Abstract

An optical field with a definite number of photons is very important for quantum metrology and quantum information. Some theoretical protocols for creating such a Fock-state have been proposed, but it is still a big challenge to produce it with a large number photons experimentally. We revisit the system of atoms inside an optical parametric oscillator that was proposed in 1990s, and it is found that for the atom ensemble, the optical Fock-state with an arbitrary number of photons can be generated. Compared to the previous proposals, the scheme presented here is simple and seems physically realizable. The system also provides the possibility to demonstrate the strong interaction between nonclassical light and atoms in a confined space.

© 2012 Optical Society of America

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  3. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
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  4. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
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  5. M. Holland and K. Burnett, “Triggered single photons from a quantum dot,” Phys. Rev. Lett. 86, 1502–1505 (2001).
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  6. K. R. Brown, K. M. Dani, D. M. Stamper-Kurn, and K. B. Whaley, “Deterministic optical Fock-state generation,” Phys. Rev. A 67, 043818 (2003).
    [CrossRef]
  7. M. N. O’Sullivan, K. W. C. Chan, V. Lakshminarayanan, and R. W. Boyd, “Conditional preparation of states containing a definite number of photons,” Phys. Rev. A 77, 023804 (2008).
    [CrossRef]
  8. J. M. Geremia, “Deterministic and nondestructively verifiable preparation of photon-number states,” Phys. Rev. Lett. 97, 073601 (2006).
    [CrossRef]
  9. I. Dotsenko, M. Mirrahimi, M. Brune, S. Haroche, J.-M. Raimond, and P. Rouchon, “Quantum feedback by discrete quantum nondemolition measurements: towards on-demand generation of photon-number states,” Phys. Rev. A 80, 013805 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  12. S. G. Lukishova, A. W. Schmid, A. J. McNamara, R. W. Boyd, and C. R. Stroud, “Room temperature single-photon source: single-dye molecule fluorescence in liquid crystal host,” IEEE J. Sel. Top. Quantum Electron. 9, 1512–1518 (2003).
    [CrossRef]
  13. J. Kim, O. Benson, H. Kan, and Y. Yamamoto, “A single-photon turnstile device,” Nature 397, 500–503 (1999).
    [CrossRef]
  14. B. T. H. Varcoe, S. Brattke, M. Weidinger, and H. Walther, “Preparing pure photon number states of the radiation field,” Nature 403, 743–746 (2000).
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  15. E. Waks, E. Diamanti, and Y. Yamamoto, “Generation of photon number states,” New J. Phys. 8, 4 (2006).
    [CrossRef]
  16. D. Achilles, C. Silberhorn, and I. A. Walmsley, “Direct, loss-tolerant characterization of nonclassical photon statistics,” Phys. Rev. Lett. 97, 043602 (2006).
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    [CrossRef]
  18. S. Jin and M. Xiao, “Extra intracavity squeezing of a degenerate optical parametric oscillator coupling with N two-level atoms,” Phys. Rev. A 49, 499–505 (1994).
    [CrossRef]
  19. F. A. Montes and M. Xiao, “Three-level atoms inside a degenerate optical parametric oscillator: steady-state behaviors,” Phys. Rev. A 62, 023818 (2000).
    [CrossRef]
  20. J. P. Clemens, P. R. Rice, P. K. Rungta, and R. J. Brecha, “Two-level atom in an optical parametric oscillator: Spectra of transmitted and fluorescent fields in the weak-driving-field limit,” Phys. Rev. A 62, 033802 (2000).
    [CrossRef]
  21. P. R. Rice, “Entanglement, teleportation, and single-photon storage with two-level atoms inside an optical parametric oscillator” J. Opt. Soc. Am. B 22, 1561–1565 (2005).
    [CrossRef]
  22. C. E. Strimbu, J. Leach, and P. R. Rice, “Conditional homodyne detection at the single-photon level: intensity-field correlations for a two-level atom in an optical parametric oscillator,” Phys. Rev. A 71, 013807 (2005).
    [CrossRef]
  23. E. Alebachew, “A coherently driven two-level atom inside a parametric oscillator,” J. Mod. Opt. 55, 1159–1173 (2008).
    [CrossRef]
  24. W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley, 1973).
  25. H. J. Carmichael, “Quantum fluctuations in absorptive bistability without adiabatic elimination,” Phys. Rev. A 33, 3262–3269 (1986).
    [CrossRef]
  26. C. W. Gardinar, Handbook of Stochastic Methods (Springer, 1982).
  27. L. Mandel and E. Wolf, Quantum Coherence and Quantum Optics (Cambridge University, 1995).
  28. J. Zhang, J. M. Wang, and T. C. Zhang, “Entanglement and nonclassicality evolution of the atom in a squeezed vacuum,” Opt. Commun. 277, 353–358 (2007).
    [CrossRef]
  29. V. Josse, A. Dantan, L. Vernac, A. Bramati, M. Pinard, and E. Giacobino, “Polarization squeezing with cold atoms,” Phys. Rev. Lett. 91, 103601 (2003).
    [CrossRef]
  30. P. D. Drummond, K. J. Mcnell, and D. F. Walls, Optica Acta 28, 211 (1981).
    [CrossRef]
  31. Q. A. Turchette, N. Ph. Georgiades, C. J. Hood, H. J. Kimble, and A. S. Parkins, “Squeezed excitation in cavity QED: experiment and theory,” Phys. Rev. A 58, 4056–4077 (1998).
    [CrossRef]

