Abstract

We propose a quantum-mechanical model of a nonlinear beam splitter having third-order nonlinearity. We show that nonclassical features, such as squeezing and sub-Poissonian photon statistics of optical fields, can be generated in the output when we mix coherent light beams via such a nonlinear beam splitter.

© 2010 Optical Society of America

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References

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  1. V. V. Dodonov, J. Opt. B 4, R1 (2002).
    [CrossRef]
  2. D. F. Walls, Nature 306, 141 (1983).
    [CrossRef]
  3. N. Chandra and H. Prakash, Phys. Rev. A 1, 1696 (1970).
    [CrossRef]
  4. H. Paul, Rev. Mod. Phys. 54, 1061 (1982).
    [CrossRef]
  5. L. Davidovich, Rev. Mod. Phys. 68, 127 (1996).
    [CrossRef]
  6. H. Prakash and D. K. Mishra, J. Phys. B 40, 2531 (2007).
    [CrossRef]
  7. H. Prakash and D. K. Mishra, J. Phys. B 39, 2291 (2006).
    [CrossRef]
  8. Y. Yamamoto and H. A. Haus, Rev. Mod. Phys. 58, 1001 (1986).
    [CrossRef]
  9. H. P. Yuen and J. H. Shapiro, IEEE Trans. Inf. Theory IT-26, 78 (1980).
    [CrossRef]
  10. S. M. Barnett and S. J. D. Phoenix, Phys. Rev. A 44, 535 (1991).
    [CrossRef] [PubMed]
  11. M. S. Kim, W. Son, V. Buzek, and P. L. Knight, Phys. Rev. A 65, 032323 (2002).
    [CrossRef]
  12. A. I. Lvovsky and J. Mlynek, Phys. Rev. Lett. 88, 250401 (2002).
    [CrossRef] [PubMed]
  13. D. K. Mishra, Acta Phys. Pol. A 112, 859 (2007).
  14. H. Prakash and D. K. Mishra, Opt. Spectrosc. 103, 145 (2007).
    [CrossRef]
  15. H. Prakash and D. K. Mishra, Eur. Phys. J. D 45, 363 (2007).
    [CrossRef]
  16. H. Prakash and D. K. Mishra, J. Phys. B 38, 665 (2005).
    [CrossRef]
  17. U. Leonhardt, Rep. Prog. Phys. 66, 1207 (2003).
    [CrossRef]
  18. M. Deutsch, Phys. Rev. A 66, 023814 (2002).
    [CrossRef]
  19. A preliminary version of this work has been reported in T. Cho, Bull. Am. Phys. Soc. 52, 100 (2007).
  20. M. Hillery, Opt. Commun. 62, 135 (1987).
    [CrossRef]
  21. H. Prakash and D. K. Mishra, Bull. Am. Phys. Soc. 53, 900 (2008).
  22. H.-A. Bachor, A Guide to Experiments in Quantum Optics (Wiley-VCH, 1998).
  23. U. Leonhardt, Phys. Rev. A 48, 3265(1993).
    [CrossRef] [PubMed]
  24. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Narosa, 2003), Vol. 1.
  25. R. Simon, N. Mukunda, and B. Dutta, Phys. Rev. A 49, 1567 (1994).
    [CrossRef] [PubMed]
  26. A. B. Dutta, N. Mukunda, and R. Simon, Phys. Rev. A 52, 1609 (1995).
    [CrossRef] [PubMed]
  27. R. W. Boyd, Nonlinear Optics (Academic, 1992).
  28. E. G. Sauter, Nonlinear Optics (Wiley, 1996).

2008

H. Prakash and D. K. Mishra, Bull. Am. Phys. Soc. 53, 900 (2008).

2007

H. Prakash and D. K. Mishra, J. Phys. B 40, 2531 (2007).
[CrossRef]

D. K. Mishra, Acta Phys. Pol. A 112, 859 (2007).

H. Prakash and D. K. Mishra, Opt. Spectrosc. 103, 145 (2007).
[CrossRef]

H. Prakash and D. K. Mishra, Eur. Phys. J. D 45, 363 (2007).
[CrossRef]

A preliminary version of this work has been reported in T. Cho, Bull. Am. Phys. Soc. 52, 100 (2007).

