Abstract

We calculate the output spectrum of a single-atom laser in a microcavity across a wide range of operating conditions. We considered both three-level and four-level atomic level structures. We used a numerical routine to calculate spectra that is more efficient than others used previously. We found that the linewidth of a single-atom laser generally scales as the inverse of the photon number and that there is no pump value at which an abrupt change occurs that might locate a lasing threshold. For a three-level gain atom we found vacuum–Rabi splitting similar to that found by Loffler et al. [Phys. Rev. A 55, 3923 (1997)] and used quantum trajectory theory to obtain a new interpretation of the results. For a four-level gain atom the vacuum–Rabi structure can appear at a small nonzero pump level and is maintained for large pumps, even when the intracavity photon number is larger than unity and the laser is on. We use the quantum trajectory approach to explain these results.

© 2004 Optical Society of America

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  1. C. Ginzel, H.-J. Briegel, U. Martini, B. Englert, and A. Schenzle, “Quantum optical master equations: the one-atom laser,” Phys. Rev. A 48, 732–738 (1993).
    [CrossRef] [PubMed]
  2. M. Loffler, G. M. Meyer, and H. Walther, “Spectral properties of the one-atom laser,” Phys. Rev. A 55, 3923–3930 (1997).
    [CrossRef]
  3. H. Mabuchi, Q. A. Turchette, M. S. Chapman, and H. J. Kimble, “Real time detection of single atoms falling through a high-finesse cavity,” Opt. Lett. 21, 1393–1395 (1996).
    [CrossRef] [PubMed]
  4. C. J. Hood, M. S. Chapman, T. W. Lynn, and H. J. Kimble, “Real-time cavity QED with single atoms,” Phys. Rev. Lett. 80, 4157–4160 (1998).
    [CrossRef]
  5. H. Mabuchi, J. Ye, and H. J. Kimble, “Full observation of single-atom dynamics in cavity QED,” Appl. Phys. B: Lasers Opt. 68, 1095–1108 (1999).
    [CrossRef]
  6. J. Ye, D. W. Vernooy, and H. J. Kimble, “Trapping of single atoms in cavity QED,” Phys. Rev. Lett. 83, 4987–4990 (1999).
    [CrossRef]
  7. S. J. van Enk, J. McKeever, H. J. Kimble, and J. Ye, “Cooling of a single atom in an optical trap inside a resonator,” Phys. Rev. A 64, 013407 (2001).
    [CrossRef]
  8. J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Naegerl, D. M. Stamper-Kurn, and H. J. Kimble, “State-insensitive cooling and trapping of single atoms in an optical cavity,” Phys. Rev. Lett. 90, 133602 (2003).
    [CrossRef] [PubMed]
  9. J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, “Experimental realization of a one-atom laser in the regime of strong coupling,” Nature (London) 425, 268–271 (2003).
    [CrossRef]
  10. H. Walther, “Single atom experiments in cavities and traps,” Proc. R. Soc. London, Ser. A 454, 431–445 (1998).
    [CrossRef]
  11. A. M. Smith and C. W. Gardiner, “Phase-space method without large-N scaling for the laser and optical bistability,” Phys. Rev. A 38, 4073–4086 (1988).
    [CrossRef] [PubMed]
  12. Y. Mu and C. Savage, “One-atom lasers,” Phys. Rev. A 46, 5944–5954 (1992).
    [CrossRef] [PubMed]
  13. T. Pellizari and H. Ritsch, “Preparation of stationary Fock states in a one-atom Raman laser,” Phys. Rev. Lett. 72, 3973–3976 (1994).
    [CrossRef]
  14. T. Pellizari and H. Ritsch, “Photon statistics of the three-level one-atom laser,” J. Mod. Opt. 41, 609–623 (1994).
    [CrossRef]
  15. G. M. Meyer, M. Loffler, and H. Walther, “Spectrum of the ion-trap laser,” Phys. Rev. A 56, R1099–R1102 (1997).
    [CrossRef]
  16. G. M. Meyer and H.-J. Briegel, “Pump-operator treatment of the ion-trap laser,” Phys. Rev. A 58, 3210–3220 (1998).
    [CrossRef]
  17. S. Ya. Kilin and T. B. Karlovich, “Single-atom laser: coherent and nonclassical effects in the regime of a strong atom field correlation,” J. Exp. Theor. Phys. 95, 805–819 (2001).
    [CrossRef]
  18. B. Jones, S. Ghose, J. Clemens, P. Rice, and L. Pedrotti, “Photon statistics of a single atom laser,” Phys. Rev. A 60, 3267–3275 (1999).
    [CrossRef]
  19. G. Bjork, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994).
    [CrossRef] [PubMed]
  20. P. R. Rice and H. J. Carmichael, “Photon statistics of a cavity-QED laser: a comment on the laser phase-transition analogy,” Phys. Rev. A 50, 4318–4329 (1994).
    [CrossRef] [PubMed]
  21. H. Haken, “Fully quantum mechanical solutions of the laser equations,” in Light and Matter, L. Genzel, ed., Vol. XXV/2c of Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, 1970), pp. 99–172.
  22. G. Koganov and R. Shuker, “Threshold and nonlinear be-havior of lasers of lambda and V configurations,” Phys. Rev. A 58, 1559–1562 (1998).
    [CrossRef]
  23. H. J. Carmichael, An Open Systems Approach to Quantum Optics (Springer-Verlag, Berlin, 1993).
  24. L. Tian and H. J. Carmichael, “Quantum trajectory simulations of two-state behavior in an optical cavity containing one atom,” Phys. Rev. A 46, R6801–R6804 (1992).
    [CrossRef] [PubMed]
  25. J. Dalibard, Y. Castin, and K. Molmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
    [CrossRef] [PubMed]
  26. R. Dum, P. Zoller, and H. Ritsch, “Monte Carlo simulation of the atomic master equation for spontaneous emission,” Phys. Rev. A 45, 4879–4887 (1992).
    [CrossRef] [PubMed]
  27. B. Misra and E. C. G. Sudarshan, “Zeno’s paradox in quantum theory,” J. Math. Phys. 18, 756–763 (1977).
    [CrossRef]