2011 (1)

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[CrossRef]

2009 (2)

K. Banaszek, R. Demkowicz-Dobrzański, and I. A. Walmsley, “Quantum states made to measure,” Nat. Photon. 3, 673–676 (2009).
[CrossRef]

I. Dotsenko, M. Mirrahimi, M. Brune, S. Haroche, J.-M. Raimond, and P. Rouchon, “Quantum feedback by discrete quantum nondemolition measurements: towards on-demand generation of photon-number states,” Phys. Rev. A 80, 013805 (2009).
[CrossRef]

2008 (2)

M. N. O’Sullivan, K. W. C. Chan, V. Lakshminarayanan, and R. W. Boyd, “Conditional preparation of states containing a definite number of photons,” Phys. Rev. A 77, 023804 (2008).
[CrossRef]

E. Alebachew, “A coherently driven two-level atom inside a parametric oscillator,” J. Mod. Opt. 55, 1159–1173 (2008).
[CrossRef]

2007 (1)

J. Zhang, J. M. Wang, and T. C. Zhang, “Entanglement and nonclassicality evolution of the atom in a squeezed vacuum,” Opt. Commun. 277, 353–358 (2007).
[CrossRef]

2006 (3)

J. M. Geremia, “Deterministic and nondestructively verifiable preparation of photon-number states,” Phys. Rev. Lett. 97, 073601 (2006).
[CrossRef]

E. Waks, E. Diamanti, and Y. Yamamoto, “Generation of photon number states,” New J. Phys. 8, 4 (2006).
[CrossRef]

D. Achilles, C. Silberhorn, and I. A. Walmsley, “Direct, loss-tolerant characterization of nonclassical photon statistics,” Phys. Rev. Lett. 97, 043602 (2006).
[CrossRef]

2005 (3)

B. Darquié, M. P. A. Jones, J. Dingjan, J. Beugnon, S. Bergamini, Y. Sortais, G. Messin, A. Browaeys, and P. Grangier, “Controlled single-photon emission from a single trapped two-level atom,” Science 309, 454–456 (2005).
[CrossRef]

C. E. Strimbu, J. Leach, and P. R. Rice, “Conditional homodyne detection at the single-photon level: intensity-field correlations for a two-level atom in an optical parametric oscillator,” Phys. Rev. A 71, 013807 (2005).
[CrossRef]

P. R. Rice, “Entanglement, teleportation, and single-photon storage with two-level atoms inside an optical parametric oscillator” J. Opt. Soc. Am. B 22, 1561–1565 (2005).
[CrossRef]

2003 (3)

V. Josse, A. Dantan, L. Vernac, A. Bramati, M. Pinard, and E. Giacobino, “Polarization squeezing with cold atoms,” Phys. Rev. Lett. 91, 103601 (2003).
[CrossRef]

S. G. Lukishova, A. W. Schmid, A. J. McNamara, R. W. Boyd, and C. R. Stroud, “Room temperature single-photon source: single-dye molecule fluorescence in liquid crystal host,” IEEE J. Sel. Top. Quantum Electron. 9, 1512–1518 (2003).
[CrossRef]

K. R. Brown, K. M. Dani, D. M. Stamper-Kurn, and K. B. Whaley, “Deterministic optical Fock-state generation,” Phys. Rev. A 67, 043818 (2003).
[CrossRef]

2002 (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

2001 (2)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef]

M. Holland and K. Burnett, “Triggered single photons from a quantum dot,” Phys. Rev. Lett. 86, 1502–1505 (2001).
[CrossRef]

2000 (3)

B. T. H. Varcoe, S. Brattke, M. Weidinger, and H. Walther, “Preparing pure photon number states of the radiation field,” Nature 403, 743–746 (2000).
[CrossRef]

F. A. Montes and M. Xiao, “Three-level atoms inside a degenerate optical parametric oscillator: steady-state behaviors,” Phys. Rev. A 62, 023818 (2000).
[CrossRef]

J. P. Clemens, P. R. Rice, P. K. Rungta, and R. J. Brecha, “Two-level atom in an optical parametric oscillator: Spectra of transmitted and fluorescent fields in the weak-driving-field limit,” Phys. Rev. A 62, 033802 (2000).
[CrossRef]

1999 (1)

J. Kim, O. Benson, H. Kan, and Y. Yamamoto, “A single-photon turnstile device,” Nature 397, 500–503 (1999).
[CrossRef]

1998 (1)

Q. A. Turchette, N. Ph. Georgiades, C. J. Hood, H. J. Kimble, and A. S. Parkins, “Squeezed excitation in cavity QED: experiment and theory,” Phys. Rev. A 58, 4056–4077 (1998).
[CrossRef]

1994 (2)

S. Jin and M. Xiao, “Extra intracavity squeezing of a degenerate optical parametric oscillator coupling with N two-level atoms,” Phys. Rev. A 49, 499–505 (1994).
[CrossRef]

C. M. Caves and P. D. Drummond, “Quantum limits on bosonic communication rates,” Rev. Mod. Phys. 66, 481–537 (1994).
[CrossRef]

1992 (1)

M. Xiao and S. Jin, “Bistable behavior in a system of an optical parametric oscillator coupling with N two-level atoms,” Phys. Rev. A 45, 483–488 (1992).
[CrossRef]

1986 (1)

H. J. Carmichael, “Quantum fluctuations in absorptive bistability without adiabatic elimination,” Phys. Rev. A 33, 3262–3269 (1986).
[CrossRef]

1981 (1)

P. D. Drummond, K. J. Mcnell, and D. F. Walls, Optica Acta 28, 211 (1981).
[CrossRef]

Achilles, D.

