Abstract

Atom-cavity coupling constant is a key parameter in cavity quantum electrodynamics for describing the interaction between an atom and a quantized electromagnetic field in a cavity. This paper reports a novel way to tune the coupling constant continuously by inducing an averaging of the atomic dipole moment over degenerate magnetic sublevels with elliptic polarization of the cavity field. We present an analytic solution of the stationary-state density matrix for this system with consideration of FF + 1 hyperfine transition under a weak excitation condition. We rigorously show that the stationary-state emission spectra of this system can be approximated by that of a non-degenerate two-level atom with an effective coupling constant as a function of the elliptic angle of the cavity field only. A precise condition for this approximation is derived and its physical meaning is interpreted in terms of a population-averaged transition strength and its variance. Our results can be used to control the coupling constant in cavity quantum electrodynamics experiments with a degenerate two-level atom with magnetic sublevels. Possible applications of our results are discussed.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Ye, D.W. Vernooy, and H. J. Kimble, “Trapping of single atoms in cavity QED,” Phys. Rev. Lett. 83, 4987-4990 (1999).
    [CrossRef]
  2. P. W. H. Pinkse, T. Fischer, P. Maunz, and G. Rempe, “Trapping an atom with single photons,” Nature 404, 365-368 (2000).
    [CrossRef] [PubMed]
  3. A. Kuhn, M. Hennrich, and G. Rempe, “Deterministic single-photon sources for distributed quantum networking,” Phys. Rev. Lett. 89, 067901 (2002).
    [CrossRef] [PubMed]
  4. J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of single photons from one atom trapped in a cavity,” Science 303, 1992-1994 (2004).
    [CrossRef] [PubMed]
  5. I. Schuster, A. Kubanek, A. Fuhrmanek, T. Puppe, P. W. H. Pinkse, K. Murr, and G. Rempe, “Nonlinear spectroscopy of photons bound to one atom,” Nature Phys. 4, 382-385 (2008).
    [CrossRef]
  6. M. Khudaverdyan, W. Alt, T. Kampschulte, S. Reick, A. Thobe, A. Widera, and D. Meschede, “Quantum jumps and spin dynamics of interacting atoms in a strongly coupled atom-cavity system,” Phys. Rev. Lett. 103, 123006 (2009).
    [CrossRef] [PubMed]
  7. . C. K. Law and J. H. Eberly, “Arbitrary control of a quantum electromagnetic field,” Phys. Rev. Lett. 76, 1055-1058 (1996).
    [CrossRef] [PubMed]
  8. T. Kato, Perturbation Theory for Linear Operators (Springer, New York, 1966).
  9. K. M. Fortier, S. Y. Kim, M. J. Gibbons, P. Ahmadi, and M. S. Chapman, “Deterministic loading of individual atoms to a high-finesse optical cavity,” Phys. Rev. Lett. 98, 233601 (2007).
    [CrossRef] [PubMed]
  10. M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schorner, A. Widera and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008).
    [CrossRef]
  11. . H. J. Carmichael, An Open Systems Approach to Quantum Optics (Springer, Berlin, 1993).
  12. A. V. Ta˘ıchenachev, A.M. Tuma˘ıkin, V. I. Yudin, and G. Nienhuis, “Steady state of atoms in a resonant field with elliptical polarization,” Phys. Rev. A 69, 033410 (2004).
    [CrossRef]
  13. H. J. Carmichael, R. J. Brecha, and P. R. Rice, “Quantum interference and collapse of the wavefunction in cavity QED,” Opt. Commun. 82, 73-79 (1991).
    [CrossRef]
  14. R. J. Brecha, P. R. Rice, and M. Xiao, “N two-level atoms in a driven optical cavity: Quantum dynamics of forward photon scattering for weak incident fields,” Phys. Rev. A 59, 2392-2417 (1999).
    [CrossRef]
  15. J. R. Morris, and B. W. Shore, “Reduction of degenerate two-level excitation to independent two-state systems,” Phys. Rev. A 27, 906-912 (1983).
    [CrossRef]
  16. G. Nienhuis, “Natural basis of magnetic substates for a radiative transition with arbitrary polarization,” Opt. Commun. 59353-356 (1986).
    [CrossRef]
  17. C. Dembowski, H. -D. Gräf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter, “Experimental observation of the topological structure of exceptional points,” Phys. Rev. Lett. 86787-790 (2001).
    [CrossRef] [PubMed]
  18. D. W. Vernooy, A. Furusawa, N. Ph. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57R2293-R2296 (1998).
    [CrossRef]
  19. S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71013817 (2005).
    [CrossRef]
  20. J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65, 016608 (2001).
    [CrossRef]
  21. A. D. Boozer, R. Miller, T. E. Northup, A. Boca, and H. J. Kimble, “Optical pumping via incoherent Raman transitions,” Phys. Rev. A 76, 063401 (2007).
    [CrossRef]
  22. T. Wilk, S. C. Webster, A. Kuhn, and G. Rempe, “Single-atom single-photon quantum interface,” Science 317, 488-490 (2007).
    [CrossRef] [PubMed]
  23. D. Jacob, M. Vallet, F. Bretenaker, A. L. Floch, and M. Oger, “Supermirror phase anisotropy measurement,” Opt. Lett. 20, 671-673 (1995).
    [CrossRef]
  24. J. Y. Lee, H-W. Lee, J. W. Kim, Y. S. Yoo, and J. W. Hahn, “Measurement of ultralow supermirror birefringence by use of the polarimetric differential cavity ringdown technique,” Applied Optics 39, 1941-1945 (2000).
    [CrossRef]
  25. E. T. Jaynes, and F.W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89-109 (1963).
    [CrossRef]
  26. K. M. Birnbaum, A. S. Parkins, and H. J. Kimble, “Cavity QED with multiple hyperfine levels,” Phys. Rev. A 74, 063802 (2006).
    [CrossRef]
  27. A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “An atom in an elliptically polarized resonant field: exact stationary solution for closed J →J + 1 transitions,” JETP 83, 949-961 (1996).
  28. A. M. Tumaikin and V. I. Yudin, “Coherent stationary states under the interaction of atoms with polarized resonant light in a magnetic field,” Sov. Phys. JETP 71, 43-47 (1990).