2003

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Naegerl, D. M. Stamper-Kurn, and H. J. Kimble, “State-insensitive cooling and trapping of single atoms in an optical cavity,” Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef] [PubMed]

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, “Experimental realization of a one-atom laser in the regime of strong coupling,” Nature (London) 425, 268–271 (2003).
[CrossRef]

2001

S. J. van Enk, J. McKeever, H. J. Kimble, and J. Ye, “Cooling of a single atom in an optical trap inside a resonator,” Phys. Rev. A 64, 013407 (2001).
[CrossRef]

S. Ya. Kilin and T. B. Karlovich, “Single-atom laser: coherent and nonclassical effects in the regime of a strong atom field correlation,” J. Exp. Theor. Phys. 95, 805–819 (2001).
[CrossRef]

1999

B. Jones, S. Ghose, J. Clemens, P. Rice, and L. Pedrotti, “Photon statistics of a single atom laser,” Phys. Rev. A 60, 3267–3275 (1999).
[CrossRef]

H. Mabuchi, J. Ye, and H. J. Kimble, “Full observation of single-atom dynamics in cavity QED,” Appl. Phys. B: Lasers Opt. 68, 1095–1108 (1999).
[CrossRef]

J. Ye, D. W. Vernooy, and H. J. Kimble, “Trapping of single atoms in cavity QED,” Phys. Rev. Lett. 83, 4987–4990 (1999).
[CrossRef]

1998

G. M. Meyer and H.-J. Briegel, “Pump-operator treatment of the ion-trap laser,” Phys. Rev. A 58, 3210–3220 (1998).
[CrossRef]

H. Walther, “Single atom experiments in cavities and traps,” Proc. R. Soc. London, Ser. A 454, 431–445 (1998).
[CrossRef]

C. J. Hood, M. S. Chapman, T. W. Lynn, and H. J. Kimble, “Real-time cavity QED with single atoms,” Phys. Rev. Lett. 80, 4157–4160 (1998).
[CrossRef]

G. Koganov and R. Shuker, “Threshold and nonlinear be-havior of lasers of lambda and V configurations,” Phys. Rev. A 58, 1559–1562 (1998).
[CrossRef]

1997

M. Loffler, G. M. Meyer, and H. Walther, “Spectral properties of the one-atom laser,” Phys. Rev. A 55, 3923–3930 (1997).
[CrossRef]

G. M. Meyer, M. Loffler, and H. Walther, “Spectrum of the ion-trap laser,” Phys. Rev. A 56, R1099–R1102 (1997).
[CrossRef]

1996

1994

T. Pellizari and H. Ritsch, “Preparation of stationary Fock states in a one-atom Raman laser,” Phys. Rev. Lett. 72, 3973–3976 (1994).
[CrossRef]

T. Pellizari and H. Ritsch, “Photon statistics of the three-level one-atom laser,” J. Mod. Opt. 41, 609–623 (1994).
[CrossRef]

G. Bjork, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994).
[CrossRef] [PubMed]

P. R. Rice and H. J. Carmichael, “Photon statistics of a cavity-QED laser: a comment on the laser phase-transition analogy,” Phys. Rev. A 50, 4318–4329 (1994).
[CrossRef] [PubMed]

1993

C. Ginzel, H.-J. Briegel, U. Martini, B. Englert, and A. Schenzle, “Quantum optical master equations: the one-atom laser,” Phys. Rev. A 48, 732–738 (1993).
[CrossRef] [PubMed]

1992

Y. Mu and C. Savage, “One-atom lasers,” Phys. Rev. A 46, 5944–5954 (1992).
[CrossRef] [PubMed]

L. Tian and H. J. Carmichael, “Quantum trajectory simulations of two-state behavior in an optical cavity containing one atom,” Phys. Rev. A 46, R6801–R6804 (1992).
[CrossRef] [PubMed]

J. Dalibard, Y. Castin, and K. Molmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
[CrossRef] [PubMed]

R. Dum, P. Zoller, and H. Ritsch, “Monte Carlo simulation of the atomic master equation for spontaneous emission,” Phys. Rev. A 45, 4879–4887 (1992).
[CrossRef] [PubMed]

1988

A. M. Smith and C. W. Gardiner, “Phase-space method without large-N scaling for the laser and optical bistability,” Phys. Rev. A 38, 4073–4086 (1988).
[CrossRef] [PubMed]

1977

B. Misra and E. C. G. Sudarshan, “Zeno’s paradox in quantum theory,” J. Math. Phys. 18, 756–763 (1977).
[CrossRef]

Bjork, G.

