Abstract

We studied the interaction between the single-mode cavity and an atomic string consisting of equidistant three-level atoms (or pairs of indistinguishable two-level atoms) that is injected at such a low flux that at most one atom at a time is present inside the cavity. We investigated the trapping effect in such systems, and we obtained the trapping conditions for the flying time inside the cavity. We derived the so-called cotangent state for the proposed systems, and we examined the properties of the electromagnetic field for such state.

© 1999 Optical Society of America

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  1. G. Rempe, H. Walther, N. Klein, “Observation of quantum collapse and revival in a one-atom maser,” Phys. Rev. Lett. 58, 353–356 (1987).
    [CrossRef] [PubMed]
  2. M. Brune, J. M. Raimond, P. Goy, L. Davidovich, S. Haroche, “Realization of a two-photon maser oscillator,” Phys. Rev. Lett. 59, 1899–1902 (1987).
    [CrossRef] [PubMed]
  3. J. J. Slosser, P. Meystre, S. Braunstein, “Harmonic oscillator driven by a quantum current,” Phys. Rev. Lett. 63, 934–937 (1989).
    [CrossRef] [PubMed]
  4. R. Short, L. Mandel, “Observation of sub-Poissonian photon statistics,” Phys. Rev. Lett. 51, 384–387 (1983);G. Rempe, F. Schmidt-Kaler, H. Walther, “Observation of sub-Poissonian photon statistics in a micromaser,” Phys. Rev. Lett. 64, 2783–2786 (1990).
    [CrossRef] [PubMed]
  5. M. Orszag, R. Ramirez, J. C. Retamal, L. Roa, “Generation of highly squeezed states in a two-photon micromaser,” Phys. Rev. A 45, 6717–6720 (1992).
    [CrossRef] [PubMed]
  6. R. Bonifacio, G. M. D’Ariano, R. Seno, N. Sterpi, “Chaotic and cooperative regimes for the micromaser,” Phys. Rev. A 47, 2464–2467 (1993).
    [CrossRef]
  7. M. Orszag, R. Ramirez, J. C. Retamal, C. Saavedra, “Quantum cooperative effects in a micromaser,” Phys. Rev. A 49, 2933–2937 (1994).
    [CrossRef] [PubMed]
  8. R. R. Puri, C. K. Law, J. H. Eberly, “Squeezed Raman micromaser model,” Phys. Rev. A 50, 4212–4218 (1994).
    [CrossRef] [PubMed]
  9. E. Wehner, R. Seno, N. Sterpi, B. Englert, H. Walther, “Atom pairs in the micromaser,” Opt. Commun. 110, 655–669 (1994).
    [CrossRef]
  10. U. Eichmann, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, W. M. Itano, D. J. Wineland, M. G. Raizen, “Young’s interference experiment with light scattered from two atoms,” Phys. Rev. Lett. 70, 2359–2362 (1993).
    [CrossRef] [PubMed]
  11. P. Kochan, H. J. Carmichael, P. R. Morrow, M. G. Raizen, “Mutual coherence and interference in resonance fluorescence,” Phys. Rev. Lett. 75, 45–48 (1995).
    [CrossRef] [PubMed]
  12. P. Filipowicz, J. Javanainen, P. Meystre, “Quantum and semiclassical steady states of a kicked cavity mode,” J. Opt. Soc. Am. B 3, 906–910 (1986).
    [CrossRef]
  13. D. Meschede, H. Walther, G. Muller, “One-atom maser,” Phys. Rev. Lett. 54, 551–554 (1985).
    [CrossRef] [PubMed]
  14. P. Filipowicz, J. Javanainen, P. Maystre, “Theory of a microscopic maser,” Phys. Rev. A 34, 3077–3087 (1986).
    [CrossRef] [PubMed]
  15. P. Meystre, G. Rempe, H. Walther, “Very-low-temperature behavior of a micromaser,” Opt. Lett. 13, 1078–1080 (1988).
    [CrossRef] [PubMed]
  16. F. Li, D. L. Lin, “Generation of higher-order squeezing in a micromaser,” J. Phys. B 30, 3719–3729 (1997).
    [CrossRef]
  17. M. Brune, J. M. Raimond, S. Haroche, “Theory of the Rydberg-atom two-photon micromaser,” Phys. Rev. A 35, 154–163 (1987).
    [CrossRef] [PubMed]
  18. N. A. Enaki, M. A. Macovei, “Cooperative emission in the process of cascade and dipole-forbidden transitions,” Phys. Rev. A 56, 3274–3285 (1997).
    [CrossRef]

