Abstract

It is shown that a two-level atom in a coherently driven optical cavity exhibits optical phase bistability in the case with strong Rabi frequencies and cavity mode damping that is fast compared with atomic damping by spontaneous emission into noncavity modes.

© 1991 Optical Society of America

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  1. V. Weisskopf, Ann. Phys. (NY.) 9, 23 (1931).
    [Crossref]
  2. S. G. Rautian and J. J. Sobelman, Soy. Phys. JETP. 41, 456 (1961); Soy. Phys. JETP. 44, 834 (1963).
  3. P. A. Apanasevich, Opt. Spectrosc. (USSR) 14, 612 (1963); Opt. Spectrosc. (USSR) 16, 709 (1964).
  4. B. R. Mollow, Phys. Rev. 188, 1969 (1969).
    [Crossref]
  5. F. Schuda, C. R. Stroud, and M. Hercher, J. Phys. B 7, L198 (1974).
    [Crossref]
  6. F. Y. Wu, R. E. Grove, and S. Ezekiel, Phys. Rev. Lett. 35, 1426 (1976).
    [Crossref]
  7. W. Harting, W. Rasmussen, R. Schieder, and H. Walther, Z. Phys. A 278, 205 (1976).
    [Crossref]
  8. H. J. Carmichael and D. F. Walls, J. Phys. B 9, 1199 (1976).
    [Crossref]
  9. H. J. Kimble, M. Dagenais, and L. Mandel, Phys. Rev. Lett. 39, 691 (1977); Phys. Rev. A 18, 201 (1978).
    [Crossref]
  10. R. Short and L. Mandel, Phys. Rev. Lett. 51, 384 (1983).
    [Crossref]
  11. D. F. Walls and P. Zoller, Phys. Rev. Lett. 47, 709 (1981).
    [Crossref]
  12. P. A. Apanasevich and S. Ya. Kilin, Phys. Lett. 62A, 83 (1977).
  13. P. Goy, J. M. Raimond, M. Gross, and S. Haroche, Phys. Rev. Lett. 50, 1903 (1983).
    [Crossref]
  14. W. Jhe, A. Anderson, E. A. Hinds, D. Meschede, L. Moi, and S. Haroche, Phys. Rev. Lett. 58, 666 (1987).
    [Crossref] [PubMed]
  15. D. P. O’Brien, P. Meystre, and H. Walther, Adv. At. Mol. 21, 1 (1985).
    [Crossref]
  16. R. G. Hulet, E. S. Hilfer, and D. Kleppner, Phys. Rev. Lett. 55, 2137 (1985).
    [Crossref] [PubMed]
  17. M. Lewenstein, T. W. Mossberg, and R. J. Glauber, Phys. Rev. Lett. 59, 775 (1987).
    [Crossref] [PubMed]
  18. Y. Zhu, A. Lezama, T. W. Mossberg, and M. Lewenstein, Phys. Rev. Lett. 61, 1946 (1988).
    [Crossref] [PubMed]
  19. J. J. Sanchez-Mondragon, N. B. Narozhny, and J. H. Eberly, Phys. Rev. Lett. 51, 550 (1983).
    [Crossref]
  20. G. S. Agarwal, Phys. Rev. Lett. 53, 1732 (1984).
    [Crossref]
  21. M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, and H. J. Carmichael, Phys. Rev. Lett. 63, 240 (1989).
    [Crossref] [PubMed]
  22. C. M. Savage, Phys. Rev. Lett. 60, 1829 (1988).
    [Crossref]
  23. P. R. Rice and H. J. Carmichael, IEEE J. Quantum Electron. 24, 1351 (1988).
    [Crossref]
  24. S. M. Barnett and P. L. Knight, Phys. Rev. A 33, 2444 (1986).
    [Crossref] [PubMed]
  25. C. M. Savage and H. J. Carmichael, IEEE J. Quantum Electron. 24, 1495 (1988).
    [Crossref]
  26. L. A. Lugiato, in Theory of Optical Bistability, Vol. 21 of Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1984), pp. 69–216.
  27. S. Ya. Kilin, J. Phys. B 13, 2653 (1980).
    [Crossref]
  28. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1964).
  29. P. Alsing and H. J. Carmichael, Department of Physics, University of Oregon, Eugene, Ore. 97403 (personal communication, October1990).
  30. P. A. Apanasevich and S. Ya. Kilin, J. Appl. Spectrosc. 29, 931 (1979).
    [Crossref]
  31. W. Nagourney, J. Sandberg, and H. Dehmelt, Phys. Rev. Lett. 56, 2727 (1986).
    [Crossref]
  32. T. Sauter, W. Newhauser, R. Blatt, and P. E. Toschek, Phys. Rev. Lett. 57, 1696 (1986).
    [Crossref] [PubMed]
  33. J. C. Bergquist, R. C. Hulet, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 57, 1699 (1986).
    [Crossref] [PubMed]
  34. S. Ya. Kilin, Quantum Optics: Fields and Their Detection, (Nauka, Minsk, 1990).
  35. R. A. Howard, IEEE Trans. Mil. Electron. MIL-8, 114 (1964).
    [Crossref]

