Abstract

We present a new technique for the detection of two-mode squeezed states of light that allows for a simple characterization of these quantum states even for arbitrary frequency separation between the modes. The proposed technique is based on the use of a bichromatic field as the local oscillator in a balanced heterodyne measurement scheme. By the proper selection of the frequencies of the bichromatic field, it is possible to arbitrarily select the frequency around which the squeezing information is located, thus making it possible to use a low-bandwidth detection system and to move away from any excess noise present in the system.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Einstein, B. Podolsky, and N. Rosen, "Can quantum-mechanical description of physical reality be considered complete?" Phys. Rev. 47, 777-780 (1935).
    [CrossRef]
  2. A. M. Marino and C. R. Stroud, Jr., "Deterministic secure communications using two-mode squeezed states," Phys. Rev. A 74, 022315 (2006).
    [CrossRef]
  3. S. L. Braunstein and H. J. Kimble, "Teleportation of continuous quantum variables," Phys. Rev. Lett. 80, 869-872 (1998).
    [CrossRef]
  4. A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
    [CrossRef] [PubMed]
  5. S. F. Pereira, Z. Y. Ou, and H. J. Kimble, "Quantum communication with correlated nonclassical states," Phys. Rev. A 62, 042311 (2000).
    [CrossRef]
  6. M. D. Reid, "Quantum cryptography with a predetermined key, using continuous-variable Einstein-Podolsky-Rosen correlations," Phys. Rev. A 62, 062308 (2000).
    [CrossRef]
  7. C. Silberhorn, N. Korolkova, and G. Leuchs, "Quantum key distribution with bright entangled beams," Phys. Rev. Lett. 88, 167902 (2002).
    [CrossRef] [PubMed]
  8. M. D. Reid, "Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification," Phys. Rev. A 40, 913-923 (1989).
    [CrossRef] [PubMed]
  9. Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, "Realization of the Einstein-Podolsky-Rosen paradox for continuous variables," Phys. Rev. Lett. 68, 3663-3666 (1992).
    [CrossRef] [PubMed]
  10. S. L. Braunstein and P. van Loock, "Quantum information with continuous variables," Rev. Mod. Phys. 77, 513-577 (2005).
    [CrossRef]
  11. C. H. Kim and P. Kumar, "Quadrature-squeezed light detection using a self-generated matched local oscillator," Phys. Rev. Lett. 73, 1605-1608 (1994).
    [CrossRef] [PubMed]
  12. D. Levandovsky, M. Vasilyev, and P. Kumar, "Perturbation theory of quantum solitons: continuum evolution and optimum squeezing by spectral filtering," Opt. Lett. 24, 43-45 (1999).
    [CrossRef]
  13. R. S. Bennink and R. W. Boyd, "Improved measurement of multimode squeezed light via an eigenmode approach," Phys. Rev. A 66, 053815 (2002).
    [CrossRef]
  14. M. B. Gray, D. A. Shaddock, C. C. Harb, and H. A. Bachor, "Photodetector designs for low-noise, broadband, and high-power applications," Rev. Sci. Instrum. 69, 3755-3762 (1998).
    [CrossRef]
  15. J. Zhang, "Einstein-Podolsky-Rosen sideband entanglement in broadband squeezed light," Phys. Rev. A 67, 054302 (2003).
    [CrossRef]
  16. C. Schori, J. L. Sorensen, and E. S. Polzik, "Narrow-band frequency tunable light source of continuous quadrature entanglement," Phys. Rev. A 66, 033802 (2002).
    [CrossRef]
  17. Throughout the paper, the fields are expressed in units of E0=√ \hbar omega/2ε0V. The frequency difference between the modes is assumed to be much smaller than the optical frequency so that E0 can be taken as a constant.
  18. R. Loudon and P. L. Knight, "Squeezed light," J. Mod. Opt. 34, 709-759 (1987).
    [CrossRef]
  19. H. P. Yuen and J. H. Shapiro, "Optical communication with two-photon coherent states--Part III: Quantum measurements realizable with photo-emissive detectors," IEEE Trans. Inf. Theory 26, 78-82 (1980).
    [CrossRef]
  20. M. J. Collett, R. Loudon, and C. W. Gardiner, "Quantum-theory of optical homodyne and heterodyne-detection," J. Mod. Opt. 34, 881-902 (1987).
    [CrossRef]
  21. H. A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics, 2nd ed. (Wiley-VCH, 2004).
    [CrossRef]
  22. S. Chelkowski, H. Vahlbruch, B. Hage, A. Franzen, N. Lastzka, K. Danzmann, and R. Schnabel, "Experimental characterization of frequency-dependent squeezed light," Phys. Rev. A 71, 013806 (2005).
    [CrossRef]
  23. K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, "Quantum noise locking," J. Opt. B 7, S421-S428 (2005).
    [CrossRef]