2009 (1)

M. Khudaverdyan, W. Alt, T. Kampschulte, S. Reick, A. Thobe, A. Widera, and D. Meschede, “Quantum jumps and spin dynamics of interacting atoms in a strongly coupled atom-cavity system,” Phys. Rev. Lett. 103, 123006 (2009).
[CrossRef] [PubMed]

2008 (2)

I. Schuster, A. Kubanek, A. Fuhrmanek, T. Puppe, P. W. H. Pinkse, K. Murr, and G. Rempe, “Nonlinear spectroscopy of photons bound to one atom,” Nature Phys. 4, 382-385 (2008).
[CrossRef]

M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schorner, A. Widera and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008).
[CrossRef]

2007 (3)

K. M. Fortier, S. Y. Kim, M. J. Gibbons, P. Ahmadi, and M. S. Chapman, “Deterministic loading of individual atoms to a high-finesse optical cavity,” Phys. Rev. Lett. 98, 233601 (2007).
[CrossRef] [PubMed]

A. D. Boozer, R. Miller, T. E. Northup, A. Boca, and H. J. Kimble, “Optical pumping via incoherent Raman transitions,” Phys. Rev. A 76, 063401 (2007).
[CrossRef]

T. Wilk, S. C. Webster, A. Kuhn, and G. Rempe, “Single-atom single-photon quantum interface,” Science 317, 488-490 (2007).
[CrossRef] [PubMed]

2006 (1)

K. M. Birnbaum, A. S. Parkins, and H. J. Kimble, “Cavity QED with multiple hyperfine levels,” Phys. Rev. A 74, 063802 (2006).
[CrossRef]

2005 (1)

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71013817 (2005).
[CrossRef]

2004 (2)

A. V. Ta˘ıchenachev, A.M. Tuma˘ıkin, V. I. Yudin, and G. Nienhuis, “Steady state of atoms in a resonant field with elliptical polarization,” Phys. Rev. A 69, 033410 (2004).
[CrossRef]

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of single photons from one atom trapped in a cavity,” Science 303, 1992-1994 (2004).
[CrossRef] [PubMed]

2002 (1)

A. Kuhn, M. Hennrich, and G. Rempe, “Deterministic single-photon sources for distributed quantum networking,” Phys. Rev. Lett. 89, 067901 (2002).
[CrossRef] [PubMed]

2001 (2)

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65, 016608 (2001).
[CrossRef]

C. Dembowski, H. -D. Gräf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter, “Experimental observation of the topological structure of exceptional points,” Phys. Rev. Lett. 86787-790 (2001).
[CrossRef] [PubMed]

2000 (2)

P. W. H. Pinkse, T. Fischer, P. Maunz, and G. Rempe, “Trapping an atom with single photons,” Nature 404, 365-368 (2000).
[CrossRef] [PubMed]

J. Y. Lee, H-W. Lee, J. W. Kim, Y. S. Yoo, and J. W. Hahn, “Measurement of ultralow supermirror birefringence by use of the polarimetric differential cavity ringdown technique,” Applied Optics 39, 1941-1945 (2000).
[CrossRef]

1999 (2)

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

R. J. Brecha, P. R. Rice, and M. Xiao, “N two-level atoms in a driven optical cavity: Quantum dynamics of forward photon scattering for weak incident fields,” Phys. Rev. A 59, 2392-2417 (1999).
[CrossRef]

1998 (1)

D. W. Vernooy, A. Furusawa, N. Ph. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57R2293-R2296 (1998).
[CrossRef]

1996 (2)

. C. K. Law and J. H. Eberly, “Arbitrary control of a quantum electromagnetic field,” Phys. Rev. Lett. 76, 1055-1058 (1996).
[CrossRef] [PubMed]

A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “An atom in an elliptically polarized resonant field: exact stationary solution for closed J →J + 1 transitions,” JETP 83, 949-961 (1996).

1995 (1)

1991 (1)

H. J. Carmichael, R. J. Brecha, and P. R. Rice, “Quantum interference and collapse of the wavefunction in cavity QED,” Opt. Commun. 82, 73-79 (1991).
[CrossRef]

1990 (1)

A. M. Tumaikin and V. I. Yudin, “Coherent stationary states under the interaction of atoms with polarized resonant light in a magnetic field,” Sov. Phys. JETP 71, 43-47 (1990).

1986 (1)

G. Nienhuis, “Natural basis of magnetic substates for a radiative transition with arbitrary polarization,” Opt. Commun. 59353-356 (1986).
[CrossRef]

1983 (1)

J. R. Morris, and B. W. Shore, “Reduction of degenerate two-level excitation to independent two-state systems,” Phys. Rev. A 27, 906-912 (1983).
[CrossRef]

1963 (1)

E. T. Jaynes, and F.W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89-109 (1963).
[CrossRef]

Ahmadi, P.

K. M. Fortier, S. Y. Kim, M. J. Gibbons, P. Ahmadi, and M. S. Chapman, “Deterministic loading of individual atoms to a high-finesse optical cavity,” Phys. Rev. Lett. 98, 233601 (2007).
[CrossRef] [PubMed]

Alt, W.

M. Khudaverdyan, W. Alt, T. Kampschulte, S. Reick, A. Thobe, A. Widera, and D. Meschede, “Quantum jumps and spin dynamics of interacting atoms in a strongly coupled atom-cavity system,” Phys. Rev. Lett. 103, 123006 (2009).
[CrossRef] [PubMed]

M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schorner, A. Widera and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008).
[CrossRef]

Birnbaum, K. M.

K. M. Birnbaum, A. S. Parkins, and H. J. Kimble, “Cavity QED with multiple hyperfine levels,” Phys. Rev. A 74, 063802 (2006).
[CrossRef]

Boca, A.

A. D. Boozer, R. Miller, T. E. Northup, A. Boca, and H. J. Kimble, “Optical pumping via incoherent Raman transitions,” Phys. Rev. A 76, 063401 (2007).
[CrossRef]

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of single photons from one atom trapped in a cavity,” Science 303, 1992-1994 (2004).
[CrossRef] [PubMed]

Boozer, A. D.