D. Achilles, C. Silberhorn, and I. A. Walmsley, “Direct, loss-tolerant characterization of nonclassical photon statistics,” Phys. Rev. Lett. 97, 043602 (2006).
[CrossRef]

Alebachew, E.

E. Alebachew, “A coherently driven two-level atom inside a parametric oscillator,” J. Mod. Opt. 55, 1159–1173 (2008).
[CrossRef]

Amini, H.

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[CrossRef]

Banaszek, K.

K. Banaszek, R. Demkowicz-Dobrzański, and I. A. Walmsley, “Quantum states made to measure,” Nat. Photon. 3, 673–676 (2009).
[CrossRef]

Benson, O.

J. Kim, O. Benson, H. Kan, and Y. Yamamoto, “A single-photon turnstile device,” Nature 397, 500–503 (1999).
[CrossRef]

Bergamini, S.

B. Darquié, M. P. A. Jones, J. Dingjan, J. Beugnon, S. Bergamini, Y. Sortais, G. Messin, A. Browaeys, and P. Grangier, “Controlled single-photon emission from a single trapped two-level atom,” Science 309, 454–456 (2005).
[CrossRef]

Beugnon, J.

B. Darquié, M. P. A. Jones, J. Dingjan, J. Beugnon, S. Bergamini, Y. Sortais, G. Messin, A. Browaeys, and P. Grangier, “Controlled single-photon emission from a single trapped two-level atom,” Science 309, 454–456 (2005).
[CrossRef]

Boyd, R. W.

M. N. O’Sullivan, K. W. C. Chan, V. Lakshminarayanan, and R. W. Boyd, “Conditional preparation of states containing a definite number of photons,” Phys. Rev. A 77, 023804 (2008).
[CrossRef]

S. G. Lukishova, A. W. Schmid, A. J. McNamara, R. W. Boyd, and C. R. Stroud, “Room temperature single-photon source: single-dye molecule fluorescence in liquid crystal host,” IEEE J. Sel. Top. Quantum Electron. 9, 1512–1518 (2003).
[CrossRef]

Bramati, A.

V. Josse, A. Dantan, L. Vernac, A. Bramati, M. Pinard, and E. Giacobino, “Polarization squeezing with cold atoms,” Phys. Rev. Lett. 91, 103601 (2003).
[CrossRef]

Brattke, S.

B. T. H. Varcoe, S. Brattke, M. Weidinger, and H. Walther, “Preparing pure photon number states of the radiation field,” Nature 403, 743–746 (2000).
[CrossRef]

Brecha, R. J.

J. P. Clemens, P. R. Rice, P. K. Rungta, and R. J. Brecha, “Two-level atom in an optical parametric oscillator: Spectra of transmitted and fluorescent fields in the weak-driving-field limit,” Phys. Rev. A 62, 033802 (2000).
[CrossRef]

Browaeys, A.

B. Darquié, M. P. A. Jones, J. Dingjan, J. Beugnon, S. Bergamini, Y. Sortais, G. Messin, A. Browaeys, and P. Grangier, “Controlled single-photon emission from a single trapped two-level atom,” Science 309, 454–456 (2005).
[CrossRef]

Brown, K. R.

K. R. Brown, K. M. Dani, D. M. Stamper-Kurn, and K. B. Whaley, “Deterministic optical Fock-state generation,” Phys. Rev. A 67, 043818 (2003).
[CrossRef]

Brune, M.

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[CrossRef]

I. Dotsenko, M. Mirrahimi, M. Brune, S. Haroche, J.-M. Raimond, and P. Rouchon, “Quantum feedback by discrete quantum nondemolition measurements: towards on-demand generation of photon-number states,” Phys. Rev. A 80, 013805 (2009).
[CrossRef]

Burnett, K.

M. Holland and K. Burnett, “Triggered single photons from a quantum dot,” Phys. Rev. Lett. 86, 1502–1505 (2001).
[CrossRef]

Carmichael, H. J.

H. J. Carmichael, “Quantum fluctuations in absorptive bistability without adiabatic elimination,” Phys. Rev. A 33, 3262–3269 (1986).
[CrossRef]

Caves, C. M.

C. M. Caves and P. D. Drummond, “Quantum limits on bosonic communication rates,” Rev. Mod. Phys. 66, 481–537 (1994).
[CrossRef]

Chan, K. W. C.

M. N. O’Sullivan, K. W. C. Chan, V. Lakshminarayanan, and R. W. Boyd, “Conditional preparation of states containing a definite number of photons,” Phys. Rev. A 77, 023804 (2008).
[CrossRef]

Clemens, J. P.

J. P. Clemens, P. R. Rice, P. K. Rungta, and R. J. Brecha, “Two-level atom in an optical parametric oscillator: Spectra of transmitted and fluorescent fields in the weak-driving-field limit,” Phys. Rev. A 62, 033802 (2000).
[CrossRef]

Dani, K. M.

K. R. Brown, K. M. Dani, D. M. Stamper-Kurn, and K. B. Whaley, “Deterministic optical Fock-state generation,” Phys. Rev. A 67, 043818 (2003).
[CrossRef]

Dantan, A.