2006 (1)

A. M. Marino and C. R. Stroud, Jr., "Deterministic secure communications using two-mode squeezed states," Phys. Rev. A 74, 022315 (2006).
[CrossRef]

2005 (3)

S. L. Braunstein and P. van Loock, "Quantum information with continuous variables," Rev. Mod. Phys. 77, 513-577 (2005).
[CrossRef]

S. Chelkowski, H. Vahlbruch, B. Hage, A. Franzen, N. Lastzka, K. Danzmann, and R. Schnabel, "Experimental characterization of frequency-dependent squeezed light," Phys. Rev. A 71, 013806 (2005).
[CrossRef]

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, "Quantum noise locking," J. Opt. B 7, S421-S428 (2005).
[CrossRef]

2003 (1)

J. Zhang, "Einstein-Podolsky-Rosen sideband entanglement in broadband squeezed light," Phys. Rev. A 67, 054302 (2003).
[CrossRef]

2002 (3)

C. Schori, J. L. Sorensen, and E. S. Polzik, "Narrow-band frequency tunable light source of continuous quadrature entanglement," Phys. Rev. A 66, 033802 (2002).
[CrossRef]

R. S. Bennink and R. W. Boyd, "Improved measurement of multimode squeezed light via an eigenmode approach," Phys. Rev. A 66, 053815 (2002).
[CrossRef]

C. Silberhorn, N. Korolkova, and G. Leuchs, "Quantum key distribution with bright entangled beams," Phys. Rev. Lett. 88, 167902 (2002).
[CrossRef] [PubMed]

2000 (2)

S. F. Pereira, Z. Y. Ou, and H. J. Kimble, "Quantum communication with correlated nonclassical states," Phys. Rev. A 62, 042311 (2000).
[CrossRef]

M. D. Reid, "Quantum cryptography with a predetermined key, using continuous-variable Einstein-Podolsky-Rosen correlations," Phys. Rev. A 62, 062308 (2000).
[CrossRef]

1999 (1)

1998 (3)

S. L. Braunstein and H. J. Kimble, "Teleportation of continuous quantum variables," Phys. Rev. Lett. 80, 869-872 (1998).
[CrossRef]

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

M. B. Gray, D. A. Shaddock, C. C. Harb, and H. A. Bachor, "Photodetector designs for low-noise, broadband, and high-power applications," Rev. Sci. Instrum. 69, 3755-3762 (1998).
[CrossRef]

1994 (1)

C. H. Kim and P. Kumar, "Quadrature-squeezed light detection using a self-generated matched local oscillator," Phys. Rev. Lett. 73, 1605-1608 (1994).
[CrossRef] [PubMed]

1992 (1)

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, "Realization of the Einstein-Podolsky-Rosen paradox for continuous variables," Phys. Rev. Lett. 68, 3663-3666 (1992).
[CrossRef] [PubMed]

1989 (1)

M. D. Reid, "Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification," Phys. Rev. A 40, 913-923 (1989).
[CrossRef] [PubMed]

1987 (2)

R. Loudon and P. L. Knight, "Squeezed light," J. Mod. Opt. 34, 709-759 (1987).
[CrossRef]

M. J. Collett, R. Loudon, and C. W. Gardiner, "Quantum-theory of optical homodyne and heterodyne-detection," J. Mod. Opt. 34, 881-902 (1987).
[CrossRef]

1980 (1)

H. P. Yuen and J. H. Shapiro, "Optical communication with two-photon coherent states--Part III: Quantum measurements realizable with photo-emissive detectors," IEEE Trans. Inf. Theory 26, 78-82 (1980).
[CrossRef]

1935 (1)

A. Einstein, B. Podolsky, and N. Rosen, "Can quantum-mechanical description of physical reality be considered complete?" Phys. Rev. 47, 777-780 (1935).
[CrossRef]

Bachor, H. A.

