Abstract

The spontaneous emission of a V-type Zeeman atom in a Fabry–Perot cavity containing left-handed materials (LHMs) is investigated. Because of the strong indirect quantum interference induced by the refocusing and phase compensation of LHMs, the population evolution and the emission spectrum are much different from that in isotropic environments at different initial conditions. For the degenerate cases, by preparing different initial states, the population decays much faster or slower than that in free vacuum, while the spontaneous emission spectra are narrowed or broadened, respectively. For large detuning cases, the population exchange between two upper levels could be weakened, and the Fano minimum appears in the emission spectrum. In addition, the influence of the dipole orientation on the spectrum is discussed.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
  3. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
    [CrossRef] [PubMed]
  4. R. Marqués, J. Martel, F. Mesa, and F. Medina, “Left-handed-media simulation and transmission of EM waves in subwavelength split-ring-resonator-loaded metallic waveguides,” Phys. Rev. Lett. 89, 183901–183904 (2002).
    [CrossRef] [PubMed]
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    [CrossRef]
  6. C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. 90, 107401–107405 (2003).
    [CrossRef] [PubMed]
  7. L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, “Optomagnetic composite medium with conducting nanoelements,” Phys. Rev. B 66, 155411–155427 (2002).
    [CrossRef]
  8. M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: creating magnetic emitters in photonic crystals,” Appl. Phys. Lett. 82, 1069–1071 (2003).
    [CrossRef]
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  10. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [CrossRef] [PubMed]
  11. D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405–077408 (2003).
    [CrossRef] [PubMed]
  12. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  21. H. T. Dung, S. Y. Buhmann, L. Knöll, and D. G. Welsch, “Electromagnetic-field quantization and spontaneous decay in left-handed media,” Phys. Rev. A 68, 043816–043830 (2003).
    [CrossRef]
  22. S. Y. Zhu, R. F. Chan, and C. P. Lee, “Spontaneous emission from a three-level atom,” Phys. Rev. A 52, 710–716 (1995).
    [CrossRef] [PubMed]
  23. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
    [CrossRef]
  24. S. Y. Zhu and M. O. Scully, “Spectral line elimination and spontaneous emission cancellation via quantum interference,” Phys. Rev. Lett. 76, 388–391 (1996).
    [CrossRef] [PubMed]

2010

J. P. Xu and Y. P. Yang, “Quantum interference of V-type three-level atom in structures made of left-handed materials and mirrors,” Phys. Rev. A 81, 013816–013823 (2010).
[CrossRef]

2009

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

2008

Y. P. Yang, J. P. Xu, H. Chen, and S. Y. Zhu, “Quantum interference enhancement with left-handed materials,” Phys. Rev. Lett. 100, 043601–043604 (2008).
[CrossRef] [PubMed]

2005

J. Kästel and M. Fleischhauer, “Suppression of spontaneous emission and superradiance over macroscopic distance in media with negative refraction,” Phys. Rev. A 71, 011804–011807(2005).
[CrossRef]

2003

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405–077408 (2003).
[CrossRef] [PubMed]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. 90, 107401–107405 (2003).
[CrossRef] [PubMed]

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: creating magnetic emitters in photonic crystals,” Appl. Phys. Lett. 82, 1069–1071 (2003).
[CrossRef]

H. T. Dung, S. Y. Buhmann, L. Knöll, and D. G. Welsch, “Electromagnetic-field quantization and spontaneous decay in left-handed media,” Phys. Rev. A 68, 043816–043830 (2003).
[CrossRef]

2002

L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, “Optomagnetic composite medium with conducting nanoelements,” Phys. Rev. B 66, 155411–155427 (2002).
[CrossRef]

R. Marqués, J. Martel, F. Mesa, and F. Medina, “Left-handed-media simulation and transmission of EM waves in subwavelength split-ring-resonator-loaded metallic waveguides,” Phys. Rev. Lett. 89, 183901–183904 (2002).
[CrossRef] [PubMed]

A. Grbic and G. V. Eleftheriades, “Experimental verification of backward-wave radiation from a negative refractive index metamaterial,” J. Appl. Phys. 92, 5930–5935 (2002).
[CrossRef]

2001

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef] [PubMed]

