Abstract

We experimentally demonstrate that the quantum entanglement between amplitude and phase quadratures of optical modes produced from a nondegenerate optical parametric amplifier (NOPA) can be enhanced and manipulated phase sensitively by means of another NOPA. When both NOPAs operate at deamplification, the entanglement degree is increased at the cavity resonance of the second NOPA. When the first NOPA operates at deamplification and the second one at amplification, the spectral features of the correlation variances are significantly changed. The experimental results are in good agreement with the theoretical expectation.

© 2010 Optical Society of America

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  1. S. L. Braunstein and P. van Loock, Rev. Mod. Phys. 77, 513 (2005).
    [CrossRef]
  2. M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, Rev. Mod. Phys. 81, 1727 (2009).
    [CrossRef]
  3. X. Y. Li, Q. Pan, J. T. Jing, J. Zhang, C. D. Xie, and K. C. Peng, Phys. Rev. Lett. 88, 047904 (2002).
    [CrossRef] [PubMed]
  4. V. D'Auria, S. Fornaro, A. Porzio, S. Solimeno, S. Olivares, and M. G. A. Paris, Phys. Rev. Lett. 102, 020502 (2009).
    [CrossRef] [PubMed]
  5. G. S. Agarwal, Phys. Rev. Lett. 97, 023601 (2006).
    [CrossRef] [PubMed]
  6. J. Zhang, C. G. Ye, F. Gao, and M. Xiao, Phys. Rev. Lett. 101, 233602 (2008).
    [CrossRef] [PubMed]
  7. U. L. Andersen, V. Josse, and G. Leuchs, Phys. Rev. Lett. 94, 240503 (2005).
    [CrossRef]
  8. R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, Phys. Rev. Lett. 103, 010501 (2009).
    [CrossRef] [PubMed]
  9. A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, Phys. Rev. Lett. 95, 243603 (2005).
    [CrossRef] [PubMed]
  10. J. T. Jing, S. Feng, R. Bloomer, and O. Pfister, Phys. Rev. A 74, 041804 (2006).
    [CrossRef]
  11. G. Keller, V. D'Auria, N. Treps, T. Coudreau, J. Laurat, and C. Fabre, Opt. Express 16, 9351 (2008).
    [CrossRef] [PubMed]
  12. H. X. Chen and J. Zhang, Phys. Rev. A 79, 063826 (2009).
    [CrossRef]
  13. Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, Phys. Rev. Lett. 68, 3663 (1992).
    [CrossRef] [PubMed]
  14. A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and P. Grangier, Phys. Rev. Lett. 98, 030502 (2007).
    [CrossRef] [PubMed]

2009 (4)

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, Rev. Mod. Phys. 81, 1727 (2009).
[CrossRef]

V. D'Auria, S. Fornaro, A. Porzio, S. Solimeno, S. Olivares, and M. G. A. Paris, Phys. Rev. Lett. 102, 020502 (2009).
[CrossRef] [PubMed]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, Phys. Rev. Lett. 103, 010501 (2009).
[CrossRef] [PubMed]

H. X. Chen and J. Zhang, Phys. Rev. A 79, 063826 (2009).
[CrossRef]

2008 (2)

2007 (1)

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and P. Grangier, Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef] [PubMed]

2006 (2)

J. T. Jing, S. Feng, R. Bloomer, and O. Pfister, Phys. Rev. A 74, 041804 (2006).
[CrossRef]

G. S. Agarwal, Phys. Rev. Lett. 97, 023601 (2006).
[CrossRef] [PubMed]

2005 (3)

U. L. Andersen, V. Josse, and G. Leuchs, Phys. Rev. Lett. 94, 240503 (2005).
[CrossRef]

A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, Phys. Rev. Lett. 95, 243603 (2005).
[CrossRef] [PubMed]

S. L. Braunstein and P. van Loock, Rev. Mod. Phys. 77, 513 (2005).
[CrossRef]

2002 (1)

X. Y. Li, Q. Pan, J. T. Jing, J. Zhang, C. D. Xie, and K. C. Peng, Phys. Rev. Lett. 88, 047904 (2002).
[CrossRef] [PubMed]

1992 (1)

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, Phys. Rev. Lett. 68, 3663 (1992).
[CrossRef] [PubMed]

Agarwal, G. S.