M. B. Gray, D. A. Shaddock, C. C. Harb, and H. A. Bachor, "Photodetector designs for low-noise, broadband, and high-power applications," Rev. Sci. Instrum. 69, 3755-3762 (1998).
[CrossRef]

H. A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics, 2nd ed. (Wiley-VCH, 2004).
[CrossRef]

Bennink, R. S.

R. S. Bennink and R. W. Boyd, "Improved measurement of multimode squeezed light via an eigenmode approach," Phys. Rev. A 66, 053815 (2002).
[CrossRef]

Boyd, R. W.

R. S. Bennink and R. W. Boyd, "Improved measurement of multimode squeezed light via an eigenmode approach," Phys. Rev. A 66, 053815 (2002).
[CrossRef]

Braunstein, S. L.

S. L. Braunstein and P. van Loock, "Quantum information with continuous variables," Rev. Mod. Phys. 77, 513-577 (2005).
[CrossRef]

S. L. Braunstein and H. J. Kimble, "Teleportation of continuous quantum variables," Phys. Rev. Lett. 80, 869-872 (1998).
[CrossRef]

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

Chelkowski, S.

S. Chelkowski, H. Vahlbruch, B. Hage, A. Franzen, N. Lastzka, K. Danzmann, and R. Schnabel, "Experimental characterization of frequency-dependent squeezed light," Phys. Rev. A 71, 013806 (2005).
[CrossRef]

Collett, M. J.

M. J. Collett, R. Loudon, and C. W. Gardiner, "Quantum-theory of optical homodyne and heterodyne-detection," J. Mod. Opt. 34, 881-902 (1987).
[CrossRef]

Danzmann, K.

S. Chelkowski, H. Vahlbruch, B. Hage, A. Franzen, N. Lastzka, K. Danzmann, and R. Schnabel, "Experimental characterization of frequency-dependent squeezed light," Phys. Rev. A 71, 013806 (2005).
[CrossRef]

Einstein, A.

A. Einstein, B. Podolsky, and N. Rosen, "Can quantum-mechanical description of physical reality be considered complete?" Phys. Rev. 47, 777-780 (1935).
[CrossRef]

Franzen, A.

S. Chelkowski, H. Vahlbruch, B. Hage, A. Franzen, N. Lastzka, K. Danzmann, and R. Schnabel, "Experimental characterization of frequency-dependent squeezed light," Phys. Rev. A 71, 013806 (2005).
[CrossRef]

Fuchs, C. A.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

Furusawa, A.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

Gardiner, C. W.

M. J. Collett, R. Loudon, and C. W. Gardiner, "Quantum-theory of optical homodyne and heterodyne-detection," J. Mod. Opt. 34, 881-902 (1987).
[CrossRef]

Goda, K.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, "Quantum noise locking," J. Opt. B 7, S421-S428 (2005).
[CrossRef]

Gray, M. B.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, "Quantum noise locking," J. Opt. B 7, S421-S428 (2005).
[CrossRef]

M. B. Gray, D. A. Shaddock, C. C. Harb, and H. A. Bachor, "Photodetector designs for low-noise, broadband, and high-power applications," Rev. Sci. Instrum. 69, 3755-3762 (1998).
[CrossRef]

Grosse, N.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, "Quantum noise locking," J. Opt. B 7, S421-S428 (2005).
[CrossRef]

Hage, B.

S. Chelkowski, H. Vahlbruch, B. Hage, A. Franzen, N. Lastzka, K. Danzmann, and R. Schnabel, "Experimental characterization of frequency-dependent squeezed light," Phys. Rev. A 71, 013806 (2005).
[CrossRef]

Harb, C. C.

M. B. Gray, D. A. Shaddock, C. C. Harb, and H. A. Bachor, "Photodetector designs for low-noise, broadband, and high-power applications," Rev. Sci. Instrum. 69, 3755-3762 (1998).
[CrossRef]

Kim, C. H.

C. H. Kim and P. Kumar, "Quadrature-squeezed light detection using a self-generated matched local oscillator," Phys. Rev. Lett. 73, 1605-1608 (1994).
[CrossRef] [PubMed]

Kimble, H. J.