2000

G. S. Agarwal, “Anisotropic vacuum-induced interference in decay channels,” Phys. Rev. Lett. 84, 5500–5503 (2000).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187(2000).
[CrossRef] [PubMed]

D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933–2936 (2000).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

1996

P. Zhou and S. Swain, “Ultranarrow spectral lines via quantum interference,” Phys. Rev. Lett. 77, 3995–3998 (1996).
[CrossRef] [PubMed]

S. Y. Zhu and M. O. Scully, “Spectral line elimination and spontaneous emission cancellation via quantum interference,” Phys. Rev. Lett. 76, 388–391 (1996).
[CrossRef] [PubMed]

1995

S. Y. Zhu, R. F. Chan, and C. P. Lee, “Spontaneous emission from a three-level atom,” Phys. Rev. A 52, 710–716 (1995).
[CrossRef] [PubMed]

1990

S. E. Harris, J. E. Field, and A. Imamoglu, “Nolinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef] [PubMed]

1989

M. O. Scully and S. Y. Zhu, “Degenerate quantum-beat laser: lasing without inversion and inversion without lasing,” Phys. Rev. Lett. 62, 2813–2816 (1989).
[CrossRef] [PubMed]

1982

P. M. Radmore and P. L. Knight, “Population trapping and dispersion in a three-level system,” J. Phys. B 15, 561–573(1982).
[CrossRef]

1968

V. G. Veselago, “Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities,” Sov. Phys. Usp. 10, 509–514 (1968).
[CrossRef]

1961

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, “Anisotropic vacuum-induced interference in decay channels,” Phys. Rev. Lett. 84, 5500–5503 (2000).
[CrossRef] [PubMed]

Buhmann, S. Y.

H. T. Dung, S. Y. Buhmann, L. Knöll, and D. G. Welsch, “Electromagnetic-field quantization and spontaneous decay in left-handed media,” Phys. Rev. A 68, 043816–043830 (2003).
[CrossRef]

Chan, R. F.

S. Y. Zhu, R. F. Chan, and C. P. Lee, “Spontaneous emission from a three-level atom,” Phys. Rev. A 52, 710–716 (1995).
[CrossRef] [PubMed]

Chen, H.

Y. P. Yang, J. P. Xu, H. Chen, and S. Y. Zhu, “Quantum interference enhancement with left-handed materials,” Phys. Rev. Lett. 100, 043601–043604 (2008).
[CrossRef] [PubMed]

Chin, J. Y.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

Cui, T. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

Dung, H. T.

H. T. Dung, S. Y. Buhmann, L. Knöll, and D. G. Welsch, “Electromagnetic-field quantization and spontaneous decay in left-handed media,” Phys. Rev. A 68, 043816–043830 (2003).
[CrossRef]

Eleftheriades, G. V.

A. Grbic and G. V. Eleftheriades, “Experimental verification of backward-wave radiation from a negative refractive index metamaterial,” J. Appl. Phys. 92, 5930–5935 (2002).
[CrossRef]

Fano, U.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[CrossRef]

Field, J. E.

S. E. Harris, J. E. Field, and A. Imamoglu, “Nolinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef] [PubMed]

Fleischhauer, M.

J. Kästel and M. Fleischhauer, “Suppression of spontaneous emission and superradiance over macroscopic distance in media with negative refraction,” Phys. Rev. A 71, 011804–011807(2005).
[CrossRef]

Grbic, A.

A. Grbic and G. V. Eleftheriades, “Experimental verification of backward-wave radiation from a negative refractive index metamaterial,” J. Appl. Phys. 92, 5930–5935 (2002).
[CrossRef]

Greegor, R. B.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. 90, 107401–107405 (2003).
[CrossRef] [PubMed]

Grigorenko, A. N.

L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, “Optomagnetic composite medium with conducting nanoelements,” Phys. Rev. B 66, 155411–155427 (2002).
[CrossRef]

Harris, S. E.

S. E. Harris, J. E. Field, and A. Imamoglu, “Nolinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef] [PubMed]

Imamoglu, A.

S. E. Harris, J. E. Field, and A. Imamoglu, “Nolinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef] [PubMed]

Ji, C.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

Joannopoulos, J. D.

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: creating magnetic emitters in photonic crystals,” Appl. Phys. Lett. 82, 1069–1071 (2003).
[CrossRef]

Johnson, S. G.