1997 (2)

F. Li, D. L. Lin, “Generation of higher-order squeezing in a micromaser,” J. Phys. B 30, 3719–3729 (1997).
[CrossRef]

N. A. Enaki, M. A. Macovei, “Cooperative emission in the process of cascade and dipole-forbidden transitions,” Phys. Rev. A 56, 3274–3285 (1997).
[CrossRef]

1995 (1)

P. Kochan, H. J. Carmichael, P. R. Morrow, M. G. Raizen, “Mutual coherence and interference in resonance fluorescence,” Phys. Rev. Lett. 75, 45–48 (1995).
[CrossRef] [PubMed]

1994 (3)

M. Orszag, R. Ramirez, J. C. Retamal, C. Saavedra, “Quantum cooperative effects in a micromaser,” Phys. Rev. A 49, 2933–2937 (1994).
[CrossRef] [PubMed]

R. R. Puri, C. K. Law, J. H. Eberly, “Squeezed Raman micromaser model,” Phys. Rev. A 50, 4212–4218 (1994).
[CrossRef] [PubMed]

E. Wehner, R. Seno, N. Sterpi, B. Englert, H. Walther, “Atom pairs in the micromaser,” Opt. Commun. 110, 655–669 (1994).
[CrossRef]

1993 (2)

U. Eichmann, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, W. M. Itano, D. J. Wineland, M. G. Raizen, “Young’s interference experiment with light scattered from two atoms,” Phys. Rev. Lett. 70, 2359–2362 (1993).
[CrossRef] [PubMed]

R. Bonifacio, G. M. D’Ariano, R. Seno, N. Sterpi, “Chaotic and cooperative regimes for the micromaser,” Phys. Rev. A 47, 2464–2467 (1993).
[CrossRef]

1992 (1)

M. Orszag, R. Ramirez, J. C. Retamal, L. Roa, “Generation of highly squeezed states in a two-photon micromaser,” Phys. Rev. A 45, 6717–6720 (1992).
[CrossRef] [PubMed]

1989 (1)

J. J. Slosser, P. Meystre, S. Braunstein, “Harmonic oscillator driven by a quantum current,” Phys. Rev. Lett. 63, 934–937 (1989).
[CrossRef] [PubMed]

1988 (1)

1987 (3)

G. Rempe, H. Walther, N. Klein, “Observation of quantum collapse and revival in a one-atom maser,” Phys. Rev. Lett. 58, 353–356 (1987).
[CrossRef] [PubMed]

M. Brune, J. M. Raimond, P. Goy, L. Davidovich, S. Haroche, “Realization of a two-photon maser oscillator,” Phys. Rev. Lett. 59, 1899–1902 (1987).
[CrossRef] [PubMed]

M. Brune, J. M. Raimond, S. Haroche, “Theory of the Rydberg-atom two-photon micromaser,” Phys. Rev. A 35, 154–163 (1987).
[CrossRef] [PubMed]

1986 (2)

1985 (1)

D. Meschede, H. Walther, G. Muller, “One-atom maser,” Phys. Rev. Lett. 54, 551–554 (1985).
[CrossRef] [PubMed]

1983 (1)

R. Short, L. Mandel, “Observation of sub-Poissonian photon statistics,” Phys. Rev. Lett. 51, 384–387 (1983);G. Rempe, F. Schmidt-Kaler, H. Walther, “Observation of sub-Poissonian photon statistics in a micromaser,” Phys. Rev. Lett. 64, 2783–2786 (1990).
[CrossRef] [PubMed]

Bergquist, J. C.

U. Eichmann, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, W. M. Itano, D. J. Wineland, M. G. Raizen, “Young’s interference experiment with light scattered from two atoms,” Phys. Rev. Lett. 70, 2359–2362 (1993).
[CrossRef] [PubMed]

Bollinger, J. J.