V. Josse, A. Dantan, L. Vernac, A. Bramati, M. Pinard, and E. Giacobino, “Polarization squeezing with cold atoms,” Phys. Rev. Lett. 91, 103601 (2003).
[CrossRef]

Darquié, B.

B. Darquié, M. P. A. Jones, J. Dingjan, J. Beugnon, S. Bergamini, Y. Sortais, G. Messin, A. Browaeys, and P. Grangier, “Controlled single-photon emission from a single trapped two-level atom,” Science 309, 454–456 (2005).
[CrossRef]

Demkowicz-Dobrzanski, R.

K. Banaszek, R. Demkowicz-Dobrzański, and I. A. Walmsley, “Quantum states made to measure,” Nat. Photon. 3, 673–676 (2009).
[CrossRef]

Diamanti, E.

E. Waks, E. Diamanti, and Y. Yamamoto, “Generation of photon number states,” New J. Phys. 8, 4 (2006).
[CrossRef]

Dingjan, J.

B. Darquié, M. P. A. Jones, J. Dingjan, J. Beugnon, S. Bergamini, Y. Sortais, G. Messin, A. Browaeys, and P. Grangier, “Controlled single-photon emission from a single trapped two-level atom,” Science 309, 454–456 (2005).
[CrossRef]

Dotsenko, I.

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[CrossRef]

I. Dotsenko, M. Mirrahimi, M. Brune, S. Haroche, J.-M. Raimond, and P. Rouchon, “Quantum feedback by discrete quantum nondemolition measurements: towards on-demand generation of photon-number states,” Phys. Rev. A 80, 013805 (2009).
[CrossRef]

Drummond, P. D.

C. M. Caves and P. D. Drummond, “Quantum limits on bosonic communication rates,” Rev. Mod. Phys. 66, 481–537 (1994).
[CrossRef]

P. D. Drummond, K. J. Mcnell, and D. F. Walls, Optica Acta 28, 211 (1981).
[CrossRef]

Gardinar, C. W.

C. W. Gardinar, Handbook of Stochastic Methods (Springer, 1982).

Geremia, J. M.

J. M. Geremia, “Deterministic and nondestructively verifiable preparation of photon-number states,” Phys. Rev. Lett. 97, 073601 (2006).
[CrossRef]

Giacobino, E.

V. Josse, A. Dantan, L. Vernac, A. Bramati, M. Pinard, and E. Giacobino, “Polarization squeezing with cold atoms,” Phys. Rev. Lett. 91, 103601 (2003).
[CrossRef]

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Gleyzes, S.

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[CrossRef]

Grangier, P.

B. Darquié, M. P. A. Jones, J. Dingjan, J. Beugnon, S. Bergamini, Y. Sortais, G. Messin, A. Browaeys, and P. Grangier, “Controlled single-photon emission from a single trapped two-level atom,” Science 309, 454–456 (2005).
[CrossRef]

Haroche, S.

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[CrossRef]

I. Dotsenko, M. Mirrahimi, M. Brune, S. Haroche, J.-M. Raimond, and P. Rouchon, “Quantum feedback by discrete quantum nondemolition measurements: towards on-demand generation of photon-number states,” Phys. Rev. A 80, 013805 (2009).
[CrossRef]

Holland, M.

M. Holland and K. Burnett, “Triggered single photons from a quantum dot,” Phys. Rev. Lett. 86, 1502–1505 (2001).
[CrossRef]

Hood, C. J.

Q. A. Turchette, N. Ph. Georgiades, C. J. Hood, H. J. Kimble, and A. S. Parkins, “Squeezed excitation in cavity QED: experiment and theory,” Phys. Rev. A 58, 4056–4077 (1998).
[CrossRef]

Jin, S.

S. Jin and M. Xiao, “Extra intracavity squeezing of a degenerate optical parametric oscillator coupling with N two-level atoms,” Phys. Rev. A 49, 499–505 (1994).
[CrossRef]

M. Xiao and S. Jin, “Bistable behavior in a system of an optical parametric oscillator coupling with N two-level atoms,” Phys. Rev. A 45, 483–488 (1992).
[CrossRef]

Jones, M. P. A.

B. Darquié, M. P. A. Jones, J. Dingjan, J. Beugnon, S. Bergamini, Y. Sortais, G. Messin, A. Browaeys, and P. Grangier, “Controlled single-photon emission from a single trapped two-level atom,” Science 309, 454–456 (2005).
[CrossRef]

Josse, V.

V. Josse, A. Dantan, L. Vernac, A. Bramati, M. Pinard, and E. Giacobino, “Polarization squeezing with cold atoms,” Phys. Rev. Lett. 91, 103601 (2003).
[CrossRef]

Kan, H.

J. Kim, O. Benson, H. Kan, and Y. Yamamoto, “A single-photon turnstile device,” Nature 397, 500–503 (1999).
[CrossRef]

Kim, J.

J. Kim, O. Benson, H. Kan, and Y. Yamamoto, “A single-photon turnstile device,” Nature 397, 500–503 (1999).
[CrossRef]

Kimble, H. J.

Q. A. Turchette, N. Ph. Georgiades, C. J. Hood, H. J. Kimble, and A. S. Parkins, “Squeezed excitation in cavity QED: experiment and theory,” Phys. Rev. A 58, 4056–4077 (1998).
[CrossRef]

Knill, E.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef]

Laflamme, R.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef]

Lakshminarayanan, V.

