Abstract

The rates of spontaneous emission and stimulated emission and absorption for a two-level atom in a dielectric microsphere are calculated for weak E1 coupling. The A coefficient for spontaneous emission is proportional to the zero-point fluctuation of the electric field ij evaluated in the previous paper [ J. Opt. Soc. Am. B 4, 1995 ( 1987)], which shows sharp resonances in frequency (Q > 104). It is verified that the ratio of the A and B coefficients is determined by the spectral density of thermal radiation. The level shift tends to repel the transition line away from the cavity resonance.

© 1987 Optical Society of America

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  1. R. D. Richtmyer, “Dielectric resonators,” J. Appl. Phys. 10, 391–398 (1939); P. Affolter and B. Eliasson, “Electromagnetic resonances and Q-factors of lossy dielectric spheres,” IEEE Trans. Microwave Theory Techn. MTT-21, 573–578 (1973).
    [CrossRef]
  2. R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980); H.-M. Tzeng, M. B. Long, and R. K. Chang, “Size and shape variations of liquid droplets deduced from morphology-dependent resonances in fluorescence spectra,” in Particle Sizing and Spray Analysis, N. Chigier and G. W. Stewart, eds., SPIE Proc. Vol. 573, 80–83 (1985); H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Evaporation and condensation rates of liquid droplets deduced from structure resonances in the fluorescence spectra,” Opt. Lett. 9, 273–275 (1984).
    [CrossRef] [PubMed]
  3. J. B. Snow, S.-X. Qian, and R. K. Chang, “Stimulated Raman scattering from individual water and ethanol droplets at morphology-dependent resonances,” Opt. Lett. 10, 37–39 (1985); S.-X. Qian, J. B. Snow, and R. K. Chang, “Coherent Raman mixing and coherent anti-Stokes Raman scattering from individual micrometer-size droplets,” Opt. Lett. 10, 499–501 (1985); S.-X. Qian and R. K. Chang, “Multiorder Stokes emission from micrometer-size droplets,” Phys. Rev. Lett. 56, 926–929 (1986).
    [CrossRef] [PubMed]
  4. H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Laser emission from individual droplets at wavelengths corresponding to morphology-dependent resonances,” Opt. Lett. 9, 499–501 (1984); S.-X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, “Lasing droplets: highlighting the liquid–air interface by laser emission,” Science 231, 486–488 (1986).
    [CrossRef] [PubMed]
  5. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
  6. S. Haroche, P. Goy, J. M. Raimond, C. Fabre, and M. Gross, “Exploration of radiative properties of very excited atoms,” Phil. Trans. Roy. Soc. London Ser. A 307, 659–672 (1982); P. Goy, J. M. Raimond, M. Gross, and S. Haroche, “Observation of cavity-enhanced single atom spontaneous emission,” Phys. Rev. Lett. 50, 1903–1906 (1983).
    [CrossRef]
  7. A. Einstein, “Zur Quantentheorie der Strahlung,” Phys. Z. 18, 121–128 (1917); R. P. Feynman, R. B. Leighton, and M. Sands, eds., The Feynman Lectures on Physics (Addison-Wesley, Reading, Mass., 1963), Vol. I.
  8. H. M. Lai, P. T. Leung, and K. Young, “Thermal spectrum in leaky cavities: a string model,” Phys. Lett. A119, 337–339 (1987).
  9. P. Ullersma, “An exactly solvable model for Brownian motion I. Derivation of the Langevin equation,” Physica 32, 27–55 (1966); “An exactly solvable model for Brownian motion II. Derivation of the Fokker–Planck equation and the master equation,” Physica 32, 56–73 (1966); “An exactly solvable model for Brownian motion III. Motion of a heavy mass in a linear chain,” Physica 32, 74–89 (1966); “An exactly solvable model for Brownian motion IV. Susceptibility and Nyquist’s theorem,” Physica 32, 90–96 (1966); R. P. Feynman and F. L. Vernon, “The theory of a general quantum system interacting with a linear dissipative system,” Ann. Phys. 24, 118–173 (1963); P. S. Riseborough, P. Hanggi, and U. Weiss, “Exact results for a damped quantum-mechanical harmonic oscillator,” Phys. Rev. A 31, 471–478 (1985); H. Grabert, U. Weiss, and P. Talkner, “Quantum theory of damped harmonic oscillator,” Z. Phys. B 55, 87–94 (1984); A. O. Caldeira and A. J. Leggett, “Quantum tunnelling in a dissipative system,” Ann. Phys. (N.Y.) 149, 374–456 (1983).
    [CrossRef] [PubMed]
  10. S. C. Ching, H. M. Lai, and K. Young, “Dielectric microspheres as optical cavities: thermal spectrum and density of states,” J. Opt. Soc. Am B 4, 1995–2003 (1987).
    [CrossRef]
  11. E. Power and T. Thiunamachandran, “Quantum electrodynamics in a cavity,” Phys. Rev. A 25, 2473–2484 (1982).
    [CrossRef]
  12. S. C. Hill and R. E. Benner, “Morphology-dependent resonances associated with stimulated processes in microspheres,” J. Opt. Soc. Am. B 3, 1509–1514 (1986).
    [CrossRef]
  13. See, e.g., A. Yariv, Introduction to Optical Electronics (Holt, Rinehart & Winston, New York, 1971).
  14. D. Kleppner, “Inhibited spontaneous emission,” Phys. Rev. Lett. 47, 233–236 (1981); R. G. Hulet, E. S. Hilfer, and D. Kleppner, “Inhibited spontaneous emission by a Rydberg atom,” Phys. Rev. Lett. 55, 2137–2140 (1985).
    [CrossRef] [PubMed]
  15. J. M. Wylie and J. E. Sipe, “Quantum electrodynamics near an interface,” Phys. Rev. A 30, 1185–1193 (1984); “Quantum electrodynamics near an interface, II,” Phys. Rev. A 32, 2030–2043 (1985); A. D. Mclachlan, “Three body dispersion forces,” Mol. Phys. 6, 423–427 (1963); “Van der Waals forces between an atom and a surface,” Mol. Phys. 7, 381–388 (1963); G. S. Agarwal, “Quantum electrodynamics in the presence of dielectrics and conductors: I. Electromagnetic-field response functions and black-body fluctuations in finite geometries,” Phys. Rev. A 11, 230–242 (1975); “Quantum electrodynamics in the presence of dielectrics and conductors: II. Theory of dispersion forces,” Phys. Rev. A 11, 243–252 (1975); “Quantum electrodynamics in the presence of dielectrics and conductors: III. Relations among one-photon transition probabilities in stationary and nonstationary fields, density of states, the field correlation functions and surface-dependent response functions,” Phys. Rev. A 11, 253–264 (1975).
    [CrossRef]
  16. M. J. Mehl and W. L. Schaich, “The Van der Waals interaction between an atom and a solid,” Surf. Sci. 99, 553–569 (1980); G. Barton, “Frequency shifts near an interface: inadequacies of two-level atomic models,” J. Phys. B 7, 2134–2142 (1974).
    [CrossRef]
  17. S. Sachdev, “Atom in a damped cavity,” Phys. Rev. A 29, 2627–2633 (1984).
    [CrossRef]
  18. R. Lang, M. O. Scully, and W. E. Lamb, “Why is the laser line so narrow? A Theory of single-quasimode laser operation,” Phys. Rev. A 7, 1788–1797 (1973); J. C. Penaforte and B. Baseia, “Quantum theory of a one-dimensional laser with output coupling: linear approximation,” Phys. Rev. A 30, 1401–1406 (1984).
    [CrossRef]
  19. A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
    [CrossRef]