U. Eichmann, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, W. M. Itano, D. J. Wineland, M. G. Raizen, “Young’s interference experiment with light scattered from two atoms,” Phys. Rev. Lett. 70, 2359–2362 (1993).
[CrossRef] [PubMed]

Bonifacio, R.

R. Bonifacio, G. M. D’Ariano, R. Seno, N. Sterpi, “Chaotic and cooperative regimes for the micromaser,” Phys. Rev. A 47, 2464–2467 (1993).
[CrossRef]

Braunstein, S.

J. J. Slosser, P. Meystre, S. Braunstein, “Harmonic oscillator driven by a quantum current,” Phys. Rev. Lett. 63, 934–937 (1989).
[CrossRef] [PubMed]

Brune, M.

M. Brune, J. M. Raimond, P. Goy, L. Davidovich, S. Haroche, “Realization of a two-photon maser oscillator,” Phys. Rev. Lett. 59, 1899–1902 (1987).
[CrossRef] [PubMed]

M. Brune, J. M. Raimond, S. Haroche, “Theory of the Rydberg-atom two-photon micromaser,” Phys. Rev. A 35, 154–163 (1987).
[CrossRef] [PubMed]

Carmichael, H. J.

P. Kochan, H. J. Carmichael, P. R. Morrow, M. G. Raizen, “Mutual coherence and interference in resonance fluorescence,” Phys. Rev. Lett. 75, 45–48 (1995).
[CrossRef] [PubMed]

D’Ariano, G. M.

R. Bonifacio, G. M. D’Ariano, R. Seno, N. Sterpi, “Chaotic and cooperative regimes for the micromaser,” Phys. Rev. A 47, 2464–2467 (1993).
[CrossRef]

Davidovich, L.

M. Brune, J. M. Raimond, P. Goy, L. Davidovich, S. Haroche, “Realization of a two-photon maser oscillator,” Phys. Rev. Lett. 59, 1899–1902 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

R. R. Puri, C. K. Law, J. H. Eberly, “Squeezed Raman micromaser model,” Phys. Rev. A 50, 4212–4218 (1994).
[CrossRef] [PubMed]

Eichmann, U.

U. Eichmann, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, W. M. Itano, D. J. Wineland, M. G. Raizen, “Young’s interference experiment with light scattered from two atoms,” Phys. Rev. Lett. 70, 2359–2362 (1993).
[CrossRef] [PubMed]

Enaki, N. A.

N. A. Enaki, M. A. Macovei, “Cooperative emission in the process of cascade and dipole-forbidden transitions,” Phys. Rev. A 56, 3274–3285 (1997).
[CrossRef]

Englert, B.

E. Wehner, R. Seno, N. Sterpi, B. Englert, H. Walther, “Atom pairs in the micromaser,” Opt. Commun. 110, 655–669 (1994).
[CrossRef]

Filipowicz, P.

Gilligan, J. M.

U. Eichmann, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, W. M. Itano, D. J. Wineland, M. G. Raizen, “Young’s interference experiment with light scattered from two atoms,” Phys. Rev. Lett. 70, 2359–2362 (1993).
[CrossRef] [PubMed]

Goy, P.

M. Brune, J. M. Raimond, P. Goy, L. Davidovich, S. Haroche, “Realization of a two-photon maser oscillator,” Phys. Rev. Lett. 59, 1899–1902 (1987).
[CrossRef] [PubMed]

Haroche, S.

M. Brune, J. M. Raimond, S. Haroche, “Theory of the Rydberg-atom two-photon micromaser,” Phys. Rev. A 35, 154–163 (1987).
[CrossRef] [PubMed]

M. Brune, J. M. Raimond, P. Goy, L. Davidovich, S. Haroche, “Realization of a two-photon maser oscillator,” Phys. Rev. Lett. 59, 1899–1902 (1987).
[CrossRef] [PubMed]

Itano, W. M.

U. Eichmann, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, W. M. Itano, D. J. Wineland, M. G. Raizen, “Young’s interference experiment with light scattered from two atoms,” Phys. Rev. Lett. 70, 2359–2362 (1993).
[CrossRef] [PubMed]

Javanainen, J.

