Abstract

We investigate, theoretically, the generation of bright and vacuum-squeezed light as well as entanglement in intracavity, type II, phase-matched second-harmonic generation. The cavity in which the crystal is embedded is resonant at the fundamental frequency but not at the second-harmonic frequency. A simple model for the process using semiclassical theory is derived, and quadrature-squeezing spectra of the involved fundamental fields are deduced. The analysis shows that vacuum squeezing reminiscent of subthreshold optical parametric oscillator squeezing is present and, in the ideal case, perfect. Under slight modifications of the operational conditions, the system is shown to produce efficient bright, squeezed light. Furthermore, we investigate the degree of polarization squeezing and find that three Stokes parameters can be squeezed simultaneously. Finally, we gauge the process for possible entanglement.

© 2003 Optical Society of America

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    [CrossRef]
  2. P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, “Optimization and transfer of vacuum squeezing from an optical parametric oscillator,” J. Opt. B: Quantum Semiclassical Opt. 1, 469–474 (1999).
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    [CrossRef]
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    [CrossRef]
  7. R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H.-A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett. 72, 3807–3810 (1994).
    [CrossRef] [PubMed]
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  31. P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
    [CrossRef]
  32. 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]
  33. M. D. Reid and P. D. Drummond, “Quantum correlations of phase in nondegenerate parametric oscillation,” Phys. Rev. Lett. 60, 2731–2733 (1988).
    [CrossRef] [PubMed]
  34. M. D. Reid, “Demonstration of the Einstein–Podolsky–Rosen paradox using nondegenerate parametric amplification,” Phys. Rev. A 40, 913–923 (1989).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  37. W. P. Bowen, P. K. Lam, and T. C. Ralph, “Biased EPR entanglement and its application to teleportation,” J. Mod. Opt. 50, 801–813 (2003).
    [CrossRef]
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    [CrossRef] [PubMed]
  39. L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
    [CrossRef] [PubMed]
  40. R. Simon, “Peres–Horodecki separability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2726–2729 (2000).
    [CrossRef] [PubMed]
  41. S. M. Tan, “Confirming entanglement in continuous variable quantum teleportation,” Phys. Rev. A 60, 2752–2758 (1999).
    [CrossRef]
  42. T. Ralph and P. K. Lam, “Teleportation with bright squeezed light,” Phys. Rev. Lett. 81, 5668–5671 (1998).
    [CrossRef]
  43. S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
    [CrossRef]
  44. F. Grosshans and P. Grangier, “Quantum cloning and teleportation criteria for continuous quantum variables,” Phys. Rev. A 64, 0103011–0103014(R) (2001).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  47. R. Paschotta, K. Fiedler, P. Kürz, R. Henking, S. Schiller, and J. Mlynek, “82% efficient continuous-wave frequency doubling of 1.06μm with a monolithic MgO:LiNbO3 resonator,” Opt. Lett. 19, 1325–1327 (1994).
    [CrossRef] [PubMed]

2003 (1)

W. P. Bowen, P. K. Lam, and T. C. Ralph, “Biased EPR entanglement and its application to teleportation,” J. Mod. Opt. 50, 801–813 (2003).
[CrossRef]

2002 (3)

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright Einstein–Podolsky–Rosen beam,” Phys. Rev. Lett. 88, 0479041–0479044 (2002).
[CrossRef]

W. P. Bowen, R. Schnabel, H.-A. Bachor, and P. K. Lam, “Polarization squeezing of continuous variable Stokes parameters,” Phys. Rev. Lett. 88, 093601/1–4 (2002).
[CrossRef]

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, “Polarization squeezing and continuous polarization entanglement,” Phys. Rev. A 65, 052306/1–12 (2002).
[CrossRef]

2001 (1)

F. Grosshans and P. Grangier, “Quantum cloning and teleportation criteria for continuous quantum variables,” Phys. Rev. A 64, 0103011–0103014(R) (2001).
[CrossRef]

2000 (4)

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef] [PubMed]

R. Simon, “Peres–Horodecki separability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2726–2729 (2000).
[CrossRef] [PubMed]

C. H. Bennett and D. P. DiVincenzo, “Quantum information and computation,” Nature 404, 247–255 (2000).
[CrossRef] [PubMed]

A. Kuzmich and E. S. Polzik, “Atomic quantum state teleportation and swapping,” Phys. Rev. Lett. 85, 5639–5642 (2000).
[CrossRef]

1999 (5)

J. Hald, J. L. Sørensen, C. Schori, and E. S. Polzik, “Spin squeezed atoms: a macroscopic entangled ensemble created by light,” Phys. Rev. Lett. 83, 1319–1322 (1999).
[CrossRef]

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[CrossRef]

P. Van Loock and S. L. Braunstein, “Unconditional teleportation of continuous-variable entanglement,” Phys. Rev. A 61, 010302/1–4 (1999).
[CrossRef]

S. M. Tan, “Confirming entanglement in continuous variable quantum teleportation,” Phys. Rev. A 60, 2752–2758 (1999).
[CrossRef]

P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, “Optimization and transfer of vacuum squeezing from an optical parametric oscillator,” J. Opt. B: Quantum Semiclassical Opt. 1, 469–474 (1999).
[CrossRef]

1998 (3)

T. Ralph and P. K. Lam, “Teleportation with bright squeezed light,” Phys. Rev. Lett. 81, 5668–5671 (1998).
[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]