A. D. Boozer, R. Miller, T. E. Northup, A. Boca, and H. J. Kimble, “Optical pumping via incoherent Raman transitions,” Phys. Rev. A 76, 063401 (2007).
[CrossRef]

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of single photons from one atom trapped in a cavity,” Science 303, 1992-1994 (2004).
[CrossRef] [PubMed]

Brecha, R. J.

R. J. Brecha, P. R. Rice, and M. Xiao, “N two-level atoms in a driven optical cavity: Quantum dynamics of forward photon scattering for weak incident fields,” Phys. Rev. A 59, 2392-2417 (1999).
[CrossRef]

H. J. Carmichael, R. J. Brecha, and P. R. Rice, “Quantum interference and collapse of the wavefunction in cavity QED,” Opt. Commun. 82, 73-79 (1991).
[CrossRef]

Bretenaker, F.

Buck, J. R.

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of single photons from one atom trapped in a cavity,” Science 303, 1992-1994 (2004).
[CrossRef] [PubMed]

Carmichael, H. J.

H. J. Carmichael, R. J. Brecha, and P. R. Rice, “Quantum interference and collapse of the wavefunction in cavity QED,” Opt. Commun. 82, 73-79 (1991).
[CrossRef]

Chapman, M. S.

K. M. Fortier, S. Y. Kim, M. J. Gibbons, P. Ahmadi, and M. S. Chapman, “Deterministic loading of individual atoms to a high-finesse optical cavity,” Phys. Rev. Lett. 98, 233601 (2007).
[CrossRef] [PubMed]

Cummings, F.W.

E. T. Jaynes, and F.W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89-109 (1963).
[CrossRef]

Dembowski, C.

C. Dembowski, H. -D. Gräf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter, “Experimental observation of the topological structure of exceptional points,” Phys. Rev. Lett. 86787-790 (2001).
[CrossRef] [PubMed]

Dotsenko, I.

M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schorner, A. Widera and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008).
[CrossRef]

Eberly, J. H.

. C. K. Law and J. H. Eberly, “Arbitrary control of a quantum electromagnetic field,” Phys. Rev. Lett. 76, 1055-1058 (1996).
[CrossRef] [PubMed]

Fischer, T.

P. W. H. Pinkse, T. Fischer, P. Maunz, and G. Rempe, “Trapping an atom with single photons,” Nature 404, 365-368 (2000).
[CrossRef] [PubMed]

Floch, A. L.

Fortier, K. M.

K. M. Fortier, S. Y. Kim, M. J. Gibbons, P. Ahmadi, and M. S. Chapman, “Deterministic loading of individual atoms to a high-finesse optical cavity,” Phys. Rev. Lett. 98, 233601 (2007).
[CrossRef] [PubMed]

Fuhrmanek, A.

I. Schuster, A. Kubanek, A. Fuhrmanek, T. Puppe, P. W. H. Pinkse, K. Murr, and G. Rempe, “Nonlinear spectroscopy of photons bound to one atom,” Nature Phys. 4, 382-385 (2008).
[CrossRef]

Furusawa, A.

D. W. Vernooy, A. Furusawa, N. Ph. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57R2293-R2296 (1998).
[CrossRef]

Georgiades, N. Ph.

D. W. Vernooy, A. Furusawa, N. Ph. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57R2293-R2296 (1998).
[CrossRef]

Gibbons, M. J.

K. M. Fortier, S. Y. Kim, M. J. Gibbons, P. Ahmadi, and M. S. Chapman, “Deterministic loading of individual atoms to a high-finesse optical cavity,” Phys. Rev. Lett. 98, 233601 (2007).
[CrossRef] [PubMed]

Goh, K. W.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71013817 (2005).
[CrossRef]

Gräf, H. -D.

C. Dembowski, H. -D. Gräf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter, “Experimental observation of the topological structure of exceptional points,” Phys. Rev. Lett. 86787-790 (2001).
[CrossRef] [PubMed]

Hahn, J. W.

J. Y. Lee, H-W. Lee, J. W. Kim, Y. S. Yoo, and J. W. Hahn, “Measurement of ultralow supermirror birefringence by use of the polarimetric differential cavity ringdown technique,” Applied Optics 39, 1941-1945 (2000).
[CrossRef]

Harney, H. L.

C. Dembowski, H. -D. Gräf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter, “Experimental observation of the topological structure of exceptional points,” Phys. Rev. Lett. 86787-790 (2001).
[CrossRef] [PubMed]

Heine, A.

C. Dembowski, H. -D. Gräf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter, “Experimental observation of the topological structure of exceptional points,” Phys. Rev. Lett. 86787-790 (2001).
[CrossRef] [PubMed]

Heiss, W. D.

C. Dembowski, H. -D. Gräf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter, “Experimental observation of the topological structure of exceptional points,” Phys. Rev. Lett. 86787-790 (2001).
[CrossRef] [PubMed]

Hennrich, M.

A. Kuhn, M. Hennrich, and G. Rempe, “Deterministic single-photon sources for distributed quantum networking,” Phys. Rev. Lett. 89, 067901 (2002).
[CrossRef] [PubMed]

Ilchenko, V. S.

D. W. Vernooy, A. Furusawa, N. Ph. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57R2293-R2296 (1998).
[CrossRef]

Jacob, D.

Jaynes, E. T.

E. T. Jaynes, and F.W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89-109 (1963).
[CrossRef]

Kampschulte, T.

M. Khudaverdyan, W. Alt, T. Kampschulte, S. Reick, A. Thobe, A. Widera, and D. Meschede, “Quantum jumps and spin dynamics of interacting atoms in a strongly coupled atom-cavity system,” Phys. Rev. Lett. 103, 123006 (2009).
[CrossRef] [PubMed]

M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schorner, A. Widera and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008).
[CrossRef]

Khudaverdyan, M.

