Abstract

An intrinsically stable type I optical parametric oscillator was built with a periodically poled KTiOPO4 crystal to generate a stable, bright, cw, broadband phase-squeezed beam. A 3.2dB sensitivity enhancement of optical interferometry was demonstrated on weak electro-optic modulation signals within a 20MHz squeezing bandwidth. This also realized a channel capacity increase beyond that of coherent optical communication.

© 2007 Optical Society of America

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References

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  1. Y. Takeno, M. Yukawa, H. Yonezawa, and A. Furusawa, "Observation of −9dB quadrature squeezing with improvement of phase stability in homodyne measurement," arXiv e-print quant-ph/0702139.
  2. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
    [CrossRef]
  3. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
    [CrossRef]
  4. R. Lifshitz, A. Arie, and A. Bahabad, "Photonic quasicrystals for nonlinear optical frequency conversion," Phys. Rev. Lett. 95, 133901 (2005).
    [CrossRef] [PubMed]
  5. R. C. Pooser and O. Pfister, "Observation of triply coincident nonlinearities in periodically poled KTiOPO4," Opt. Lett. 30, 2635 (2005).
    [CrossRef] [PubMed]
  6. N. C. Menicucci, S. T. Flammia, H. Zaidi, and O. Pfister, "Ultracompact generation of continuous-variable cluster states," Phys. Rev. A 76, 010302 (R) (2007).
    [CrossRef]
  7. C. M. Caves, "Quantum-mechanical noise in an interferometer," Phys. Rev. D 23, 1693-1708 (1981).
    [CrossRef]
  8. M. Xiao, L.-A. Wu, and H. J. Kimble, "Precision measurement beyond the shot-noise limit," Phys. Rev. Lett. 59, 278-281 (1987).
    [CrossRef] [PubMed]
  9. P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, "Squeezed-light-enhanced polarization interferometer," Phys. Rev. Lett. 59, 2153-2156 (1987).
    [CrossRef] [PubMed]
  10. S. Feng and O. Pfister, "Sub-shot-noise heterodyne polarimetry," Opt. Lett. 29, 2800-2802 (2004).
    [CrossRef] [PubMed]
  11. T. J. Kane and R. L. Byer, "Monolithic unidirectional single-mode Nd:YAG ring laser," Opt. Lett. 10, 65-67 (1985).
    [CrossRef] [PubMed]
  12. K. Schneider, R. Bruckmeier, H. Hansen, S. Schiller, and J. Mlynek, "Bright squeezed-light generation by a continuous-wave semimonolithic parametric amplifier," Opt. Lett. 21, 1396-1398 (1996).
    [CrossRef] [PubMed]
  13. H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, "Coherent control of vacuum squeezing in the gravitational-wave detection band," Phys. Rev. Lett. 97, 011101 (2006).
    [CrossRef] [PubMed]
  14. D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1994).
  15. A. Yariv, Quantum Electronics, 3rd ed. (Wiley, 1988).
  16. 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, 047904 (2002).
    [CrossRef] [PubMed]
  17. S. F. Pereira, Z. Y. Ou, and H. J. Kimble, "Quantum communication with correlated nonclassical states," Phys. Rev. A 62, 042311 (2000).
    [CrossRef]
  18. T. C. Ralph and E. H. Huntington, "Unconditional continuous-variable dense coding," Phys. Rev. A 66, 042321 (2002).
    [CrossRef]
  19. J. G. Webb, T. C. Ralph, and E. H. Huntington, "Homodyne measurement of the average photon number," Phys. Rev. A 73, 033808 (2006).
    [CrossRef]
  20. S. L. Braunstein and H. J. Kimble, "Dense coding for continuous variables," Phys. Rev. A 61, 042302 (2000).
    [CrossRef]

2007 (1)

N. C. Menicucci, S. T. Flammia, H. Zaidi, and O. Pfister, "Ultracompact generation of continuous-variable cluster states," Phys. Rev. A 76, 010302 (R) (2007).
[CrossRef]

2006 (2)

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, "Coherent control of vacuum squeezing in the gravitational-wave detection band," Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

J. G. Webb, T. C. Ralph, and E. H. Huntington, "Homodyne measurement of the average photon number," Phys. Rev. A 73, 033808 (2006).
[CrossRef]

2005 (2)