1987 (2)

H. M. Lai, P. T. Leung, and K. Young, “Thermal spectrum in leaky cavities: a string model,” Phys. Lett. A119, 337–339 (1987).

S. C. Ching, H. M. Lai, and K. Young, “Dielectric microspheres as optical cavities: thermal spectrum and density of states,” J. Opt. Soc. Am B 4, 1995–2003 (1987).
[CrossRef]

1986 (1)

1985 (1)

1984 (3)

H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Laser emission from individual droplets at wavelengths corresponding to morphology-dependent resonances,” Opt. Lett. 9, 499–501 (1984); S.-X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, “Lasing droplets: highlighting the liquid–air interface by laser emission,” Science 231, 486–488 (1986).
[CrossRef] [PubMed]

J. M. Wylie and J. E. Sipe, “Quantum electrodynamics near an interface,” Phys. Rev. A 30, 1185–1193 (1984); “Quantum electrodynamics near an interface, II,” Phys. Rev. A 32, 2030–2043 (1985); A. D. Mclachlan, “Three body dispersion forces,” Mol. Phys. 6, 423–427 (1963); “Van der Waals forces between an atom and a surface,” Mol. Phys. 7, 381–388 (1963); G. S. Agarwal, “Quantum electrodynamics in the presence of dielectrics and conductors: I. Electromagnetic-field response functions and black-body fluctuations in finite geometries,” Phys. Rev. A 11, 230–242 (1975); “Quantum electrodynamics in the presence of dielectrics and conductors: II. Theory of dispersion forces,” Phys. Rev. A 11, 243–252 (1975); “Quantum electrodynamics in the presence of dielectrics and conductors: III. Relations among one-photon transition probabilities in stationary and nonstationary fields, density of states, the field correlation functions and surface-dependent response functions,” Phys. Rev. A 11, 253–264 (1975).
[CrossRef]