Klein, N.

G. Rempe, H. Walther, N. Klein, “Observation of quantum collapse and revival in a one-atom maser,” Phys. Rev. Lett. 58, 353–356 (1987).
[CrossRef] [PubMed]

Kochan, P.

P. Kochan, H. J. Carmichael, P. R. Morrow, M. G. Raizen, “Mutual coherence and interference in resonance fluorescence,” Phys. Rev. Lett. 75, 45–48 (1995).
[CrossRef] [PubMed]

Law, C. K.

R. R. Puri, C. K. Law, J. H. Eberly, “Squeezed Raman micromaser model,” Phys. Rev. A 50, 4212–4218 (1994).
[CrossRef] [PubMed]

Li, F.

F. Li, D. L. Lin, “Generation of higher-order squeezing in a micromaser,” J. Phys. B 30, 3719–3729 (1997).
[CrossRef]

Lin, D. L.

F. Li, D. L. Lin, “Generation of higher-order squeezing in a micromaser,” J. Phys. B 30, 3719–3729 (1997).
[CrossRef]

Macovei, M. A.

N. A. Enaki, M. A. Macovei, “Cooperative emission in the process of cascade and dipole-forbidden transitions,” Phys. Rev. A 56, 3274–3285 (1997).
[CrossRef]

Mandel, L.

R. Short, L. Mandel, “Observation of sub-Poissonian photon statistics,” Phys. Rev. Lett. 51, 384–387 (1983);G. Rempe, F. Schmidt-Kaler, H. Walther, “Observation of sub-Poissonian photon statistics in a micromaser,” Phys. Rev. Lett. 64, 2783–2786 (1990).
[CrossRef] [PubMed]

Maystre, P.

P. Filipowicz, J. Javanainen, P. Maystre, “Theory of a microscopic maser,” Phys. Rev. A 34, 3077–3087 (1986).
[CrossRef] [PubMed]

Meschede, D.

D. Meschede, H. Walther, G. Muller, “One-atom maser,” Phys. Rev. Lett. 54, 551–554 (1985).
[CrossRef] [PubMed]

Meystre, P.

Morrow, P. R.

P. Kochan, H. J. Carmichael, P. R. Morrow, M. G. Raizen, “Mutual coherence and interference in resonance fluorescence,” Phys. Rev. Lett. 75, 45–48 (1995).
[CrossRef] [PubMed]

Muller, G.

D. Meschede, H. Walther, G. Muller, “One-atom maser,” Phys. Rev. Lett. 54, 551–554 (1985).
[CrossRef] [PubMed]

Orszag, M.

M. Orszag, R. Ramirez, J. C. Retamal, C. Saavedra, “Quantum cooperative effects in a micromaser,” Phys. Rev. A 49, 2933–2937 (1994).
[CrossRef] [PubMed]

M. Orszag, R. Ramirez, J. C. Retamal, L. Roa, “Generation of highly squeezed states in a two-photon micromaser,” Phys. Rev. A 45, 6717–6720 (1992).
[CrossRef] [PubMed]

Puri, R. R.

R. R. Puri, C. K. Law, J. H. Eberly, “Squeezed Raman micromaser model,” Phys. Rev. A 50, 4212–4218 (1994).
[CrossRef] [PubMed]

Raimond, J. M.

M. Brune, J. M. Raimond, P. Goy, L. Davidovich, S. Haroche, “Realization of a two-photon maser oscillator,” Phys. Rev. Lett. 59, 1899–1902 (1987).
[CrossRef] [PubMed]

M. Brune, J. M. Raimond, S. Haroche, “Theory of the Rydberg-atom two-photon micromaser,” Phys. Rev. A 35, 154–163 (1987).
[CrossRef] [PubMed]

Raizen, M. G.

P. Kochan, H. J. Carmichael, P. R. Morrow, M. G. Raizen, “Mutual coherence and interference in resonance fluorescence,” Phys. Rev. Lett. 75, 45–48 (1995).
[CrossRef] [PubMed]

U. Eichmann, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, W. M. Itano, D. J. Wineland, M. G. Raizen, “Young’s interference experiment with light scattered from two atoms,” Phys. Rev. Lett. 70, 2359–2362 (1993).
[CrossRef] [PubMed]

Ramirez, R.