M. N. O’Sullivan, K. W. C. Chan, V. Lakshminarayanan, and R. W. Boyd, “Conditional preparation of states containing a definite number of photons,” Phys. Rev. A 77, 023804 (2008).
[CrossRef]

Leach, J.

C. E. Strimbu, J. Leach, and P. R. Rice, “Conditional homodyne detection at the single-photon level: intensity-field correlations for a two-level atom in an optical parametric oscillator,” Phys. Rev. A 71, 013807 (2005).
[CrossRef]

Louisell, W. H.

W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley, 1973).

Lukishova, S. G.

S. G. Lukishova, A. W. Schmid, A. J. McNamara, R. W. Boyd, and C. R. Stroud, “Room temperature single-photon source: single-dye molecule fluorescence in liquid crystal host,” IEEE J. Sel. Top. Quantum Electron. 9, 1512–1518 (2003).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Quantum Coherence and Quantum Optics (Cambridge University, 1995).

McNamara, A. J.

S. G. Lukishova, A. W. Schmid, A. J. McNamara, R. W. Boyd, and C. R. Stroud, “Room temperature single-photon source: single-dye molecule fluorescence in liquid crystal host,” IEEE J. Sel. Top. Quantum Electron. 9, 1512–1518 (2003).
[CrossRef]

Mcnell, K. J.

P. D. Drummond, K. J. Mcnell, and D. F. Walls, Optica Acta 28, 211 (1981).
[CrossRef]

Messin, G.

B. Darquié, M. P. A. Jones, J. Dingjan, J. Beugnon, S. Bergamini, Y. Sortais, G. Messin, A. Browaeys, and P. Grangier, “Controlled single-photon emission from a single trapped two-level atom,” Science 309, 454–456 (2005).
[CrossRef]

Milburn, G. J.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef]

Mirrahimi, M.

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[CrossRef]

I. Dotsenko, M. Mirrahimi, M. Brune, S. Haroche, J.-M. Raimond, and P. Rouchon, “Quantum feedback by discrete quantum nondemolition measurements: towards on-demand generation of photon-number states,” Phys. Rev. A 80, 013805 (2009).
[CrossRef]

Montes, F. A.

F. A. Montes and M. Xiao, “Three-level atoms inside a degenerate optical parametric oscillator: steady-state behaviors,” Phys. Rev. A 62, 023818 (2000).
[CrossRef]

O’Sullivan, M. N.

M. N. O’Sullivan, K. W. C. Chan, V. Lakshminarayanan, and R. W. Boyd, “Conditional preparation of states containing a definite number of photons,” Phys. Rev. A 77, 023804 (2008).
[CrossRef]

Parkins, A. S.

Q. A. Turchette, N. Ph. Georgiades, C. J. Hood, H. J. Kimble, and A. S. Parkins, “Squeezed excitation in cavity QED: experiment and theory,” Phys. Rev. A 58, 4056–4077 (1998).
[CrossRef]

Peaudecerf, B.

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[CrossRef]

Ph. Georgiades, N.

Q. A. Turchette, N. Ph. Georgiades, C. J. Hood, H. J. Kimble, and A. S. Parkins, “Squeezed excitation in cavity QED: experiment and theory,” Phys. Rev. A 58, 4056–4077 (1998).
[CrossRef]

Pinard, M.

V. Josse, A. Dantan, L. Vernac, A. Bramati, M. Pinard, and E. Giacobino, “Polarization squeezing with cold atoms,” Phys. Rev. Lett. 91, 103601 (2003).
[CrossRef]

Raimond, J.

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[CrossRef]

Raimond, J.-M.

I. Dotsenko, M. Mirrahimi, M. Brune, S. Haroche, J.-M. Raimond, and P. Rouchon, “Quantum feedback by discrete quantum nondemolition measurements: towards on-demand generation of photon-number states,” Phys. Rev. A 80, 013805 (2009).
[CrossRef]

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Rice, P. R.

P. R. Rice, “Entanglement, teleportation, and single-photon storage with two-level atoms inside an optical parametric oscillator” J. Opt. Soc. Am. B 22, 1561–1565 (2005).
[CrossRef]

C. E. Strimbu, J. Leach, and P. R. Rice, “Conditional homodyne detection at the single-photon level: intensity-field correlations for a two-level atom in an optical parametric oscillator,” Phys. Rev. A 71, 013807 (2005).
[CrossRef]

J. P. Clemens, P. R. Rice, P. K. Rungta, and R. J. Brecha, “Two-level atom in an optical parametric oscillator: Spectra of transmitted and fluorescent fields in the weak-driving-field limit,” Phys. Rev. A 62, 033802 (2000).
[CrossRef]

Rouchon, P.

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[CrossRef]

I. Dotsenko, M. Mirrahimi, M. Brune, S. Haroche, J.-M. Raimond, and P. Rouchon, “Quantum feedback by discrete quantum nondemolition measurements: towards on-demand generation of photon-number states,” Phys. Rev. A 80, 013805 (2009).
[CrossRef]

Rungta, P. K.

J. P. Clemens, P. R. Rice, P. K. Rungta, and R. J. Brecha, “Two-level atom in an optical parametric oscillator: Spectra of transmitted and fluorescent fields in the weak-driving-field limit,” Phys. Rev. A 62, 033802 (2000).
[CrossRef]

Rybarczyk, T.

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[CrossRef]

Sayrin, C.

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[CrossRef]

Schmid, A. W.