1989 (1)

M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, and H. J. Carmichael, Phys. Rev. Lett. 63, 240 (1989).
[Crossref] [PubMed]

1988 (4)

C. M. Savage, Phys. Rev. Lett. 60, 1829 (1988).
[Crossref]

P. R. Rice and H. J. Carmichael, IEEE J. Quantum Electron. 24, 1351 (1988).
[Crossref]

C. M. Savage and H. J. Carmichael, IEEE J. Quantum Electron. 24, 1495 (1988).
[Crossref]

Y. Zhu, A. Lezama, T. W. Mossberg, and M. Lewenstein, Phys. Rev. Lett. 61, 1946 (1988).
[Crossref] [PubMed]

1987 (2)

M. Lewenstein, T. W. Mossberg, and R. J. Glauber, Phys. Rev. Lett. 59, 775 (1987).
[Crossref] [PubMed]

W. Jhe, A. Anderson, E. A. Hinds, D. Meschede, L. Moi, and S. Haroche, Phys. Rev. Lett. 58, 666 (1987).
[Crossref] [PubMed]

1986 (4)

S. M. Barnett and P. L. Knight, Phys. Rev. A 33, 2444 (1986).
[Crossref] [PubMed]

W. Nagourney, J. Sandberg, and H. Dehmelt, Phys. Rev. Lett. 56, 2727 (1986).
[Crossref]

T. Sauter, W. Newhauser, R. Blatt, and P. E. Toschek, Phys. Rev. Lett. 57, 1696 (1986).
[Crossref] [PubMed]

J. C. Bergquist, R. C. Hulet, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 57, 1699 (1986).
[Crossref] [PubMed]

1985 (2)

D. P. O’Brien, P. Meystre, and H. Walther, Adv. At. Mol. 21, 1 (1985).
[Crossref]

R. G. Hulet, E. S. Hilfer, and D. Kleppner, Phys. Rev. Lett. 55, 2137 (1985).
[Crossref] [PubMed]

1984 (1)

G. S. Agarwal, Phys. Rev. Lett. 53, 1732 (1984).
[Crossref]

1983 (3)

R. Short and L. Mandel, Phys. Rev. Lett. 51, 384 (1983).
[Crossref]

P. Goy, J. M. Raimond, M. Gross, and S. Haroche, Phys. Rev. Lett. 50, 1903 (1983).
[Crossref]

J. J. Sanchez-Mondragon, N. B. Narozhny, and J. H. Eberly, Phys. Rev. Lett. 51, 550 (1983).
[Crossref]

1981 (1)

D. F. Walls and P. Zoller, Phys. Rev. Lett. 47, 709 (1981).
[Crossref]

1980 (1)

S. Ya. Kilin, J. Phys. B 13, 2653 (1980).
[Crossref]

1979 (1)

P. A. Apanasevich and S. Ya. Kilin, J. Appl. Spectrosc. 29, 931 (1979).
[Crossref]

1977 (2)

P. A. Apanasevich and S. Ya. Kilin, Phys. Lett. 62A, 83 (1977).

H. J. Kimble, M. Dagenais, and L. Mandel, Phys. Rev. Lett. 39, 691 (1977); Phys. Rev. A 18, 201 (1978).
[Crossref]

1976 (3)

F. Y. Wu, R. E. Grove, and S. Ezekiel, Phys. Rev. Lett. 35, 1426 (1976).
[Crossref]

W. Harting, W. Rasmussen, R. Schieder, and H. Walther, Z. Phys. A 278, 205 (1976).
[Crossref]

H. J. Carmichael and D. F. Walls, J. Phys. B 9, 1199 (1976).
[Crossref]

1974 (1)