S. F. Pereira, Z. Y. Ou, and H. J. Kimble, "Quantum communication with correlated nonclassical states," Phys. Rev. A 62, 042311 (2000).
[CrossRef]

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

S. L. Braunstein and H. J. Kimble, "Teleportation of continuous quantum variables," Phys. Rev. Lett. 80, 869-872 (1998).
[CrossRef]

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, "Realization of the Einstein-Podolsky-Rosen paradox for continuous variables," Phys. Rev. Lett. 68, 3663-3666 (1992).
[CrossRef] [PubMed]

Knight, P. L.

R. Loudon and P. L. Knight, "Squeezed light," J. Mod. Opt. 34, 709-759 (1987).
[CrossRef]

Korolkova, N.

C. Silberhorn, N. Korolkova, and G. Leuchs, "Quantum key distribution with bright entangled beams," Phys. Rev. Lett. 88, 167902 (2002).
[CrossRef] [PubMed]

Kumar, P.

D. Levandovsky, M. Vasilyev, and P. Kumar, "Perturbation theory of quantum solitons: continuum evolution and optimum squeezing by spectral filtering," Opt. Lett. 24, 43-45 (1999).
[CrossRef]

C. H. Kim and P. Kumar, "Quadrature-squeezed light detection using a self-generated matched local oscillator," Phys. Rev. Lett. 73, 1605-1608 (1994).
[CrossRef] [PubMed]

Lam, P. K.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, "Quantum noise locking," J. Opt. B 7, S421-S428 (2005).
[CrossRef]

Lastzka, N.

S. Chelkowski, H. Vahlbruch, B. Hage, A. Franzen, N. Lastzka, K. Danzmann, and R. Schnabel, "Experimental characterization of frequency-dependent squeezed light," Phys. Rev. A 71, 013806 (2005).
[CrossRef]

Leuchs, G.

C. Silberhorn, N. Korolkova, and G. Leuchs, "Quantum key distribution with bright entangled beams," Phys. Rev. Lett. 88, 167902 (2002).
[CrossRef] [PubMed]

Levandovsky, D.

Loudon, R.

R. Loudon and P. L. Knight, "Squeezed light," J. Mod. Opt. 34, 709-759 (1987).
[CrossRef]

M. J. Collett, R. Loudon, and C. W. Gardiner, "Quantum-theory of optical homodyne and heterodyne-detection," J. Mod. Opt. 34, 881-902 (1987).
[CrossRef]

Marino, A. M.

A. M. Marino and C. R. Stroud, Jr., "Deterministic secure communications using two-mode squeezed states," Phys. Rev. A 74, 022315 (2006).
[CrossRef]

Mavalvala, N.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, "Quantum noise locking," J. Opt. B 7, S421-S428 (2005).
[CrossRef]

McClelland, D. E.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, "Quantum noise locking," J. Opt. B 7, S421-S428 (2005).
[CrossRef]

McKenzie, K.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, "Quantum noise locking," J. Opt. B 7, S421-S428 (2005).
[CrossRef]

Mikhailov, E. E.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, "Quantum noise locking," J. Opt. B 7, S421-S428 (2005).
[CrossRef]

Ou, Z. Y.

S. F. Pereira, Z. Y. Ou, and H. J. Kimble, "Quantum communication with correlated nonclassical states," Phys. Rev. A 62, 042311 (2000).
[CrossRef]

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, "Realization of the Einstein-Podolsky-Rosen paradox for continuous variables," Phys. Rev. Lett. 68, 3663-3666 (1992).
[CrossRef] [PubMed]

Peng, K. C.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, "Realization of the Einstein-Podolsky-Rosen paradox for continuous variables," Phys. Rev. Lett. 68, 3663-3666 (1992).
[CrossRef] [PubMed]

Pereira, S. F.

S. F. Pereira, Z. Y. Ou, and H. J. Kimble, "Quantum communication with correlated nonclassical states," Phys. Rev. A 62, 042311 (2000).
[CrossRef]

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, "Realization of the Einstein-Podolsky-Rosen paradox for continuous variables," Phys. Rev. Lett. 68, 3663-3666 (1992).
[CrossRef] [PubMed]

Podolsky, B.