M. Khudaverdyan, W. Alt, T. Kampschulte, S. Reick, A. Thobe, A. Widera, and D. Meschede, “Quantum jumps and spin dynamics of interacting atoms in a strongly coupled atom-cavity system,” Phys. Rev. Lett. 103, 123006 (2009).
[CrossRef] [PubMed]

M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schorner, A. Widera and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008).
[CrossRef]

Kim, J. W.

J. Y. Lee, H-W. Lee, J. W. Kim, Y. S. Yoo, and J. W. Hahn, “Measurement of ultralow supermirror birefringence by use of the polarimetric differential cavity ringdown technique,” Applied Optics 39, 1941-1945 (2000).
[CrossRef]

Kim, S. Y.

K. M. Fortier, S. Y. Kim, M. J. Gibbons, P. Ahmadi, and M. S. Chapman, “Deterministic loading of individual atoms to a high-finesse optical cavity,” Phys. Rev. Lett. 98, 233601 (2007).
[CrossRef] [PubMed]

Kimble, H. J.

A. D. Boozer, R. Miller, T. E. Northup, A. Boca, and H. J. Kimble, “Optical pumping via incoherent Raman transitions,” Phys. Rev. A 76, 063401 (2007).
[CrossRef]

K. M. Birnbaum, A. S. Parkins, and H. J. Kimble, “Cavity QED with multiple hyperfine levels,” Phys. Rev. A 74, 063802 (2006).
[CrossRef]

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71013817 (2005).
[CrossRef]

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of single photons from one atom trapped in a cavity,” Science 303, 1992-1994 (2004).
[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]

D. W. Vernooy, A. Furusawa, N. Ph. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57R2293-R2296 (1998).
[CrossRef]

Kippenberg, T. J.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71013817 (2005).
[CrossRef]

Kubanek, A.

I. Schuster, A. Kubanek, A. Fuhrmanek, T. Puppe, P. W. H. Pinkse, K. Murr, and G. Rempe, “Nonlinear spectroscopy of photons bound to one atom,” Nature Phys. 4, 382-385 (2008).
[CrossRef]

Kuhn, A.

T. Wilk, S. C. Webster, A. Kuhn, and G. Rempe, “Single-atom single-photon quantum interface,” Science 317, 488-490 (2007).
[CrossRef] [PubMed]

A. Kuhn, M. Hennrich, and G. Rempe, “Deterministic single-photon sources for distributed quantum networking,” Phys. Rev. Lett. 89, 067901 (2002).
[CrossRef] [PubMed]

Kuzmich, A.

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of single photons from one atom trapped in a cavity,” Science 303, 1992-1994 (2004).
[CrossRef] [PubMed]

Law, C. K.

. C. K. Law and J. H. Eberly, “Arbitrary control of a quantum electromagnetic field,” Phys. Rev. Lett. 76, 1055-1058 (1996).
[CrossRef] [PubMed]

Lee, H-W.

J. Y. Lee, H-W. Lee, J. W. Kim, Y. S. Yoo, and J. W. Hahn, “Measurement of ultralow supermirror birefringence by use of the polarimetric differential cavity ringdown technique,” Applied Optics 39, 1941-1945 (2000).
[CrossRef]

Lee, J. Y.

J. Y. Lee, H-W. Lee, J. W. Kim, Y. S. Yoo, and J. W. Hahn, “Measurement of ultralow supermirror birefringence by use of the polarimetric differential cavity ringdown technique,” Applied Optics 39, 1941-1945 (2000).
[CrossRef]

Lenhard, K.

M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schorner, A. Widera and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008).
[CrossRef]

Loncar, M.

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65, 016608 (2001).
[CrossRef]

Mabuchi, H.

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65, 016608 (2001).
[CrossRef]

Maunz, P.

P. W. H. Pinkse, T. Fischer, P. Maunz, and G. Rempe, “Trapping an atom with single photons,” Nature 404, 365-368 (2000).
[CrossRef] [PubMed]

McKeever, J.

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of single photons from one atom trapped in a cavity,” Science 303, 1992-1994 (2004).
[CrossRef] [PubMed]

Meschede, D.

M. Khudaverdyan, W. Alt, T. Kampschulte, S. Reick, A. Thobe, A. Widera, and D. Meschede, “Quantum jumps and spin dynamics of interacting atoms in a strongly coupled atom-cavity system,” Phys. Rev. Lett. 103, 123006 (2009).
[CrossRef] [PubMed]

M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schorner, A. Widera and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008).
[CrossRef]

Miller, R.

A. D. Boozer, R. Miller, T. E. Northup, A. Boca, and H. J. Kimble, “Optical pumping via incoherent Raman transitions,” Phys. Rev. A 76, 063401 (2007).
[CrossRef]

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of single photons from one atom trapped in a cavity,” Science 303, 1992-1994 (2004).
[CrossRef] [PubMed]

Morris, J. R.

J. R. Morris, and B. W. Shore, “Reduction of degenerate two-level excitation to independent two-state systems,” Phys. Rev. A 27, 906-912 (1983).
[CrossRef]

Murr, K.

I. Schuster, A. Kubanek, A. Fuhrmanek, T. Puppe, P. W. H. Pinkse, K. Murr, and G. Rempe, “Nonlinear spectroscopy of photons bound to one atom,” Nature Phys. 4, 382-385 (2008).
[CrossRef]

Nienhuis, G.

A. V. Ta˘ıchenachev, A.M. Tuma˘ıkin, V. I. Yudin, and G. Nienhuis, “Steady state of atoms in a resonant field with elliptical polarization,” Phys. Rev. A 69, 033410 (2004).
[CrossRef]

G. Nienhuis, “Natural basis of magnetic substates for a radiative transition with arbitrary polarization,” Opt. Commun. 59353-356 (1986).
[CrossRef]

Northup, T. E.

A. D. Boozer, R. Miller, T. E. Northup, A. Boca, and H. J. Kimble, “Optical pumping via incoherent Raman transitions,” Phys. Rev. A 76, 063401 (2007).
[CrossRef]

Oger, M.

Parkins, A. S.

K. M. Birnbaum, A. S. Parkins, and H. J. Kimble, “Cavity QED with multiple hyperfine levels,” Phys. Rev. A 74, 063802 (2006).
[CrossRef]

Pinkse, P. W. H.