R. Lifshitz, A. Arie, and A. Bahabad, "Photonic quasicrystals for nonlinear optical frequency conversion," Phys. Rev. Lett. 95, 133901 (2005).
[CrossRef] [PubMed]

R. C. Pooser and O. Pfister, "Observation of triply coincident nonlinearities in periodically poled KTiOPO4," Opt. Lett. 30, 2635 (2005).
[CrossRef] [PubMed]

2004 (1)

2002 (2)

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, 047904 (2002).
[CrossRef] [PubMed]

T. C. Ralph and E. H. Huntington, "Unconditional continuous-variable dense coding," Phys. Rev. A 66, 042321 (2002).
[CrossRef]

2000 (2)

S. L. Braunstein and H. J. Kimble, "Dense coding for continuous variables," Phys. Rev. A 61, 042302 (2000).
[CrossRef]

S. F. Pereira, Z. Y. Ou, and H. J. Kimble, "Quantum communication with correlated nonclassical states," Phys. Rev. A 62, 042311 (2000).
[CrossRef]

1996 (1)

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

1987 (2)

M. Xiao, L.-A. Wu, and H. J. Kimble, "Precision measurement beyond the shot-noise limit," Phys. Rev. Lett. 59, 278-281 (1987).
[CrossRef] [PubMed]

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

1985 (1)

1981 (1)

C. M. Caves, "Quantum-mechanical noise in an interferometer," Phys. Rev. D 23, 1693-1708 (1981).
[CrossRef]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Arie, A.

R. Lifshitz, A. Arie, and A. Bahabad, "Photonic quasicrystals for nonlinear optical frequency conversion," Phys. Rev. Lett. 95, 133901 (2005).
[CrossRef] [PubMed]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Bahabad, A.

R. Lifshitz, A. Arie, and A. Bahabad, "Photonic quasicrystals for nonlinear optical frequency conversion," Phys. Rev. Lett. 95, 133901 (2005).
[CrossRef] [PubMed]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Braunstein, S. L.

S. L. Braunstein and H. J. Kimble, "Dense coding for continuous variables," Phys. Rev. A 61, 042302 (2000).
[CrossRef]

Bruckmeier, R.

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

T. J. Kane and R. L. Byer, "Monolithic unidirectional single-mode Nd:YAG ring laser," Opt. Lett. 10, 65-67 (1985).
[CrossRef] [PubMed]

Caves, C. M.

C. M. Caves, "Quantum-mechanical noise in an interferometer," Phys. Rev. D 23, 1693-1708 (1981).
[CrossRef]

Chelkowski, S.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, "Coherent control of vacuum squeezing in the gravitational-wave detection band," Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

Danzmann, K.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, "Coherent control of vacuum squeezing in the gravitational-wave detection band," Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Feng, S.

Flammia, S. T.

N. C. Menicucci, S. T. Flammia, H. Zaidi, and O. Pfister, "Ultracompact generation of continuous-variable cluster states," Phys. Rev. A 76, 010302 (R) (2007).
[CrossRef]

Franzen, A.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, "Coherent control of vacuum squeezing in the gravitational-wave detection band," Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

Furusawa, A.

Y. Takeno, M. Yukawa, H. Yonezawa, and A. Furusawa, "Observation of −9dB quadrature squeezing with improvement of phase stability in homodyne measurement," arXiv e-print quant-ph/0702139.

Grangier, P.

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

Hage, B.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, "Coherent control of vacuum squeezing in the gravitational-wave detection band," Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

Hansen, H.

Huntington, E. H.

J. G. Webb, T. C. Ralph, and E. H. Huntington, "Homodyne measurement of the average photon number," Phys. Rev. A 73, 033808 (2006).
[CrossRef]

T. C. Ralph and E. H. Huntington, "Unconditional continuous-variable dense coding," Phys. Rev. A 66, 042321 (2002).
[CrossRef]

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, 047904 (2002).
[CrossRef] [PubMed]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Kane, T. J.

Kimble, H. J.

S. F. Pereira, Z. Y. Ou, and H. J. Kimble, "Quantum communication with correlated nonclassical states," Phys. Rev. A 62, 042311 (2000).
[CrossRef]

S. L. Braunstein and H. J. Kimble, "Dense coding for continuous variables," Phys. Rev. A 61, 042302 (2000).
[CrossRef]

M. Xiao, L.-A. Wu, and H. J. Kimble, "Precision measurement beyond the shot-noise limit," Phys. Rev. Lett. 59, 278-281 (1987).
[CrossRef] [PubMed]

LaPorta, A.