S. G. Lukishova, A. W. Schmid, A. J. McNamara, R. W. Boyd, and C. R. Stroud, “Room temperature single-photon source: single-dye molecule fluorescence in liquid crystal host,” IEEE J. Sel. Top. Quantum Electron. 9, 1512–1518 (2003).
[CrossRef]

Silberhorn, C.

D. Achilles, C. Silberhorn, and I. A. Walmsley, “Direct, loss-tolerant characterization of nonclassical photon statistics,” Phys. Rev. Lett. 97, 043602 (2006).
[CrossRef]

Sortais, Y.

B. Darquié, M. P. A. Jones, J. Dingjan, J. Beugnon, S. Bergamini, Y. Sortais, G. Messin, A. Browaeys, and P. Grangier, “Controlled single-photon emission from a single trapped two-level atom,” Science 309, 454–456 (2005).
[CrossRef]

Stamper-Kurn, D. M.

K. R. Brown, K. M. Dani, D. M. Stamper-Kurn, and K. B. Whaley, “Deterministic optical Fock-state generation,” Phys. Rev. A 67, 043818 (2003).
[CrossRef]

Strimbu, C. E.

C. E. Strimbu, J. Leach, and P. R. Rice, “Conditional homodyne detection at the single-photon level: intensity-field correlations for a two-level atom in an optical parametric oscillator,” Phys. Rev. A 71, 013807 (2005).
[CrossRef]

Stroud, C. R.

S. G. Lukishova, A. W. Schmid, A. J. McNamara, R. W. Boyd, and C. R. Stroud, “Room temperature single-photon source: single-dye molecule fluorescence in liquid crystal host,” IEEE J. Sel. Top. Quantum Electron. 9, 1512–1518 (2003).
[CrossRef]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Turchette, Q. A.

Q. A. Turchette, N. Ph. Georgiades, C. J. Hood, H. J. Kimble, and A. S. Parkins, “Squeezed excitation in cavity QED: experiment and theory,” Phys. Rev. A 58, 4056–4077 (1998).
[CrossRef]

Varcoe, B. T. H.

B. T. H. Varcoe, S. Brattke, M. Weidinger, and H. Walther, “Preparing pure photon number states of the radiation field,” Nature 403, 743–746 (2000).
[CrossRef]

Vernac, L.

V. Josse, A. Dantan, L. Vernac, A. Bramati, M. Pinard, and E. Giacobino, “Polarization squeezing with cold atoms,” Phys. Rev. Lett. 91, 103601 (2003).
[CrossRef]

Waks, E.

E. Waks, E. Diamanti, and Y. Yamamoto, “Generation of photon number states,” New J. Phys. 8, 4 (2006).
[CrossRef]

Walls, D. F.

P. D. Drummond, K. J. Mcnell, and D. F. Walls, Optica Acta 28, 211 (1981).
[CrossRef]

Walmsley, I. A.

K. Banaszek, R. Demkowicz-Dobrzański, and I. A. Walmsley, “Quantum states made to measure,” Nat. Photon. 3, 673–676 (2009).
[CrossRef]

D. Achilles, C. Silberhorn, and I. A. Walmsley, “Direct, loss-tolerant characterization of nonclassical photon statistics,” Phys. Rev. Lett. 97, 043602 (2006).
[CrossRef]

Walther, H.

B. T. H. Varcoe, S. Brattke, M. Weidinger, and H. Walther, “Preparing pure photon number states of the radiation field,” Nature 403, 743–746 (2000).
[CrossRef]

Wang, J. M.

J. Zhang, J. M. Wang, and T. C. Zhang, “Entanglement and nonclassicality evolution of the atom in a squeezed vacuum,” Opt. Commun. 277, 353–358 (2007).
[CrossRef]

Weidinger, M.

B. T. H. Varcoe, S. Brattke, M. Weidinger, and H. Walther, “Preparing pure photon number states of the radiation field,” Nature 403, 743–746 (2000).
[CrossRef]

Whaley, K. B.

K. R. Brown, K. M. Dani, D. M. Stamper-Kurn, and K. B. Whaley, “Deterministic optical Fock-state generation,” Phys. Rev. A 67, 043818 (2003).
[CrossRef]

Wolf, E.

L. Mandel and E. Wolf, Quantum Coherence and Quantum Optics (Cambridge University, 1995).

Xiao, M.

F. A. Montes and M. Xiao, “Three-level atoms inside a degenerate optical parametric oscillator: steady-state behaviors,” Phys. Rev. A 62, 023818 (2000).
[CrossRef]

S. Jin and M. Xiao, “Extra intracavity squeezing of a degenerate optical parametric oscillator coupling with N two-level atoms,” Phys. Rev. A 49, 499–505 (1994).
[CrossRef]

M. Xiao and S. Jin, “Bistable behavior in a system of an optical parametric oscillator coupling with N two-level atoms,” Phys. Rev. A 45, 483–488 (1992).
[CrossRef]

Yamamoto, Y.

E. Waks, E. Diamanti, and Y. Yamamoto, “Generation of photon number states,” New J. Phys. 8, 4 (2006).
[CrossRef]

J. Kim, O. Benson, H. Kan, and Y. Yamamoto, “A single-photon turnstile device,” Nature 397, 500–503 (1999).
[CrossRef]

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Zhang, J.

J. Zhang, J. M. Wang, and T. C. Zhang, “Entanglement and nonclassicality evolution of the atom in a squeezed vacuum,” Opt. Commun. 277, 353–358 (2007).
[CrossRef]

Zhang, T. C.