M. Orszag, R. Ramirez, J. C. Retamal, C. Saavedra, “Quantum cooperative effects in a micromaser,” Phys. Rev. A 49, 2933–2937 (1994).
[CrossRef] [PubMed]

M. Orszag, R. Ramirez, J. C. Retamal, L. Roa, “Generation of highly squeezed states in a two-photon micromaser,” Phys. Rev. A 45, 6717–6720 (1992).
[CrossRef] [PubMed]

Rempe, G.

P. Meystre, G. Rempe, H. Walther, “Very-low-temperature behavior of a micromaser,” Opt. Lett. 13, 1078–1080 (1988).
[CrossRef] [PubMed]

G. Rempe, H. Walther, N. Klein, “Observation of quantum collapse and revival in a one-atom maser,” Phys. Rev. Lett. 58, 353–356 (1987).
[CrossRef] [PubMed]

Retamal, J. C.

M. Orszag, R. Ramirez, J. C. Retamal, C. Saavedra, “Quantum cooperative effects in a micromaser,” Phys. Rev. A 49, 2933–2937 (1994).
[CrossRef] [PubMed]

M. Orszag, R. Ramirez, J. C. Retamal, L. Roa, “Generation of highly squeezed states in a two-photon micromaser,” Phys. Rev. A 45, 6717–6720 (1992).
[CrossRef] [PubMed]

Roa, L.

M. Orszag, R. Ramirez, J. C. Retamal, L. Roa, “Generation of highly squeezed states in a two-photon micromaser,” Phys. Rev. A 45, 6717–6720 (1992).
[CrossRef] [PubMed]

Saavedra, C.

M. Orszag, R. Ramirez, J. C. Retamal, C. Saavedra, “Quantum cooperative effects in a micromaser,” Phys. Rev. A 49, 2933–2937 (1994).
[CrossRef] [PubMed]

Seno, R.

E. Wehner, R. Seno, N. Sterpi, B. Englert, H. Walther, “Atom pairs in the micromaser,” Opt. Commun. 110, 655–669 (1994).
[CrossRef]

R. Bonifacio, G. M. D’Ariano, R. Seno, N. Sterpi, “Chaotic and cooperative regimes for the micromaser,” Phys. Rev. A 47, 2464–2467 (1993).
[CrossRef]

Short, R.

R. Short, L. Mandel, “Observation of sub-Poissonian photon statistics,” Phys. Rev. Lett. 51, 384–387 (1983);G. Rempe, F. Schmidt-Kaler, H. Walther, “Observation of sub-Poissonian photon statistics in a micromaser,” Phys. Rev. Lett. 64, 2783–2786 (1990).
[CrossRef] [PubMed]

Slosser, J. J.

J. J. Slosser, P. Meystre, S. Braunstein, “Harmonic oscillator driven by a quantum current,” Phys. Rev. Lett. 63, 934–937 (1989).
[CrossRef] [PubMed]

Sterpi, N.

E. Wehner, R. Seno, N. Sterpi, B. Englert, H. Walther, “Atom pairs in the micromaser,” Opt. Commun. 110, 655–669 (1994).
[CrossRef]

R. Bonifacio, G. M. D’Ariano, R. Seno, N. Sterpi, “Chaotic and cooperative regimes for the micromaser,” Phys. Rev. A 47, 2464–2467 (1993).
[CrossRef]

Walther, H.

E. Wehner, R. Seno, N. Sterpi, B. Englert, H. Walther, “Atom pairs in the micromaser,” Opt. Commun. 110, 655–669 (1994).
[CrossRef]

P. Meystre, G. Rempe, H. Walther, “Very-low-temperature behavior of a micromaser,” Opt. Lett. 13, 1078–1080 (1988).
[CrossRef] [PubMed]

G. Rempe, H. Walther, N. Klein, “Observation of quantum collapse and revival in a one-atom maser,” Phys. Rev. Lett. 58, 353–356 (1987).
[CrossRef] [PubMed]

D. Meschede, H. Walther, G. Muller, “One-atom maser,” Phys. Rev. Lett. 54, 551–554 (1985).
[CrossRef] [PubMed]

Wehner, E.