F. Schuda, C. R. Stroud, and M. Hercher, J. Phys. B 7, L198 (1974).
[Crossref]

1969 (1)

B. R. Mollow, Phys. Rev. 188, 1969 (1969).
[Crossref]

1964 (1)

R. A. Howard, IEEE Trans. Mil. Electron. MIL-8, 114 (1964).
[Crossref]

1963 (1)

P. A. Apanasevich, Opt. Spectrosc. (USSR) 14, 612 (1963); Opt. Spectrosc. (USSR) 16, 709 (1964).

1961 (1)

S. G. Rautian and J. J. Sobelman, Soy. Phys. JETP. 41, 456 (1961); Soy. Phys. JETP. 44, 834 (1963).

1931 (1)

V. Weisskopf, Ann. Phys. (NY.) 9, 23 (1931).
[Crossref]

Agarwal, G. S.

G. S. Agarwal, Phys. Rev. Lett. 53, 1732 (1984).
[Crossref]

Alsing, P.

P. Alsing and H. J. Carmichael, Department of Physics, University of Oregon, Eugene, Ore. 97403 (personal communication, October1990).

Anderson, A.

W. Jhe, A. Anderson, E. A. Hinds, D. Meschede, L. Moi, and S. Haroche, Phys. Rev. Lett. 58, 666 (1987).
[Crossref] [PubMed]

Apanasevich, P. A.

P. A. Apanasevich and S. Ya. Kilin, J. Appl. Spectrosc. 29, 931 (1979).
[Crossref]

P. A. Apanasevich and S. Ya. Kilin, Phys. Lett. 62A, 83 (1977).

P. A. Apanasevich, Opt. Spectrosc. (USSR) 14, 612 (1963); Opt. Spectrosc. (USSR) 16, 709 (1964).

Barnett, S. M.

S. M. Barnett and P. L. Knight, Phys. Rev. A 33, 2444 (1986).
[Crossref] [PubMed]

Bergquist, J. C.

J. C. Bergquist, R. C. Hulet, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 57, 1699 (1986).
[Crossref] [PubMed]

Blatt, R.

T. Sauter, W. Newhauser, R. Blatt, and P. E. Toschek, Phys. Rev. Lett. 57, 1696 (1986).
[Crossref] [PubMed]

Brecha, R. J.

M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, and H. J. Carmichael, Phys. Rev. Lett. 63, 240 (1989).
[Crossref] [PubMed]

Carmichael, H. J.

M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, and H. J. Carmichael, Phys. Rev. Lett. 63, 240 (1989).
[Crossref] [PubMed]

P. R. Rice and H. J. Carmichael, IEEE J. Quantum Electron. 24, 1351 (1988).
[Crossref]

C. M. Savage and H. J. Carmichael, IEEE J. Quantum Electron. 24, 1495 (1988).
[Crossref]

H. J. Carmichael and D. F. Walls, J. Phys. B 9, 1199 (1976).
[Crossref]

P. Alsing and H. J. Carmichael, Department of Physics, University of Oregon, Eugene, Ore. 97403 (personal communication, October1990).

Dagenais, M.

H. J. Kimble, M. Dagenais, and L. Mandel, Phys. Rev. Lett. 39, 691 (1977); Phys. Rev. A 18, 201 (1978).
[Crossref]

Dehmelt, H.

W. Nagourney, J. Sandberg, and H. Dehmelt, Phys. Rev. Lett. 56, 2727 (1986).
[Crossref]

Eberly, J. H.

J. J. Sanchez-Mondragon, N. B. Narozhny, and J. H. Eberly, Phys. Rev. Lett. 51, 550 (1983).
[Crossref]

Ezekiel, S.

F. Y. Wu, R. E. Grove, and S. Ezekiel, Phys. Rev. Lett. 35, 1426 (1976).
[Crossref]

Glauber, R. J.

M. Lewenstein, T. W. Mossberg, and R. J. Glauber, Phys. Rev. Lett. 59, 775 (1987).
[Crossref] [PubMed]

Goy, P.

P. Goy, J. M. Raimond, M. Gross, and S. Haroche, Phys. Rev. Lett. 50, 1903 (1983).
[Crossref]

Gross, M.

P. Goy, J. M. Raimond, M. Gross, and S. Haroche, Phys. Rev. Lett. 50, 1903 (1983).
[Crossref]

Grove, R. E.