J. Zhang, J. M. Wang, and T. C. Zhang, “Entanglement and nonclassicality evolution of the atom in a squeezed vacuum,” Opt. Commun. 277, 353–358 (2007).
[CrossRef]

Zhou, X.

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

S. G. Lukishova, A. W. Schmid, A. J. McNamara, R. W. Boyd, and C. R. Stroud, “Room temperature single-photon source: single-dye molecule fluorescence in liquid crystal host,” IEEE J. Sel. Top. Quantum Electron. 9, 1512–1518 (2003).
[CrossRef]

J. Mod. Opt. (1)

E. Alebachew, “A coherently driven two-level atom inside a parametric oscillator,” J. Mod. Opt. 55, 1159–1173 (2008).
[CrossRef]

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

Nat. Photon. (1)

K. Banaszek, R. Demkowicz-Dobrzański, and I. A. Walmsley, “Quantum states made to measure,” Nat. Photon. 3, 673–676 (2009).
[CrossRef]

Nature (4)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef]

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[CrossRef]

J. Kim, O. Benson, H. Kan, and Y. Yamamoto, “A single-photon turnstile device,” Nature 397, 500–503 (1999).
[CrossRef]

B. T. H. Varcoe, S. Brattke, M. Weidinger, and H. Walther, “Preparing pure photon number states of the radiation field,” Nature 403, 743–746 (2000).
[CrossRef]

New J. Phys. (1)

E. Waks, E. Diamanti, and Y. Yamamoto, “Generation of photon number states,” New J. Phys. 8, 4 (2006).
[CrossRef]

Opt. Commun. (1)

J. Zhang, J. M. Wang, and T. C. Zhang, “Entanglement and nonclassicality evolution of the atom in a squeezed vacuum,” Opt. Commun. 277, 353–358 (2007).
[CrossRef]

Optica Acta (1)

P. D. Drummond, K. J. Mcnell, and D. F. Walls, Optica Acta 28, 211 (1981).
[CrossRef]

Phys. Rev. A (10)

Q. A. Turchette, N. Ph. Georgiades, C. J. Hood, H. J. Kimble, and A. S. Parkins, “Squeezed excitation in cavity QED: experiment and theory,” Phys. Rev. A 58, 4056–4077 (1998).
[CrossRef]

H. J. Carmichael, “Quantum fluctuations in absorptive bistability without adiabatic elimination,” Phys. Rev. A 33, 3262–3269 (1986).
[CrossRef]

I. Dotsenko, M. Mirrahimi, M. Brune, S. Haroche, J.-M. Raimond, and P. Rouchon, “Quantum feedback by discrete quantum nondemolition measurements: towards on-demand generation of photon-number states,” Phys. Rev. A 80, 013805 (2009).
[CrossRef]

M. Xiao and S. Jin, “Bistable behavior in a system of an optical parametric oscillator coupling with N two-level atoms,” Phys. Rev. A 45, 483–488 (1992).
[CrossRef]

S. Jin and M. Xiao, “Extra intracavity squeezing of a degenerate optical parametric oscillator coupling with N two-level atoms,” Phys. Rev. A 49, 499–505 (1994).
[CrossRef]

F. A. Montes and M. Xiao, “Three-level atoms inside a degenerate optical parametric oscillator: steady-state behaviors,” Phys. Rev. A 62, 023818 (2000).
[CrossRef]

J. P. Clemens, P. R. Rice, P. K. Rungta, and R. J. Brecha, “Two-level atom in an optical parametric oscillator: Spectra of transmitted and fluorescent fields in the weak-driving-field limit,” Phys. Rev. A 62, 033802 (2000).
[CrossRef]

C. E. Strimbu, J. Leach, and P. R. Rice, “Conditional homodyne detection at the single-photon level: intensity-field correlations for a two-level atom in an optical parametric oscillator,” Phys. Rev. A 71, 013807 (2005).
[CrossRef]

K. R. Brown, K. M. Dani, D. M. Stamper-Kurn, and K. B. Whaley, “Deterministic optical Fock-state generation,” Phys. Rev. A 67, 043818 (2003).
[CrossRef]

M. N. O’Sullivan, K. W. C. Chan, V. Lakshminarayanan, and R. W. Boyd, “Conditional preparation of states containing a definite number of photons,” Phys. Rev. A 77, 023804 (2008).
[CrossRef]

Phys. Rev. Lett. (4)

J. M. Geremia, “Deterministic and nondestructively verifiable preparation of photon-number states,” Phys. Rev. Lett. 97, 073601 (2006).
[CrossRef]

M. Holland and K. Burnett, “Triggered single photons from a quantum dot,” Phys. Rev. Lett. 86, 1502–1505 (2001).
[CrossRef]

D. Achilles, C. Silberhorn, and I. A. Walmsley, “Direct, loss-tolerant characterization of nonclassical photon statistics,” Phys. Rev. Lett. 97, 043602 (2006).
[CrossRef]

V. Josse, A. Dantan, L. Vernac, A. Bramati, M. Pinard, and E. Giacobino, “Polarization squeezing with cold atoms,” Phys. Rev. Lett. 91, 103601 (2003).
[CrossRef]

Rev. Mod. Phys. (2)

C. M. Caves and P. D. Drummond, “Quantum limits on bosonic communication rates,” Rev. Mod. Phys. 66, 481–537 (1994).
[CrossRef]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Science (1)

B. Darquié, M. P. A. Jones, J. Dingjan, J. Beugnon, S. Bergamini, Y. Sortais, G. Messin, A. Browaeys, and P. Grangier, “Controlled single-photon emission from a single trapped two-level atom,” Science 309, 454–456 (2005).
[CrossRef]

Other (3)

C. W. Gardinar, Handbook of Stochastic Methods (Springer, 1982).

L. Mandel and E. Wolf, Quantum Coherence and Quantum Optics (Cambridge University, 1995).

W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley, 1973).