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: creating magnetic emitters in photonic crystals,” Appl. Phys. Lett. 82, 1069–1071 (2003).
[CrossRef]

Kästel, J.

J. Kästel and M. Fleischhauer, “Suppression of spontaneous emission and superradiance over macroscopic distance in media with negative refraction,” Phys. Rev. A 71, 011804–011807(2005).
[CrossRef]

Knight, P. L.

P. M. Radmore and P. L. Knight, “Population trapping and dispersion in a three-level system,” J. Phys. B 15, 561–573(1982).
[CrossRef]

Knöll, L.

H. T. Dung, S. Y. Buhmann, L. Knöll, and D. G. Welsch, “Electromagnetic-field quantization and spontaneous decay in left-handed media,” Phys. Rev. A 68, 043816–043830 (2003).
[CrossRef]

Koltenbah, B. E. C.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. 90, 107401–107405 (2003).
[CrossRef] [PubMed]

Kroll, N.

D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933–2936 (2000).
[CrossRef] [PubMed]

Lee, C. P.

S. Y. Zhu, R. F. Chan, and C. P. Lee, “Spontaneous emission from a three-level atom,” Phys. Rev. A 52, 710–716 (1995).
[CrossRef] [PubMed]

Li, K.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. 90, 107401–107405 (2003).
[CrossRef] [PubMed]

Liu, R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

Makhnovskiy, D. P.

L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, “Optomagnetic composite medium with conducting nanoelements,” Phys. Rev. B 66, 155411–155427 (2002).
[CrossRef]

Marqués, R.

R. Marqués, J. Martel, F. Mesa, and F. Medina, “Left-handed-media simulation and transmission of EM waves in subwavelength split-ring-resonator-loaded metallic waveguides,” Phys. Rev. Lett. 89, 183901–183904 (2002).
[CrossRef] [PubMed]

Martel, J.

R. Marqués, J. Martel, F. Mesa, and F. Medina, “Left-handed-media simulation and transmission of EM waves in subwavelength split-ring-resonator-loaded metallic waveguides,” Phys. Rev. Lett. 89, 183901–183904 (2002).
[CrossRef] [PubMed]

Medina, F.

R. Marqués, J. Martel, F. Mesa, and F. Medina, “Left-handed-media simulation and transmission of EM waves in subwavelength split-ring-resonator-loaded metallic waveguides,” Phys. Rev. Lett. 89, 183901–183904 (2002).
[CrossRef] [PubMed]

Mesa, F.

R. Marqués, J. Martel, F. Mesa, and F. Medina, “Left-handed-media simulation and transmission of EM waves in subwavelength split-ring-resonator-loaded metallic waveguides,” Phys. Rev. Lett. 89, 183901–183904 (2002).
[CrossRef] [PubMed]

Mock, J. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187(2000).
[CrossRef] [PubMed]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187(2000).
[CrossRef] [PubMed]

Panina, L. V.

L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, “Optomagnetic composite medium with conducting nanoelements,” Phys. Rev. B 66, 155411–155427 (2002).
[CrossRef]

Parazzoli, C. G.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. 90, 107401–107405 (2003).
[CrossRef] [PubMed]

Pendry, J. B.

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: creating magnetic emitters in photonic crystals,” Appl. Phys. Lett. 82, 1069–1071 (2003).
[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

Povinelli, M. L.

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: creating magnetic emitters in photonic crystals,” Appl. Phys. Lett. 82, 1069–1071 (2003).
[CrossRef]

Radmore, P. M.

P. M. Radmore and P. L. Knight, “Population trapping and dispersion in a three-level system,” J. Phys. B 15, 561–573(1982).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187(2000).
[CrossRef] [PubMed]

Schurig, D.

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405–077408 (2003).
[CrossRef] [PubMed]

Scully, M. O.

S. Y. Zhu and M. O. Scully, “Spectral line elimination and spontaneous emission cancellation via quantum interference,” Phys. Rev. Lett. 76, 388–391 (1996).
[CrossRef] [PubMed]

M. O. Scully and S. Y. Zhu, “Degenerate quantum-beat laser: lasing without inversion and inversion without lasing,” Phys. Rev. Lett. 62, 2813–2816 (1989).
[CrossRef] [PubMed]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef] [PubMed]

Smith, D. R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405–077408 (2003).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187(2000).
[CrossRef] [PubMed]

D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933–2936 (2000).
[CrossRef] [PubMed]

Swain, S.