2006

H. Prakash and D. K. Mishra, J. Phys. B 39, 2291 (2006).
[CrossRef]

2005

H. Prakash and D. K. Mishra, J. Phys. B 38, 665 (2005).
[CrossRef]

2003

U. Leonhardt, Rep. Prog. Phys. 66, 1207 (2003).
[CrossRef]

R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Narosa, 2003), Vol. 1.

2002

M. Deutsch, Phys. Rev. A 66, 023814 (2002).
[CrossRef]

M. S. Kim, W. Son, V. Buzek, and P. L. Knight, Phys. Rev. A 65, 032323 (2002).
[CrossRef]

A. I. Lvovsky and J. Mlynek, Phys. Rev. Lett. 88, 250401 (2002).
[CrossRef] [PubMed]

V. V. Dodonov, J. Opt. B 4, R1 (2002).
[CrossRef]

1998

H.-A. Bachor, A Guide to Experiments in Quantum Optics (Wiley-VCH, 1998).

1996

E. G. Sauter, Nonlinear Optics (Wiley, 1996).

L. Davidovich, Rev. Mod. Phys. 68, 127 (1996).
[CrossRef]

1995

A. B. Dutta, N. Mukunda, and R. Simon, Phys. Rev. A 52, 1609 (1995).
[CrossRef] [PubMed]

1994

R. Simon, N. Mukunda, and B. Dutta, Phys. Rev. A 49, 1567 (1994).
[CrossRef] [PubMed]

1993

U. Leonhardt, Phys. Rev. A 48, 3265(1993).
[CrossRef] [PubMed]

1992

R. W. Boyd, Nonlinear Optics (Academic, 1992).

1991

S. M. Barnett and S. J. D. Phoenix, Phys. Rev. A 44, 535 (1991).
[CrossRef] [PubMed]

1987

M. Hillery, Opt. Commun. 62, 135 (1987).
[CrossRef]

1986

Y. Yamamoto and H. A. Haus, Rev. Mod. Phys. 58, 1001 (1986).
[CrossRef]

1983

D. F. Walls, Nature 306, 141 (1983).
[CrossRef]

1982

H. Paul, Rev. Mod. Phys. 54, 1061 (1982).
[CrossRef]

1980

H. P. Yuen and J. H. Shapiro, IEEE Trans. Inf. Theory IT-26, 78 (1980).
[CrossRef]

1970

N. Chandra and H. Prakash, Phys. Rev. A 1, 1696 (1970).
[CrossRef]

Bachor, H.-A.

H.-A. Bachor, A Guide to Experiments in Quantum Optics (Wiley-VCH, 1998).

Barnett, S. M.

S. M. Barnett and S. J. D. Phoenix, Phys. Rev. A 44, 535 (1991).
[CrossRef] [PubMed]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 1992).

Buzek, V.

M. S. Kim, W. Son, V. Buzek, and P. L. Knight, Phys. Rev. A 65, 032323 (2002).
[CrossRef]

Chandra, N.

N. Chandra and H. Prakash, Phys. Rev. A 1, 1696 (1970).
[CrossRef]

Cho, T.

A preliminary version of this work has been reported in T. Cho, Bull. Am. Phys. Soc. 52, 100 (2007).

Davidovich, L.

L. Davidovich, Rev. Mod. Phys. 68, 127 (1996).
[CrossRef]

Deutsch, M.

M. Deutsch, Phys. Rev. A 66, 023814 (2002).
[CrossRef]

Dodonov, V. V.

V. V. Dodonov, J. Opt. B 4, R1 (2002).
[CrossRef]

Dutta, A. B.

A. B. Dutta, N. Mukunda, and R. Simon, Phys. Rev. A 52, 1609 (1995).
[CrossRef] [PubMed]

Dutta, B.