G. S. Agarwal, Phys. Rev. Lett. 97, 023601 (2006).
[CrossRef] [PubMed]

Andersen, U. L.

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, Rev. Mod. Phys. 81, 1727 (2009).
[CrossRef]

U. L. Andersen, V. Josse, and G. Leuchs, Phys. Rev. Lett. 94, 240503 (2005).
[CrossRef]

Bachor, H. A.

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, Rev. Mod. Phys. 81, 1727 (2009).
[CrossRef]

Bloomer, R.

J. T. Jing, S. Feng, R. Bloomer, and O. Pfister, Phys. Rev. A 74, 041804 (2006).
[CrossRef]

Bowen, W. P.

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, Rev. Mod. Phys. 81, 1727 (2009).
[CrossRef]

Boyer, V.

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, Phys. Rev. Lett. 103, 010501 (2009).
[CrossRef] [PubMed]

Braunstein, S. L.

S. L. Braunstein and P. van Loock, Rev. Mod. Phys. 77, 513 (2005).
[CrossRef]

Cassemiro, K. N.

A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, Phys. Rev. Lett. 95, 243603 (2005).
[CrossRef] [PubMed]

Cavalcanti, E. G.

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, Rev. Mod. Phys. 81, 1727 (2009).
[CrossRef]

Chen, H. X.

H. X. Chen and J. Zhang, Phys. Rev. A 79, 063826 (2009).
[CrossRef]

Coudreau, T.

Cruz, L. S.

A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, Phys. Rev. Lett. 95, 243603 (2005).
[CrossRef] [PubMed]

Dantan, A.

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and P. Grangier, Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef] [PubMed]

D'Auria, V.

V. D'Auria, S. Fornaro, A. Porzio, S. Solimeno, S. Olivares, and M. G. A. Paris, Phys. Rev. Lett. 102, 020502 (2009).
[CrossRef] [PubMed]

G. Keller, V. D'Auria, N. Treps, T. Coudreau, J. Laurat, and C. Fabre, Opt. Express 16, 9351 (2008).
[CrossRef] [PubMed]

Drummond, P. D.

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, Rev. Mod. Phys. 81, 1727 (2009).
[CrossRef]

Fabre, C.

Feng, S.

J. T. Jing, S. Feng, R. Bloomer, and O. Pfister, Phys. Rev. A 74, 041804 (2006).
[CrossRef]

Fornaro, S.

V. D'Auria, S. Fornaro, A. Porzio, S. Solimeno, S. Olivares, and M. G. A. Paris, Phys. Rev. Lett. 102, 020502 (2009).
[CrossRef] [PubMed]

Gao, F.

J. Zhang, C. G. Ye, F. Gao, and M. Xiao, Phys. Rev. Lett. 101, 233602 (2008).
[CrossRef] [PubMed]

Grangier, P.

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and P. Grangier, Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef] [PubMed]

Jing, J. T.

J. T. Jing, S. Feng, R. Bloomer, and O. Pfister, Phys. Rev. A 74, 041804 (2006).
[CrossRef]

X. Y. Li, Q. Pan, J. T. Jing, J. Zhang, C. D. Xie, and K. C. Peng, Phys. Rev. Lett. 88, 047904 (2002).
[CrossRef] [PubMed]

Jones, K. M.

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, Phys. Rev. Lett. 103, 010501 (2009).
[CrossRef] [PubMed]

Josse, V.

U. L. Andersen, V. Josse, and G. Leuchs, Phys. Rev. Lett. 94, 240503 (2005).
[CrossRef]

Keller, G.

Kimble, H. J.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, Phys. Rev. Lett. 68, 3663 (1992).
[CrossRef] [PubMed]

Lam, P. K.