1997 (2)

1996 (2)

M. W. Jack, M. J. Collett, and D. F. Walls, “Asymmetrically pumped nondegenerate second-harmonic generation inside a cavity,” Phys. Rev. A 53, 1801–1811 (1996).
[CrossRef] [PubMed]

A. Peres, “Separability criterion for density matrices,” Phys. Rev. Lett. 77, 1413–1415 (1996).
[CrossRef] [PubMed]

1995 (5)

D. P. Di Vincenzo, “Quantum computation,” Science 270, 255–261 (1995).
[CrossRef]

J. I. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett. 74, 4091–4094 (1995).
[CrossRef] [PubMed]

M. Marte, “Sub-Poissonian twin beams via competing nonlinearities,” Phys. Rev. Lett. 74, 4815–4818 (1995).
[CrossRef] [PubMed]

H. Tsuchida, “Generation of amplitude-squeezed light at 432 nm from a singly resonant frequency doubler,” Opt. Lett. 20, 2240–2242 (1995).
[CrossRef]

L. Shiv, J. L. Sørensen, E. S. Polzik, and G. Mizell, Opt. Lett. 20, 2270–2272 (1995).
[CrossRef]

1994 (4)

R. Paschotta, K. Fiedler, P. Kürz, R. Henking, S. Schiller, and J. Mlynek, “82% efficient continuous-wave frequency doubling of 1.06μm with a monolithic MgO:LiNbO3 resonator,” Opt. Lett. 19, 1325–1327 (1994).
[CrossRef] [PubMed]

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H.-A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett. 72, 3807–3810 (1994).
[CrossRef] [PubMed]

Z. Y. Ou, “Quantum-nondemolition measurement and squeezing in type-II harmonic generation with triple resonance,” Phys. Rev. A 49, 4902–4911 (1994).
[CrossRef] [PubMed]

A. Eschmann and M. D. Reid, “Squeezing of intensity fluctuations in frequency summation,” Phys. Rev. A 49, 2881–2890 (1994).
[CrossRef] [PubMed]

1993 (2)

P. Kürz, P. Paschotta, K. Fiedler, and J. Mlynek, “Bright squeezed light by second-harmonic generation in a monolithic resonator,” Europhys. Lett. 24, 449–454 (1993).
[CrossRef]

A. S. Chirkin, A. A. Orlov, and D. Yu. Paraschuk, “Quantum theory of two-mode interactions in optically anisotropic media with cubic nonlinearities: generation of quadrature- and polarization-squeezed light,” Kvant. Elektron. 20, 999–1004 (1993).

1992 (2)

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]

Z. Y. Ou, S. F. Pereira, E. S. Polzik, and H. J. Kimble, “85% efficiency for cw frequency doubling from 1.08 to 0.54 μm,” Opt. Lett. 17, 640–642 (1992).
[CrossRef] [PubMed]

1991 (1)

M. J. Collett and R. B. Levien, “Two-photon-loss model ofintracavity second-harmonic generation,” Phys. Rev. A 43, 5068–5072 (1991).
[CrossRef] [PubMed]

1990 (1)

A. Sizmann, R. J. Horowicz, G. Wagner, and G. Leuchs, “Observation of amplitude squeezing of the up-converted mode in second harmonic generation,” Opt. Commun. 80, 138–142 (1990).
[CrossRef]

1989 (2)

G. S. Agarwal and R. R. Puri, “Quantum theory of propagation of elliptically polarized light through a Kerr medium,” Phys. Rev. A 40, 5179–5186 (1989).
[CrossRef] [PubMed]

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

1988 (2)

M. D. Reid and P. D. Drummond, “Quantum correlations of phase in nondegenerate parametric oscillation,” Phys. Rev. Lett. 60, 2731–2733 (1988).
[CrossRef] [PubMed]

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A 38, 4931–4934 (1988).
[CrossRef] [PubMed]

1987 (2)

P. Grangier, R. E. Slusher, B. Yurke, and LaPorta, “Squeezed light-enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).
[CrossRef] [PubMed]

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

1985 (2)

M. J. Collett and D. F. Walls, “Squeezing spectra for nonlinear optical systems,” Phys. Rev. A 32, 2887–2892 (1985).
[CrossRef] [PubMed]

C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
[CrossRef] [PubMed]

1984 (1)

B. Yurke, “Use of cavities in squeezed-state generation,” Phys. Rev. A 29, 408–410 (1984).
[CrossRef]

1983 (1)

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]

Agarwal, G. S.

G. S. Agarwal and R. R. Puri, “Quantum theory of propagation of elliptically polarized light through a Kerr medium,” Phys. Rev. A 40, 5179–5186 (1989).
[CrossRef] [PubMed]

Anderson, M. E.

Appelbaum, I.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[CrossRef]

Bachor, H.-A.

W. P. Bowen, R. Schnabel, H.-A. Bachor, and P. K. Lam, “Polarization squeezing of continuous variable Stokes parameters,” Phys. Rev. Lett. 88, 093601/1–4 (2002).
[CrossRef]

P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, “Optimization and transfer of vacuum squeezing from an optical parametric oscillator,” J. Opt. B: Quantum Semiclassical Opt. 1, 469–474 (1999).
[CrossRef]

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H.-A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett. 72, 3807–3810 (1994).
[CrossRef] [PubMed]

Bennett, C. H.