R. Simon, N. Mukunda, and B. Dutta, Phys. Rev. A 49, 1567 (1994).
[CrossRef] [PubMed]

Feynman, R. P.

R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Narosa, 2003), Vol. 1.

Haus, H. A.

Y. Yamamoto and H. A. Haus, Rev. Mod. Phys. 58, 1001 (1986).
[CrossRef]

Hillery, M.

M. Hillery, Opt. Commun. 62, 135 (1987).
[CrossRef]

Kim, M. S.

M. S. Kim, W. Son, V. Buzek, and P. L. Knight, Phys. Rev. A 65, 032323 (2002).
[CrossRef]

Knight, P. L.

M. S. Kim, W. Son, V. Buzek, and P. L. Knight, Phys. Rev. A 65, 032323 (2002).
[CrossRef]

Leighton, R. B.

R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Narosa, 2003), Vol. 1.

Leonhardt, U.

U. Leonhardt, Rep. Prog. Phys. 66, 1207 (2003).
[CrossRef]

U. Leonhardt, Phys. Rev. A 48, 3265(1993).
[CrossRef] [PubMed]

Lvovsky, A. I.

A. I. Lvovsky and J. Mlynek, Phys. Rev. Lett. 88, 250401 (2002).
[CrossRef] [PubMed]

Mishra, D. K.

H. Prakash and D. K. Mishra, Bull. Am. Phys. Soc. 53, 900 (2008).

H. Prakash and D. K. Mishra, Eur. Phys. J. D 45, 363 (2007).
[CrossRef]

H. Prakash and D. K. Mishra, J. Phys. B 40, 2531 (2007).
[CrossRef]

D. K. Mishra, Acta Phys. Pol. A 112, 859 (2007).

H. Prakash and D. K. Mishra, Opt. Spectrosc. 103, 145 (2007).
[CrossRef]

H. Prakash and D. K. Mishra, J. Phys. B 39, 2291 (2006).
[CrossRef]

H. Prakash and D. K. Mishra, J. Phys. B 38, 665 (2005).
[CrossRef]

Mlynek, J.

A. I. Lvovsky and J. Mlynek, Phys. Rev. Lett. 88, 250401 (2002).
[CrossRef] [PubMed]

Mukunda, N.

A. B. Dutta, N. Mukunda, and R. Simon, Phys. Rev. A 52, 1609 (1995).
[CrossRef] [PubMed]

R. Simon, N. Mukunda, and B. Dutta, Phys. Rev. A 49, 1567 (1994).
[CrossRef] [PubMed]

Paul, H.

H. Paul, Rev. Mod. Phys. 54, 1061 (1982).
[CrossRef]

Phoenix, S. J. D.

S. M. Barnett and S. J. D. Phoenix, Phys. Rev. A 44, 535 (1991).
[CrossRef] [PubMed]

Prakash, H.

H. Prakash and D. K. Mishra, Bull. Am. Phys. Soc. 53, 900 (2008).

H. Prakash and D. K. Mishra, Eur. Phys. J. D 45, 363 (2007).
[CrossRef]

H. Prakash and D. K. Mishra, J. Phys. B 40, 2531 (2007).
[CrossRef]

H. Prakash and D. K. Mishra, Opt. Spectrosc. 103, 145 (2007).
[CrossRef]

H. Prakash and D. K. Mishra, J. Phys. B 39, 2291 (2006).
[CrossRef]

H. Prakash and D. K. Mishra, J. Phys. B 38, 665 (2005).
[CrossRef]

N. Chandra and H. Prakash, Phys. Rev. A 1, 1696 (1970).
[CrossRef]

Sands, M.

R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Narosa, 2003), Vol. 1.

Sauter, E. G.

E. G. Sauter, Nonlinear Optics (Wiley, 1996).

Shapiro, J. H.

H. P. Yuen and J. H. Shapiro, IEEE Trans. Inf. Theory IT-26, 78 (1980).
[CrossRef]

Simon, R.

