their respective noise level to aid visualization. Electronic noise of the verifying detector is subtracted from the measurements. Resolution bandwidth, 100 kHz ; video bandwidth, 3 kHz . All traces are averaged 100 times.

Fig. 3
Fig. 3

Conditional variance V s m versus optical noise gain G. The measured squeezing level is represented by the solid line (0.54).

Fig. 4
Fig. 4

Signal transfer versus conditional variance. QND operation is associated with the region defined by T s + m > 1 and V s m < 1 .

Equations (4)

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

T s ( m ) = SNR s ( m ) out SNR s in ,
Δ 2 X s m = Δ 2 X s , out ( 1 C s m 2 ) .
T m = η , T s = η g 2 Δ 2 X m + g 2 ,
Δ 2 X s m = Δ 2 X m .

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