Abstract

We discuss the possibility of generating noncritical quadrature squeezing by spontaneous polarization symmetry breaking. We first consider Type II frequency-degenerate optical parametric oscillators but discard them for a number of reasons. Then we propose a four-wave-mixing cavity, in which the polarization of the output mode is always linear but has an arbitrary orientation. We show that in such a cavity, complete noise suppression in a quadrature of the output field occurs, irrespective of the parameter values.

© 2010 Optical Society of America

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  1. C. Navarrete-Benlloch, E. Roldán, and G. J. de Valcárcel, Phys. Rev. Lett. 100, 203601 (2008).
    [CrossRef] [PubMed]
  2. C. Navarrete-Benlloch, A. Romanelli, E. Roldán, and G. J. de Valcárcel, Phys. Rev. A 81, 043829 (2010).
    [CrossRef]
  3. F. V. Garcia-Ferrer, C. Navarrete-Benlloch, G. J. de Valcárcel, and E. Roldán, IEEE J. Quantum Electron. 45, 1404 (2009).
    [CrossRef]
  4. I. Pérez-Arjona, E. Roldán, and G. J. de Valcárcel, Europhys. Lett. 74, 247 (2006).
    [CrossRef]
  5. I. Pérez-Arjona, E. Roldán, and G. J. de Valcárcel, Phys. Rev. A 75, 063802 (2007).
    [CrossRef]
  6. The FPP might be, e.g., the eccentricity or the orientation of the polarization ellipse. We are reminded that continuous variations of these parameters correspond to rotations on the Poincaré sphere, defined by the Stokes parameters .
  7. R. D. Guenther, Modern Optics (Wiley, 1990).
  8. R. W. Boyd, Nonlinear Optics (Academic, 2003).
  9. S. Reynaud, C. Fabre, and E. Giacobino, J. Opt. Soc. Am. B 4, 1520 (1987).
    [CrossRef]
  10. A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, Phys. Rev. Lett. 59, 2555 (1987).
    [CrossRef] [PubMed]
  11. S. Feng and O. Pfister, J. Opt. B 5, 262 (2003).
    [CrossRef]
  12. L. Longchambon, J. Laurat, T. Coudreau, and C. Fabre, Eur. Phys. J. D 30, 287 (2004).
    [CrossRef]
  13. J. Laurat, L. Longchambon, C. Fabre, and T. Coudreau, Opt. Lett. 30, 1177 (2005).
    [CrossRef] [PubMed]
  14. M. Vallet, M. Pinard, and G. Grynberg, Europhys. Lett. 11, 739 (1990).
    [CrossRef]
  15. The explicit form of the χ(3) nonlinear susceptibility tensor, taking into account these considerations, is χijkl(ωa+ωb−ωc;ωa,ωb,−ωc)=χxxyy(δijδkl+δikδjl)+χxyyxδilδjk, irrespective of the frequencies involved in the particular process .
  16. In fact, in the Type II OPO experiment commented on above , 4.5dB of noise reduction was found in the dark mode, even though the polarization symmetry was broken, as explained in the text.
  17. N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, Phys. Rev. A 65, 052306 (2002).
    [CrossRef]
  18. F. V. Garcia-Ferrer, I. Pérez-Arjona, G. J. de Valcárcel, and E. Roldán, Phys. Rev. A 75, 063823 (2007).
    [CrossRef]

2010

C. Navarrete-Benlloch, A. Romanelli, E. Roldán, and G. J. de Valcárcel, Phys. Rev. A 81, 043829 (2010).
[CrossRef]

2009

F. V. Garcia-Ferrer, C. Navarrete-Benlloch, G. J. de Valcárcel, and E. Roldán, IEEE J. Quantum Electron. 45, 1404 (2009).
[CrossRef]