A. Einstein, B. Podolsky, and N. Rosen, "Can quantum-mechanical description of physical reality be considered complete?" Phys. Rev. 47, 777-780 (1935).
[CrossRef]

Polzik, E. S.

C. Schori, J. L. Sorensen, and E. S. Polzik, "Narrow-band frequency tunable light source of continuous quadrature entanglement," Phys. Rev. A 66, 033802 (2002).
[CrossRef]

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

Ralph, T. C.

H. A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics, 2nd ed. (Wiley-VCH, 2004).
[CrossRef]

Reid, M. D.

M. D. Reid, "Quantum cryptography with a predetermined key, using continuous-variable Einstein-Podolsky-Rosen correlations," Phys. Rev. A 62, 062308 (2000).
[CrossRef]

M. D. Reid, "Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification," Phys. Rev. A 40, 913-923 (1989).
[CrossRef] [PubMed]

Rosen, N.

A. Einstein, B. Podolsky, and N. Rosen, "Can quantum-mechanical description of physical reality be considered complete?" Phys. Rev. 47, 777-780 (1935).
[CrossRef]

Schnabel, R.

S. Chelkowski, H. Vahlbruch, B. Hage, A. Franzen, N. Lastzka, K. Danzmann, and R. Schnabel, "Experimental characterization of frequency-dependent squeezed light," Phys. Rev. A 71, 013806 (2005).
[CrossRef]

Schori, C.

C. Schori, J. L. Sorensen, and E. S. Polzik, "Narrow-band frequency tunable light source of continuous quadrature entanglement," Phys. Rev. A 66, 033802 (2002).
[CrossRef]

Shaddock, D. A.

M. B. Gray, D. A. Shaddock, C. C. Harb, and H. A. Bachor, "Photodetector designs for low-noise, broadband, and high-power applications," Rev. Sci. Instrum. 69, 3755-3762 (1998).
[CrossRef]

Shapiro, J. H.

H. P. Yuen and J. H. Shapiro, "Optical communication with two-photon coherent states--Part III: Quantum measurements realizable with photo-emissive detectors," IEEE Trans. Inf. Theory 26, 78-82 (1980).
[CrossRef]

Silberhorn, C.

C. Silberhorn, N. Korolkova, and G. Leuchs, "Quantum key distribution with bright entangled beams," Phys. Rev. Lett. 88, 167902 (2002).
[CrossRef] [PubMed]

Sorensen, J. L.

C. Schori, J. L. Sorensen, and E. S. Polzik, "Narrow-band frequency tunable light source of continuous quadrature entanglement," Phys. Rev. A 66, 033802 (2002).
[CrossRef]

Sørensen, J. L.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

Stroud, C. R.

A. M. Marino and C. R. Stroud, Jr., "Deterministic secure communications using two-mode squeezed states," Phys. Rev. A 74, 022315 (2006).
[CrossRef]

Vahlbruch, H.

S. Chelkowski, H. Vahlbruch, B. Hage, A. Franzen, N. Lastzka, K. Danzmann, and R. Schnabel, "Experimental characterization of frequency-dependent squeezed light," Phys. Rev. A 71, 013806 (2005).
[CrossRef]

van Loock, P.

S. L. Braunstein and P. van Loock, "Quantum information with continuous variables," Rev. Mod. Phys. 77, 513-577 (2005).
[CrossRef]

Vasilyev, M.

Yuen, H. P.

H. P. Yuen and J. H. Shapiro, "Optical communication with two-photon coherent states--Part III: Quantum measurements realizable with photo-emissive detectors," IEEE Trans. Inf. Theory 26, 78-82 (1980).
[CrossRef]

Zhang, J.