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, Rev. Mod. Phys. 81, 1727 (2009).
[CrossRef]

Laurat, J.

Lett, P. D.

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, Phys. Rev. Lett. 103, 010501 (2009).
[CrossRef] [PubMed]

Leuchs, G.

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, Rev. Mod. Phys. 81, 1727 (2009).
[CrossRef]

U. L. Andersen, V. Josse, and G. Leuchs, Phys. Rev. Lett. 94, 240503 (2005).
[CrossRef]

Li, X. Y.

X. Y. Li, Q. Pan, J. T. Jing, J. Zhang, C. D. Xie, and K. C. Peng, Phys. Rev. Lett. 88, 047904 (2002).
[CrossRef] [PubMed]

Marino, A. M.

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, Phys. Rev. Lett. 103, 010501 (2009).
[CrossRef] [PubMed]

Martinelli, M.

A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, Phys. Rev. Lett. 95, 243603 (2005).
[CrossRef] [PubMed]

Nussenzveig, P.

A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, Phys. Rev. Lett. 95, 243603 (2005).
[CrossRef] [PubMed]

Olivares, S.

V. D'Auria, S. Fornaro, A. Porzio, S. Solimeno, S. Olivares, and M. G. A. Paris, Phys. Rev. Lett. 102, 020502 (2009).
[CrossRef] [PubMed]

Ou, Z. Y.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, Phys. Rev. Lett. 68, 3663 (1992).
[CrossRef] [PubMed]

Ourjoumtsev, A.

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and P. Grangier, Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef] [PubMed]

Pan, Q.

X. Y. Li, Q. Pan, J. T. Jing, J. Zhang, C. D. Xie, and K. C. Peng, Phys. Rev. Lett. 88, 047904 (2002).
[CrossRef] [PubMed]

Paris, M. G. A.

V. D'Auria, S. Fornaro, A. Porzio, S. Solimeno, S. Olivares, and M. G. A. Paris, Phys. Rev. Lett. 102, 020502 (2009).
[CrossRef] [PubMed]

Peng, K. C.

X. Y. Li, Q. Pan, J. T. Jing, J. Zhang, C. D. Xie, and K. C. Peng, Phys. Rev. Lett. 88, 047904 (2002).
[CrossRef] [PubMed]

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, Phys. Rev. Lett. 68, 3663 (1992).
[CrossRef] [PubMed]

Pereira, S. F.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, Phys. Rev. Lett. 68, 3663 (1992).
[CrossRef] [PubMed]

Pfister, O.

J. T. Jing, S. Feng, R. Bloomer, and O. Pfister, Phys. Rev. A 74, 041804 (2006).
[CrossRef]

Pooser, R. C.

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, Phys. Rev. Lett. 103, 010501 (2009).
[CrossRef] [PubMed]

Porzio, A.

V. D'Auria, S. Fornaro, A. Porzio, S. Solimeno, S. Olivares, and M. G. A. Paris, Phys. Rev. Lett. 102, 020502 (2009).
[CrossRef] [PubMed]

Reid, M. D.

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, Rev. Mod. Phys. 81, 1727 (2009).
[CrossRef]

Solimeno, S.

V. D'Auria, S. Fornaro, A. Porzio, S. Solimeno, S. Olivares, and M. G. A. Paris, Phys. Rev. Lett. 102, 020502 (2009).
[CrossRef] [PubMed]

Treps, N.

Tualle-Brouri, R.

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and P. Grangier, Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef] [PubMed]

van Loock, P.

S. L. Braunstein and P. van Loock, Rev. Mod. Phys. 77, 513 (2005).
[CrossRef]

Villar, A. S.

A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, Phys. Rev. Lett. 95, 243603 (2005).
[CrossRef] [PubMed]

Xiao, M.

J. Zhang, C. G. Ye, F. Gao, and M. Xiao, Phys. Rev. Lett. 101, 233602 (2008).
[CrossRef] [PubMed]

Xie, C. D.