P. Zhou and S. Swain, “Ultranarrow spectral lines via quantum interference,” Phys. Rev. Lett. 77, 3995–3998 (1996).
[CrossRef] [PubMed]

Tanielian, M.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. 90, 107401–107405 (2003).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, “Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities,” Sov. Phys. Usp. 10, 509–514 (1968).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187(2000).
[CrossRef] [PubMed]

Welsch, D. G.

H. T. Dung, S. Y. Buhmann, L. Knöll, and D. G. Welsch, “Electromagnetic-field quantization and spontaneous decay in left-handed media,” Phys. Rev. A 68, 043816–043830 (2003).
[CrossRef]

Xu, J. P.

J. P. Xu and Y. P. Yang, “Quantum interference of V-type three-level atom in structures made of left-handed materials and mirrors,” Phys. Rev. A 81, 013816–013823 (2010).
[CrossRef]

Y. P. Yang, J. P. Xu, H. Chen, and S. Y. Zhu, “Quantum interference enhancement with left-handed materials,” Phys. Rev. Lett. 100, 043601–043604 (2008).
[CrossRef] [PubMed]

Yang, Y. P.

J. P. Xu and Y. P. Yang, “Quantum interference of V-type three-level atom in structures made of left-handed materials and mirrors,” Phys. Rev. A 81, 013816–013823 (2010).
[CrossRef]

Y. P. Yang, J. P. Xu, H. Chen, and S. Y. Zhu, “Quantum interference enhancement with left-handed materials,” Phys. Rev. Lett. 100, 043601–043604 (2008).
[CrossRef] [PubMed]

Zhou, P.

P. Zhou and S. Swain, “Ultranarrow spectral lines via quantum interference,” Phys. Rev. Lett. 77, 3995–3998 (1996).
[CrossRef] [PubMed]

Zhu, S. Y.

Y. P. Yang, J. P. Xu, H. Chen, and S. Y. Zhu, “Quantum interference enhancement with left-handed materials,” Phys. Rev. Lett. 100, 043601–043604 (2008).
[CrossRef] [PubMed]

S. Y. Zhu and M. O. Scully, “Spectral line elimination and spontaneous emission cancellation via quantum interference,” Phys. Rev. Lett. 76, 388–391 (1996).
[CrossRef] [PubMed]

S. Y. Zhu, R. F. Chan, and C. P. Lee, “Spontaneous emission from a three-level atom,” Phys. Rev. A 52, 710–716 (1995).
[CrossRef] [PubMed]

M. O. Scully and S. Y. Zhu, “Degenerate quantum-beat laser: lasing without inversion and inversion without lasing,” Phys. Rev. Lett. 62, 2813–2816 (1989).
[CrossRef] [PubMed]

Appl. Phys. Lett.

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: creating magnetic emitters in photonic crystals,” Appl. Phys. Lett. 82, 1069–1071 (2003).
[CrossRef]

J. Appl. Phys.

A. Grbic and G. V. Eleftheriades, “Experimental verification of backward-wave radiation from a negative refractive index metamaterial,” J. Appl. Phys. 92, 5930–5935 (2002).
[CrossRef]

J. Phys. B

P. M. Radmore and P. L. Knight, “Population trapping and dispersion in a three-level system,” J. Phys. B 15, 561–573(1982).
[CrossRef]

Phys. Rev.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[CrossRef]

Phys. Rev. A

J. P. Xu and Y. P. Yang, “Quantum interference of V-type three-level atom in structures made of left-handed materials and mirrors,” Phys. Rev. A 81, 013816–013823 (2010).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Zeeman atom with two upper levels | a , | b and a ground level | c is placed in the middle of two LHM slabs attached on two perfect mirrors. The thickness of the LHM slab is d A , and the distance between the slabs is 2 d A .

Fig. 2
Fig. 2

Evolution of | C a ( t ) | 2 (dotted curve), | C b ( t ) | 2 (dashed curve), and | C a ( t ) | 2 + | C b ( t ) | 2 (dashed–dotted curve) of a Zeeman atom in the LHM cavity and | C a ( t ) | 2 (solid curve) in free vacuum with C a ( 0 ) = 1 , C b ( 0 ) = 0 .