C. H. Bennett and D. P. DiVincenzo, “Quantum information and computation,” Nature 404, 247–255 (2000).
[CrossRef] [PubMed]

Bowen, W. P.

W. P. Bowen, P. K. Lam, and T. C. Ralph, “Biased EPR entanglement and its application to teleportation,” J. Mod. Opt. 50, 801–813 (2003).
[CrossRef]

W. P. Bowen, R. Schnabel, H.-A. Bachor, and P. K. Lam, “Polarization squeezing of continuous variable Stokes parameters,” Phys. Rev. Lett. 88, 093601/1–4 (2002).
[CrossRef]

Braunstein, S. L.

P. Van Loock and S. L. Braunstein, “Unconditional teleportation of continuous-variable entanglement,” Phys. Rev. A 61, 010302/1–4 (1999).
[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]

Buchler, B. C.

P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, “Optimization and transfer of vacuum squeezing from an optical parametric oscillator,” J. Opt. B: Quantum Semiclassical Opt. 1, 469–474 (1999).
[CrossRef]

Chirkin, A. S.

A. S. Chirkin, A. A. Orlov, and D. Yu. Paraschuk, “Quantum theory of two-mode interactions in optically anisotropic media with cubic nonlinearities: generation of quadrature- and polarization-squeezed light,” Kvant. Elektron. 20, 999–1004 (1993).

Cirac, J. I.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef] [PubMed]

J. I. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett. 74, 4091–4094 (1995).
[CrossRef] [PubMed]

Collett, M.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H.-A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett. 72, 3807–3810 (1994).
[CrossRef] [PubMed]

Collett, M. J.

M. W. Jack, M. J. Collett, and D. F. Walls, “Asymmetrically pumped nondegenerate second-harmonic generation inside a cavity,” Phys. Rev. A 53, 1801–1811 (1996).
[CrossRef] [PubMed]

M. J. Collett and R. B. Levien, “Two-photon-loss model ofintracavity second-harmonic generation,” Phys. Rev. A 43, 5068–5072 (1991).
[CrossRef] [PubMed]

M. J. Collett and D. F. Walls, “Squeezing spectra for nonlinear optical systems,” Phys. Rev. A 32, 2887–2892 (1985).
[CrossRef] [PubMed]

C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
[CrossRef] [PubMed]

De Martini, F.

Di Vincenzo, D. P.

D. P. Di Vincenzo, “Quantum computation,” Science 270, 255–261 (1995).
[CrossRef]

DiVincenzo, D. P.

C. H. Bennett and D. P. DiVincenzo, “Quantum information and computation,” Nature 404, 247–255 (2000).
[CrossRef] [PubMed]

Drummond, P. D.

M. D. Reid and P. D. Drummond, “Quantum correlations of phase in nondegenerate parametric oscillation,” Phys. Rev. Lett. 60, 2731–2733 (1988).
[CrossRef] [PubMed]

Duan, L.-M.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef] [PubMed]

Eberhard, P. H.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[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]

Eschmann, A.

A. Eschmann and M. D. Reid, “Squeezing of intensity fluctuations in frequency summation,” Phys. Rev. A 49, 2881–2890 (1994).
[CrossRef] [PubMed]

Fiedler, K.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H.-A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett. 72, 3807–3810 (1994).
[CrossRef] [PubMed]

R. Paschotta, K. Fiedler, P. Kürz, R. Henking, S. Schiller, and J. Mlynek, “82% efficient continuous-wave frequency doubling of 1.06μm with a monolithic MgO:LiNbO3 resonator,” Opt. Lett. 19, 1325–1327 (1994).
[CrossRef] [PubMed]

P. Kürz, P. Paschotta, K. Fiedler, and J. Mlynek, “Bright squeezed light by second-harmonic generation in a monolithic resonator,” Europhys. Lett. 24, 449–454 (1993).
[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]

Gao, J.

P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, “Optimization and transfer of vacuum squeezing from an optical parametric oscillator,” J. Opt. B: Quantum Semiclassical Opt. 1, 469–474 (1999).
[CrossRef]

Gardiner, C. W.

C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
[CrossRef] [PubMed]

Giedke, G.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef] [PubMed]

Grangier, P.

F. Grosshans and P. Grangier, “Quantum cloning and teleportation criteria for continuous quantum variables,” Phys. Rev. A 64, 0103011–0103014(R) (2001).
[CrossRef]

P. Grangier, R. E. Slusher, B. Yurke, and LaPorta, “Squeezed light-enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).
[CrossRef] [PubMed]

Grosshans, F.

F. Grosshans and P. Grangier, “Quantum cloning and teleportation criteria for continuous quantum variables,” Phys. Rev. A 64, 0103011–0103014(R) (2001).
[CrossRef]

Gupta, M. C.

Hald, J.

J. Hald, J. L. Sørensen, C. Schori, and E. S. Polzik, “Spin squeezed atoms: a macroscopic entangled ensemble created by light,” Phys. Rev. Lett. 83, 1319–1322 (1999).
[CrossRef]

Hall, J. L.

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A 38, 4931–4934 (1988).
[CrossRef] [PubMed]

Henking, R.

Horowicz, R. J.