2008

C. Navarrete-Benlloch, E. Roldán, and G. J. de Valcárcel, Phys. Rev. Lett. 100, 203601 (2008).
[CrossRef] [PubMed]

2007

I. Pérez-Arjona, E. Roldán, and G. J. de Valcárcel, Phys. Rev. A 75, 063802 (2007).
[CrossRef]

F. V. Garcia-Ferrer, I. Pérez-Arjona, G. J. de Valcárcel, and E. Roldán, Phys. Rev. A 75, 063823 (2007).
[CrossRef]

2006

I. Pérez-Arjona, E. Roldán, and G. J. de Valcárcel, Europhys. Lett. 74, 247 (2006).
[CrossRef]

2005

2004

L. Longchambon, J. Laurat, T. Coudreau, and C. Fabre, Eur. Phys. J. D 30, 287 (2004).
[CrossRef]

2003

S. Feng and O. Pfister, J. Opt. B 5, 262 (2003).
[CrossRef]

R. W. Boyd, Nonlinear Optics (Academic, 2003).

2002

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, Phys. Rev. A 65, 052306 (2002).
[CrossRef]

1990

M. Vallet, M. Pinard, and G. Grynberg, Europhys. Lett. 11, 739 (1990).
[CrossRef]

R. D. Guenther, Modern Optics (Wiley, 1990).

1987

S. Reynaud, C. Fabre, and E. Giacobino, J. Opt. Soc. Am. B 4, 1520 (1987).
[CrossRef]

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef] [PubMed]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 2003).

Camy, G.

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef] [PubMed]

Coudreau, T.

J. Laurat, L. Longchambon, C. Fabre, and T. Coudreau, Opt. Lett. 30, 1177 (2005).
[CrossRef] [PubMed]

L. Longchambon, J. Laurat, T. Coudreau, and C. Fabre, Eur. Phys. J. D 30, 287 (2004).
[CrossRef]

de Valcárcel, G. J.

C. Navarrete-Benlloch, A. Romanelli, E. Roldán, and G. J. de Valcárcel, Phys. Rev. A 81, 043829 (2010).
[CrossRef]

F. V. Garcia-Ferrer, C. Navarrete-Benlloch, G. J. de Valcárcel, and E. Roldán, IEEE J. Quantum Electron. 45, 1404 (2009).
[CrossRef]

C. Navarrete-Benlloch, E. Roldán, and G. J. de Valcárcel, Phys. Rev. Lett. 100, 203601 (2008).
[CrossRef] [PubMed]

I. Pérez-Arjona, E. Roldán, and G. J. de Valcárcel, Phys. Rev. A 75, 063802 (2007).
[CrossRef]

F. V. Garcia-Ferrer, I. Pérez-Arjona, G. J. de Valcárcel, and E. Roldán, Phys. Rev. A 75, 063823 (2007).
[CrossRef]

I. Pérez-Arjona, E. Roldán, and G. J. de Valcárcel, Europhys. Lett. 74, 247 (2006).
[CrossRef]

Fabre, C.

J. Laurat, L. Longchambon, C. Fabre, and T. Coudreau, Opt. Lett. 30, 1177 (2005).
[CrossRef] [PubMed]

L. Longchambon, J. Laurat, T. Coudreau, and C. Fabre, Eur. Phys. J. D 30, 287 (2004).
[CrossRef]

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef] [PubMed]

S. Reynaud, C. Fabre, and E. Giacobino, J. Opt. Soc. Am. B 4, 1520 (1987).
[CrossRef]

Feng, S.

S. Feng and O. Pfister, J. Opt. B 5, 262 (2003).
[CrossRef]

Garcia-Ferrer, F. V.

F. V. Garcia-Ferrer, C. Navarrete-Benlloch, G. J. de Valcárcel, and E. Roldán, IEEE J. Quantum Electron. 45, 1404 (2009).
[CrossRef]

F. V. Garcia-Ferrer, I. Pérez-Arjona, G. J. de Valcárcel, and E. Roldán, Phys. Rev. A 75, 063823 (2007).
[CrossRef]

Giacobino, E.

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef] [PubMed]

S. Reynaud, C. Fabre, and E. Giacobino, J. Opt. Soc. Am. B 4, 1520 (1987).
[CrossRef]

Grynberg, G.

M. Vallet, M. Pinard, and G. Grynberg, Europhys. Lett. 11, 739 (1990).
[CrossRef]

Guenther, R. D.

R. D. Guenther, Modern Optics (Wiley, 1990).

Heidmann, A.

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef] [PubMed]

Horowicz, R. J.

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef] [PubMed]

Korolkova, N.

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, Phys. Rev. A 65, 052306 (2002).
[CrossRef]

Laurat, J.