G. Bjork, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994).
[CrossRef] [PubMed]

Boca, A.

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, “Experimental realization of a one-atom laser in the regime of strong coupling,” Nature (London) 425, 268–271 (2003).
[CrossRef]

Boozer, A. D.

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, “Experimental realization of a one-atom laser in the regime of strong coupling,” Nature (London) 425, 268–271 (2003).
[CrossRef]

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Naegerl, D. M. Stamper-Kurn, and H. J. Kimble, “State-insensitive cooling and trapping of single atoms in an optical cavity,” Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef] [PubMed]

Briegel, H.-J.

G. M. Meyer and H.-J. Briegel, “Pump-operator treatment of the ion-trap laser,” Phys. Rev. A 58, 3210–3220 (1998).
[CrossRef]

C. Ginzel, H.-J. Briegel, U. Martini, B. Englert, and A. Schenzle, “Quantum optical master equations: the one-atom laser,” Phys. Rev. A 48, 732–738 (1993).
[CrossRef] [PubMed]

Buck, J. R.

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Naegerl, D. M. Stamper-Kurn, and H. J. Kimble, “State-insensitive cooling and trapping of single atoms in an optical cavity,” Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef] [PubMed]

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, “Experimental realization of a one-atom laser in the regime of strong coupling,” Nature (London) 425, 268–271 (2003).
[CrossRef]

Carmichael, H. J.

P. R. Rice and H. J. Carmichael, “Photon statistics of a cavity-QED laser: a comment on the laser phase-transition analogy,” Phys. Rev. A 50, 4318–4329 (1994).
[CrossRef] [PubMed]

L. Tian and H. J. Carmichael, “Quantum trajectory simulations of two-state behavior in an optical cavity containing one atom,” Phys. Rev. A 46, R6801–R6804 (1992).
[CrossRef] [PubMed]

Castin, Y.

J. Dalibard, Y. Castin, and K. Molmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
[CrossRef] [PubMed]

Chapman, M. S.

C. J. Hood, M. S. Chapman, T. W. Lynn, and H. J. Kimble, “Real-time cavity QED with single atoms,” Phys. Rev. Lett. 80, 4157–4160 (1998).
[CrossRef]

H. Mabuchi, Q. A. Turchette, M. S. Chapman, and H. J. Kimble, “Real time detection of single atoms falling through a high-finesse cavity,” Opt. Lett. 21, 1393–1395 (1996).
[CrossRef] [PubMed]

Clemens, J.

B. Jones, S. Ghose, J. Clemens, P. Rice, and L. Pedrotti, “Photon statistics of a single atom laser,” Phys. Rev. A 60, 3267–3275 (1999).
[CrossRef]

Dalibard, J.

J. Dalibard, Y. Castin, and K. Molmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
[CrossRef] [PubMed]

Dum, R.

R. Dum, P. Zoller, and H. Ritsch, “Monte Carlo simulation of the atomic master equation for spontaneous emission,” Phys. Rev. A 45, 4879–4887 (1992).
[CrossRef] [PubMed]

Englert, B.

C. Ginzel, H.-J. Briegel, U. Martini, B. Englert, and A. Schenzle, “Quantum optical master equations: the one-atom laser,” Phys. Rev. A 48, 732–738 (1993).
[CrossRef] [PubMed]

Gardiner, C. W.

A. M. Smith and C. W. Gardiner, “Phase-space method without large-N scaling for the laser and optical bistability,” Phys. Rev. A 38, 4073–4086 (1988).
[CrossRef] [PubMed]

Ghose, S.

B. Jones, S. Ghose, J. Clemens, P. Rice, and L. Pedrotti, “Photon statistics of a single atom laser,” Phys. Rev. A 60, 3267–3275 (1999).
[CrossRef]

Ginzel, C.

C. Ginzel, H.-J. Briegel, U. Martini, B. Englert, and A. Schenzle, “Quantum optical master equations: the one-atom laser,” Phys. Rev. A 48, 732–738 (1993).
[CrossRef] [PubMed]

Hood, C. J.

C. J. Hood, M. S. Chapman, T. W. Lynn, and H. J. Kimble, “Real-time cavity QED with single atoms,” Phys. Rev. Lett. 80, 4157–4160 (1998).
[CrossRef]

Jones, B.

B. Jones, S. Ghose, J. Clemens, P. Rice, and L. Pedrotti, “Photon statistics of a single atom laser,” Phys. Rev. A 60, 3267–3275 (1999).
[CrossRef]

Karlovich, T. B.