E. Wehner, R. Seno, N. Sterpi, B. Englert, H. Walther, “Atom pairs in the micromaser,” Opt. Commun. 110, 655–669 (1994).
[CrossRef]

Wineland, D. J.

U. Eichmann, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, W. M. Itano, D. J. Wineland, M. G. Raizen, “Young’s interference experiment with light scattered from two atoms,” Phys. Rev. Lett. 70, 2359–2362 (1993).
[CrossRef] [PubMed]

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

J. Phys. B (1)

F. Li, D. L. Lin, “Generation of higher-order squeezing in a micromaser,” J. Phys. B 30, 3719–3729 (1997).
[CrossRef]

Opt. Commun. (1)

E. Wehner, R. Seno, N. Sterpi, B. Englert, H. Walther, “Atom pairs in the micromaser,” Opt. Commun. 110, 655–669 (1994).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (7)

M. Brune, J. M. Raimond, S. Haroche, “Theory of the Rydberg-atom two-photon micromaser,” Phys. Rev. A 35, 154–163 (1987).
[CrossRef] [PubMed]

N. A. Enaki, M. A. Macovei, “Cooperative emission in the process of cascade and dipole-forbidden transitions,” Phys. Rev. A 56, 3274–3285 (1997).
[CrossRef]

M. Orszag, R. Ramirez, J. C. Retamal, L. Roa, “Generation of highly squeezed states in a two-photon micromaser,” Phys. Rev. A 45, 6717–6720 (1992).
[CrossRef] [PubMed]

R. Bonifacio, G. M. D’Ariano, R. Seno, N. Sterpi, “Chaotic and cooperative regimes for the micromaser,” Phys. Rev. A 47, 2464–2467 (1993).
[CrossRef]

M. Orszag, R. Ramirez, J. C. Retamal, C. Saavedra, “Quantum cooperative effects in a micromaser,” Phys. Rev. A 49, 2933–2937 (1994).
[CrossRef] [PubMed]

R. R. Puri, C. K. Law, J. H. Eberly, “Squeezed Raman micromaser model,” Phys. Rev. A 50, 4212–4218 (1994).
[CrossRef] [PubMed]

P. Filipowicz, J. Javanainen, P. Maystre, “Theory of a microscopic maser,” Phys. Rev. A 34, 3077–3087 (1986).
[CrossRef] [PubMed]

Phys. Rev. Lett. (7)

G. Rempe, H. Walther, N. Klein, “Observation of quantum collapse and revival in a one-atom maser,” Phys. Rev. Lett. 58, 353–356 (1987).
[CrossRef] [PubMed]

M. Brune, J. M. Raimond, P. Goy, L. Davidovich, S. Haroche, “Realization of a two-photon maser oscillator,” Phys. Rev. Lett. 59, 1899–1902 (1987).
[CrossRef] [PubMed]

J. J. Slosser, P. Meystre, S. Braunstein, “Harmonic oscillator driven by a quantum current,” Phys. Rev. Lett. 63, 934–937 (1989).
[CrossRef] [PubMed]

R. Short, L. Mandel, “Observation of sub-Poissonian photon statistics,” Phys. Rev. Lett. 51, 384–387 (1983);G. Rempe, F. Schmidt-Kaler, H. Walther, “Observation of sub-Poissonian photon statistics in a micromaser,” Phys. Rev. Lett. 64, 2783–2786 (1990).
[CrossRef] [PubMed]

U. Eichmann, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, W. M. Itano, D. J. Wineland, M. G. Raizen, “Young’s interference experiment with light scattered from two atoms,” Phys. Rev. Lett. 70, 2359–2362 (1993).
[CrossRef] [PubMed]

P. Kochan, H. J. Carmichael, P. R. Morrow, M. G. Raizen, “Mutual coherence and interference in resonance fluorescence,” Phys. Rev. Lett. 75, 45–48 (1995).
[CrossRef] [PubMed]

D. Meschede, H. Walther, G. Muller, “One-atom maser,” Phys. Rev. Lett. 54, 551–554 (1985).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Solid curve, mean excitation 〈n〉 of the cotangent states as a function of the population of the second excited state |α|2. Solid curve with dots, fluctuations in the mean excitations σ=(n2-n2)/n, showing sub-Poissonian statistics when σ<1. Here Nu=3, |γ|2=0.25, and τk=22π.