I. Schuster, A. Kubanek, A. Fuhrmanek, T. Puppe, P. W. H. Pinkse, K. Murr, and G. Rempe, “Nonlinear spectroscopy of photons bound to one atom,” Nature Phys. 4, 382-385 (2008).
[CrossRef]

P. W. H. Pinkse, T. Fischer, P. Maunz, and G. Rempe, “Trapping an atom with single photons,” Nature 404, 365-368 (2000).
[CrossRef] [PubMed]

Puppe, T.

I. Schuster, A. Kubanek, A. Fuhrmanek, T. Puppe, P. W. H. Pinkse, K. Murr, and G. Rempe, “Nonlinear spectroscopy of photons bound to one atom,” Nature Phys. 4, 382-385 (2008).
[CrossRef]

Rauschenbeutel, A.

M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schorner, A. Widera and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008).
[CrossRef]

Rehfeld, H.

C. Dembowski, H. -D. Gräf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter, “Experimental observation of the topological structure of exceptional points,” Phys. Rev. Lett. 86787-790 (2001).
[CrossRef] [PubMed]

Reick, S.

M. Khudaverdyan, W. Alt, T. Kampschulte, S. Reick, A. Thobe, A. Widera, and D. Meschede, “Quantum jumps and spin dynamics of interacting atoms in a strongly coupled atom-cavity system,” Phys. Rev. Lett. 103, 123006 (2009).
[CrossRef] [PubMed]

M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schorner, A. Widera and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008).
[CrossRef]

Rempe, G.

I. Schuster, A. Kubanek, A. Fuhrmanek, T. Puppe, P. W. H. Pinkse, K. Murr, and G. Rempe, “Nonlinear spectroscopy of photons bound to one atom,” Nature Phys. 4, 382-385 (2008).
[CrossRef]

T. Wilk, S. C. Webster, A. Kuhn, and G. Rempe, “Single-atom single-photon quantum interface,” Science 317, 488-490 (2007).
[CrossRef] [PubMed]

A. Kuhn, M. Hennrich, and G. Rempe, “Deterministic single-photon sources for distributed quantum networking,” Phys. Rev. Lett. 89, 067901 (2002).
[CrossRef] [PubMed]

P. W. H. Pinkse, T. Fischer, P. Maunz, and G. Rempe, “Trapping an atom with single photons,” Nature 404, 365-368 (2000).
[CrossRef] [PubMed]

Rice, P. R.

R. J. Brecha, P. R. Rice, and M. Xiao, “N two-level atoms in a driven optical cavity: Quantum dynamics of forward photon scattering for weak incident fields,” Phys. Rev. A 59, 2392-2417 (1999).
[CrossRef]

H. J. Carmichael, R. J. Brecha, and P. R. Rice, “Quantum interference and collapse of the wavefunction in cavity QED,” Opt. Commun. 82, 73-79 (1991).
[CrossRef]

Richter, A.

C. Dembowski, H. -D. Gräf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter, “Experimental observation of the topological structure of exceptional points,” Phys. Rev. Lett. 86787-790 (2001).
[CrossRef] [PubMed]

Scherer, A.

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65, 016608 (2001).
[CrossRef]

Schorner, K.

M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schorner, A. Widera and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008).
[CrossRef]

Schuster, I.

I. Schuster, A. Kubanek, A. Fuhrmanek, T. Puppe, P. W. H. Pinkse, K. Murr, and G. Rempe, “Nonlinear spectroscopy of photons bound to one atom,” Nature Phys. 4, 382-385 (2008).
[CrossRef]

Shore, B. W.

J. R. Morris, and B. W. Shore, “Reduction of degenerate two-level excitation to independent two-state systems,” Phys. Rev. A 27, 906-912 (1983).
[CrossRef]

Spillane, S. M.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71013817 (2005).
[CrossRef]

Ta?ichenachev, A. V.

A. V. Ta˘ıchenachev, A.M. Tuma˘ıkin, V. I. Yudin, and G. Nienhuis, “Steady state of atoms in a resonant field with elliptical polarization,” Phys. Rev. A 69, 033410 (2004).
[CrossRef]

Taichenachev, A. V.

A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “An atom in an elliptically polarized resonant field: exact stationary solution for closed J →J + 1 transitions,” JETP 83, 949-961 (1996).

Thobe, A.

M. Khudaverdyan, W. Alt, T. Kampschulte, S. Reick, A. Thobe, A. Widera, and D. Meschede, “Quantum jumps and spin dynamics of interacting atoms in a strongly coupled atom-cavity system,” Phys. Rev. Lett. 103, 123006 (2009).
[CrossRef] [PubMed]

Tuma?ikin, A.M.

A. V. Ta˘ıchenachev, A.M. Tuma˘ıkin, V. I. Yudin, and G. Nienhuis, “Steady state of atoms in a resonant field with elliptical polarization,” Phys. Rev. A 69, 033410 (2004).
[CrossRef]

Tumaikin, A. M.

A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “An atom in an elliptically polarized resonant field: exact stationary solution for closed J →J + 1 transitions,” JETP 83, 949-961 (1996).

A. M. Tumaikin and V. I. Yudin, “Coherent stationary states under the interaction of atoms with polarized resonant light in a magnetic field,” Sov. Phys. JETP 71, 43-47 (1990).

Vahala, K. J.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71013817 (2005).
[CrossRef]

Vallet, M.

Vernooy, D. W.

D. W. Vernooy, A. Furusawa, N. Ph. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57R2293-R2296 (1998).
[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]

Vuckovic, J.

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65, 016608 (2001).
[CrossRef]

Webster, S. C.

T. Wilk, S. C. Webster, A. Kuhn, and G. Rempe, “Single-atom single-photon quantum interface,” Science 317, 488-490 (2007).
[CrossRef] [PubMed]

Widera, A.