S. Ya. Kilin and T. B. Karlovich, “Single-atom laser: coherent and nonclassical effects in the regime of a strong atom field correlation,” J. Exp. Theor. Phys. 95, 805–819 (2001).
[CrossRef]

Karlsson, A.

G. Bjork, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994).
[CrossRef] [PubMed]

Kilin, S. Ya.

S. Ya. Kilin and T. B. Karlovich, “Single-atom laser: coherent and nonclassical effects in the regime of a strong atom field correlation,” J. Exp. Theor. Phys. 95, 805–819 (2001).
[CrossRef]

Kimble, H. J.

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, “Experimental realization of a one-atom laser in the regime of strong coupling,” Nature (London) 425, 268–271 (2003).
[CrossRef]

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Naegerl, D. M. Stamper-Kurn, and H. J. Kimble, “State-insensitive cooling and trapping of single atoms in an optical cavity,” Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef] [PubMed]

S. J. van Enk, J. McKeever, H. J. Kimble, and J. Ye, “Cooling of a single atom in an optical trap inside a resonator,” Phys. Rev. A 64, 013407 (2001).
[CrossRef]

H. Mabuchi, J. Ye, and H. J. Kimble, “Full observation of single-atom dynamics in cavity QED,” Appl. Phys. B: Lasers Opt. 68, 1095–1108 (1999).
[CrossRef]

J. Ye, D. W. Vernooy, and H. J. Kimble, “Trapping of single atoms in cavity QED,” Phys. Rev. Lett. 83, 4987–4990 (1999).
[CrossRef]

C. J. Hood, M. S. Chapman, T. W. Lynn, and H. J. Kimble, “Real-time cavity QED with single atoms,” Phys. Rev. Lett. 80, 4157–4160 (1998).
[CrossRef]

H. Mabuchi, Q. A. Turchette, M. S. Chapman, and H. J. Kimble, “Real time detection of single atoms falling through a high-finesse cavity,” Opt. Lett. 21, 1393–1395 (1996).
[CrossRef] [PubMed]

Koganov, G.

G. Koganov and R. Shuker, “Threshold and nonlinear be-havior of lasers of lambda and V configurations,” Phys. Rev. A 58, 1559–1562 (1998).
[CrossRef]

Kuzmich, A.

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Naegerl, D. M. Stamper-Kurn, and H. J. Kimble, “State-insensitive cooling and trapping of single atoms in an optical cavity,” Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef] [PubMed]

Loffler, M.

M. Loffler, G. M. Meyer, and H. Walther, “Spectral properties of the one-atom laser,” Phys. Rev. A 55, 3923–3930 (1997).
[CrossRef]

G. M. Meyer, M. Loffler, and H. Walther, “Spectrum of the ion-trap laser,” Phys. Rev. A 56, R1099–R1102 (1997).
[CrossRef]

Lynn, T. W.

C. J. Hood, M. S. Chapman, T. W. Lynn, and H. J. Kimble, “Real-time cavity QED with single atoms,” Phys. Rev. Lett. 80, 4157–4160 (1998).
[CrossRef]

Mabuchi, H.

H. Mabuchi, J. Ye, and H. J. Kimble, “Full observation of single-atom dynamics in cavity QED,” Appl. Phys. B: Lasers Opt. 68, 1095–1108 (1999).
[CrossRef]

H. Mabuchi, Q. A. Turchette, M. S. Chapman, and H. J. Kimble, “Real time detection of single atoms falling through a high-finesse cavity,” Opt. Lett. 21, 1393–1395 (1996).
[CrossRef] [PubMed]

Martini, U.

C. Ginzel, H.-J. Briegel, U. Martini, B. Englert, and A. Schenzle, “Quantum optical master equations: the one-atom laser,” Phys. Rev. A 48, 732–738 (1993).
[CrossRef] [PubMed]

McKeever, J.

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, “Experimental realization of a one-atom laser in the regime of strong coupling,” Nature (London) 425, 268–271 (2003).
[CrossRef]

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Naegerl, D. M. Stamper-Kurn, and H. J. Kimble, “State-insensitive cooling and trapping of single atoms in an optical cavity,” Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef] [PubMed]

S. J. van Enk, J. McKeever, H. J. Kimble, and J. Ye, “Cooling of a single atom in an optical trap inside a resonator,” Phys. Rev. A 64, 013407 (2001).
[CrossRef]

Meyer, G. M.

G. M. Meyer and H.-J. Briegel, “Pump-operator treatment of the ion-trap laser,” Phys. Rev. A 58, 3210–3220 (1998).
[CrossRef]

G. M. Meyer, M. Loffler, and H. Walther, “Spectrum of the ion-trap laser,” Phys. Rev. A 56, R1099–R1102 (1997).
[CrossRef]

M. Loffler, G. M. Meyer, and H. Walther, “Spectral properties of the one-atom laser,” Phys. Rev. A 55, 3923–3930 (1997).
[CrossRef]

Misra, B.

B. Misra and E. C. G. Sudarshan, “Zeno’s paradox in quantum theory,” J. Math. Phys. 18, 756–763 (1977).
[CrossRef]

Molmer, K.