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Figures (4)

Fig. 1.
Fig. 1.

A schematic of the physical system under consideration.

Fig. 2.
Fig. 2.

Typical bistable curve of the intracavity intensity X versus pumping intensity Y; (a) normal optical absorptive bistability with C=5, (b) atoms in DOPO with Δ=0, C=5, and r=0.5. The turning points have been pointed out.

Fig. 3.
Fig. 3.

The second order degree of coherence for zero delay time g(2)(0) and Mandel Q versus intracavity intensity with different cavity-decay rates (N=10000). (a) and (c) are for OAB, C=5; (b) and (d) are for atoms in DOPO, C=5 and r=0.5.

Fig. 4.
Fig. 4.

The second order degree of coherence g(2)(0) and Mandel Q versus intracavity intensity with different atomic-cooperative parameter C (N=10000). (a) and (c) are for OAB, μ=1; (b) and (d) are for atoms in DOPO, μ=1 and r=0.5.

Equations (19)

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

H^=i=14H^i,H^1=ωca^+a^+12ωaμσ^μz+ω2a^2+a^2,H^2=iμg(a^+σ^μeiϕa^σ^μ+eiϕ)+iκ2(a^+2a^2a^2a^2+),H^3=i(ε2a^2+eiωptε2a^2eiωpt),H^4=μσ^μz(Γ^aσ^μ++Γ^a+σ^μ)+a^2B^2++a^2+B^2+a^B^1++a^+B^1,
(a^,a^+,a^2,a^2+,J^,J^+,J^z)(α,α+,α2,α2+,J,J+,Jz),
J^zμσ^μz,J^±=μe±iϕσ^μ±,
dαdt=γ1α+gJ+κα+α2+Γα(t),dα+dt=γ1α++gJ++καα2++Γα+(t),dα2dt=γ2α2κ2α2+ε2,dα2+dt=γ2α2+κ2α+2+ε2*,dJdt=(γ+iΔa)J+gαJz+Γ(t),dJdt=(γ+iΔa)J++gα+Jz+Γ+(t),dJzdt=2γ(N+Jz)2g(α+J+αJ+)+Γz(t),
Γα(t)Γα(t)=κα2δ(tt),Γα+(t)Γα+(t)=κα2+δ(tt),Γ(t)Γ(t)=2gαJδ(tt),Γ+(t)Γ+(t)=2gα+J+δ(tt),Γz(t)Γz(t)=[4γ(N+Jz)4g(α+J+αJ+)]δ(tt),
ΔΔaγ,CNg22γγ1,Nsγγ4g2,n02γ1γ2κ2,|ε0|γ1γ2κ,
x=αNs,y=ε2ε0.
τ=γt,J=N2υ,J+=N2υ*,Jz=N2m,
dxdτ=μx+μ(yrx¯*·x¯)x*+2μCυ,dx*dτ=μx*+μ(yrx¯*·x¯)x+2μCυ*,dυdτ=(1+iΔ)υ+12xm,dυ*dτ=(1+iΔ)υ*+12x*m,dmdτ=2m42(x*υ+xυ*).
υ¯=(1iΔ)x¯1+Δ2+x¯·x¯*,υ¯*=(1+iΔ)x¯*1+Δ2+x¯·x¯*,m¯=2(1+Δ2)1+Δ2+x¯·x¯*,y=x¯x¯*[1+2C(1iΔ)1+Δ2+x¯·x¯*]+rx¯·x¯*.
[1+2C1+Δ2+X+rX]2+[2CΔ1+Δ2+X]2=Y,X=0.
|ε¯c|=|ε0|{[1+2C1+Δ2]2+[2CΔ1+Δ2]2}1/2.
du^dτ=A̲u^+D̲1/2η^(τ),
u=(x,x*,υ,υ*,m)T,u¯=(x¯,x¯,x¯1+x¯2,x¯1+x¯2,21+x¯2)T,ξ=(Δx,Δx*,Δυ,Δυ*,Δm)T,
A̲=(μμ(1+2C1+x¯22rx¯2)2μC00μ(1+2C1+x¯22rx¯2)μ02μC011+x¯2010x¯/2011+x¯201x¯/22x¯1+x¯22x¯1+x¯22x¯2x¯2),
D̲=N1diag(4μ2C(1+2C1+x¯22rx¯2),4μ2C(1+2C1+x¯22rx¯2),2x¯21+x¯2,-2x¯21+x¯2,32x¯21+x¯2).
A̲G̲+G̲A̲T=D̲.
g(2)(0)=a+2a2a+a2=(a¯++Δa+)2(a¯+Δa)2(a¯++Δa+)(a¯+Δa)2=1+a¯+2Δa2+a¯2Δa+2+2a¯+a¯Δa+Δa+Δa+2Δa2Δa+Δa2(a¯+a¯+Δa+Δa)2,Q=N4μC(g(2)(0)1).
g(2)(0)1+2(ΔxΔx+Δx*Δx)x¯2,QN4μC2(ΔxΔx+Δx*Δx)x¯2.

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