S. Sachdev, “Atom in a damped cavity,” Phys. Rev. A 29, 2627–2633 (1984).
[CrossRef]

1982 (2)

E. Power and T. Thiunamachandran, “Quantum electrodynamics in a cavity,” Phys. Rev. A 25, 2473–2484 (1982).
[CrossRef]

S. Haroche, P. Goy, J. M. Raimond, C. Fabre, and M. Gross, “Exploration of radiative properties of very excited atoms,” Phil. Trans. Roy. Soc. London Ser. A 307, 659–672 (1982); P. Goy, J. M. Raimond, M. Gross, and S. Haroche, “Observation of cavity-enhanced single atom spontaneous emission,” Phys. Rev. Lett. 50, 1903–1906 (1983).
[CrossRef]

1981 (1)

D. Kleppner, “Inhibited spontaneous emission,” Phys. Rev. Lett. 47, 233–236 (1981); R. G. Hulet, E. S. Hilfer, and D. Kleppner, “Inhibited spontaneous emission by a Rydberg atom,” Phys. Rev. Lett. 55, 2137–2140 (1985).
[CrossRef] [PubMed]

1980 (2)

M. J. Mehl and W. L. Schaich, “The Van der Waals interaction between an atom and a solid,” Surf. Sci. 99, 553–569 (1980); G. Barton, “Frequency shifts near an interface: inadequacies of two-level atomic models,” J. Phys. B 7, 2134–2142 (1974).
[CrossRef]

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980); H.-M. Tzeng, M. B. Long, and R. K. Chang, “Size and shape variations of liquid droplets deduced from morphology-dependent resonances in fluorescence spectra,” in Particle Sizing and Spray Analysis, N. Chigier and G. W. Stewart, eds., SPIE Proc. Vol. 573, 80–83 (1985); H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Evaporation and condensation rates of liquid droplets deduced from structure resonances in the fluorescence spectra,” Opt. Lett. 9, 273–275 (1984).
[CrossRef] [PubMed]

1973 (1)

R. Lang, M. O. Scully, and W. E. Lamb, “Why is the laser line so narrow? A Theory of single-quasimode laser operation,” Phys. Rev. A 7, 1788–1797 (1973); J. C. Penaforte and B. Baseia, “Quantum theory of a one-dimensional laser with output coupling: linear approximation,” Phys. Rev. A 30, 1401–1406 (1984).
[CrossRef]

1966 (1)

P. Ullersma, “An exactly solvable model for Brownian motion I. Derivation of the Langevin equation,” Physica 32, 27–55 (1966); “An exactly solvable model for Brownian motion II. Derivation of the Fokker–Planck equation and the master equation,” Physica 32, 56–73 (1966); “An exactly solvable model for Brownian motion III. Motion of a heavy mass in a linear chain,” Physica 32, 74–89 (1966); “An exactly solvable model for Brownian motion IV. Susceptibility and Nyquist’s theorem,” Physica 32, 90–96 (1966); R. P. Feynman and F. L. Vernon, “The theory of a general quantum system interacting with a linear dissipative system,” Ann. Phys. 24, 118–173 (1963); P. S. Riseborough, P. Hanggi, and U. Weiss, “Exact results for a damped quantum-mechanical harmonic oscillator,” Phys. Rev. A 31, 471–478 (1985); H. Grabert, U. Weiss, and P. Talkner, “Quantum theory of damped harmonic oscillator,” Z. Phys. B 55, 87–94 (1984); A. O. Caldeira and A. J. Leggett, “Quantum tunnelling in a dissipative system,” Ann. Phys. (N.Y.) 149, 374–456 (1983).
[CrossRef] [PubMed]

1961 (1)

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
[CrossRef]

1946 (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

1939 (1)

R. D. Richtmyer, “Dielectric resonators,” J. Appl. Phys. 10, 391–398 (1939); P. Affolter and B. Eliasson, “Electromagnetic resonances and Q-factors of lossy dielectric spheres,” IEEE Trans. Microwave Theory Techn. MTT-21, 573–578 (1973).
[CrossRef]

1917 (1)

A. Einstein, “Zur Quantentheorie der Strahlung,” Phys. Z. 18, 121–128 (1917); R. P. Feynman, R. B. Leighton, and M. Sands, eds., The Feynman Lectures on Physics (Addison-Wesley, Reading, Mass., 1963), Vol. I.

Barber, P. W.