F. Y. Wu, R. E. Grove, and S. Ezekiel, Phys. Rev. Lett. 35, 1426 (1976).
[Crossref]

Haroche, S.

W. Jhe, A. Anderson, E. A. Hinds, D. Meschede, L. Moi, and S. Haroche, Phys. Rev. Lett. 58, 666 (1987).
[Crossref] [PubMed]

P. Goy, J. M. Raimond, M. Gross, and S. Haroche, Phys. Rev. Lett. 50, 1903 (1983).
[Crossref]

Harting, W.

W. Harting, W. Rasmussen, R. Schieder, and H. Walther, Z. Phys. A 278, 205 (1976).
[Crossref]

Hercher, M.

F. Schuda, C. R. Stroud, and M. Hercher, J. Phys. B 7, L198 (1974).
[Crossref]

Hilfer, E. S.

R. G. Hulet, E. S. Hilfer, and D. Kleppner, Phys. Rev. Lett. 55, 2137 (1985).
[Crossref] [PubMed]

Hinds, E. A.

W. Jhe, A. Anderson, E. A. Hinds, D. Meschede, L. Moi, and S. Haroche, Phys. Rev. Lett. 58, 666 (1987).
[Crossref] [PubMed]

Howard, R. A.

R. A. Howard, IEEE Trans. Mil. Electron. MIL-8, 114 (1964).
[Crossref]

Hulet, R. C.

J. C. Bergquist, R. C. Hulet, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 57, 1699 (1986).
[Crossref] [PubMed]

Hulet, R. G.

R. G. Hulet, E. S. Hilfer, and D. Kleppner, Phys. Rev. Lett. 55, 2137 (1985).
[Crossref] [PubMed]

Itano, W. M.

J. C. Bergquist, R. C. Hulet, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 57, 1699 (1986).
[Crossref] [PubMed]

Jhe, W.

W. Jhe, A. Anderson, E. A. Hinds, D. Meschede, L. Moi, and S. Haroche, Phys. Rev. Lett. 58, 666 (1987).
[Crossref] [PubMed]

Kilin, S. Ya.

S. Ya. Kilin, J. Phys. B 13, 2653 (1980).
[Crossref]

P. A. Apanasevich and S. Ya. Kilin, J. Appl. Spectrosc. 29, 931 (1979).
[Crossref]

P. A. Apanasevich and S. Ya. Kilin, Phys. Lett. 62A, 83 (1977).

S. Ya. Kilin, Quantum Optics: Fields and Their Detection, (Nauka, Minsk, 1990).

Kimble, H. J.

M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, and H. J. Carmichael, Phys. Rev. Lett. 63, 240 (1989).
[Crossref] [PubMed]

H. J. Kimble, M. Dagenais, and L. Mandel, Phys. Rev. Lett. 39, 691 (1977); Phys. Rev. A 18, 201 (1978).
[Crossref]

Kleppner, D.

R. G. Hulet, E. S. Hilfer, and D. Kleppner, Phys. Rev. Lett. 55, 2137 (1985).
[Crossref] [PubMed]

Knight, P. L.

S. M. Barnett and P. L. Knight, Phys. Rev. A 33, 2444 (1986).
[Crossref] [PubMed]

Lewenstein, M.

Y. Zhu, A. Lezama, T. W. Mossberg, and M. Lewenstein, Phys. Rev. Lett. 61, 1946 (1988).
[Crossref] [PubMed]

M. Lewenstein, T. W. Mossberg, and R. J. Glauber, Phys. Rev. Lett. 59, 775 (1987).
[Crossref] [PubMed]

Lezama, A.

Y. Zhu, A. Lezama, T. W. Mossberg, and M. Lewenstein, Phys. Rev. Lett. 61, 1946 (1988).
[Crossref] [PubMed]

Lugiato, L. A.

L. A. Lugiato, in Theory of Optical Bistability, Vol. 21 of Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1984), pp. 69–216.

Mandel, L.

R. Short and L. Mandel, Phys. Rev. Lett. 51, 384 (1983).
[Crossref]

H. J. Kimble, M. Dagenais, and L. Mandel, Phys. Rev. Lett. 39, 691 (1977); Phys. Rev. A 18, 201 (1978).
[Crossref]

Meschede, D.

W. Jhe, A. Anderson, E. A. Hinds, D. Meschede, L. Moi, and S. Haroche, Phys. Rev. Lett. 58, 666 (1987).
[Crossref] [PubMed]

Meystre, P.