A. Sizmann, R. J. Horowicz, G. Wagner, and G. Leuchs, “Observation of amplitude squeezing of the up-converted mode in second harmonic generation,” Opt. Commun. 80, 138–142 (1990).
[CrossRef]

Jack, M. W.

M. W. Jack, M. J. Collett, and D. F. Walls, “Asymmetrically pumped nondegenerate second-harmonic generation inside a cavity,” Phys. Rev. A 53, 1801–1811 (1996).
[CrossRef] [PubMed]

Jing, J.

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright Einstein–Podolsky–Rosen beam,” Phys. Rev. Lett. 88, 0479041–0479044 (2002).
[CrossRef]

Kimble, H. J.

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]

Z. Y. Ou, S. F. Pereira, E. S. Polzik, and H. J. Kimble, “85% efficiency for cw frequency doubling from 1.08 to 0.54 μm,” Opt. Lett. 17, 640–642 (1992).
[CrossRef] [PubMed]

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A 38, 4931–4934 (1988).
[CrossRef] [PubMed]

Knight, P. L.

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

Korolkova, N.

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, “Polarization squeezing and continuous polarization entanglement,” Phys. Rev. A 65, 052306/1–12 (2002).
[CrossRef]

Kürz, P.

R. Paschotta, K. Fiedler, P. Kürz, R. Henking, S. Schiller, and J. Mlynek, “82% efficient continuous-wave frequency doubling of 1.06μm with a monolithic MgO:LiNbO3 resonator,” Opt. Lett. 19, 1325–1327 (1994).
[CrossRef] [PubMed]

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H.-A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett. 72, 3807–3810 (1994).
[CrossRef] [PubMed]

P. Kürz, P. Paschotta, K. Fiedler, and J. Mlynek, “Bright squeezed light by second-harmonic generation in a monolithic resonator,” Europhys. Lett. 24, 449–454 (1993).
[CrossRef]

Kuzmich, A.

A. Kuzmich and E. S. Polzik, “Atomic quantum state teleportation and swapping,” Phys. Rev. Lett. 85, 5639–5642 (2000).
[CrossRef]

Kwiat, P. G.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[CrossRef]

Lam, P. K.

W. P. Bowen, P. K. Lam, and T. C. Ralph, “Biased EPR entanglement and its application to teleportation,” J. Mod. Opt. 50, 801–813 (2003).
[CrossRef]

W. P. Bowen, R. Schnabel, H.-A. Bachor, and P. K. Lam, “Polarization squeezing of continuous variable Stokes parameters,” Phys. Rev. Lett. 88, 093601/1–4 (2002).
[CrossRef]

P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, “Optimization and transfer of vacuum squeezing from an optical parametric oscillator,” J. Opt. B: Quantum Semiclassical Opt. 1, 469–474 (1999).
[CrossRef]

T. Ralph and P. K. Lam, “Teleportation with bright squeezed light,” Phys. Rev. Lett. 81, 5668–5671 (1998).
[CrossRef]

LaPorta,

P. Grangier, R. E. Slusher, B. Yurke, and LaPorta, “Squeezed light-enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).
[CrossRef] [PubMed]

Leuchs, G.

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, “Polarization squeezing and continuous polarization entanglement,” Phys. Rev. A 65, 052306/1–12 (2002).
[CrossRef]

A. Sizmann, R. J. Horowicz, G. Wagner, and G. Leuchs, “Observation of amplitude squeezing of the up-converted mode in second harmonic generation,” Opt. Commun. 80, 138–142 (1990).
[CrossRef]

Levien, R. B.

M. J. Collett and R. B. Levien, “Two-photon-loss model ofintracavity second-harmonic generation,” Phys. Rev. A 43, 5068–5072 (1991).
[CrossRef] [PubMed]

Li, X.

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright Einstein–Podolsky–Rosen beam,” Phys. Rev. Lett. 88, 0479041–0479044 (2002).
[CrossRef]

Loudon, R.

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, “Polarization squeezing and continuous polarization entanglement,” Phys. Rev. A 65, 052306/1–12 (2002).
[CrossRef]

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

Lugiato, L. A.

Marte, M.

M. Marte, “Sub-Poissonian twin beams via competing nonlinearities,” Phys. Rev. Lett. 74, 4815–4818 (1995).
[CrossRef] [PubMed]

McAlister, D. F.

McClelland, D. E.

P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, “Optimization and transfer of vacuum squeezing from an optical parametric oscillator,” J. Opt. B: Quantum Semiclassical Opt. 1, 469–474 (1999).
[CrossRef]

Mizell, G.

Mlynek, J.

R. Paschotta, K. Fiedler, P. Kürz, R. Henking, S. Schiller, and J. Mlynek, “82% efficient continuous-wave frequency doubling of 1.06μm with a monolithic MgO:LiNbO3 resonator,” Opt. Lett. 19, 1325–1327 (1994).
[CrossRef] [PubMed]

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H.-A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett. 72, 3807–3810 (1994).
[CrossRef] [PubMed]

P. Kürz, P. Paschotta, K. Fiedler, and J. Mlynek, “Bright squeezed light by second-harmonic generation in a monolithic resonator,” Europhys. Lett. 24, 449–454 (1993).
[CrossRef]

Orlov, A. A.