X. Y. Li, Q. Pan, J. T. Jing, J. Zhang, C. D. Xie, and K. C. Peng, Phys. Rev. Lett. 88, 047904 (2002).
[CrossRef] [PubMed]

Ye, C. G.

J. Zhang, C. G. Ye, F. Gao, and M. Xiao, Phys. Rev. Lett. 101, 233602 (2008).
[CrossRef] [PubMed]

Zhang, J.

H. X. Chen and J. Zhang, Phys. Rev. A 79, 063826 (2009).
[CrossRef]

J. Zhang, C. G. Ye, F. Gao, and M. Xiao, Phys. Rev. Lett. 101, 233602 (2008).
[CrossRef] [PubMed]

X. Y. Li, Q. Pan, J. T. Jing, J. Zhang, C. D. Xie, and K. C. Peng, Phys. Rev. Lett. 88, 047904 (2002).
[CrossRef] [PubMed]

Opt. Express (1)

Phys. Rev. A (2)

J. T. Jing, S. Feng, R. Bloomer, and O. Pfister, Phys. Rev. A 74, 041804 (2006).
[CrossRef]

H. X. Chen and J. Zhang, Phys. Rev. A 79, 063826 (2009).
[CrossRef]

Phys. Rev. Lett. (9)

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, Phys. Rev. Lett. 68, 3663 (1992).
[CrossRef] [PubMed]

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and P. Grangier, Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef] [PubMed]

X. Y. Li, Q. Pan, J. T. Jing, J. Zhang, C. D. Xie, and K. C. Peng, Phys. Rev. Lett. 88, 047904 (2002).
[CrossRef] [PubMed]

V. D'Auria, S. Fornaro, A. Porzio, S. Solimeno, S. Olivares, and M. G. A. Paris, Phys. Rev. Lett. 102, 020502 (2009).
[CrossRef] [PubMed]

G. S. Agarwal, Phys. Rev. Lett. 97, 023601 (2006).
[CrossRef] [PubMed]

J. Zhang, C. G. Ye, F. Gao, and M. Xiao, Phys. Rev. Lett. 101, 233602 (2008).
[CrossRef] [PubMed]

U. L. Andersen, V. Josse, and G. Leuchs, Phys. Rev. Lett. 94, 240503 (2005).
[CrossRef]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, Phys. Rev. Lett. 103, 010501 (2009).
[CrossRef] [PubMed]

A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, Phys. Rev. Lett. 95, 243603 (2005).
[CrossRef] [PubMed]

Rev. Mod. Phys. (2)

S. L. Braunstein and P. van Loock, Rev. Mod. Phys. 77, 513 (2005).
[CrossRef]

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, Rev. Mod. Phys. 81, 1727 (2009).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Experimental setup. laser, Nd:YAP/KTP laser source; HW, λ / 2 wave plate; PBS, polarizing beam splitter; BS1–BS2, 50/50 beam splitter; D1–D4, ETX500 InGaAs photodiode detectors; + / , positive/negative power combiner; MC, mode cleaner; M0–M6, different mirrors (see text for details); PZT, piezoelectric transducer; SA, spectrum analyzer.

Fig. 2
Fig. 2

Noise powers of the correlation variances of the output beams from NOPA2 operated at deamplification versus cavity detuning: (a) for amplitude sum δ 2 ( X ̂ b 1 + X ̂ b 2 ) , (b) for phase difference δ 2 ( Y ̂ b 1 Y ̂ b 2 ) . Trace i, SNL; trace ii, theoretically calculated results; trace iii, measured variance spectrum with the cavity detuning; trace iv, measured variance power with the cavity locked on resonance.

Fig. 3
Fig. 3

Noise powers of the correlation variances of the output beams from NOPA2 operated at amplification versus cavity detuning: (a) for amplitude difference δ 2 ( X ̂ b 1 X ̂ b 2 ) , (b) for phase sum δ 2 ( Y ̂ b 1 + Y ̂ b 2 ) . Trace i, SNL; trace ii, theoretically calculated results; trace iii, measured variance spectrum with the cavity detuning; trace iv, measured variance power with the cavity locked on resonance.

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