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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 20, Iss. 9 — Sep. 1, 2003
  • pp: 1947–1958

Squeezing and entanglement in doubly resonant, type II, second-harmonic generation

Ulrik L. Andersen and Preben Buchhave  »View Author Affiliations

JOSA B, Vol. 20, Issue 9, pp. 1947-1958 (2003)

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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

OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4970) Nonlinear optics : Parametric oscillators and amplifiers
(270.2500) Quantum optics : Fluctuations, relaxations, and noise
(270.6570) Quantum optics : Squeezed states

Ulrik L. Andersen and Preben Buchhave, "Squeezing and entanglement in doubly resonant, type II, second-harmonic generation," J. Opt. Soc. Am. B 20, 1947-1958 (2003)

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  1. R. Loudon and P. L. Knight, “Squeezed light,” J. Mod. Opt. 34, 709–759 (1987). [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). [CrossRef]
  3. L. A. Lugiato, G. Strini, and F. De Martini, “Squeezed states in second-harmonic generation,” Opt. Lett. 8, 256–258 (1983). [CrossRef] [PubMed]
  4. 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]
  5. 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]
  6. 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]
  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]
  8. H. Tsuchida, “Generation of amplitude-squeezed light at 432 nm from a singly resonant frequency doubler,” Opt. Lett. 20, 2240–2242 (1995). [CrossRef]
  9. 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]
  10. A. Eschmann and M. D. Reid, “Squeezing of intensity fluctuations in frequency summation,” Phys. Rev. A 49, 2881–2890 (1994). [CrossRef] [PubMed]
  11. 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]
  12. 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]
  13. C. H. Bennett and D. P. DiVincenzo, “Quantum information and computation,” Nature 404, 247–255 (2000). [CrossRef] [PubMed]
  14. 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]
  15. 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]
  16. 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]
  17. M. J. Collett and R. B. Levien, “Two-photon-loss model ofintracavity second-harmonic generation,” Phys. Rev. A 43, 5068–5072 (1991). [CrossRef] [PubMed]
  18. B. Yurke, “Use of cavities in squeezed-state generation,” Phys. Rev. A 29, 408–410 (1984). [CrossRef]
  19. K. Schneider and S. Schiller, “Multiple conversion and optical limiting in a subharmonic-pumped parametric oscillator,” Opt. Lett. 22, 363–365 (1997). [CrossRef] [PubMed]
  20. M. Marte, “Sub-Poissonian twin beams via competing nonlinearities,” Phys. Rev. Lett. 74, 4815–4818 (1995). [CrossRef] [PubMed]
  21. M. J. Collett and D. F. Walls, “Squeezing spectra for nonlinear optical systems,” Phys. Rev. A 32, 2887–2892 (1985). [CrossRef] [PubMed]
  22. 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]
  23. 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).
  24. P. Grangier, R. E. Slusher, B. Yurke, and LaPorta, “Squeezed light-enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987). [CrossRef] [PubMed]
  25. 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]
  26. D. P. Di Vincenzo, “Quantum computation,” Science 270, 255–261 (1995). [CrossRef]
  27. J. I. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett. 74, 4091–4094 (1995). [CrossRef] [PubMed]
  28. A. Kuzmich and E. S. Polzik, “Atomic quantum state teleportation and swapping,” Phys. Rev. Lett. 85, 5639–5642 (2000). [CrossRef]
  29. 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]
  30. 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]
  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]
  35. A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?,” Phys. Rev. 47, 777–780 (1935). [CrossRef]
  36. P. Van Loock and S. L. Braunstein, “Unconditional teleportation of continuous-variable entanglement,” Phys. Rev. A 61, 010302/1–4 (1999). [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]
  38. A. Peres, “Separability criterion for density matrices,” Phys. Rev. Lett. 77, 1413–1415 (1996). [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]
  45. L. Shiv, J. L. Sørensen, E. S. Polzik, and G. Mizell, Opt. Lett. 20, 2270–2272 (1995). [CrossRef]
  46. M. E. Anderson, D. F. McAlister, M. G. Raymer, and M. C. Gupta, “Pulsed squeezed-light generation in χ(2) nonlinear waveguides,” J. Opt. Soc. Am. B 14, 3180–3190 (1997). [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]

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