A. S. Chirkin, A. A. Orlov, and D. Yu. Paraschuk, “Quantum theory of two-mode interactions in optically anisotropic media with cubic nonlinearities: generation of quadrature- and polarization-squeezed light,” Kvant. Elektron. 20, 999–1004 (1993).

Ou, Z. Y.

Z. Y. Ou, “Quantum-nondemolition measurement and squeezing in type-II harmonic generation with triple resonance,” Phys. Rev. A 49, 4902–4911 (1994).
[CrossRef] [PubMed]

Z. Y. Ou, S. F. Pereira, E. S. Polzik, and H. J. Kimble, “85% efficiency for cw frequency doubling from 1.08 to 0.54 μm,” Opt. Lett. 17, 640–642 (1992).
[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]

Pan, Q.

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright Einstein–Podolsky–Rosen beam,” Phys. Rev. Lett. 88, 0479041–0479044 (2002).
[CrossRef]

Paraschuk, D. Yu.

A. S. Chirkin, A. A. Orlov, and D. Yu. Paraschuk, “Quantum theory of two-mode interactions in optically anisotropic media with cubic nonlinearities: generation of quadrature- and polarization-squeezed light,” Kvant. Elektron. 20, 999–1004 (1993).

Paschotta, P.

P. Kürz, P. Paschotta, K. Fiedler, and J. Mlynek, “Bright squeezed light by second-harmonic generation in a monolithic resonator,” Europhys. Lett. 24, 449–454 (1993).
[CrossRef]

Paschotta, R.

R. Paschotta, K. Fiedler, P. Kürz, R. Henking, S. Schiller, and J. Mlynek, “82% efficient continuous-wave frequency doubling of 1.06μm with a monolithic MgO:LiNbO3 resonator,” Opt. Lett. 19, 1325–1327 (1994).
[CrossRef] [PubMed]

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H.-A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett. 72, 3807–3810 (1994).
[CrossRef] [PubMed]

Peng, K.

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright Einstein–Podolsky–Rosen beam,” Phys. Rev. Lett. 88, 0479041–0479044 (2002).
[CrossRef]

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.

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]

Z. Y. Ou, S. F. Pereira, E. S. Polzik, and H. J. Kimble, “85% efficiency for cw frequency doubling from 1.08 to 0.54 μm,” Opt. Lett. 17, 640–642 (1992).
[CrossRef] [PubMed]

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A 38, 4931–4934 (1988).
[CrossRef] [PubMed]

Peres, A.

A. Peres, “Separability criterion for density matrices,” Phys. Rev. Lett. 77, 1413–1415 (1996).
[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.

A. Kuzmich and E. S. Polzik, “Atomic quantum state teleportation and swapping,” Phys. Rev. Lett. 85, 5639–5642 (2000).
[CrossRef]

J. Hald, J. L. Sørensen, C. Schori, and E. S. Polzik, “Spin squeezed atoms: a macroscopic entangled ensemble created by light,” Phys. Rev. Lett. 83, 1319–1322 (1999).
[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]

L. Shiv, J. L. Sørensen, E. S. Polzik, and G. Mizell, Opt. Lett. 20, 2270–2272 (1995).
[CrossRef]

Z. Y. Ou, S. F. Pereira, E. S. Polzik, and H. J. Kimble, “85% efficiency for cw frequency doubling from 1.08 to 0.54 μm,” Opt. Lett. 17, 640–642 (1992).
[CrossRef] [PubMed]

Puri, R. R.

G. S. Agarwal and R. R. Puri, “Quantum theory of propagation of elliptically polarized light through a Kerr medium,” Phys. Rev. A 40, 5179–5186 (1989).
[CrossRef] [PubMed]

Ralph, T.

T. Ralph and P. K. Lam, “Teleportation with bright squeezed light,” Phys. Rev. Lett. 81, 5668–5671 (1998).
[CrossRef]

Ralph, T. C.

W. P. Bowen, P. K. Lam, and T. C. Ralph, “Biased EPR entanglement and its application to teleportation,” J. Mod. Opt. 50, 801–813 (2003).
[CrossRef]

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, “Polarization squeezing and continuous polarization entanglement,” Phys. Rev. A 65, 052306/1–12 (2002).
[CrossRef]

P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, “Optimization and transfer of vacuum squeezing from an optical parametric oscillator,” J. Opt. B: Quantum Semiclassical Opt. 1, 469–474 (1999).
[CrossRef]

Raymer, M. G.

Reid, M. D.

A. Eschmann and M. D. Reid, “Squeezing of intensity fluctuations in frequency summation,” Phys. Rev. A 49, 2881–2890 (1994).
[CrossRef] [PubMed]

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

M. D. Reid and P. D. Drummond, “Quantum correlations of phase in nondegenerate parametric oscillation,” Phys. Rev. Lett. 60, 2731–2733 (1988).
[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]

Schiller, S.

Schnabel, R.

W. P. Bowen, R. Schnabel, H.-A. Bachor, and P. K. Lam, “Polarization squeezing of continuous variable Stokes parameters,” Phys. Rev. Lett. 88, 093601/1–4 (2002).
[CrossRef]

Schneider, K.

Schori, C.

J. Hald, J. L. Sørensen, C. Schori, and E. S. Polzik, “Spin squeezed atoms: a macroscopic entangled ensemble created by light,” Phys. Rev. Lett. 83, 1319–1322 (1999).
[CrossRef]

Shiv, L.

Silberhorn, C.