J. Zhang, "Einstein-Podolsky-Rosen sideband entanglement in broadband squeezed light," Phys. Rev. A 67, 054302 (2003).
[CrossRef]

IEEE Trans. Inf. Theory (1)

H. P. Yuen and J. H. Shapiro, "Optical communication with two-photon coherent states--Part III: Quantum measurements realizable with photo-emissive detectors," IEEE Trans. Inf. Theory 26, 78-82 (1980).
[CrossRef]

J. Mod. Opt. (2)

M. J. Collett, R. Loudon, and C. W. Gardiner, "Quantum-theory of optical homodyne and heterodyne-detection," J. Mod. Opt. 34, 881-902 (1987).
[CrossRef]

R. Loudon and P. L. Knight, "Squeezed light," J. Mod. Opt. 34, 709-759 (1987).
[CrossRef]

J. Opt. B (1)

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, "Quantum noise locking," J. Opt. B 7, S421-S428 (2005).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

A. Einstein, B. Podolsky, and N. Rosen, "Can quantum-mechanical description of physical reality be considered complete?" Phys. Rev. 47, 777-780 (1935).
[CrossRef]

Phys. Rev. A (8)

A. M. Marino and C. R. Stroud, Jr., "Deterministic secure communications using two-mode squeezed states," Phys. Rev. A 74, 022315 (2006).
[CrossRef]

S. F. Pereira, Z. Y. Ou, and H. J. Kimble, "Quantum communication with correlated nonclassical states," Phys. Rev. A 62, 042311 (2000).
[CrossRef]

M. D. Reid, "Quantum cryptography with a predetermined key, using continuous-variable Einstein-Podolsky-Rosen correlations," Phys. Rev. A 62, 062308 (2000).
[CrossRef]

M. D. Reid, "Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification," Phys. Rev. A 40, 913-923 (1989).
[CrossRef] [PubMed]

R. S. Bennink and R. W. Boyd, "Improved measurement of multimode squeezed light via an eigenmode approach," Phys. Rev. A 66, 053815 (2002).
[CrossRef]

J. Zhang, "Einstein-Podolsky-Rosen sideband entanglement in broadband squeezed light," Phys. Rev. A 67, 054302 (2003).
[CrossRef]

C. Schori, J. L. Sorensen, and E. S. Polzik, "Narrow-band frequency tunable light source of continuous quadrature entanglement," Phys. Rev. A 66, 033802 (2002).
[CrossRef]

S. Chelkowski, H. Vahlbruch, B. Hage, A. Franzen, N. Lastzka, K. Danzmann, and R. Schnabel, "Experimental characterization of frequency-dependent squeezed light," Phys. Rev. A 71, 013806 (2005).
[CrossRef]

Phys. Rev. Lett. (4)

C. H. Kim and P. Kumar, "Quadrature-squeezed light detection using a self-generated matched local oscillator," Phys. Rev. Lett. 73, 1605-1608 (1994).
[CrossRef] [PubMed]

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, "Realization of the Einstein-Podolsky-Rosen paradox for continuous variables," Phys. Rev. Lett. 68, 3663-3666 (1992).
[CrossRef] [PubMed]

C. Silberhorn, N. Korolkova, and G. Leuchs, "Quantum key distribution with bright entangled beams," Phys. Rev. Lett. 88, 167902 (2002).
[CrossRef] [PubMed]

S. L. Braunstein and H. J. Kimble, "Teleportation of continuous quantum variables," Phys. Rev. Lett. 80, 869-872 (1998).
[CrossRef]

Rev. Mod. Phys. (1)

S. L. Braunstein and P. van Loock, "Quantum information with continuous variables," Rev. Mod. Phys. 77, 513-577 (2005).
[CrossRef]

Rev. Sci. Instrum. (1)

M. B. Gray, D. A. Shaddock, C. C. Harb, and H. A. Bachor, "Photodetector designs for low-noise, broadband, and high-power applications," Rev. Sci. Instrum. 69, 3755-3762 (1998).
[CrossRef]

Science (1)

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

Other (2)

Throughout the paper, the fields are expressed in units of E0=√ \hbar omega/2ε0V. The frequency difference between the modes is assumed to be much smaller than the optical frequency so that E0 can be taken as a constant.

H. A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics, 2nd ed. (Wiley-VCH, 2004).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Balanced heterodyne detection scheme used for the characterization of squeezed light. LO, local oscillator; BS, beam splitter.

Fig. 2
Fig. 2

Frequency components involved in a heterodyne measurement of a TMSS. The frequencies of the two modes of the squeezed state are given by ω and ω + while the frequency of the LO is represented by ω L . To get a measurement that is independent of time, the frequency of the LO has to be selected between the frequencies of the two modes of the squeezed state.