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980); H.-M. Tzeng, M. B. Long, and R. K. Chang, “Size and shape variations of liquid droplets deduced from morphology-dependent resonances in fluorescence spectra,” in Particle Sizing and Spray Analysis, N. Chigier and G. W. Stewart, eds., SPIE Proc. Vol. 573, 80–83 (1985); H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Evaporation and condensation rates of liquid droplets deduced from structure resonances in the fluorescence spectra,” Opt. Lett. 9, 273–275 (1984).
[CrossRef] [PubMed]

Benner, R. E.

S. C. Hill and R. E. Benner, “Morphology-dependent resonances associated with stimulated processes in microspheres,” J. Opt. Soc. Am. B 3, 1509–1514 (1986).
[CrossRef]

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980); H.-M. Tzeng, M. B. Long, and R. K. Chang, “Size and shape variations of liquid droplets deduced from morphology-dependent resonances in fluorescence spectra,” in Particle Sizing and Spray Analysis, N. Chigier and G. W. Stewart, eds., SPIE Proc. Vol. 573, 80–83 (1985); H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Evaporation and condensation rates of liquid droplets deduced from structure resonances in the fluorescence spectra,” Opt. Lett. 9, 273–275 (1984).
[CrossRef] [PubMed]

Chang, R. K.

J. B. Snow, S.-X. Qian, and R. K. Chang, “Stimulated Raman scattering from individual water and ethanol droplets at morphology-dependent resonances,” Opt. Lett. 10, 37–39 (1985); S.-X. Qian, J. B. Snow, and R. K. Chang, “Coherent Raman mixing and coherent anti-Stokes Raman scattering from individual micrometer-size droplets,” Opt. Lett. 10, 499–501 (1985); S.-X. Qian and R. K. Chang, “Multiorder Stokes emission from micrometer-size droplets,” Phys. Rev. Lett. 56, 926–929 (1986).
[CrossRef] [PubMed]

H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Laser emission from individual droplets at wavelengths corresponding to morphology-dependent resonances,” Opt. Lett. 9, 499–501 (1984); S.-X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, “Lasing droplets: highlighting the liquid–air interface by laser emission,” Science 231, 486–488 (1986).
[CrossRef] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980); H.-M. Tzeng, M. B. Long, and R. K. Chang, “Size and shape variations of liquid droplets deduced from morphology-dependent resonances in fluorescence spectra,” in Particle Sizing and Spray Analysis, N. Chigier and G. W. Stewart, eds., SPIE Proc. Vol. 573, 80–83 (1985); H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Evaporation and condensation rates of liquid droplets deduced from structure resonances in the fluorescence spectra,” Opt. Lett. 9, 273–275 (1984).
[CrossRef] [PubMed]

Ching, S. C.

S. C. Ching, H. M. Lai, and K. Young, “Dielectric microspheres as optical cavities: thermal spectrum and density of states,” J. Opt. Soc. Am B 4, 1995–2003 (1987).
[CrossRef]

Einstein, A.

A. Einstein, “Zur Quantentheorie der Strahlung,” Phys. Z. 18, 121–128 (1917); R. P. Feynman, R. B. Leighton, and M. Sands, eds., The Feynman Lectures on Physics (Addison-Wesley, Reading, Mass., 1963), Vol. I.

Fabre, C.

S. Haroche, P. Goy, J. M. Raimond, C. Fabre, and M. Gross, “Exploration of radiative properties of very excited atoms,” Phil. Trans. Roy. Soc. London Ser. A 307, 659–672 (1982); P. Goy, J. M. Raimond, M. Gross, and S. Haroche, “Observation of cavity-enhanced single atom spontaneous emission,” Phys. Rev. Lett. 50, 1903–1906 (1983).
[CrossRef]

Fox, A. G.

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
[CrossRef]

Goy, P.

S. Haroche, P. Goy, J. M. Raimond, C. Fabre, and M. Gross, “Exploration of radiative properties of very excited atoms,” Phil. Trans. Roy. Soc. London Ser. A 307, 659–672 (1982); P. Goy, J. M. Raimond, M. Gross, and S. Haroche, “Observation of cavity-enhanced single atom spontaneous emission,” Phys. Rev. Lett. 50, 1903–1906 (1983).
[CrossRef]

Gross, M.

S. Haroche, P. Goy, J. M. Raimond, C. Fabre, and M. Gross, “Exploration of radiative properties of very excited atoms,” Phil. Trans. Roy. Soc. London Ser. A 307, 659–672 (1982); P. Goy, J. M. Raimond, M. Gross, and S. Haroche, “Observation of cavity-enhanced single atom spontaneous emission,” Phys. Rev. Lett. 50, 1903–1906 (1983).
[CrossRef]

Haroche, S.