Fig. 2
Fig. 2

Same as Fig. 1, but for |γ|2=0.65.

Fig. 3
Fig. 3

Same as Fig. 1, but for Nu=23.

Fig. 4
Fig. 4

Same as Fig. 2, but for Nu=23.

Equations (39)

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

ρ(k+1)=Tra[U(tint)ρaU0(τp-tint)ρ(k)].
|Ψ(t)=n=NdNusn|n(α|e2+β|e1+γ|g).
i t |Ψ(t)=H|Ψ(t),t>t.
H=ω0Sz+ωaa+k(aS-+aS+).
S+=12 (|e2e1|+|e1g|,
S-=12 (|ge1|+|e1e2|),
Sz=|e2e2|-|gg|.
x=S(τ)|e2,y=S(τ)|g,z=S(τ)|e1.
d2xdτ2=-x k2aa2-y k2aa2,
d2ydτ2=-y k2aa2-x k2a22,
d2zdτ2=-z k22 (1+2aa),
x=Cx1 cosτk2aa+32+Cx2 sinτk2aa+32+Cx3,
y=Cy1 cosτk2aa-12+Cy2 sinτk2aa-12+Cy3,
z=Cz1 cosτk2aa+12+Cz2 sinτk2aa+12,
Cx1=|e2aa 12aa+3+|gaa 12aa+3,
Cx2=-i|e1a 1(2aa+3)1/2,
Cx3=|e2-Cx1,
Cy1=|gaa 12aa-1+|e2aa 12aa-1,
Cy2=-i|e1a 1(2aa-1)1/2,
Cy3=|g-Cy1,
Cz1=|e1,
Cz2=-i|e2a 1(2aa+1)1/2-i|ga 1(2aa+1)1/2.
|Ψ(t+τ)=exp(-iHτ/)|Ψ(t)
=exp[-i(ω0Sz+ω0aa)τ]×n=NdNusnα1+(n+1)(2n+3)×cosτk2n+32-1|n-iβ n2n+1 sinτk2n+12|n-1+γ n(n-1)(2n-1)×cosτk2n-12-1|n-2|e2+n=NdNusnβ cosτk2n+12|n-iα n+12n+3 sinτk2n+32|n+1-iγ n2n-1×sinτk2n-12|n-1|e1+n=NdNusnγ+γn(2n-1)×cosτk2n-12-1|n+α n+1n+2(2n+3)×cosτk2n+32-1|n+2-iβ n+12n+1×sinτk2n+12|n+1|g.
sn=-i βγ cot12 τk2n-12 2n-1n sn-1-αγ n-1n sn-2
τk2Nd-12=qπforevenintegralq,
τk2Nu+32=pπforevenintegralp.
|Ψ(t+τ)=exp[-i(ω0Sz+ω0aa)τ]×n=NdNusn|n(α|e2-β|e1+γ|g)
Φp=n=1Nusnn,
P2=-i βγ cot12 τk32 32.
P3=-i βγ cot12 τk52 53-αγ 23-i βγ cot12 τk32 32.
P4=-i βγ cot12 τk72 74-αγ 34-i βγ cot12 τk52 53-αγ 23-i βγ cot12 τk32 32.
sn=m=2nPms1.
Pm=-i βγ cot12 τk2m-12 2m-1m-αγ m-1mb(τ)-αγ m-2m-1c(τ)--i βγ cot12 τk32 32,
b(τ)=-i βγ cot12 τk2m-32 2m-3m-1,
c(τ)=-i βγ cot12 τk2m-52 2m-5m-2.
n=n,n=1Nusn*snn|aa|n=n=1Nu|sn|2n,
n2=n=1Nu|sn|2n2,
σ=n2-n2n.

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