Fig. 3
Fig. 3

Evolution of | C a ( t ) | 2 + | C b ( t ) | 2 with C a ( 0 ) = C b ( 0 ) = 2 / 2 (dashed curve), C a ( 0 ) = C b ( 0 ) = 2 / 2 (dotted curve) of a Zeeman atom in the LHM cavity and C a ( 0 ) = ± C b ( 0 ) = 2 / 2 (solid curve) in free vacuum.

Fig. 4
Fig. 4

Spontaneous emission spectrum with ω a b = 0 and C a ( 0 ) = 1 , C b ( 0 ) = 0 .

Fig. 5
Fig. 5

Spontaneous emission spectrum with ω a b = 0 and C a ( 0 ) = C b ( 0 ) = 2 / 2 (dashed curve) and C a ( 0 ) = C b ( 0 ) = 2 / 2 (solid curve).

Fig. 6
Fig. 6

Evolution of | C a ( t ) | 2 (solid curve), | C b ( t ) | 2 (dotted curve) with ω a b = 2 Γ a 0 , and | C a ( t ) | 2 (dashed curve), | C b ( t ) | 2 (dashed–dotted curve) with ω a b = 8 Γ a 0 .

Fig. 7
Fig. 7

Population evolution of | C b ( t ) | 2 with C a ( 0 ) = 1 , C b ( 0 ) = 0 , and ω a b = 20 Γ a 0 .

Fig. 8
Fig. 8

Spontaneous emission spectrum with C a ( 0 ) = 1 , C b ( 0 ) = 0 , and ω a b = 2 Γ a 0 (dotted curve), 4 Γ a 0 (dashed–dotted curve), 8 Γ a 0 (solid curve).

Fig. 9
Fig. 9

Spontaneous emission spectrum with C a ( 0 ) = C b ( 0 ) = 2 / 2 and ω a b = 1 Γ a 0 (solid curve), 3 Γ a 0 (dashed–dotted curve), and 6 Γ a 0 (dotted curve).

Fig. 10
Fig. 10

Strength of quantum interference of a Zeeman atom in the LHM cavity varying with θ.

Fig. 11
Fig. 11

Spontaneous emission spectrum with C a ( 0 ) = 1 , C b ( 0 ) = 0 , ω a b = 2 Γ a 0 , and θ = π / 6 (dotted curve), π / 4 (solid curve), and π / 3 (dashed–dotted curve).

Equations (26)