J. Dalibard, Y. Castin, and K. Molmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
[CrossRef] [PubMed]

Mu, Y.

Y. Mu and C. Savage, “One-atom lasers,” Phys. Rev. A 46, 5944–5954 (1992).
[CrossRef] [PubMed]

Naegerl, H.-C.

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Naegerl, D. M. Stamper-Kurn, and H. J. Kimble, “State-insensitive cooling and trapping of single atoms in an optical cavity,” Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef] [PubMed]

Pedrotti, L.

B. Jones, S. Ghose, J. Clemens, P. Rice, and L. Pedrotti, “Photon statistics of a single atom laser,” Phys. Rev. A 60, 3267–3275 (1999).
[CrossRef]

Pellizari, T.

T. Pellizari and H. Ritsch, “Preparation of stationary Fock states in a one-atom Raman laser,” Phys. Rev. Lett. 72, 3973–3976 (1994).
[CrossRef]

T. Pellizari and H. Ritsch, “Photon statistics of the three-level one-atom laser,” J. Mod. Opt. 41, 609–623 (1994).
[CrossRef]

Rice, P.

B. Jones, S. Ghose, J. Clemens, P. Rice, and L. Pedrotti, “Photon statistics of a single atom laser,” Phys. Rev. A 60, 3267–3275 (1999).
[CrossRef]

Rice, P. R.

P. R. Rice and H. J. Carmichael, “Photon statistics of a cavity-QED laser: a comment on the laser phase-transition analogy,” Phys. Rev. A 50, 4318–4329 (1994).
[CrossRef] [PubMed]

Ritsch, H.

T. Pellizari and H. Ritsch, “Photon statistics of the three-level one-atom laser,” J. Mod. Opt. 41, 609–623 (1994).
[CrossRef]

T. Pellizari and H. Ritsch, “Preparation of stationary Fock states in a one-atom Raman laser,” Phys. Rev. Lett. 72, 3973–3976 (1994).
[CrossRef]

R. Dum, P. Zoller, and H. Ritsch, “Monte Carlo simulation of the atomic master equation for spontaneous emission,” Phys. Rev. A 45, 4879–4887 (1992).
[CrossRef] [PubMed]

Savage, C.

Y. Mu and C. Savage, “One-atom lasers,” Phys. Rev. A 46, 5944–5954 (1992).
[CrossRef] [PubMed]

Schenzle, A.

C. Ginzel, H.-J. Briegel, U. Martini, B. Englert, and A. Schenzle, “Quantum optical master equations: the one-atom laser,” Phys. Rev. A 48, 732–738 (1993).
[CrossRef] [PubMed]

Shuker, R.

G. Koganov and R. Shuker, “Threshold and nonlinear be-havior of lasers of lambda and V configurations,” Phys. Rev. A 58, 1559–1562 (1998).
[CrossRef]

Smith, A. M.

A. M. Smith and C. W. Gardiner, “Phase-space method without large-N scaling for the laser and optical bistability,” Phys. Rev. A 38, 4073–4086 (1988).
[CrossRef] [PubMed]

Stamper-Kurn, D. M.

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Naegerl, D. M. Stamper-Kurn, and H. J. Kimble, “State-insensitive cooling and trapping of single atoms in an optical cavity,” Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef] [PubMed]

Sudarshan, E. C. G.

B. Misra and E. C. G. Sudarshan, “Zeno’s paradox in quantum theory,” J. Math. Phys. 18, 756–763 (1977).
[CrossRef]

Tian, L.

L. Tian and H. J. Carmichael, “Quantum trajectory simulations of two-state behavior in an optical cavity containing one atom,” Phys. Rev. A 46, R6801–R6804 (1992).
[CrossRef] [PubMed]

Turchette, Q. A.

van Enk, S. J.

S. J. van Enk, J. McKeever, H. J. Kimble, and J. Ye, “Cooling of a single atom in an optical trap inside a resonator,” Phys. Rev. A 64, 013407 (2001).
[CrossRef]

Vernooy, D. W.

J. Ye, D. W. Vernooy, and H. J. Kimble, “Trapping of single atoms in cavity QED,” Phys. Rev. Lett. 83, 4987–4990 (1999).
[CrossRef]

Walther, H.

H. Walther, “Single atom experiments in cavities and traps,” Proc. R. Soc. London, Ser. A 454, 431–445 (1998).
[CrossRef]

G. M. Meyer, M. Loffler, and H. Walther, “Spectrum of the ion-trap laser,” Phys. Rev. A 56, R1099–R1102 (1997).
[CrossRef]

M. Loffler, G. M. Meyer, and H. Walther, “Spectral properties of the one-atom laser,” Phys. Rev. A 55, 3923–3930 (1997).
[CrossRef]

Yamamoto, Y.

G. Bjork, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994).
[CrossRef] [PubMed]

Ye, J.