J. Laurat, L. Longchambon, C. Fabre, and T. Coudreau, Opt. Lett. 30, 1177 (2005).
[CrossRef] [PubMed]

L. Longchambon, J. Laurat, T. Coudreau, and C. Fabre, Eur. Phys. J. D 30, 287 (2004).
[CrossRef]

Leuchs, G.

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, Phys. Rev. A 65, 052306 (2002).
[CrossRef]

Longchambon, L.

J. Laurat, L. Longchambon, C. Fabre, and T. Coudreau, Opt. Lett. 30, 1177 (2005).
[CrossRef] [PubMed]

L. Longchambon, J. Laurat, T. Coudreau, and C. Fabre, Eur. Phys. J. D 30, 287 (2004).
[CrossRef]

Loudon, R.

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, Phys. Rev. A 65, 052306 (2002).
[CrossRef]

Navarrete-Benlloch, C.

C. Navarrete-Benlloch, A. Romanelli, E. Roldán, and G. J. de Valcárcel, Phys. Rev. A 81, 043829 (2010).
[CrossRef]

F. V. Garcia-Ferrer, C. Navarrete-Benlloch, G. J. de Valcárcel, and E. Roldán, IEEE J. Quantum Electron. 45, 1404 (2009).
[CrossRef]

C. Navarrete-Benlloch, E. Roldán, and G. J. de Valcárcel, Phys. Rev. Lett. 100, 203601 (2008).
[CrossRef] [PubMed]

Pérez-Arjona, I.

I. Pérez-Arjona, E. Roldán, and G. J. de Valcárcel, Phys. Rev. A 75, 063802 (2007).
[CrossRef]

F. V. Garcia-Ferrer, I. Pérez-Arjona, G. J. de Valcárcel, and E. Roldán, Phys. Rev. A 75, 063823 (2007).
[CrossRef]

I. Pérez-Arjona, E. Roldán, and G. J. de Valcárcel, Europhys. Lett. 74, 247 (2006).
[CrossRef]

Pfister, O.

S. Feng and O. Pfister, J. Opt. B 5, 262 (2003).
[CrossRef]

Pinard, M.

M. Vallet, M. Pinard, and G. Grynberg, Europhys. Lett. 11, 739 (1990).
[CrossRef]

Ralph, T. C.

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, Phys. Rev. A 65, 052306 (2002).
[CrossRef]

Reynaud, S.

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef] [PubMed]

S. Reynaud, C. Fabre, and E. Giacobino, J. Opt. Soc. Am. B 4, 1520 (1987).
[CrossRef]

Roldán, E.

C. Navarrete-Benlloch, A. Romanelli, E. Roldán, and G. J. de Valcárcel, Phys. Rev. A 81, 043829 (2010).
[CrossRef]

F. V. Garcia-Ferrer, C. Navarrete-Benlloch, G. J. de Valcárcel, and E. Roldán, IEEE J. Quantum Electron. 45, 1404 (2009).
[CrossRef]

C. Navarrete-Benlloch, E. Roldán, and G. J. de Valcárcel, Phys. Rev. Lett. 100, 203601 (2008).
[CrossRef] [PubMed]

I. Pérez-Arjona, E. Roldán, and G. J. de Valcárcel, Phys. Rev. A 75, 063802 (2007).
[CrossRef]

F. V. Garcia-Ferrer, I. Pérez-Arjona, G. J. de Valcárcel, and E. Roldán, Phys. Rev. A 75, 063823 (2007).
[CrossRef]

I. Pérez-Arjona, E. Roldán, and G. J. de Valcárcel, Europhys. Lett. 74, 247 (2006).
[CrossRef]

Romanelli, A.

C. Navarrete-Benlloch, A. Romanelli, E. Roldán, and G. J. de Valcárcel, Phys. Rev. A 81, 043829 (2010).
[CrossRef]

Silberhorn, C.

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, Phys. Rev. A 65, 052306 (2002).
[CrossRef]

Vallet, M.

M. Vallet, M. Pinard, and G. Grynberg, Europhys. Lett. 11, 739 (1990).
[CrossRef]

Eur. Phys. J. D

L. Longchambon, J. Laurat, T. Coudreau, and C. Fabre, Eur. Phys. J. D 30, 287 (2004).
[CrossRef]

Europhys. Lett.