D. P. O’Brien, P. Meystre, and H. Walther, Adv. At. Mol. 21, 1 (1985).
[Crossref]

Moi, L.

W. Jhe, A. Anderson, E. A. Hinds, D. Meschede, L. Moi, and S. Haroche, Phys. Rev. Lett. 58, 666 (1987).
[Crossref] [PubMed]

Mollow, B. R.

B. R. Mollow, Phys. Rev. 188, 1969 (1969).
[Crossref]

Mossberg, T. W.

Y. Zhu, A. Lezama, T. W. Mossberg, and M. Lewenstein, Phys. Rev. Lett. 61, 1946 (1988).
[Crossref] [PubMed]

M. Lewenstein, T. W. Mossberg, and R. J. Glauber, Phys. Rev. Lett. 59, 775 (1987).
[Crossref] [PubMed]

Nagourney, W.

W. Nagourney, J. Sandberg, and H. Dehmelt, Phys. Rev. Lett. 56, 2727 (1986).
[Crossref]

Narozhny, N. B.

J. J. Sanchez-Mondragon, N. B. Narozhny, and J. H. Eberly, Phys. Rev. Lett. 51, 550 (1983).
[Crossref]

Newhauser, W.

T. Sauter, W. Newhauser, R. Blatt, and P. E. Toschek, Phys. Rev. Lett. 57, 1696 (1986).
[Crossref] [PubMed]

O’Brien, D. P.

D. P. O’Brien, P. Meystre, and H. Walther, Adv. At. Mol. 21, 1 (1985).
[Crossref]

Raimond, J. M.

P. Goy, J. M. Raimond, M. Gross, and S. Haroche, Phys. Rev. Lett. 50, 1903 (1983).
[Crossref]

Raizen, M. G.

M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, and H. J. Carmichael, Phys. Rev. Lett. 63, 240 (1989).
[Crossref] [PubMed]

Rasmussen, W.

W. Harting, W. Rasmussen, R. Schieder, and H. Walther, Z. Phys. A 278, 205 (1976).
[Crossref]

Rautian, S. G.

S. G. Rautian and J. J. Sobelman, Soy. Phys. JETP. 41, 456 (1961); Soy. Phys. JETP. 44, 834 (1963).

Rice, P. R.

P. R. Rice and H. J. Carmichael, IEEE J. Quantum Electron. 24, 1351 (1988).
[Crossref]

Sanchez-Mondragon, J. J.

J. J. Sanchez-Mondragon, N. B. Narozhny, and J. H. Eberly, Phys. Rev. Lett. 51, 550 (1983).
[Crossref]

Sandberg, J.

W. Nagourney, J. Sandberg, and H. Dehmelt, Phys. Rev. Lett. 56, 2727 (1986).
[Crossref]

Sauter, T.

T. Sauter, W. Newhauser, R. Blatt, and P. E. Toschek, Phys. Rev. Lett. 57, 1696 (1986).
[Crossref] [PubMed]

Savage, C. M.

C. M. Savage and H. J. Carmichael, IEEE J. Quantum Electron. 24, 1495 (1988).
[Crossref]

C. M. Savage, Phys. Rev. Lett. 60, 1829 (1988).
[Crossref]

Schieder, R.

W. Harting, W. Rasmussen, R. Schieder, and H. Walther, Z. Phys. A 278, 205 (1976).
[Crossref]

Schuda, F.

F. Schuda, C. R. Stroud, and M. Hercher, J. Phys. B 7, L198 (1974).
[Crossref]

Short, R.

R. Short and L. Mandel, Phys. Rev. Lett. 51, 384 (1983).
[Crossref]

Sobelman, J. J.

S. G. Rautian and J. J. Sobelman, Soy. Phys. JETP. 41, 456 (1961); Soy. Phys. JETP. 44, 834 (1963).

Stroud, C. R.

F. Schuda, C. R. Stroud, and M. Hercher, J. Phys. B 7, L198 (1974).
[Crossref]

Thompson, R. J.

M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, and H. J. Carmichael, Phys. Rev. Lett. 63, 240 (1989).
[Crossref] [PubMed]

Toschek, P. E.

T. Sauter, W. Newhauser, R. Blatt, and P. E. Toschek, Phys. Rev. Lett. 57, 1696 (1986).
[Crossref] [PubMed]

Walls, D. F.