A. B. Dutta, N. Mukunda, and R. Simon, Phys. Rev. A 52, 1609 (1995).
[CrossRef] [PubMed]

R. Simon, N. Mukunda, and B. Dutta, Phys. Rev. A 49, 1567 (1994).
[CrossRef] [PubMed]

Son, W.

M. S. Kim, W. Son, V. Buzek, and P. L. Knight, Phys. Rev. A 65, 032323 (2002).
[CrossRef]

Walls, D. F.

D. F. Walls, Nature 306, 141 (1983).
[CrossRef]

Yamamoto, Y.

Y. Yamamoto and H. A. Haus, Rev. Mod. Phys. 58, 1001 (1986).
[CrossRef]

Yuen, H. P.

H. P. Yuen and J. H. Shapiro, IEEE Trans. Inf. Theory IT-26, 78 (1980).
[CrossRef]

Acta Phys. Pol. A

D. K. Mishra, Acta Phys. Pol. A 112, 859 (2007).

Bull. Am. Phys. Soc.

A preliminary version of this work has been reported in T. Cho, Bull. Am. Phys. Soc. 52, 100 (2007).

H. Prakash and D. K. Mishra, Bull. Am. Phys. Soc. 53, 900 (2008).

Eur. Phys. J. D

H. Prakash and D. K. Mishra, Eur. Phys. J. D 45, 363 (2007).
[CrossRef]

IEEE Trans. Inf. Theory

H. P. Yuen and J. H. Shapiro, IEEE Trans. Inf. Theory IT-26, 78 (1980).
[CrossRef]

J. Opt. B

V. V. Dodonov, J. Opt. B 4, R1 (2002).
[CrossRef]

J. Phys. B

H. Prakash and D. K. Mishra, J. Phys. B 38, 665 (2005).
[CrossRef]

H. Prakash and D. K. Mishra, J. Phys. B 40, 2531 (2007).
[CrossRef]

H. Prakash and D. K. Mishra, J. Phys. B 39, 2291 (2006).
[CrossRef]

Nature

D. F. Walls, Nature 306, 141 (1983).
[CrossRef]

Opt. Commun.

M. Hillery, Opt. Commun. 62, 135 (1987).
[CrossRef]

Opt. Spectrosc.

H. Prakash and D. K. Mishra, Opt. Spectrosc. 103, 145 (2007).
[CrossRef]

Phys. Rev. A

N. Chandra and H. Prakash, Phys. Rev. A 1, 1696 (1970).
[CrossRef]

S. M. Barnett and S. J. D. Phoenix, Phys. Rev. A 44, 535 (1991).
[CrossRef] [PubMed]

M. S. Kim, W. Son, V. Buzek, and P. L. Knight, Phys. Rev. A 65, 032323 (2002).
[CrossRef]

U. Leonhardt, Phys. Rev. A 48, 3265(1993).
[CrossRef] [PubMed]

R. Simon, N. Mukunda, and B. Dutta, Phys. Rev. A 49, 1567 (1994).
[CrossRef] [PubMed]

A. B. Dutta, N. Mukunda, and R. Simon, Phys. Rev. A 52, 1609 (1995).
[CrossRef] [PubMed]

M. Deutsch, Phys. Rev. A 66, 023814 (2002).
[CrossRef]

Phys. Rev. Lett.

A. I. Lvovsky and J. Mlynek, Phys. Rev. Lett. 88, 250401 (2002).
[CrossRef] [PubMed]

Rep. Prog. Phys.

U. Leonhardt, Rep. Prog. Phys. 66, 1207 (2003).
[CrossRef]

Rev. Mod. Phys.

Y. Yamamoto and H. A. Haus, Rev. Mod. Phys. 58, 1001 (1986).
[CrossRef]

H. Paul, Rev. Mod. Phys. 54, 1061 (1982).
[CrossRef]

L. Davidovich, Rev. Mod. Phys. 68, 127 (1996).
[CrossRef]

Other

R. W. Boyd, Nonlinear Optics (Academic, 1992).

E. G. Sauter, Nonlinear Optics (Wiley, 1996).

R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Narosa, 2003), Vol. 1.