S. Haroche, P. Goy, J. M. Raimond, C. Fabre, and M. Gross, “Exploration of radiative properties of very excited atoms,” Phil. Trans. Roy. Soc. London Ser. A 307, 659–672 (1982); P. Goy, J. M. Raimond, M. Gross, and S. Haroche, “Observation of cavity-enhanced single atom spontaneous emission,” Phys. Rev. Lett. 50, 1903–1906 (1983).
[CrossRef]

Hill, S. C.

Kleppner, D.

D. Kleppner, “Inhibited spontaneous emission,” Phys. Rev. Lett. 47, 233–236 (1981); R. G. Hulet, E. S. Hilfer, and D. Kleppner, “Inhibited spontaneous emission by a Rydberg atom,” Phys. Rev. Lett. 55, 2137–2140 (1985).
[CrossRef] [PubMed]

Lai, H. M.

S. C. Ching, H. M. Lai, and K. Young, “Dielectric microspheres as optical cavities: thermal spectrum and density of states,” J. Opt. Soc. Am B 4, 1995–2003 (1987).
[CrossRef]

H. M. Lai, P. T. Leung, and K. Young, “Thermal spectrum in leaky cavities: a string model,” Phys. Lett. A119, 337–339 (1987).

Lamb, W. E.

R. Lang, M. O. Scully, and W. E. Lamb, “Why is the laser line so narrow? A Theory of single-quasimode laser operation,” Phys. Rev. A 7, 1788–1797 (1973); J. C. Penaforte and B. Baseia, “Quantum theory of a one-dimensional laser with output coupling: linear approximation,” Phys. Rev. A 30, 1401–1406 (1984).
[CrossRef]

Lang, R.

R. Lang, M. O. Scully, and W. E. Lamb, “Why is the laser line so narrow? A Theory of single-quasimode laser operation,” Phys. Rev. A 7, 1788–1797 (1973); J. C. Penaforte and B. Baseia, “Quantum theory of a one-dimensional laser with output coupling: linear approximation,” Phys. Rev. A 30, 1401–1406 (1984).
[CrossRef]

Leung, P. T.

H. M. Lai, P. T. Leung, and K. Young, “Thermal spectrum in leaky cavities: a string model,” Phys. Lett. A119, 337–339 (1987).

Li, T.

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
[CrossRef]

Long, M. B.

Mehl, M. J.

M. J. Mehl and W. L. Schaich, “The Van der Waals interaction between an atom and a solid,” Surf. Sci. 99, 553–569 (1980); G. Barton, “Frequency shifts near an interface: inadequacies of two-level atomic models,” J. Phys. B 7, 2134–2142 (1974).
[CrossRef]

Owen, J. F.

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980); H.-M. Tzeng, M. B. Long, and R. K. Chang, “Size and shape variations of liquid droplets deduced from morphology-dependent resonances in fluorescence spectra,” in Particle Sizing and Spray Analysis, N. Chigier and G. W. Stewart, eds., SPIE Proc. Vol. 573, 80–83 (1985); H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Evaporation and condensation rates of liquid droplets deduced from structure resonances in the fluorescence spectra,” Opt. Lett. 9, 273–275 (1984).
[CrossRef] [PubMed]

Power, E.

E. Power and T. Thiunamachandran, “Quantum electrodynamics in a cavity,” Phys. Rev. A 25, 2473–2484 (1982).
[CrossRef]

Purcell, E. M.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Qian, S.-X.

Raimond, J. M.

S. Haroche, P. Goy, J. M. Raimond, C. Fabre, and M. Gross, “Exploration of radiative properties of very excited atoms,” Phil. Trans. Roy. Soc. London Ser. A 307, 659–672 (1982); P. Goy, J. M. Raimond, M. Gross, and S. Haroche, “Observation of cavity-enhanced single atom spontaneous emission,” Phys. Rev. Lett. 50, 1903–1906 (1983).
[CrossRef]

Richtmyer, R. D.

R. D. Richtmyer, “Dielectric resonators,” J. Appl. Phys. 10, 391–398 (1939); P. Affolter and B. Eliasson, “Electromagnetic resonances and Q-factors of lossy dielectric spheres,” IEEE Trans. Microwave Theory Techn. MTT-21, 573–578 (1973).
[CrossRef]

Sachdev, S.

S. Sachdev, “Atom in a damped cavity,” Phys. Rev. A 29, 2627–2633 (1984).
[CrossRef]

Schaich, W. L.

M. J. Mehl and W. L. Schaich, “The Van der Waals interaction between an atom and a solid,” Surf. Sci. 99, 553–569 (1980); G. Barton, “Frequency shifts near an interface: inadequacies of two-level atomic models,” J. Phys. B 7, 2134–2142 (1974).
[CrossRef]

Scully, M. O.