M. Khudaverdyan, W. Alt, T. Kampschulte, S. Reick, A. Thobe, A. Widera, and D. Meschede, “Quantum jumps and spin dynamics of interacting atoms in a strongly coupled atom-cavity system,” Phys. Rev. Lett. 103, 123006 (2009).
[CrossRef] [PubMed]

M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schorner, A. Widera and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008).
[CrossRef]

Wilcut, E.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71013817 (2005).
[CrossRef]

Wilk, T.

T. Wilk, S. C. Webster, A. Kuhn, and G. Rempe, “Single-atom single-photon quantum interface,” Science 317, 488-490 (2007).
[CrossRef] [PubMed]

Xiao, M.

R. J. Brecha, P. R. Rice, and M. Xiao, “N two-level atoms in a driven optical cavity: Quantum dynamics of forward photon scattering for weak incident fields,” Phys. Rev. A 59, 2392-2417 (1999).
[CrossRef]

Ye, J.

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

Yoo, Y. S.

J. Y. Lee, H-W. Lee, J. W. Kim, Y. S. Yoo, and J. W. Hahn, “Measurement of ultralow supermirror birefringence by use of the polarimetric differential cavity ringdown technique,” Applied Optics 39, 1941-1945 (2000).
[CrossRef]

Yudin, V. I.

A. V. Ta˘ıchenachev, A.M. Tuma˘ıkin, V. I. Yudin, and G. Nienhuis, “Steady state of atoms in a resonant field with elliptical polarization,” Phys. Rev. A 69, 033410 (2004).
[CrossRef]

A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “An atom in an elliptically polarized resonant field: exact stationary solution for closed J →J + 1 transitions,” JETP 83, 949-961 (1996).

A. M. Tumaikin and V. I. Yudin, “Coherent stationary states under the interaction of atoms with polarized resonant light in a magnetic field,” Sov. Phys. JETP 71, 43-47 (1990).

Applied Optics (1)

J. Y. Lee, H-W. Lee, J. W. Kim, Y. S. Yoo, and J. W. Hahn, “Measurement of ultralow supermirror birefringence by use of the polarimetric differential cavity ringdown technique,” Applied Optics 39, 1941-1945 (2000).
[CrossRef]

JETP (1)

A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “An atom in an elliptically polarized resonant field: exact stationary solution for closed J →J + 1 transitions,” JETP 83, 949-961 (1996).

Nature (1)

P. W. H. Pinkse, T. Fischer, P. Maunz, and G. Rempe, “Trapping an atom with single photons,” Nature 404, 365-368 (2000).
[CrossRef] [PubMed]

Nature Phys. (1)

I. Schuster, A. Kubanek, A. Fuhrmanek, T. Puppe, P. W. H. Pinkse, K. Murr, and G. Rempe, “Nonlinear spectroscopy of photons bound to one atom,” Nature Phys. 4, 382-385 (2008).
[CrossRef]

New J. Phys. (1)

M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schorner, A. Widera and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008).
[CrossRef]

Opt. Commun. (2)

H. J. Carmichael, R. J. Brecha, and P. R. Rice, “Quantum interference and collapse of the wavefunction in cavity QED,” Opt. Commun. 82, 73-79 (1991).
[CrossRef]

G. Nienhuis, “Natural basis of magnetic substates for a radiative transition with arbitrary polarization,” Opt. Commun. 59353-356 (1986).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (7)

A. V. Ta˘ıchenachev, A.M. Tuma˘ıkin, V. I. Yudin, and G. Nienhuis, “Steady state of atoms in a resonant field with elliptical polarization,” Phys. Rev. A 69, 033410 (2004).
[CrossRef]

K. M. Birnbaum, A. S. Parkins, and H. J. Kimble, “Cavity QED with multiple hyperfine levels,” Phys. Rev. A 74, 063802 (2006).
[CrossRef]

A. D. Boozer, R. Miller, T. E. Northup, A. Boca, and H. J. Kimble, “Optical pumping via incoherent Raman transitions,” Phys. Rev. A 76, 063401 (2007).
[CrossRef]

D. W. Vernooy, A. Furusawa, N. Ph. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57R2293-R2296 (1998).
[CrossRef]

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71013817 (2005).
[CrossRef]

R. J. Brecha, P. R. Rice, and M. Xiao, “N two-level atoms in a driven optical cavity: Quantum dynamics of forward photon scattering for weak incident fields,” Phys. Rev. A 59, 2392-2417 (1999).
[CrossRef]

J. R. Morris, and B. W. Shore, “Reduction of degenerate two-level excitation to independent two-state systems,” Phys. Rev. A 27, 906-912 (1983).
[CrossRef]

Phys. Rev. E (1)

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65, 016608 (2001).
[CrossRef]

Phys. Rev. Lett. (6)

C. Dembowski, H. -D. Gräf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter, “Experimental observation of the topological structure of exceptional points,” Phys. Rev. Lett. 86787-790 (2001).
[CrossRef] [PubMed]

M. Khudaverdyan, W. Alt, T. Kampschulte, S. Reick, A. Thobe, A. Widera, and D. Meschede, “Quantum jumps and spin dynamics of interacting atoms in a strongly coupled atom-cavity system,” Phys. Rev. Lett. 103, 123006 (2009).
[CrossRef] [PubMed]

. C. K. Law and J. H. Eberly, “Arbitrary control of a quantum electromagnetic field,” Phys. Rev. Lett. 76, 1055-1058 (1996).
[CrossRef] [PubMed]

A. Kuhn, M. Hennrich, and G. Rempe, “Deterministic single-photon sources for distributed quantum networking,” Phys. Rev. Lett. 89, 067901 (2002).
[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]

K. M. Fortier, S. Y. Kim, M. J. Gibbons, P. Ahmadi, and M. S. Chapman, “Deterministic loading of individual atoms to a high-finesse optical cavity,” Phys. Rev. Lett. 98, 233601 (2007).
[CrossRef] [PubMed]

Proc. IEEE (1)

E. T. Jaynes, and F.W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89-109 (1963).
[CrossRef]

Science (2)

T. Wilk, S. C. Webster, A. Kuhn, and G. Rempe, “Single-atom single-photon quantum interface,” Science 317, 488-490 (2007).
[CrossRef] [PubMed]

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of single photons from one atom trapped in a cavity,” Science 303, 1992-1994 (2004).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

A. M. Tumaikin and V. I. Yudin, “Coherent stationary states under the interaction of atoms with polarized resonant light in a magnetic field,” Sov. Phys. JETP 71, 43-47 (1990).