S. J. van Enk, J. McKeever, H. J. Kimble, and J. Ye, “Cooling of a single atom in an optical trap inside a resonator,” Phys. Rev. A 64, 013407 (2001).
[CrossRef]

J. Ye, D. W. Vernooy, and H. J. Kimble, “Trapping of single atoms in cavity QED,” Phys. Rev. Lett. 83, 4987–4990 (1999).
[CrossRef]

H. Mabuchi, J. Ye, and H. J. Kimble, “Full observation of single-atom dynamics in cavity QED,” Appl. Phys. B: Lasers Opt. 68, 1095–1108 (1999).
[CrossRef]

Zoller, P.

R. Dum, P. Zoller, and H. Ritsch, “Monte Carlo simulation of the atomic master equation for spontaneous emission,” Phys. Rev. A 45, 4879–4887 (1992).
[CrossRef] [PubMed]

Appl. Phys. B: Lasers Opt.

H. Mabuchi, J. Ye, and H. J. Kimble, “Full observation of single-atom dynamics in cavity QED,” Appl. Phys. B: Lasers Opt. 68, 1095–1108 (1999).
[CrossRef]

J. Exp. Theor. Phys.

S. Ya. Kilin and T. B. Karlovich, “Single-atom laser: coherent and nonclassical effects in the regime of a strong atom field correlation,” J. Exp. Theor. Phys. 95, 805–819 (2001).
[CrossRef]

J. Math. Phys.

B. Misra and E. C. G. Sudarshan, “Zeno’s paradox in quantum theory,” J. Math. Phys. 18, 756–763 (1977).
[CrossRef]

J. Mod. Opt.

T. Pellizari and H. Ritsch, “Photon statistics of the three-level one-atom laser,” J. Mod. Opt. 41, 609–623 (1994).
[CrossRef]

Nature (London)

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, “Experimental realization of a one-atom laser in the regime of strong coupling,” Nature (London) 425, 268–271 (2003).
[CrossRef]

Opt. Lett.

Phys. Rev. A

C. Ginzel, H.-J. Briegel, U. Martini, B. Englert, and A. Schenzle, “Quantum optical master equations: the one-atom laser,” Phys. Rev. A 48, 732–738 (1993).
[CrossRef] [PubMed]

M. Loffler, G. M. Meyer, and H. Walther, “Spectral properties of the one-atom laser,” Phys. Rev. A 55, 3923–3930 (1997).
[CrossRef]

S. J. van Enk, J. McKeever, H. J. Kimble, and J. Ye, “Cooling of a single atom in an optical trap inside a resonator,” Phys. Rev. A 64, 013407 (2001).
[CrossRef]

A. M. Smith and C. W. Gardiner, “Phase-space method without large-N scaling for the laser and optical bistability,” Phys. Rev. A 38, 4073–4086 (1988).
[CrossRef] [PubMed]

Y. Mu and C. Savage, “One-atom lasers,” Phys. Rev. A 46, 5944–5954 (1992).
[CrossRef] [PubMed]

B. Jones, S. Ghose, J. Clemens, P. Rice, and L. Pedrotti, “Photon statistics of a single atom laser,” Phys. Rev. A 60, 3267–3275 (1999).
[CrossRef]

G. Bjork, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994).
[CrossRef] [PubMed]

P. R. Rice and H. J. Carmichael, “Photon statistics of a cavity-QED laser: a comment on the laser phase-transition analogy,” Phys. Rev. A 50, 4318–4329 (1994).
[CrossRef] [PubMed]

G. M. Meyer, M. Loffler, and H. Walther, “Spectrum of the ion-trap laser,” Phys. Rev. A 56, R1099–R1102 (1997).
[CrossRef]

G. M. Meyer and H.-J. Briegel, “Pump-operator treatment of the ion-trap laser,” Phys. Rev. A 58, 3210–3220 (1998).
[CrossRef]

G. Koganov and R. Shuker, “Threshold and nonlinear be-havior of lasers of lambda and V configurations,” Phys. Rev. A 58, 1559–1562 (1998).
[CrossRef]

R. Dum, P. Zoller, and H. Ritsch, “Monte Carlo simulation of the atomic master equation for spontaneous emission,” Phys. Rev. A 45, 4879–4887 (1992).
[CrossRef] [PubMed]

L. Tian and H. J. Carmichael, “Quantum trajectory simulations of two-state behavior in an optical cavity containing one atom,” Phys. Rev. A 46, R6801–R6804 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett.

J. Dalibard, Y. Castin, and K. Molmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
[CrossRef] [PubMed]

T. Pellizari and H. Ritsch, “Preparation of stationary Fock states in a one-atom Raman laser,” Phys. Rev. Lett. 72, 3973–3976 (1994).
[CrossRef]

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Naegerl, D. M. Stamper-Kurn, and H. J. Kimble, “State-insensitive cooling and trapping of single atoms in an optical cavity,” Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef] [PubMed]

J. Ye, D. W. Vernooy, and H. J. Kimble, “Trapping of single atoms in cavity QED,” Phys. Rev. Lett. 83, 4987–4990 (1999).
[CrossRef]

C. J. Hood, M. S. Chapman, T. W. Lynn, and H. J. Kimble, “Real-time cavity QED with single atoms,” Phys. Rev. Lett. 80, 4157–4160 (1998).
[CrossRef]

Proc. R. Soc. London, Ser. A

H. Walther, “Single atom experiments in cavities and traps,” Proc. R. Soc. London, Ser. A 454, 431–445 (1998).
[CrossRef]

Other

H. Haken, “Fully quantum mechanical solutions of the laser equations,” in Light and Matter, L. Genzel, ed., Vol. XXV/2c of Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, 1970), pp. 99–172.