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, “Polarization squeezing and continuous polarization entanglement,” Phys. Rev. A 65, 052306/1–12 (2002).
[CrossRef]

Simon, R.

R. Simon, “Peres–Horodecki separability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2726–2729 (2000).
[CrossRef] [PubMed]

Sizmann, A.

A. Sizmann, R. J. Horowicz, G. Wagner, and G. Leuchs, “Observation of amplitude squeezing of the up-converted mode in second harmonic generation,” Opt. Commun. 80, 138–142 (1990).
[CrossRef]

Slusher, R. E.

P. Grangier, R. E. Slusher, B. Yurke, and LaPorta, “Squeezed light-enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).
[CrossRef] [PubMed]

Sørensen, J. L.

J. Hald, J. L. Sørensen, C. Schori, and E. S. Polzik, “Spin squeezed atoms: a macroscopic entangled ensemble created by light,” Phys. Rev. Lett. 83, 1319–1322 (1999).
[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]

L. Shiv, J. L. Sørensen, E. S. Polzik, and G. Mizell, Opt. Lett. 20, 2270–2272 (1995).
[CrossRef]

Strini, G.

Tan, S. M.

S. M. Tan, “Confirming entanglement in continuous variable quantum teleportation,” Phys. Rev. A 60, 2752–2758 (1999).
[CrossRef]

Tsuchida, H.

Van Loock, P.

P. Van Loock and S. L. Braunstein, “Unconditional teleportation of continuous-variable entanglement,” Phys. Rev. A 61, 010302/1–4 (1999).
[CrossRef]

Wagner, G.

A. Sizmann, R. J. Horowicz, G. Wagner, and G. Leuchs, “Observation of amplitude squeezing of the up-converted mode in second harmonic generation,” Opt. Commun. 80, 138–142 (1990).
[CrossRef]

Waks, E.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[CrossRef]

Walls, D. F.

M. W. Jack, M. J. Collett, and D. F. Walls, “Asymmetrically pumped nondegenerate second-harmonic generation inside a cavity,” Phys. Rev. A 53, 1801–1811 (1996).
[CrossRef] [PubMed]

M. J. Collett and D. F. Walls, “Squeezing spectra for nonlinear optical systems,” Phys. Rev. A 32, 2887–2892 (1985).
[CrossRef] [PubMed]

White, A. G.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[CrossRef]

Xiao, M.

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A 38, 4931–4934 (1988).
[CrossRef] [PubMed]

Xie, C.

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright Einstein–Podolsky–Rosen beam,” Phys. Rev. Lett. 88, 0479041–0479044 (2002).
[CrossRef]

Yurke, B.

P. Grangier, R. E. Slusher, B. Yurke, and LaPorta, “Squeezed light-enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).
[CrossRef] [PubMed]

B. Yurke, “Use of cavities in squeezed-state generation,” Phys. Rev. A 29, 408–410 (1984).
[CrossRef]

Zhang, J.

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright Einstein–Podolsky–Rosen beam,” Phys. Rev. Lett. 88, 0479041–0479044 (2002).
[CrossRef]

Zoller, P.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef] [PubMed]

J. I. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett. 74, 4091–4094 (1995).
[CrossRef] [PubMed]

Europhys. Lett. (1)

P. Kürz, P. Paschotta, K. Fiedler, and J. Mlynek, “Bright squeezed light by second-harmonic generation in a monolithic resonator,” Europhys. Lett. 24, 449–454 (1993).
[CrossRef]

J. Mod. Opt. (2)

W. P. Bowen, P. K. Lam, and T. C. Ralph, “Biased EPR entanglement and its application to teleportation,” J. Mod. Opt. 50, 801–813 (2003).
[CrossRef]

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

J. Opt. B: Quantum Semiclassical Opt. (1)

P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H.-A. Bachor, and J. Gao, “Optimization and transfer of vacuum squeezing from an optical parametric oscillator,” J. Opt. B: Quantum Semiclassical Opt. 1, 469–474 (1999).
[CrossRef]

J. Opt. Soc. Am. B (1)

Kvant. Elektron. (1)

A. S. Chirkin, A. A. Orlov, and D. Yu. Paraschuk, “Quantum theory of two-mode interactions in optically anisotropic media with cubic nonlinearities: generation of quadrature- and polarization-squeezed light,” Kvant. Elektron. 20, 999–1004 (1993).

Nature (1)

C. H. Bennett and D. P. DiVincenzo, “Quantum information and computation,” Nature 404, 247–255 (2000).
[CrossRef] [PubMed]

Opt. Commun. (1)

A. Sizmann, R. J. Horowicz, G. Wagner, and G. Leuchs, “Observation of amplitude squeezing of the up-converted mode in second harmonic generation,” Opt. Commun. 80, 138–142 (1990).
[CrossRef]

Opt. Lett. (6)

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 (15)

P. Van Loock and S. L. Braunstein, “Unconditional teleportation of continuous-variable entanglement,” Phys. Rev. A 61, 010302/1–4 (1999).
[CrossRef]

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

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, “Polarization squeezing and continuous polarization entanglement,” Phys. Rev. A 65, 052306/1–12 (2002).
[CrossRef]

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[CrossRef]

M. J. Collett and D. F. Walls, “Squeezing spectra for nonlinear optical systems,” Phys. Rev. A 32, 2887–2892 (1985).
[CrossRef] [PubMed]