Other (2)

T. Kato, Perturbation Theory for Linear Operators (Springer, New York, 1966).

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

(a) Elliptic angle ε of arbitrary elliptic polarization in a coordinate frame with quantization axis parallel to the propagation direction of the cavity field. (b) A two-level atom (FF + 1) with Zeeman sublevel degeneracy with a decay rate γ interacts with a quantized cavity field with a decay rate κ. (c) Collective dressed-state representation with the number of quantum limited up to one.

Fig. 2.
Fig. 2.

(Color Online) (a) Plot of δ(ε) for various F. (b) Variation of g′ /g 0 as elliptic angle ε. (c) Excitation spectrum of the cavity transmission for linear polarization (ε = 0) when F = 3. For a fixed value of γ/g 0 = 0.1, the value of κ/g 0 is varied. Solid line represents the spectrum given by Eq. (8) while the dotted line shows the equivalent non-degenerate two-level system with a coupling constant equal to g′.

Fig. 3.
Fig. 3.

(a) Conventional Zeeman basis and the transition linkage by the elliptical polarization ê in Fig. 1. (b) Natural basis and the corresponding transition strength λi . Two rightmost sublevels of the upper state manifold are uncoupled in the natural basis.

Fig. 4.
Fig. 4.

Plot of λi 2 and πi (a) for various F values when ε = 0. As F increases, the differences in λi 2 among three most-contributing sublevels (i = F,F + 1,F + 2) decrease, and accordingly, the dispersion Δλ 2 decreases.

Fig. 5.
Fig. 5.

Real and imaginary parts of quasi-eigenenergies of the atom-cavity system vs. the atom-cavity detuning for three representative coupling constants, with κ= 8γ and g 0 = 4γ: (a) g = 0.73g 0 in a weak coupling regime, (b) g = γ = 0.88g 0 at the critical coupling, and (c) g = 1.0g 0 in a strong coupling regime. Also shown are the cavity transmission (T cav) spectra when ωA = ωC . Although the spectra do not change much, the associated real and imaginary parts of the quasi-eigenenergies exhibit a dramatic transition across the critical coupling g = γ . The transition can be observed experimentally by measuring the spectra with high signal-to-noise ratio and then by fitting them to the theory to extract quasi-eigenenergies.

Tables (1)

Tables Icon

Table 1. Maximum values of δ(ε) for various angular momenta F and corresponding atomic species. They have D2 lines of (Fg = F) ↔ (Fe = F + 1) closed transition.

Equations (78)