R. Lang, M. O. Scully, and W. E. Lamb, “Why is the laser line so narrow? A Theory of single-quasimode laser operation,” Phys. Rev. A 7, 1788–1797 (1973); J. C. Penaforte and B. Baseia, “Quantum theory of a one-dimensional laser with output coupling: linear approximation,” Phys. Rev. A 30, 1401–1406 (1984).
[CrossRef]

Sipe, J. E.

J. M. Wylie and J. E. Sipe, “Quantum electrodynamics near an interface,” Phys. Rev. A 30, 1185–1193 (1984); “Quantum electrodynamics near an interface, II,” Phys. Rev. A 32, 2030–2043 (1985); A. D. Mclachlan, “Three body dispersion forces,” Mol. Phys. 6, 423–427 (1963); “Van der Waals forces between an atom and a surface,” Mol. Phys. 7, 381–388 (1963); G. S. Agarwal, “Quantum electrodynamics in the presence of dielectrics and conductors: I. Electromagnetic-field response functions and black-body fluctuations in finite geometries,” Phys. Rev. A 11, 230–242 (1975); “Quantum electrodynamics in the presence of dielectrics and conductors: II. Theory of dispersion forces,” Phys. Rev. A 11, 243–252 (1975); “Quantum electrodynamics in the presence of dielectrics and conductors: III. Relations among one-photon transition probabilities in stationary and nonstationary fields, density of states, the field correlation functions and surface-dependent response functions,” Phys. Rev. A 11, 253–264 (1975).
[CrossRef]

Snow, J. B.

Thiunamachandran, T.

E. Power and T. Thiunamachandran, “Quantum electrodynamics in a cavity,” Phys. Rev. A 25, 2473–2484 (1982).
[CrossRef]

Tzeng, H.-M.

Ullersma, P.

P. Ullersma, “An exactly solvable model for Brownian motion I. Derivation of the Langevin equation,” Physica 32, 27–55 (1966); “An exactly solvable model for Brownian motion II. Derivation of the Fokker–Planck equation and the master equation,” Physica 32, 56–73 (1966); “An exactly solvable model for Brownian motion III. Motion of a heavy mass in a linear chain,” Physica 32, 74–89 (1966); “An exactly solvable model for Brownian motion IV. Susceptibility and Nyquist’s theorem,” Physica 32, 90–96 (1966); R. P. Feynman and F. L. Vernon, “The theory of a general quantum system interacting with a linear dissipative system,” Ann. Phys. 24, 118–173 (1963); P. S. Riseborough, P. Hanggi, and U. Weiss, “Exact results for a damped quantum-mechanical harmonic oscillator,” Phys. Rev. A 31, 471–478 (1985); H. Grabert, U. Weiss, and P. Talkner, “Quantum theory of damped harmonic oscillator,” Z. Phys. B 55, 87–94 (1984); A. O. Caldeira and A. J. Leggett, “Quantum tunnelling in a dissipative system,” Ann. Phys. (N.Y.) 149, 374–456 (1983).
[CrossRef] [PubMed]

Wall, K. F.

Wylie, J. M.

J. M. Wylie and J. E. Sipe, “Quantum electrodynamics near an interface,” Phys. Rev. A 30, 1185–1193 (1984); “Quantum electrodynamics near an interface, II,” Phys. Rev. A 32, 2030–2043 (1985); A. D. Mclachlan, “Three body dispersion forces,” Mol. Phys. 6, 423–427 (1963); “Van der Waals forces between an atom and a surface,” Mol. Phys. 7, 381–388 (1963); G. S. Agarwal, “Quantum electrodynamics in the presence of dielectrics and conductors: I. Electromagnetic-field response functions and black-body fluctuations in finite geometries,” Phys. Rev. A 11, 230–242 (1975); “Quantum electrodynamics in the presence of dielectrics and conductors: II. Theory of dispersion forces,” Phys. Rev. A 11, 243–252 (1975); “Quantum electrodynamics in the presence of dielectrics and conductors: III. Relations among one-photon transition probabilities in stationary and nonstationary fields, density of states, the field correlation functions and surface-dependent response functions,” Phys. Rev. A 11, 253–264 (1975).
[CrossRef]

Yariv, A.

See, e.g., A. Yariv, Introduction to Optical Electronics (Holt, Rinehart & Winston, New York, 1971).

Young, K.

S. C. Ching, H. M. Lai, and K. Young, “Dielectric microspheres as optical cavities: thermal spectrum and density of states,” J. Opt. Soc. Am B 4, 1995–2003 (1987).
[CrossRef]

H. M. Lai, P. T. Leung, and K. Young, “Thermal spectrum in leaky cavities: a string model,” Phys. Lett. A119, 337–339 (1987).