P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, "Squeezed-light-enhanced polarization interferometer," Phys. Rev. Lett. 59, 2153-2156 (1987).
[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, 047904 (2002).
[CrossRef] [PubMed]

Lifshitz, R.

R. Lifshitz, A. Arie, and A. Bahabad, "Photonic quasicrystals for nonlinear optical frequency conversion," Phys. Rev. Lett. 95, 133901 (2005).
[CrossRef] [PubMed]

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Menicucci, N. C.

N. C. Menicucci, S. T. Flammia, H. Zaidi, and O. Pfister, "Ultracompact generation of continuous-variable cluster states," Phys. Rev. A 76, 010302 (R) (2007).
[CrossRef]

Milburn, G. J.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1994).

Mlynek, J.

Ou, Z. Y.

S. F. Pereira, Z. Y. Ou, and H. J. Kimble, "Quantum communication with correlated nonclassical states," Phys. Rev. A 62, 042311 (2000).
[CrossRef]

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, 047904 (2002).
[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, 047904 (2002).
[CrossRef] [PubMed]

Pereira, S. F.

S. F. Pereira, Z. Y. Ou, and H. J. Kimble, "Quantum communication with correlated nonclassical states," Phys. Rev. A 62, 042311 (2000).
[CrossRef]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Pfister, O.

Pooser, R. C.

Ralph, T. C.

J. G. Webb, T. C. Ralph, and E. H. Huntington, "Homodyne measurement of the average photon number," Phys. Rev. A 73, 033808 (2006).
[CrossRef]

T. C. Ralph and E. H. Huntington, "Unconditional continuous-variable dense coding," Phys. Rev. A 66, 042321 (2002).
[CrossRef]

Schiller, S.

Schnabel, R.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, "Coherent control of vacuum squeezing in the gravitational-wave detection band," Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

Schneider, K.

Slusher, R. E.

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

Takeno, Y.

Y. Takeno, M. Yukawa, H. Yonezawa, and A. Furusawa, "Observation of −9dB quadrature squeezing with improvement of phase stability in homodyne measurement," arXiv e-print quant-ph/0702139.

Vahlbruch, H.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, "Coherent control of vacuum squeezing in the gravitational-wave detection band," Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

Walls, D. F.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1994).

Webb, J. G.

J. G. Webb, T. C. Ralph, and E. H. Huntington, "Homodyne measurement of the average photon number," Phys. Rev. A 73, 033808 (2006).
[CrossRef]

Wu, L.-A.

M. Xiao, L.-A. Wu, and H. J. Kimble, "Precision measurement beyond the shot-noise limit," Phys. Rev. Lett. 59, 278-281 (1987).
[CrossRef] [PubMed]

Xiao, M.

M. Xiao, L.-A. Wu, and H. J. Kimble, "Precision measurement beyond the shot-noise limit," Phys. Rev. Lett. 59, 278-281 (1987).
[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, 047904 (2002).
[CrossRef] [PubMed]

Yariv, A.

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, 1988).

Yonezawa, H.

Y. Takeno, M. Yukawa, H. Yonezawa, and A. Furusawa, "Observation of −9dB quadrature squeezing with improvement of phase stability in homodyne measurement," arXiv e-print quant-ph/0702139.

Yukawa, M.

Y. Takeno, M. Yukawa, H. Yonezawa, and A. Furusawa, "Observation of −9dB quadrature squeezing with improvement of phase stability in homodyne measurement," arXiv e-print quant-ph/0702139.

Yurke, B.

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

Zaidi, H.

N. C. Menicucci, S. T. Flammia, H. Zaidi, and O. Pfister, "Ultracompact generation of continuous-variable cluster states," Phys. Rev. A 76, 010302 (R) (2007).
[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, 047904 (2002).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Phys. Rev. A (5)

N. C. Menicucci, S. T. Flammia, H. Zaidi, and O. Pfister, "Ultracompact generation of continuous-variable cluster states," Phys. Rev. A 76, 010302 (R) (2007).
[CrossRef]

S. F. Pereira, Z. Y. Ou, and H. J. Kimble, "Quantum communication with correlated nonclassical states," Phys. Rev. A 62, 042311 (2000).
[CrossRef]