G. S. Agarwal and R. R. Puri, “Quantum theory of propagation of elliptically polarized light through a Kerr medium,” Phys. Rev. A 40, 5179–5186 (1989).
[CrossRef] [PubMed]

Z. Y. Ou, “Quantum-nondemolition measurement and squeezing in type-II harmonic generation with triple resonance,” Phys. Rev. A 49, 4902–4911 (1994).
[CrossRef] [PubMed]

A. Eschmann and M. D. Reid, “Squeezing of intensity fluctuations in frequency summation,” Phys. Rev. A 49, 2881–2890 (1994).
[CrossRef] [PubMed]

M. W. Jack, M. J. Collett, and D. F. Walls, “Asymmetrically pumped nondegenerate second-harmonic generation inside a cavity,” Phys. Rev. A 53, 1801–1811 (1996).
[CrossRef] [PubMed]

S. M. Tan, “Confirming entanglement in continuous variable quantum teleportation,” Phys. Rev. A 60, 2752–2758 (1999).
[CrossRef]

F. Grosshans and P. Grangier, “Quantum cloning and teleportation criteria for continuous quantum variables,” Phys. Rev. A 64, 0103011–0103014(R) (2001).
[CrossRef]

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A 38, 4931–4934 (1988).
[CrossRef] [PubMed]

C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
[CrossRef] [PubMed]

M. J. Collett and R. B. Levien, “Two-photon-loss model ofintracavity second-harmonic generation,” Phys. Rev. A 43, 5068–5072 (1991).
[CrossRef] [PubMed]

B. Yurke, “Use of cavities in squeezed-state generation,” Phys. Rev. A 29, 408–410 (1984).
[CrossRef]

Phys. Rev. Lett. (15)

T. Ralph and P. K. Lam, “Teleportation with bright squeezed light,” Phys. Rev. Lett. 81, 5668–5671 (1998).
[CrossRef]

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

A. Peres, “Separability criterion for density matrices,” Phys. Rev. Lett. 77, 1413–1415 (1996).
[CrossRef] [PubMed]

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef] [PubMed]

R. Simon, “Peres–Horodecki separability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2726–2729 (2000).
[CrossRef] [PubMed]

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H.-A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett. 72, 3807–3810 (1994).
[CrossRef] [PubMed]

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright Einstein–Podolsky–Rosen beam,” Phys. Rev. Lett. 88, 0479041–0479044 (2002).
[CrossRef]

J. I. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett. 74, 4091–4094 (1995).
[CrossRef] [PubMed]

A. Kuzmich and E. S. Polzik, “Atomic quantum state teleportation and swapping,” Phys. Rev. Lett. 85, 5639–5642 (2000).
[CrossRef]

J. Hald, J. L. Sørensen, C. Schori, and E. S. Polzik, “Spin squeezed atoms: a macroscopic entangled ensemble created by light,” Phys. Rev. Lett. 83, 1319–1322 (1999).
[CrossRef]

P. Grangier, R. E. Slusher, B. Yurke, and LaPorta, “Squeezed light-enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).
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Figures (10)

Fig. 1
Fig. 1

Schematic diagram of the setup. PBS, polarizing beam splitter; ain, pumping mode; a,, intracavity modes; a,out, output modes; γ,, decay rates of coupling mirror.

Fig. 2
Fig. 2

Original basis (a1, a2) along the ordinary and extraordinary axes of the crystal and the rotated basis (a, a) rotated by 45° with respect to the crystal axes. The pump beam ain is linearly polarized with an angle θ with respect to the rotated basis.

Fig. 3
Fig. 3

Fundamental field α is here plotted against the pumping power with thin curves corresponding to θ=0 and thick curves corresponding to θ=π/30. Stable and unstable solutions are associated with solid and dashed lines, respectively.

Fig. 4
Fig. 4

Normalized spectral variance of the orthogonal-polarized fundamental field in the symmetric pumping case as a function of the pump power at three different frequencies.

Fig. 5
Fig. 5

Normalized spectral variance of the phase quadrature of the orthogonal-polarized fundamental field in the asymmetric pumping case as a function of the pump power normalized to the threshold power DOPO. Four different polarizations of the pump beam are shown.

Fig. 6
Fig. 6

Normalized spectral variance of the amplitude quadrature of the orthogonal-polarized fundamental field in the asymmetric pumping case as a function of the pump power normalized to the threshold power of the DOPO. Four different polarizations of the pump beam are shown.

Fig. 7
Fig. 7

Demonstration of the EPR paradox by means of the Heisenberg-like inequality as a function of the normalized pump power. Dashed curve, a single DOPO; dotted curve, interference of two DOPOs; solid curve, type II doubly resonant SHG.

Fig. 8
Fig. 8

Domain of entanglement according to the Peres–Horodecki measure is here plotted as a function of the normalized pump power for different systems. Dotted curve, a single DOPO; dashed curve, interference of two DOPOs; solid curve, type II doubly resonant SHG.

Fig. 9
Fig. 9

Squeezing product in relations (36) and (37) for type II SHG is here represented by the solid curve, together with the borderlines for inseparability (dashed line) and EPR entanglement (dotted curve).