D. F. Walls and P. Zoller, Phys. Rev. Lett. 47, 709 (1981).
[Crossref]

H. J. Carmichael and D. F. Walls, J. Phys. B 9, 1199 (1976).
[Crossref]

Walther, H.

D. P. O’Brien, P. Meystre, and H. Walther, Adv. At. Mol. 21, 1 (1985).
[Crossref]

W. Harting, W. Rasmussen, R. Schieder, and H. Walther, Z. Phys. A 278, 205 (1976).
[Crossref]

Weisskopf, V.

V. Weisskopf, Ann. Phys. (NY.) 9, 23 (1931).
[Crossref]

Wineland, D. J.

J. C. Bergquist, R. C. Hulet, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 57, 1699 (1986).
[Crossref] [PubMed]

Wu, F. Y.

F. Y. Wu, R. E. Grove, and S. Ezekiel, Phys. Rev. Lett. 35, 1426 (1976).
[Crossref]

Zhu, Y.

Y. Zhu, A. Lezama, T. W. Mossberg, and M. Lewenstein, Phys. Rev. Lett. 61, 1946 (1988).
[Crossref] [PubMed]

Zoller, P.

D. F. Walls and P. Zoller, Phys. Rev. Lett. 47, 709 (1981).
[Crossref]

Adv. At. Mol. (1)

D. P. O’Brien, P. Meystre, and H. Walther, Adv. At. Mol. 21, 1 (1985).
[Crossref]

Ann. Phys. (NY.) (1)

V. Weisskopf, Ann. Phys. (NY.) 9, 23 (1931).
[Crossref]

IEEE J. Quantum Electron. (2)

P. R. Rice and H. J. Carmichael, IEEE J. Quantum Electron. 24, 1351 (1988).
[Crossref]

C. M. Savage and H. J. Carmichael, IEEE J. Quantum Electron. 24, 1495 (1988).
[Crossref]

IEEE Trans. Mil. Electron. (1)

R. A. Howard, IEEE Trans. Mil. Electron. MIL-8, 114 (1964).
[Crossref]

J. Appl. Spectrosc. (1)

P. A. Apanasevich and S. Ya. Kilin, J. Appl. Spectrosc. 29, 931 (1979).
[Crossref]

J. Phys. B (3)

S. Ya. Kilin, J. Phys. B 13, 2653 (1980).
[Crossref]

F. Schuda, C. R. Stroud, and M. Hercher, J. Phys. B 7, L198 (1974).
[Crossref]

H. J. Carmichael and D. F. Walls, J. Phys. B 9, 1199 (1976).
[Crossref]

Opt. Spectrosc. (USSR) (1)

P. A. Apanasevich, Opt. Spectrosc. (USSR) 14, 612 (1963); Opt. Spectrosc. (USSR) 16, 709 (1964).

Phys. Lett. (1)

P. A. Apanasevich and S. Ya. Kilin, Phys. Lett. 62A, 83 (1977).

Phys. Rev. (1)

B. R. Mollow, Phys. Rev. 188, 1969 (1969).
[Crossref]

Phys. Rev. A (1)

S. M. Barnett and P. L. Knight, Phys. Rev. A 33, 2444 (1986).
[Crossref] [PubMed]

Phys. Rev. Lett. (16)

P. Goy, J. M. Raimond, M. Gross, and S. Haroche, Phys. Rev. Lett. 50, 1903 (1983).
[Crossref]

W. Jhe, A. Anderson, E. A. Hinds, D. Meschede, L. Moi, and S. Haroche, Phys. Rev. Lett. 58, 666 (1987).
[Crossref] [PubMed]

F. Y. Wu, R. E. Grove, and S. Ezekiel, Phys. Rev. Lett. 35, 1426 (1976).
[Crossref]

W. Nagourney, J. Sandberg, and H. Dehmelt, Phys. Rev. Lett. 56, 2727 (1986).
[Crossref]

T. Sauter, W. Newhauser, R. Blatt, and P. E. Toschek, Phys. Rev. Lett. 57, 1696 (1986).
[Crossref] [PubMed]

J. C. Bergquist, R. C. Hulet, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 57, 1699 (1986).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Schematic representation of the possible values for the steady-state intracavity coherent amplitude 〈a〉. The value of 〈a〉 can be situated only in the hatched region of the phase plane. The vertical filled arrow indicates the field amplitude of the empty driven resonator E/k, while the open arrow indicates the maximum of the amplitude of the atomic reradiated field g/2k. Points 1 and 2 correspond to the intracavity field amplitude 〈a〉 when the atom is in the dressed states 1 = ( - - + ) / 2 and 2 = ( + + - ) / 2 ( Δ ω = 0 ).