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d = d ( A a c e 1 + A b c e 2 ) + H . c . ,
e 1 , 2 = ( e z ± i e x ) / 2 ,
H ^ = λ = e , m d 3 r 0 d ω ω f ^ λ + ( r , ω ) f ^ λ ( r , ω ) + ω a | a a | + ω b | b b | [ | a c | d a · 0 d ω E ^ ( + ) ( r A , ω ) + | b c | d b · 0 d ω E ^ ( + ) ( r A , ω ) + H . c . ] .
[ f ^ λ , i ( r , ω ) , f ^ λ , j + ( r , ω ) ] = δ λ λ ' δ i j δ ( r r ) δ ( ω ω ) ,
[ f ^ λ , i ( r , ω ) , f ^ λ , j ( r , ω ) ] = 0 ,
E ^ ( + ) ( r , ω ) = i ω μ 0 d 3 r G ( r , r , ω ) · j ^ N ( r , ω ) .
j ^ N ( r , ω ) = ω ε 0 π Im ε ( r , ω ) f ^ e ( r , ω ) + × π μ 0 Im [ 1 / μ ( r , ω ) ] f ^ m ( r , ω ) ,
[ × 1 μ ( r , ω ) × ω 2 c 2 ε ( r , ω ) ] G ( r , r , ω ) = I δ ( r r ) .
| ψ ( t ) = C a ( t ) e i ω a t | { 0 } | a + C b ( t ) e i ω b t | { 0 } | b + λ = e , m d 3 r 0 d ω e i ω t C λ c ( r , ω , t ) · | 1 λ ( r , ω ) | c ,
C ˙ a ( t ) = 1 π ε 0 0 d ω e i ( ω ω a ) t ω c d 3 r · d a · { ω c Im ε ( r , ω ) G ( r A , r , ω ) · C e c ( r , ω , t ) + Im [ 1 / μ ( r , ω ) ] [ G ( r A , r , ω ) × r ] · C m c ( r , ω , t ) } ,
C ˙ b ( t ) = 1 π ε 0 0 d ω e i ( ω ω b ) t ω c d 3 r · d b · { ω c Im ε ( r , ω ) G ( r A , r , ω ) · C e c ( r , ω , t ) + Im [ 1 / μ ( r , ω ) ] [ G ( r A , r , ω ) × r ] · C m c ( r , ω , t ) } ,
C ˙ e c ( r , ω , t ) = 1 π ε 0 ω 2 c 2 Im ε ( r , ω ) G * ( r , r A , ω ) · [ d a * C a ( t ) e i ( ω a ω ) t + d b * C b ( t ) e i ( ω b ω ) t ] ,
C ˙ m c ( r , ω , t ) = 1 π ε 0 ω c Im [ 1 / μ ( r , ω ) ] [ r × G * ( r , r A , ω ) ] · [ d a * C a ( t ) e i ( ω a ω ) t + d b * C b ( t ) e i ( ω b ω ) t ] .
C ˙ a ( t ) = γ a 2 C a ( t ) κ a 2 C b ( t ) e i ω a b t ,
C ˙ b ( t ) = γ b 2 C b ( t ) κ b 2 C a ( t ) e i ω b a t ,
γ i = 2 ω i 2 ε 0 c 2 d i * · Im G ( r A , r A , ω i ) · d i ,
κ i = 2 ω j 2 ε 0 c 2 d i * · Im G ( r A , r A , ω j ) · d j .
Γ = 3 4 Γ 0 Re μ 0 n 0 0 d k k 0 k β 0 { ( 1 + 2 r L TE r R TE e 4 i β 0 d A + r L TE e 2 i β 0 d A + r R TE e 2 i β 0 d A 1 r L TE r R TE e 4 i β 0 d A ) + β 0 2 k 0 2 ( 1 + 2 r L TM r R TM e 4 i β 0 d A r L TM e 2 i β 0 d A r R TM e 2 i β 0 d A 1 r L TM r R TM e 4 i β 0 d A ) } ,
Γ = 3 2 Γ 0 Re μ 0 n 0 0 d k k 0 3 k 3 β 0 ( 1 + 2 r L TM r R TM e 4 i β 0 d A + r L TM e 2 i β 0 d A + r R TM e 2 i β 0 d A 1 r L TM r R TM e 4 i β 0 d A ) ,
C a ( t ) = C 1 e s 1 t + C 2 e s 2 t ,
C b ( t ) = 2 γ a b [ ( s 1 + γ a 2 ) C 1 e s 1 t + ( s 2 + γ a 2 ) C 2 e s 2 t ] e i ω a b t ,
s 1 , 2 = [ ( γ a 2 + γ b 2 ) + i ω a b ± D ] / 2 , D = ( γ a 2 γ b 2 + i ω a b ) 2 + κ a κ b , C 1 , 2 = ( ) [ ( γ a 2 + s 2 , 1 ) C a ( 0 ) + κ a 2 C b ( 0 ) ] / D .
S ( r , ω ) = lim t ψ ( t ) | E ^ ( ) ( r , ω ) E ^ ( + ) ( r , ω ) | ψ ( t ) = ω 4 μ 0 2 π 2 | Im G ( r , r A ω ) · [ d a ( 2 s 1 + γ a ) d b / κ a ω ω a i s 1 C 1 + d a ( 2 s 2 + γ a ) d b / κ a ω ω a i s 2 C 2 ] | 2 .
S ( r , ω ) = ω 4 μ 0 2 d 2 2 π 2 | Im G ( r , r A , ω ) · ( e z ω ω a + i Γ 2 + i e x ω ω a + i Γ 2 ) | 2 .
S ( r , ω ) = ω 4 μ 0 2 d 2 π 2 | Im G ( r , r A , ω ) · e z ω ω a + i Γ 2 | 2 for     C a ( 0 ) = C b ( 0 ) = 2 / 2 ,
S ( r , ω ) = ω 4 μ 0 2 d 2 π 2 | Im G ( r , r A , ω ) · e x ω ω a + i Γ | 2 | 2 for   C a ( 0 ) = C b ( 0 ) = 2 / 2.

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