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A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
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R. D. Richtmyer, “Dielectric resonators,” J. Appl. Phys. 10, 391–398 (1939); P. Affolter and B. Eliasson, “Electromagnetic resonances and Q-factors of lossy dielectric spheres,” IEEE Trans. Microwave Theory Techn. MTT-21, 573–578 (1973).
[CrossRef]

J. Opt. Soc. Am B (1)

S. C. Ching, H. M. Lai, and K. Young, “Dielectric microspheres as optical cavities: thermal spectrum and density of states,” J. Opt. Soc. Am B 4, 1995–2003 (1987).
[CrossRef]

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

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Phil. Trans. Roy. Soc. London Ser. A (1)

S. Haroche, P. Goy, J. M. Raimond, C. Fabre, and M. Gross, “Exploration of radiative properties of very excited atoms,” Phil. Trans. Roy. Soc. London Ser. A 307, 659–672 (1982); P. Goy, J. M. Raimond, M. Gross, and S. Haroche, “Observation of cavity-enhanced single atom spontaneous emission,” Phys. Rev. Lett. 50, 1903–1906 (1983).
[CrossRef]

Phys. Lett. (1)

H. M. Lai, P. T. Leung, and K. Young, “Thermal spectrum in leaky cavities: a string model,” Phys. Lett. A119, 337–339 (1987).

Phys. Rev. (1)

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E. Power and T. Thiunamachandran, “Quantum electrodynamics in a cavity,” Phys. Rev. A 25, 2473–2484 (1982).
[CrossRef]

J. M. Wylie and J. E. Sipe, “Quantum electrodynamics near an interface,” Phys. Rev. A 30, 1185–1193 (1984); “Quantum electrodynamics near an interface, II,” Phys. Rev. A 32, 2030–2043 (1985); A. D. Mclachlan, “Three body dispersion forces,” Mol. Phys. 6, 423–427 (1963); “Van der Waals forces between an atom and a surface,” Mol. Phys. 7, 381–388 (1963); G. S. Agarwal, “Quantum electrodynamics in the presence of dielectrics and conductors: I. Electromagnetic-field response functions and black-body fluctuations in finite geometries,” Phys. Rev. A 11, 230–242 (1975); “Quantum electrodynamics in the presence of dielectrics and conductors: II. Theory of dispersion forces,” Phys. Rev. A 11, 243–252 (1975); “Quantum electrodynamics in the presence of dielectrics and conductors: III. Relations among one-photon transition probabilities in stationary and nonstationary fields, density of states, the field correlation functions and surface-dependent response functions,” Phys. Rev. A 11, 253–264 (1975).
[CrossRef]

S. Sachdev, “Atom in a damped cavity,” Phys. Rev. A 29, 2627–2633 (1984).
[CrossRef]

R. Lang, M. O. Scully, and W. E. Lamb, “Why is the laser line so narrow? A Theory of single-quasimode laser operation,” Phys. Rev. A 7, 1788–1797 (1973); J. C. Penaforte and B. Baseia, “Quantum theory of a one-dimensional laser with output coupling: linear approximation,” Phys. Rev. A 30, 1401–1406 (1984).
[CrossRef]

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R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980); H.-M. Tzeng, M. B. Long, and R. K. Chang, “Size and shape variations of liquid droplets deduced from morphology-dependent resonances in fluorescence spectra,” in Particle Sizing and Spray Analysis, N. Chigier and G. W. Stewart, eds., SPIE Proc. Vol. 573, 80–83 (1985); H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Evaporation and condensation rates of liquid droplets deduced from structure resonances in the fluorescence spectra,” Opt. Lett. 9, 273–275 (1984).
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D. Kleppner, “Inhibited spontaneous emission,” Phys. Rev. Lett. 47, 233–236 (1981); R. G. Hulet, E. S. Hilfer, and D. Kleppner, “Inhibited spontaneous emission by a Rydberg atom,” Phys. Rev. Lett. 55, 2137–2140 (1985).
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M. J. Mehl and W. L. Schaich, “The Van der Waals interaction between an atom and a solid,” Surf. Sci. 99, 553–569 (1980); G. Barton, “Frequency shifts near an interface: inadequacies of two-level atomic models,” J. Phys. B 7, 2134–2142 (1974).
[CrossRef]

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See, e.g., A. Yariv, Introduction to Optical Electronics (Holt, Rinehart & Winston, New York, 1971).