M. Vallet, M. Pinard, and G. Grynberg, Europhys. Lett. 11, 739 (1990).
[CrossRef]

I. Pérez-Arjona, E. Roldán, and G. J. de Valcárcel, Europhys. Lett. 74, 247 (2006).
[CrossRef]

IEEE J. Quantum Electron.

F. V. Garcia-Ferrer, C. Navarrete-Benlloch, G. J. de Valcárcel, and E. Roldán, IEEE J. Quantum Electron. 45, 1404 (2009).
[CrossRef]

J. Opt. B

S. Feng and O. Pfister, J. Opt. B 5, 262 (2003).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. A

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, Phys. Rev. A 65, 052306 (2002).
[CrossRef]

F. V. Garcia-Ferrer, I. Pérez-Arjona, G. J. de Valcárcel, and E. Roldán, Phys. Rev. A 75, 063823 (2007).
[CrossRef]

C. Navarrete-Benlloch, A. Romanelli, E. Roldán, and G. J. de Valcárcel, Phys. Rev. A 81, 043829 (2010).
[CrossRef]

I. Pérez-Arjona, E. Roldán, and G. J. de Valcárcel, Phys. Rev. A 75, 063802 (2007).
[CrossRef]

Phys. Rev. Lett.

C. Navarrete-Benlloch, E. Roldán, and G. J. de Valcárcel, Phys. Rev. Lett. 100, 203601 (2008).
[CrossRef] [PubMed]

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef] [PubMed]

Other

The FPP might be, e.g., the eccentricity or the orientation of the polarization ellipse. We are reminded that continuous variations of these parameters correspond to rotations on the Poincaré sphere, defined by the Stokes parameters .

R. D. Guenther, Modern Optics (Wiley, 1990).

R. W. Boyd, Nonlinear Optics (Academic, 2003).

The explicit form of the χ(3) nonlinear susceptibility tensor, taking into account these considerations, is χijkl(ωa+ωb−ωc;ωa,ωb,−ωc)=χxxyy(δijδkl+δikδjl)+χxyyxδilδjk, irrespective of the frequencies involved in the particular process .

In fact, in the Type II OPO experiment commented on above , 4.5dB of noise reduction was found in the dark mode, even though the polarization symmetry was broken, as explained in the text.

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Equations (12)

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H ^ OPO = i ( E p b ^ + χ b ^ a ^ x a ^ y ) + H.c. ,
E p = i F G ( r ) j = 1 , 2 ( e x α j x + e y α j y ) e i ω j t + c.c ,
E ^ s = i F G ( r ) [ e x a ^ x ( t ) + e y a ^ y ( t ) ] e i ω s t + H.c. ,
H ^ 0 = δ ( a ^ x a ^ x + a ^ y a ^ y ) ,
H ^ int = 3 4 g ( H ^ spm + H ^ cpm + H ^ fwm ) ,
H ^ spm = a ^ x 2 a ^ x 2 + a ^ y 2 a ^ y 2 ,
H ^ cpm = j = 1 , 2 4 ( | α j x | 2 + A | α j y | 2 ) a ^ x a ^ x + j = 1 , 2 4 ( | α j y | 2 + A | α j x | 2 ) a ^ y a ^ y + 4 A a ^ x a ^ x a ^ y a ^ y ,
H ^ fwm = B a ^ x 2 a ^ y 2 + 2 ( α 1 x α 2 x + B α 1 y α 2 y ) a ^ x 2 + 2 ( α 1 y α 2 y + B α 1 x α 2 x ) a ^ y 2 + j = 1 , 2 4 ( B α j x * α j y + A α j x α j y * ) a ^ x a ^ y + 4 A ( α 1 x α 2 y + α 1 y α 2 x ) a ^ x a ^ y + H.c. ,
H ^ 0 = δ ( a ^ + a ^ + + a ^ a ^ ) ,
H ^ spm = ( 1 B ) ( a ^ + 2 a ^ + 2 + a ^ 2 a ^ 2 ) ,
H ^ cpm = 2 ( 1 + B ) a ^ + a ^ + a ^ a ^ + 2 ρ 2 ( 3 B ) ( a ^ + a ^ + + a ^ a ^ ) ,
H ^ fwm = 2 ρ 2 ( 1 + B ) ( a ^ + a ^ + a ^ + a ^ ) .

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