Fig. 2
Fig. 2

Schematic representation of the trajectories of the vector (〈σx〉, 〈σy〉, 〈σz〉) on the Bloch sphere at a large Rabi frequency Ω. This vector rotates with the frequency Ω about the B axis, defined by the polar angle θ = arctan(2νω) and the azimuthal angle ϕ = 0. The steady-state points 1 and 2 correspond to the dressed states of Eqs. (18a) and (18b).

Fig. 3
Fig. 3

distribution of the field resonator mode in the steady state [Eq. (9)] at Δω = 0 and g = k. (a) γ/4k = 2, (b) γ/4k = 1, (c) −γ/4k = 0.5.

Fig. 4
Fig. 4

(a) Phase space for the coherently driven atom inside the cavity in the case of a large Rabi frequency. (b) Stochastic realization of the resonator field mode movement for the representation.

Fig. 5
Fig. 5

Steady-state intracavity field amplitude 〈a〉 versus the steady-state amplitude E/k of the empty driven resonator calculated from the point of view of the semiclassical treatment: (a) in the absence of absorptive optical bistability (g = k and γ/k= 2; thus C = 0.5); (b) with the absorptive optical bistability (g = k and γ/k = 0.1; thus C = 10). The dotted vertical lines correspond to equal values of the two characteristic times Ω−1 and γ−1. The dashed vertical lines indicate the equality of the Rabi frequencies induced by the empty driven resonator field (E/k) and by the atomic reradiated field (g/2k). The region where the optical phase bistability is observable in a pure form is at the right of both the dashed and dotted lines [see inequalities (14a) and (14b)].

Equations (57)