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

ρ bb = η 2 g 0 2 + O ( 4 )
ρ aa = η 2 E A 2 ( VV ) 1 + O ( 𝓔 4 )
ρ 00 = η { E A E C 2 ( VV ) 1 2 Re [ E A E C ] g 0 2 + g 0 4 VV } + O ( 𝓔 2 ) ,
V = V .
[ , VV ] = 0 , [ , V V ] = 0 .
η = 1 E A E C 2 α 0 2 Re [ E A E C ] α 1 g 0 2 + α 2 g 0 4 + O ( 2 ) ,
α 0 = Tr [ ( VV ) 1 ] , α 1 = Tr [ ] = Tr [ ] , α 2 = Tr [ VV ] .
T cav = Tr [ a ] = Tr [ ρ aa ]
= 2 E A 2 E A E C 2 2 Re [ E A E C ] ( α 1 / α 0 ) g 0 2 + ( α 2 / α 0 ) g 0 4 + O ( 4 ) ,
T sp = Tr [ q D q D q ρ ] = Tr [ ρ bb ]
= 2 ( α 1 / α 0 ) g 0 2 E A E C 2 Re [ E A E C ] ( α 1 / α 0 ) g 0 2 + ( α 2 / α 0 ) g 0 4 + O ( 4 ) .
T cav ( ε = ± π / 4 ) = 2 E A E A E C g 0 2 2 + O ( 𝓔 4 ) ,
T sp ( ε = ± π / 4 ) = 2 g 0 E A E C g 0 2 2 + O ( 4 ) .
g = α 1 α 0 g 0 ,
E A E C g 2 2 + δ ( ε ) g 4 ,
E A E C g 2 2 = ( Δ C Δ A g 2 ) 2 + ( Δ A κ ) 2 + ( Δ C γ ) 2 + [ ( κγ + g 2 ) 2 g 4 ] .
4 κγ g 2 4 κγ g 0 2 δ ( ε ) ,
VV = i = 1 2 F + 1 λ i , ( a ) 2 ( a ) i ( a ) i , V V = j = 1 2 F + 3 λ j , ( b ) 2 ( b ) j ( b ) j .
V = i λ i ( a ) i ( b ) i , V = i λ i ( b ) i ( a ) i ,
= i = 1 2 F + 1 ν i ( a ) i ( a ) i , = j = 1 2 F + 3 ν j ( b ) j ( b ) j ,
π i ( a ) ν i / λ i 2 i ν i / λ i 2 , i π i ( a ) = 1 ,
α 0 = i ν i / λ i 2 , α 1 = i ν i , α 2 = i ν i λ i 2 .
g = α 1 α 0 g 0 = i λ i 2 π i ( a ) g 0 = λ 2 ¯ g 0 ,
δ ( ε ) = α 0 α 2 / α 1 2 1
= ( i λ i 4 π i ( a ) ) ( i λ i 2 π i ( a ) ) 2 ( i λ i 2 π i ( a ) ) 2
= [ ( Δ λ 2 ) λ 2 ] 2 ,
λ i 2 = ( 2 F + 2 i ) i ( F + 1 ) ( 2 F + 1 ) ,
e ̂ = q = 1 + 1 e q e ̂ q
e ̂ = sin ( ε + π / 4 ) e ̂ + 1 + cos ( ε + π / 4 ) e ̂ 1
H / h ¯ = Δ C a a + Δ A q = 1 + 1 D q D q + g 0 ( V a a V ) + ( a + a ) ,
D q = m F , m F C F g m F 1q F e m F ' g , m F e , m F ,
C jm j m JM = ( 1 ) j j + M 2 J + 1 j j J m m M .
V = ( q = 1 + 1 D q e ̂ q ) · e ̂ .
0 col = m F ξ m F 0 g , m F atom 0 field
a col = m F ξ m F a g , m F atom 1 field
b col = m F ξ m F b e , m F atom 0 field ,
H = h ¯ [ Δ A I 2 F + 3 g 0 V 0 g 0 V Δ C I 2 F + 1 I 2 F + 1 0 I 2 F + 1 0 ] ,
ρ = [ ρ bb ρ ba ρ b 0 ρ ab ρ aa ρ a 0 ρ 0 b ρ 0 a ρ 00 ] ,
ρ ˙ = [ ρ ] = 1 ih [ H , ρ ] + κ ( 2 a a ρ a a )
+ γ q = 1 + 1 ( 2 D q ρ D q D q D q ρ ρ D q D q ) ,
ρ ˙ bb = 2 γ ρ bb i g 0 ( V ρ ab ρ ba V )
ρ ˙ aa = 2 κ ρ aa i g 0 ( V ρ ba ρ ab V ) i퓔 ( ρ 0 a ρ a 0 )
ρ ˙ 00 = 2 κ ρ aa + 2 γ q D q ρ bb D q + i퓔 ( ρ 0 a ρ a 0 )
ρ ˙ ab = ( ρ ˙ ba ) = i ( E A * E C ) ρ ab i g 0 ( V ρ bb ρ aa V ) i퓔 ρ 0 b
ρ ˙ 0 b = ( ρ ˙ b 0 ) = i E A * ρ 0 b + i g 0 ρ 0 a V i𝓔 ρ ab
ρ ˙ 0 a = ( ρ ˙ a 0 ) = i E C * ρ 0 a + i g 0 ρ 0 b V + i퓔 ( ρ 00 ρ aa )
ρ ab = ( ρ ba ) = i s * g 0 ( V ρ bb ρ aa V ) + i s * g 0 𝓔 2 ρ 00 V X 1 + O ( 𝓔 4 ) ,
ρ 0 b = ( ρ b 0 ) = g 0 ρ 00 V X 1 + O ( 𝓔 3 ) ,
ρ 0 a = ( ρ a 0 ) = E A * ρ 00 Y 1 + O ( 3 ) ,
X = E A * E C * I 2 F + 3 g 0 2 V V ,
Y = E A * E C * I 2 F + 1 g 0 2 V V .
X V = V Y , VX = YV .
2 γ ρ bb [ s * g 0 2 V ( ρ aa 2 ρ 00 Y 1 ) V s * g 0 2 V V ρ bb + h . c . ] = 0 ,
2 κ ρ aa + [ s * g 0 2 ( ρ aa 2 ρ 00 Y 1 ) V V s * g 0 2 V ρ bb V + i E A * 2 ρ 00 Y 1 + h . c . ] = 0 ,
2 κ ρ aa + 2 γ q D q ρ bb D q [ i E A * 2 ρ 00 Y 1 + h . c . ] = 0 ,
V ρ bb V V V q D q ρ bb D q = 0 .
= ρ bb η 2 g 0 2 , = q D q D q ,
V퓑 V = V V 𝓐 ,
ρ bb = η 𝓔 2 g 0 2 𝓑 + O ( 𝓔 4 )
ρ aa = η 𝓔 2 E A 2 ( VV ) 1 𝓐 + O ( 𝓔 4 )
ρ 00 = η ( YY ) ( VV ) 1 𝓐 O ( 2 ) .
e ̂ = cos 2 ε e ̂ 0 2 sin ε e ̂ + 1 .
ij = k = F 1 Min [ i , j ] 1 ( i k ) ! ( j k ) !
× ( 2 F + 1 + i k ) ! ( 2 F + 1 + j k ) ! ( 2 F + 1 i + k ) ! ( 2 F + 1 j + k ) !
× C Fi ( F + 1 ) k ( 2 F + 1 ) ( i k ) C Fj ( F + 1 ) k ( 2 F + 1 ) ( j k ) ( sin ε cos 2 ε ) i + j 2 k ,
ij = k = F Min [ i , j ] 1 ( i k ) ! ( j k ) !
× ( 2 F + 1 + i k ) ! ( 2 F + 1 + j k ) ! ( 2 F + 1 i + k ) ! ( 2 F + 1 j + k ) !
× C ( F + 1 ) i F k ( 2 F + 1 ) ( i k ) C ( F + 1 ) j F k ( 2 F + 1 ) ( j k ) ( sin ε cos 2 ε ) i + j 2 k .
α 0 = 1 cos 2 ε l = 0 F C 2 l 2 P 2 l ( 1 / cos 2 ε )
α 1 = P 2 F + 1 ( 1 / cos 2 ε )
α 2 = cos 2 ε l = 2 F 2 F + 2 D l 2 P l ( 1 / cos 2 ε ) ,
C 1 = ( 2 l + 1 ) ( 2 F 1 ) ! ( 2 F + l + 1 ) ! ( 2 F + 1 ) ( 4 F + 1 ) !
D 1 = ( 2 F + 3 ) ( 4 F + 3 ) C 10 2 F + 10 l 0 × l 1 2 F + 1 F F + 1 F + 1 ,
lim ε ± π 4 α 1 α 0 = lim ε ± π 4 α 2 α 0 = 1 .
( 2 l + 1 ) x P l ( x ) = ( l + 1 ) P l + 1 ( x ) + l P l 1 ( x ) ,
α 0 = α 1 + 2 F 2 F + 1 P 2 F 1 ( 1 / cos 2 ε ) + 1 cos 2 ε l = 0 F 1 C 2 l 2 P 2 l ( 1 / cos 2 ε ) ,
α 2 = α 1 2 F cos 2 ε 4 F + 1 P 2 F ( 1 / cos 2 ε ) ,
α 0 α 1 α 2 .

Metrics