H. J. Carmichael, An Open Systems Approach to Quantum Optics (Springer-Verlag, Berlin, 1993).

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Figures (11)

Fig. 1
Fig. 1

Single-atom laser: a pumped, stationary atom in a lossy cavity, with spontaneous emission through the side of the cavity.

Fig. 2
Fig. 2

Schematic diagram of a single three-level atom in a cavity with an incoherent pump and with level four adiabatically eliminated. For the four-level system the values of γij are spontaneous-emission rates from levels i to j, and Γ is a pump rate. For the three-level system Γ is an effective pump rate and γ is the spontaneous-emission rate on the lasing transition. For both systems, κ is the cavity decay rate and g is the atom–field coupling strength.

Fig. 3
Fig. 3

Linewidth of the single three-level incoherently pumped laser as a function of pump strength Γ/γ for κ/γ=0.1 and g/γ=0.6 (solid curve). Dashed curve, plot of κ/2n for the same parameters. Inset, mean intracavity photon number for the incoherently pumped three-level laser as a function of pump strength for the same parameters.

Fig. 4
Fig. 4

Output spectrum of the single three-level incoherently pumped laser for g/γ=1.414 and κ/γ=0.1 as a function of pumping strength Γ/γ. This plot is for small pumping strengths.

Fig. 5
Fig. 5

Output spectrum of the single three-level incoherently pumped laser for g/γ=1.414 and κ/γ=0.1 as a function of pumping strength Γ/γ. Here we show the behavior over a broad range of pump values and the mean intracavity photon number for the same parameters.

Fig. 6
Fig. 6

Conditioned dipole on the lasing transition for the three-level incoherently pumped laser with (a) Γ/γ=0.1, g/γ=1.414, and κ/γ=0.1 and with (b) Γ/γ=10.0, g/γ=1.414, and κ/γ=0.1.

Fig. 7
Fig. 7

Schematic diagram of a single four-level atom in a cavity with an incoherent pump and with level four adiabatically eliminated. For the four-level system the values of γij are spontaneous-emission rates from level i to level j and Γ is a pump rate. For the three-level system Γ is an effective pump rate, γ is the spontaneous-emission rate on the lasing transition, and γf is the spontaneous-emission rate from the lower lasing level. For both systems κ is the cavity decay rate and g is the atom–field coupling strength.

Fig. 8
Fig. 8

Linewidth of the single four-level incoherently pumped laser as a function of pumping strength Γ/γ for κ/γ=0.1 and g/γ=0.6 for (a) β=0.3, (b) β=0.4, and (c) β=0.5. Dashed curves are plots of κ/2n for the same γf/γ, κ/γ, and (d) β=0.3, (e) β=0.4, and (f) β=0.5.

Fig. 9
Fig. 9

Linewidth of the single four-level incoherently pumped laser as a function of pumping strength Γ/γ for κ/γ=0.1 and g/γ=0.6 for (a) β=0.6, (b) β=0.7, (c) β=0.8, and (d) β=0.9. In (e) β=0.998, with γf/γ=100.0 and κ/γ=0.1.

Fig. 10
Fig. 10

Output spectrum of the single four-level incoherently pumped laser for g/γ=10.0, κ/γ=0.1, and γf/γ=2.0, as a function of pumping strength Γ/γ.

Fig. 11
Fig. 11

Plot of the conditioned dipole on the lasing transition for (a) Γ/γ=1.0, g/γ=10.0, and κ/γ=0.1 and for (b) Γ/γ=10.0, g/γ=10.0, and κ/γ=0.1.

Equations (44)