H.-A. Bachor, A Guide to Experiments in Quantum Optics (Wiley-VCH, 1998).

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Equations (9)

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c ^ = t a ^ + i r b ^ , d ^ = t b ^ + i r a ^ ,
c ^ = t a ^ + i r b ^ + ( z 1 a ^ + z 2 b ^ ) ( a ^ 2 + b ^ 2 ) + ( z 3 a ^ + z 4 b ^ ) ( a ^ 2 b ^ 2 ) + ( z 5 a ^ + z 6 b ^ ) a ^ b ^ ,
d ^ = t b ^ + i r a ^ + ( z 1 b ^ + z 2 a ^ ) ( a ^ 2 + b ^ 2 ) ( z 3 a ^ + z 4 b ^ ) ( a ^ 2 b ^ 2 ) + ( z 5 b ^ + z 6 a ^ ) a ^ b ^ ,
a ^ = t c ^ i r d ^ ( t z 1 i r z 2 ) ( t c ^ + i r d ^ ) [ ( t 2 r 2 ) ( c ^ 2 + d ^ 2 ) 4 i r t c ^ d ^ ] ( t z 2 i r z 1 ) ( t d ^ + i r c ^ ) [ ( t 2 r 2 ) ( c ^ 2 + d ^ 2 ) 4 i r t c ^ d ^ ] ( t z 3 + i r z 4 ) ( t c ^ + i r d ^ ) ( c ^ 2 d ^ 2 ) ( t z 4 + i r z 3 ) ( t d ^ + i r c ^ ) ( c ^ 2 d ^ 2 ) ( t z 5 i r z 6 ) ( t c ^ + i r d ^ ) [ ( t 2 r 2 ) c ^ d ^ i r t ( c ^ 2 + d ^ 2 ) ] ( t z 6 i r z 5 ) ( t d ^ + i r c ^ ) [ ( t 2 r 2 ) c ^ d ^ i r t ( c ^ 2 + d ^ 2 ) ] .
a ^ = t c ^ i r d ^ + ( z 1 * c ^ + z 2 * d ^ ) ( c ^ 2 + d ^ 2 ) + ( z 3 * c ^ + z 4 * d ^ ) ( c ^ 2 d ^ 2 ) + ( z 5 * c ^ + z 6 * d ^ ) c ^ d ^ ] ,
c ^ = t a ^ + i r b ^ + [ ( r p 1 + i t q 1 ) a ^ + ( r p 2 + i t q 2 ) b ^ ] ( a ^ 2 + b ^ 2 ) + [ ( r p 3 + i t q 3 ) a ^ + ( r q 3 + i t p 3 ) b ^ ] ( a ^ 2 b ^ 2 ) 2 [ ( r q 2 + i t p 2 ) a ^ + ( r q 1 + i t p 1 ) b ^ ] a ^ b ^ ,
d ^ = t b ^ + i r a ^ + [ ( r p 1 + i t q 1 ) a ^ + ( r p 2 + i t q 2 ) b ^ ] ( a ^ 2 + b ^ 2 ) + [ ( r p 3 + i t q 3 ) a ^ + ( r q 3 + i t p 3 ) b ^ ] ( a ^ 2 b ^ 2 ) 2 [ ( r q 1 + i t p 1 ) b ^ + ( r q 2 + i t p 2 ) a ^ ] a ^ b ^ .
c ^ = t a ^ + i r b ^ + p [ r b ^ ( a ^ 2 + b ^ 2 ) 2 i t a ^ b ^ b ^ ] + q ( r b ^ + i t a ^ ) ( a ^ 2 b ^ 2 ) ,
d ^ = t b ^ + i r a ^ + p [ r a ^ ( a ^ 2 + b ^ 2 ) 2 i t a ^ a ^ b ^ ] q ( r a ^ + i t b ^ ) ( a ^ 2 b ^ 2 ) .

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