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d ρ / d t = E [ a + - a , ρ ] - i Δ ω [ σ z , ρ ] - i g [ a + σ - + a σ + , ρ ] + ( L a + L f ) ρ , L a ρ = ( γ / 2 ) ( [ σ - , ρ σ + ] + [ σ - ρ , σ + ] , L f ρ = k ( [ a , ρ a + ] + [ a ρ , a + ] ) ,
a ˙ = E - k a - i g σ - ,
σ ˙ - = i Δ ω σ - + 2 i g σ s a - γ σ - / 2 ,
σ ˙ z = - i g ( σ + a - σ - a + - γ ( σ z + 1 / 2 ) .
σ i 1 / 2             ( i = ± , z ) .
E - < E < E + ,
E ± = k a ± ( 1 + 2 C 1 + 8 G 2 σ ± 2 / γ 2 ) , a ± = γ [ C - 1 ± ( C 2 - 4 C ) 1 / 2 ] 1 / 2 / 2 g 2 ,
a low < a - .
a low < γ / 2 g 2 .
a up > ( a + ) .
a up > g / 2 k C .
d ρ ¯ / d t = - 2 i ν [ σ x , ρ ] - i Δ ω [ σ z , ρ ¯ ] - i g [ a + σ - + a σ + , ρ ¯ ] + ( L a + L f ) ρ ¯ ,
ρ ¯ = exp ( - i Ω σ z t ) ρ exp ( i Ω σ z t ) ,
σ + ( t ) = s σ z + ( 1 + c ) σ + exp ( i Ω t ) / 2 - ( 1 - c ) σ - exp ( - i Ω t ) / 2 ,
σ z ( t ) = c σ z - ( s / 2 ) σ + exp ( i Ω t ) - ( s / 2 ) σ - exp ( - i Ω t ) ,
Ω k ,             Ω γ .
Ω g 2 / k ,
d ρ / d t = - i g s [ ( a + + a ) σ z , ρ ] + L f ρ + ( γ s 2 / 2 ) ( [ σ z , ρ σ z ] + [ σ z ρ , σ z ] ) + d 12 ( [ σ + , ρ σ - ] + [ σ + ρ , σ - ] ) + d 21 ( [ σ - , ρ σ + ] + [ σ - ρ , σ + ] ) ,
d ρ 11 d t = i ( g s / 2 ) [ a + + a , ρ 11 ] + L f ρ 11 + d 21 ρ 22 - d 12 ρ 11
d ρ 22 d t = - i ( g s / 2 ) [ a + + a , ρ 22 ] + L f ρ 22 + d 12 ρ 11 - d 21 ρ 22 .
2 σ x 1 , 2 = s ,             σ y 1 , 2 = 0 ,             2 σ z 1 , 2 = c .
1 = exp ( - i θ σ y ) - = cos ( θ / 2 ) - - sin ( θ / 2 ) + ,
2 = exp ( - i θ σ y ) + = cos ( θ / 2 ) + + sin ( θ / 2 ) - ,
1 g ( a σ + + a + σ - ) 1 = - ( g s / 2 ) ( a + a + ) , 2 g ( a σ + + a + σ - ) 2 = + ( g s / 2 ) ( a + a + ) .
F i j ( λ , t ) = Sp [ exp ( λ a + ) exp ( - λ * a ) D ( E / k ) ρ i j D - 1 ( E / k ) ]
P ( α ) = P 0 - 1 δ ( Re α - ɛ R ) Θ ( Im 2 α - ɛ I 2 ) × ( 1 - Im α / ɛ I ) d 21 / k - 1 ( 1 - Im α / ɛ I ) d 12 / k - 1 ,
P ( α ) = P 11 ( α ) + P 22 ( α ) , P i i ( α ) = π - 2 d 2 λ exp ( λ * a - λ a * ) F i i ( λ , t ) ,
E / k - i g σ ¯ - t / k = E / k - i g s σ z / k E / k - i g s / 2 k .
Δ ϕ = 2 arctan ( g s / 2 E ) .
g E = 2 2 C Y = γ 2 ν 12 ( k 0 w ) 2 F π ,
P 11 t = x [ ( k x - E ) P 11 ] + y [ ( k y + g s 2 ) P 11 ] + d 21 P 22 - d 12 P 11 ,
P 22 t = x [ ( k x - E ) P 22 ] + y [ ( k y - g s 2 ) P 22 ] + d 21 P 22 - d 12 P 11 ,
h i 1 i 1 , i 2 i 2 , , i n i n ( α 1 , t 1 ; α 2 , t 2 ; ; α n , t n ) = P i 1 i 1 , i 2 i 2 ( α 1 , t 1 α 2 , t 2 ) P i n - 1 i n - 1 , i n i n ( α n - 2 , t n - 1 α n , t n ) P i n i n ( α n , t n ) .
y + g s 2 k = const . × ( x - E k ) , y - g s 2 k = const . × ( x - E k )
c j j , i i ( t + τ t ) = c j i ( τ ) = d i j exp ( - γ i i τ ) ,
τ i j ( n ) = - ( 1 / γ i i ) ln ( γ i i x n / d i j ) ,
α ( t ) - α 01 = exp [ - k ( t - t n ) ] [ α ( t n ) - α 01 ]
α ( t ) - α 02 = exp [ - k ( t - t n ) ] [ α ( t n ) - α 02 ]
2 ν / γ = 10 ,             k = γ
σ ¯ - = ( 4 i g / γ ) σ ¯ z a ¯ ,
2 σ ¯ z = - ( 1 + 2 2 g a ¯ / γ 2 ) - 1 .
E / k = a ¯ ( 1 + 2 C / ( 1 + 2 2 g a ¯ / γ 2 ) ,
C = g 2 / k γ 1
E + < E < E - ,
E ± = k a ± [ 1 + 2 C / ( 1 + 8 g 2 a ± 2 / γ 2 ) ] ,
p ˙ i = k j d k i p i - k d i k p i .
j N π i j = 1 ,
π i j 0.
p j i ( t 0 ) = δ i j w i ( t 0 ) + k = 1 N π i k 0 t d τ f i k ( τ ) p j k ( t - τ 0 ) ,
w i ( t 0 ) = j = 1 N t π i j f i j ( τ ) d τ = 1 - 0 t j = 1 N π i j f i j ( τ ) d τ .
p i j [ s ] = 0 d τ p i j ( t + τ t ) exp ( - s τ )
P ˜ [ s ] = ( s I + d diag - d ) - 1 ,
P ˜ [ s ] = ( I - C ˜ diag [ s ] ) / s ( I - C ˜ [ s ] ) ,
C ˜ [ s ] = ( s I + d diag ) - 1 d ,
c j i ( τ ) = d i j exp ( - γ i i τ )
π i j = d i j / γ i i ,
f i j ( τ ) = γ i i exp ( - γ i i τ ) ,

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