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ρ˙=-i[Hs, ρ]+κ(2aρa-aaρ-ρaa)+γ2(2σ-ρσ+-σ+σ-ρ-ρσ+σ-)+Γ2(2σ+ρσ--σ-σ+ρ-ρσ-σ+).
HS=ig(aσ--aσ+).
S(ω)=-dτ exp(iωτ)a(0)a(τ)=2R0dτ exp(iωτ)a(0)a(τ).
dρn,1;n,1dt=2κ(n+1)ρn+1,1;n+1,1-(2κn+Γ)ρn,1;n,1+γρn,2;n,2-2n+1gρn,1;n-1,2,
dρn,2;n,2dt=2κ(n+1)ρn+1,2;n+1,2-{2κn+γ}ρn,2;n,2+Γρn,1;n,1+2ngρn,1;n-1,2,
dρn,1;n-1,2dt=2κn(n-1)ρn+1,2;n,1-κ(2n-1)+Γ+γ2ρn,2;n-1,1+ng(ρn-1,2;n-1,2-ρn,1;n,1).
β=2g2/(γ+Γ+2κ)2g2/(γ+Γ+2κ)+γ/2.
a+(0)a(τ)=Tr[a(0)A(τ)]=i,nn+1i, n+1|A(τ)|i, n,
dAn+1,1;n,1dt=2κ[(n+2)(n+1)]1/2An+2,1;n+1,1-[κ(2n+1)+Γ]An+1,1;n,1+γAn+1,2;n,2+gn+1An,2;n,1+gnAn+1,1;n-1,2,
dAn+1,2;n,2dt=2κ[(n+2)(n+1)]1/2An+2,2;n+1,1-[κ(2n+1)+γ]An+1,2;n,2+ΓAn+1,1;n,1-gn+2An+2,1;n,2-gn+1An+1,2,n+1,1,
dAn+2,1;n,2dt=2κ[(n+3)(n+1)]1/2An+3,1;n+1,2-[κ(2n+1)+γ/2+Γ/2]An+2,1;1,2+gn+2An+1,2;n,2-gn+1An+2,1;n+1,1,
dAn,2;n,1dt=2κ(n+1)An+1,2;n,1-(2κ+γ/2+κ/2)+gnAn,2;n-1,2-gn+1An+1,1;n,1.
B=An+1,1;n,1An+1,2;n,2An+2,1;n,2An,2;n,1.
dBdt=MB.
B˜(ω)={M-iωI}-1B(0),
S(ω)=i,nn+1i, n+1|RA˜(ω)|i, n.
|ψc(t)=n=0C1,n(t)exp(-iE1,nt)|1, n+C2,n(t)exp(-iE2,nt)|2, n.
HD=(ω-iκ)aa+ig(aσ32-aσ-)-iγ2σ+σ--iΓ2σ-σ+.
F1=γσ-,
F2=Γσ+,
F3=2κa.
ρ˙=-i[Hs, ρ]+κ(2aρa-aaρ-ρaa)+Γ2(2σ13ρσ31-σ31σ13ρ-ρσ31σ13)+γ2(2σ32ρσ23-σ23σ32ρ-ρσ23σ32)+γf2(2σ21ρσ12-σ12σ21ρ-ρσ12σ21),
HS=ig(aσ32-aσ23)
σij=|ji|.
dρn,1;n,1dt=2κ(n+1)ρn+1,1;n+1,1-{2κn+Γ}ρn,1;n,1+γfρn,2;n,2,
dρn,2;n,2dt=2κ(n+1)ρn+1,2;n+1,2-{2κn+γf}ρn,2;n,2+γρn,3;n,3+2ngρn,2;n-1,3,
dρn,3;n,3dt=2κ(n+1)ρn+1,3;n+1,3-{2κn+γ}ρn,3;n,3+Γρn,1;n,1-2n+1gρn,3;n+1,2,
dρn,2;n-1,3dt=2κn(n-1)ρn+1,2;n,3-κ(2n-1)+γ2ρn,2;n-1,3+ng{ρn-1,3;n-1,3-ρn,2;n,2}.
dAn+1,1;n,1dt=2κ[(n+2)(n+1)]1/2An+2,1;n+1,1-[κ(2n+1)+Γ]An=1,1;n,1+γfAn+1,2;n,2,
dAn+1,2;n,2dt=2κ[(n+2)(n+1)]1/2An+2,2;n+1,2-[κ(2n+1)+γf]An+1,2;n,2+γAn+1,3;n,3+gn+1An,3;n,2+gnAn+1,2;n-1,3,
dAn+3,1;n,3dt=2κ[(n+2)(n+1)]1/2An+2,3;n+1,3-[κ(2n+1)+γ]An+1,3;n,3+ΓAn+1,1;n,1-gn+2An+2,2;n,3-gn+1An+1,3;n+1,2,
dAn+2,2;n,3dt=2κ[(n+3)(n+1)]1/2An+3,2;n+1,3-[κ(2n+2)+γ/2+γf/2]An+2,2;n,3+gn+2An+1,3;n,3-gn+1An+2,2;n+1,2,
dAn,3;n,2dt=2κ(n+1)An+1,3;n+1,2-(2κn+γ/2γf/2)An,3;n,2+gnAn,3;n-1,3-gn+1An+1,2;n,3.
|ψc(t)=n=0C1,n(t)exp(-iE1,nt)|1, n+C2,n(t)exp(-iE2,nt)|2, n+C3,n(t)exp(-iE3,nt)|3, n,
HD=(ω-iκ)aa+ig(aσ32-aσ23)-iγ2σ23σ32-iγf2σ12σ21-iΓ2σ31σ13.
F1=γσ32,
F2=γfσ21,
F3=Γσ13,
F4=2κa.
C˙1,n=-Γ2+nκC1,n,
C˙2,n+1=-γf2+(n+1)κC2,n+1+gn+1C3,n,
C˙3,n=-γ2+nκC3,n-gn+1C2,n+1.
C˙3,n=-γ2+nκC3,n-g2κ(n+1)+γf/2(n+1)C1,n+1.
β=2g2/(γf+2κ)2g2/(γf+2κ)+γ/2

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