Fig. 3
Fig. 3

Frequency components for the characterization of a TMSS using a BLO. The frequencies of the modes of the LO are chosen close to each of the modes of the squeezed field. It is necessary to include in the analysis the influence of the image bands associated with each mode of the squeezed state. The image bands are represented by the dashed lines. The curves centered around the modes of the TMSS represent the squeezing spectrum of the state. The image bands will be correlated as long as they are within the squeezing spectrum.

Fig. 4
Fig. 4

Effect of changing the measurement frequency on the amount of squeezing measured with the BLO technique. As long as the measurement frequency is less than the squeezing bandwidth σ there will not be a significant amount of excess noise.

Equations (19)

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

d ̂ 1 = t E ̂ S + r E ̂ L O ,
d ̂ 2 = r E ̂ S + t E ̂ L O ,
I ̂ 12 = d ̂ 1 d ̂ 1 d ̂ 2 d ̂ 2 = i ( E ̂ S E ̂ L O E ̂ L O E ̂ S ) .
E ̂ S = a ̂ + e i ( ω + t ϕ + ) + a ̂ e i ( ω t ϕ ) ,
X ̂ = 1 2 2 ( a ̂ + + a ̂ + + a ̂ + a ̂ ) ,
Y ̂ = 1 i 2 2 ( a ̂ + a ̂ + + a ̂ a ̂ ) .
( Δ X ̂ ) 2 = 1 4 ( e 2 s cos 2 θ 2 + e 2 s sin 2 θ 2 ) ,
( Δ Y ̂ ) 2 = 1 4 ( e 2 s sin 2 θ 2 + e 2 s cos 2 θ 2 ) ,
( Δ X ̂ ) 2 min = 1 4 e 2 s ,
( Δ Y ̂ ) 2 max = 1 4 e 2 s .
E ̂ L O = b ̂ e i ω L t ,
( Δ I ̂ 12 ) 2 = 2 β 2 [ e 2 s cos 2 ( χ θ 2 ) + e 2 s sin 2 ( χ θ 2 ) ] ,
E ̂ L O = b ̂ 1 e i ω L 1 t + b ̂ 2 e i ω L 2 t ,
( Δ I ̂ 12 ) 2 = { ( Δ E ̂ S ) 2 ( β 1 2 e i 2 ω L 1 t + β 2 2 e i 2 ω L 2 t + 2 β 1 β 2 e i ( ω L 1 + ω L 2 ) t ) ( E ̂ S E ̂ S E ̂ S E ̂ S ) ( β 1 2 + β 2 2 + β 1 β 2 * e i ( ω L 1 ω L 2 ) t + β 1 * β 2 e i ( ω L 1 ω L 2 ) t ) + H.c. } + 2 E ̂ S E ̂ S ,
E ̂ S = a ̂ + e i ( ω + t ϕ + ) + a ̂ v + e i ( ω v + ϕ + ) t + a ̂ e i ( ω t ϕ ) + a ̂ v e i ( ω v ϕ ) t ,
( Δ I ̂ 12 ) 2 = ( β 1 2 + β 2 2 ) ( 4 sinh 2 s o + 4 sinh 2 s v + 4 ) + [ 4 β 1 β 2 e i ( Δ 1 + Δ 2 ) t e i ( θ + ϕ + + ϕ ) sinh s o cosh s o + 4 β 1 β 2 e i ( Δ 1 + Δ 2 ) t e i ( θ + ϕ v + + ϕ v ) sinh s v cosh s v + c.c. ] ,
( Δ I ̂ 12 ) 2 = 4 β 2 [ ( e 2 s o + e 2 s v ) cos 2 ( χ 1 + χ 2 θ 2 ) + ( e 2 s o + e 2 s v ) sin 2 ( χ 1 + χ 2 θ o 2 ) + E ̂ s E ̂ s 2 β 2 ] ,
s ( Ω ) = s o exp ( Ω 2 2 σ 2 ) ,
( Δ I ̂ 12 ) 2 = 4 β 2 { ( 1 + δ β β ) [ ( e 2 s o + e 2 s v ) cos 2 ( χ 1 + χ 2 θ 2 ) + ( e 2 s o + e 2 s v ) sin 2 ( χ 1 + χ 2 θ 2 ) ] + 1 2 ( δ β β ) 2 ( cosh 2 s o + cosh 2 s v ) } .

Metrics