T. C. Ralph and E. H. Huntington, "Unconditional continuous-variable dense coding," Phys. Rev. A 66, 042321 (2002).
[CrossRef]

J. G. Webb, T. C. Ralph, and E. H. Huntington, "Homodyne measurement of the average photon number," Phys. Rev. A 73, 033808 (2006).
[CrossRef]

S. L. Braunstein and H. J. Kimble, "Dense coding for continuous variables," Phys. Rev. A 61, 042302 (2000).
[CrossRef]

Phys. Rev. D (1)

C. M. Caves, "Quantum-mechanical noise in an interferometer," Phys. Rev. D 23, 1693-1708 (1981).
[CrossRef]

Phys. Rev. Lett. (5)

M. Xiao, L.-A. Wu, and H. J. Kimble, "Precision measurement beyond the shot-noise limit," Phys. Rev. Lett. 59, 278-281 (1987).
[CrossRef] [PubMed]

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

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, "Coherent control of vacuum squeezing in the gravitational-wave detection band," Phys. Rev. Lett. 97, 011101 (2006).
[CrossRef] [PubMed]

R. Lifshitz, A. Arie, and A. Bahabad, "Photonic quasicrystals for nonlinear optical frequency conversion," Phys. Rev. Lett. 95, 133901 (2005).
[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, 047904 (2002).
[CrossRef] [PubMed]

Other (3)

Y. Takeno, M. Yukawa, H. Yonezawa, and A. Furusawa, "Observation of −9dB quadrature squeezing with improvement of phase stability in homodyne measurement," arXiv e-print quant-ph/0702139.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1994).

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, 1988).

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Figures (4)

Fig. 1
Fig. 1

Experimental setup. CLL, cavity lock loop; EOM, electro-optic modulator; FR, Faraday rotator ( 45 ° ) ; H(Q)WP, half(quarter)-wave plate; LO, local oscillator; MC, mode cleaner; PBS, polarizing beam splitter; PZT, piezoelectric transducer; T, temperature controller.

Fig. 2
Fig. 2

Photocurrent power spectrum of the balanced homodyne detection. (i) OPA amplitude quadrature. (ii) Shot-noise level. (iii) OPA phase quadrature. (iv) Electronic detection noise (no light). Resolution bandwidth, 30 kHz : video bandwidth, 10 kHz ; 100-sweep average. Peaks at 11.5 and 12 MHz are modulation signals for locking the mode-cleaner cavities.

Fig. 3
Fig. 3

Photodetection noise with a small phase modulation at Ω 2 π = 4.5 MHz . (i) LO beam interferes with a coherent beam. (ii) LO beam interferes with a squeezed beam. In both cases, the average optical power P O P A α 2 is the same. Resolution bandwidth, 30 kHz ; video bandwidth, 10 kHz ; 100-sweep average.

Fig. 4
Fig. 4

Channel capacity versus average photon number in different cases. Dotted curve, classical coherent limit; solid curve, 3.2 dB squeezed limit (this work); dashed curve, Holevo bound.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

N = ( a + b e i θ ) ( a + b e i θ ) 2 ( a b e i θ ) ( a b e i θ ) 2 = a b e i θ + a b e i θ 2 α β cos θ + α δ B θ + β δ A θ ,
V ( N ) = ( Δ N ) 2 = α 2 δ B θ 2 + β 2 δ A θ 2
V ( N ) = ( Δ N ) 2 = α 2 + β 2 ( e 2 r sin 2 θ + e 2 r cos 2 θ ) ,
V ( N ) s q V ( N ) s n = α 2 + β 2 e 2 r β 2 = P O P A P L O + e 2 r .
δ θ 0 = ( n Z 3 r 33 E Z + n Y 3 r 23 E Z ) l π λ ,
V ( N ) s q V ( N ) s n = α 2 + β 2 e 2 r α 2 + β 2 ,
C = 1 2 log 2 ( 1 + V S V N ) ,
n ¯ = a a = 1 4 ( V 0 + V π 2 ) 1 2 ,
C c o h = 1 2 log 2 ( 1 + 4 n ¯ ) .
C c o h s q = 1 2 log 2 ( 1 + 4 e 2 r n ¯ ) .
C s q = 1 2 log 2 [ 1 + 4 e 2 r ( n ¯ sinh 2 r ) ] ,
C H = ( 1 + n ¯ ) log 2 ( 1 + n ¯ ) n ¯ log 2 n ¯ ,

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