Fig. 10
Fig. 10

Expected fidelity for quantum teleportation in the ideal case for three different systems. Dashed curve, a single DOPO; dotted curve, interference of two DOPOs; solid curve, Type II, doubly resonant SHG.

Equations (63)

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Hsys=Hfree+Hint,
Hfree=ω0a1a1+ω0a2a2+2ω0bb,
Hint=i κ2 (ba1a2-ba1a2),
a=12 (a1+a2),
a=12 (a1-a2).
Hint=i κ4 (ba2-ba2-H.c.).
dadt=-γa+κab+2γlain1+2γcain2,
dadt=-γa-κab+2γlain1+2γcain2,
dbdt=-γbb-κ2 (a2-a2)+2γbbin,
aiin1(t)ajin1(t)=aiin2(t)ajin2(t)=δijδ(t-t),
biin(t)bjin(t)=δijδ(t-t).
b=-κ2γb (a2-a2)+2γb bin,
dadt=-γa+2μabin-μa(a2-a2)+2γlain1+2γcain2,
dadt=-γa-2μabin+μa(a2-a2)+2γlain1+2γcain2.
aiout=2γicai-aiin,
dαdt=-γα-μα(α2-α2)+2γcαincos θ,
dαdt=-γα+μα(α2-α2)+2γcαinsin θ,
2γcαincos θ=α(γ+μ(α2-α2),
2γcαinsin θ=α(γ-μ(α2-α2).
ddtδXδX=M+δXδX,ddtδYδY=M-δYδY,
M±=-c±2μαα2μαα-c,
λ1,2=-12 b11±1-4b2b12,
b2>0.
α=0,α(γ+μα2)=2γcαin,
α=±2γc(αin)2(γ+γ)2-γμ,α=2γcαinγ+γ,
dδZdt=-c±δZ+2μααδZ+2μαδZbin+2γlδZin1+2γcδZin2,
dδZdt=-c±δZ+2μααδZ-2μαδZbin+2γlδZin1+2γcδZin2,
δZiout(ω)=2γicδZi(ω)-δZiin(ω).
VδZout(ω)δ(ω+ω)=δZiout(ω)δZiout(ω),
δZiin(ω)δZiin(ω)=δ(ω-ω).
VδZiout(ω)=1|Di(ω)|2j=15FjZi(ω)|δZj|2,
(δZ1, δZ2, δZ3, δZ4, δZ5)
=(δZbin, δZin1, δZin2, δZin1, δZin2),
VδZ±(ω)=14γcμα2(γ+2μ|α|2±μ|α|2)2+ω2,
VδZ±(ω)=1±4γcμα2(γμ|α|2)2+ω2,
VδY=8γμα2[μ2(α2+α2)2-4μ2α2α2+γ2+2γμα2]+[γ2-μ2(α2-α2)2]2[γ2+2μγ(α2+α2)+μ2(α2-α2)2]2.
S0=aa+aa,S1=aa-aa,
S2=aa+aa,S3=iaa-iaa.
S×S=2iS,
VδS0=VδS1=α2VδX,
VδS2=α2VδX,
VδS3=α2VδY.
VδZ1|δZ2=VδZ1-|δZ1δZ2|2VδZ2,
VδZ1|δZ2=2 VδZVδZVδZ+VδZ.
gZ=ΔZ1δZ2|δZ1|2=VδZ-VδZVδZ+VδZ.
VδX1|δX2VδY1|δY2<1.
(δX2-δX1)2+(δY2+δY1)2<4,
(δX2-δX1)2(δY2+δY1)2<4.
VδXVδY<1.
VδXVδY<(VδX+VδX)(VδY+VδY)4VδXVδY.
Pthin=(T+L)(T+T+2L)24ΓnlT,
F1XF1Y=2γc-4μμα2α+2μαγ+2μα2+-1+1(α2-α2)2+4μα2ω2,
F2X=F2Y=16μ2α2α2γcγl,
F3X=F3Y=16μ2α2α2γcγc,
F4XF4Y=4γlγcγ+2μα2+-1+1μ(α2-α2)2+4γlγcω2,
F5XF5Y=2γcγ+2μα2+-1+1μ(α2-α2)-γγ++1-1μ(α2-α2)(γ-γ)-2μ(γα2+γα2)+-+3-1μ2(α2-α2)2+ω22+ω2[γ+γ+2μ(α2+α2)-2γ2]2,
|D|2=[γγ+μ(γ-γ)2(α2-α2)+2μ(α2γ+α2γ)+μ2(α2-α2)-ω2]2+ω2[γ+γ+2μ(α2+α2)]2,
F1XF1Y=2γc4μμα2α-2μαγ+2μα2++1-1(α2-α2)2+4μα2ω2,
F2X=F2Y=16μ2α2α2γcγl,
F3X=F3Y=16μ2α2α2γcγc,
F4XF4Y=4γlγcγ+2μα2++1-1μα2-α22+4γlγcω2,
F5XF5Y=2γcγ+2μα2++1-1μ(α2-α2)-γγ++1-1μ(α2-α2)(γ-γ)-2μ(γα2+γα2)++3-1μ2(α2-α2)2+ω22+ω2[γ+γ+2μ(α2+α2)-2γc]2,
|D|2=[γγ-μ(γ-γ)(α2-α2)+2μ(α2γ+α2γ)-3μ2(α2-α2)2-ω2]2+ω2[γ+γ+2μ(α2+α2)]2.

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