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Equations (51)

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matrix    element 2 ×    density    of    states .
V ρ vac ( ω ) = V ω 2 / π 2 c 3 ,
ρ C ( ω ) ~ D / γ ~ D Q / ω ,
K ~ ρ C ( ω ) V ρ vac ( ω ) ~ D Q 8 π λ 3 V
V = - f P · E ( r 0 ) ,
E ( r ) = s ω s - 1 d α ( s , t ) / d t e ( s , r ) ,
d 2 α ( s , t ) / d t 2 = - ω s 2 α ( s , t ) ,
H r = s 1 2 { 1 ω s 2 [ d α ( s , t ) d t ] 2 + α ( s , t ) 2 } ω s .
π ( s , t ) = ω s d α ( s , t ) d t ,
a s ( t ) = 1 2 [ α ( s , t ) + i π ( s , t ) ] ,
E ( r ) = - i 2 s ( a s - a s + ) e ( s , r ) .
A = 2 π d a s a s V b 2 δ ( Ω - ω s ) ,
a s V b = - i f 2 a P i b e i ( s , r 0 ) .
A = 4 π 2 f 2 d a M i j i j ( Ω , r 0 ) Ω .
M i j = a P i b b P j a
i j ( ω , r ) = ( 1 / 4 π ω ) s e i ( s , r ) e j ( s , r ) δ ( ω s - ω )
( ω , r ) i i i ( ω , r ) = ρ vac ( ω ) ,
vac E i ( r , t ) E j ( r , t ) vac = 2 π 0 d ω i j ( ω , r ) ω exp [ - i ω ( t - t ) ] .
A / A vac = ( f / n ) 2 h E ( Ω a / c , r 0 / a ) ,
h E = n 2 / ρ vac
( Ω , r 0 ) ~ ρ ( Ω , r 0 ) ρ C ( Ω ) / V eff ( r 0 ) ,
t decay time ~ A - 1 .
d ω i j ( ω ) ω sin ( ω - Ω ) t ( ω - Ω ) ,
t γ - 1 ,
A γ .
Rate = f 2 2 d a M i j P ˜ i j ( Ω ) = f 2 2 d a M P ˜ ( Ω ) ,
E i ( r 0 , t ) E j ( r 0 , t ) = ( 1 / π ) 0 d ω P ˜ i j ( ω ) cos ω ( t - t ) .
rate ( b a ) = B ( b a ) [ ( c / 2 π ) P ˜ ( Ω ) ]
B ( b a ) = 2 π c f 2 2 d a M .
A ( b a ) B ( b a ) = ( e β Ω - 1 ) c 2 π P ˜ ( Ω ) .
π s e ( s , r 0 ) · e ( s , r 0 ) δ ( ω s - Ω ) = 4 π 2 Ω ( Ω ) ,
δ E b = s a s V b 2 ( Ω - ω s ) ,
δ E b = 2 π f 2 M d a d ω ω ( ω , r 0 ) Ω - ω + i ,
- vac ,
( f / n ) 2 h E = K ( γ / 2 ) 2 ( ω - ω 0 ) 2 + ( γ / 2 ) 2 .
δ E b = K M d a ω 0 3 c 3 Δ γ Δ 2 + ( γ / 2 ) 2 ,
δ E b = K M d a ω 0 3 c 3 = K 4 τ 0 ,
Ω - ω 0 ~ Δ + δ E b / ~ Δ + K γ 4 τ 0 Δ Δ ,
A / A vac ~ ( f / n ) 2 h E ( Ω a / c , r 0 / a ) ~ K ( γ / 2 ) 2 ( Δ ) 2 γ Q - 1 ,
V = - P · d ( r 0 ) + ( 2 / 3 π ) P 2 0 d k k 2 ,
d ( r ) = E l ( r ) + 4 π P δ 3 ( r - r 0 ) + 4 π P med ( r ) ,
E l ( r 0 ) = f E ( r 0 ) ,             f = 3 n 2 / ( 2 n 2 + 1 ) .
V ( t ) = - d ω 2 π V ˜ ( ω ) e - i ω t ,             V ˜ ( - ω ) = V ˜ ( ω ) + .
V ( t ) V ( t ) = F ( t - t ) = 0 d ω 2 π F ˜ ( ω ) 2 cos ω ( t - t ) ,
V ˜ ( ω ) V ˜ ( ω ) + = F ˜ ( ω ) 2 π δ ( ω - ω ) .
C F ( t ) = - 1 - d ω 2 π F V ˜ ( ω ) I exp [ i ( Ω - ω ) t ] - 1 Ω - ω ,
C F ( t ) 2 = 1 2 d ω 2 π F ˜ ( ω ) 4 sin 2 ( Ω - ω ) t / 2 ( Ω - ω ) 2 ,
rate = ( 1 / 2 ) F ˜ ( Ω ) .
rate = f 2 2 M i j P ˜ i j ( Ω ) ,
E i ( r 0 , t ) E j ( r 0 , t ) = P i j ( t - t ) = 0 d ω 2 π P ˜ i j ( ω ) 2 cos ω ( t - t ) .
I = ( c / 4 π ) P ( 0 ) = 0 d ω 2 π ( c / 2 π ) P ˜ ( ω ) .

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