Abstract

A four-level atomic system with two closely lying upper levels driven by two coherent fields is considered. We show that, in the presence of a weak incoherent pump, steady-state gain can be achieved as a result of quantum interference from spontaneous emission. The gain depends on the relative phase between the two fields, so it can be modulated by control of the relative phase. Also, by controlling the relative phase, one can always obtain a large index of refraction with zero absorption.

© 2003 Optical Society of America

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  1. J. Javanainen, “Effect of state superpositions created by spontaneous emission on laser-driven transitions,” Europhys. Lett. 17, 407–412 (1992).
    [CrossRef]
  2. S. Menon and G. S. Agarwal, “Effects of spontaneously generated coherence on the pump-probe response of a Λ system,” Phys. Rev. A 57, 4014–4018 (1998).
    [CrossRef]
  3. E. Paspalakis, S. Q. Gong, and P. L. Knight, “Spontaneous emission-induced coherent effects in absorption and dispersion of a V-type three-level atom,” Opt. Commun. 152, 293–298 (1998).
    [CrossRef]
  4. S. Menon and G. S. Agarwal, “Gain components in the Autler-Townes doublet from quantum interferences in decay channels,” Phys. Rev. A 61, 013807 (1999).
    [CrossRef]
  5. X.-M. Hu and J.-S. Peng, “Quantum interference from spontaneous decay in Λ systems: realization in the dressed-state picture,” J. Phys. B 33, 921–931 (2000).
    [CrossRef]
  6. E. Paspalakis and P. L. Knight, “Spontaneous emission properties of a quasi-continuum,” Opt. Commun. 179, 257–265 (2000).
    [CrossRef]
  7. J. Evers, D. Bullock, and C. H. Keitel, “Dark state suppression and narrow fluorescent feature in a laser-driven Λ atom,” Opt. Commun. 209, 173–179 (2002).
    [CrossRef]
  8. J.-H. Wu and J.-Y. Gao, “Phase control of light amplification without inversion in a Λ system with spontaneously generated coherence,” Phys. Rev. A 65, 063807 (2002).
    [CrossRef]
  9. S.-Y. Zhu, R. C. F. Chan, and C. P. Lee, “Spontaneous emission from a three-level atom,” Phys. Rev. A 52, 710–716 (1995).
    [CrossRef] [PubMed]
  10. P. Zhou and S. Swain, “Quantum interference in probe absorption: narrow resonances, transparency, and gain without population inversion,” Phys. Rev. Lett. 78, 832–835 (1997).
    [CrossRef]
  11. P. Zhou and S. Swain, “Quantum interference in resonance fluorescence for a driven V atom,” Phys. Rev. A 56, 3011–3021 (1997).
    [CrossRef]
  12. H. Lee, P. Polynkin, M. O. Scully, and S.-Y. Zhu, “Quenchingof spontaneous emission via quantum interference,” Phys. Rev. A 55, 4454–4465 (1997).
    [CrossRef]
  13. 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]
  14. E. Paspalakis and P. L. Knight, “Phase control of spontaneous emission,” Phys. Rev. Lett. 81, 293–296 (1998).
    [CrossRef]
  15. F.-L. Li and S.-Y. Zhu, “Effects of quantum interference on coherent population trapping states of a four-level atom interacting with coherent fields,” Opt. Commun. 162, 155–161 (1999).
    [CrossRef]
  16. E. Paspalakis, N. J. Kylstra, and P. L. Knight, “Transparency induced via decay interference,” Phys. Rev. Lett. 82, 2079–2082 (1999).
    [CrossRef]
  17. G. S. Agarwal and S. Menon, “Quantum interferences and the question of thermodynamic equilibrium,” Phys. Rev. A 63, 023818 (2001).
    [CrossRef]
  18. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, 1997).
  19. H. R. Xia, C. Y. Ye, and S. Y. Zhu, “Experimental observation of spontaneous emission cancellation,” Phys. Rev. Lett. 77, 1032–1037 (1996).
    [CrossRef] [PubMed]
  20. K. Hakuta, L. Marmet, and B. P. Stoicheff, “Nonlinear optical generation with reduced absorption using electric-field coupling in atomic hydrogen,” Phys. Rev. A 45, 5152–5159 (1992).
    [CrossRef] [PubMed]
  21. K. Hakuta, L. Marmet, and B. P. Stoicheff, “Electric-field-induced second-harmonic generation with reduced absorption in atomic hydrogen,” Phys. Rev. Lett. 66, 596–599 (1991).
    [CrossRef] [PubMed]
  22. P. R. Berman, “Analysis of dynamical suppression of spontaneous emission,” Phys. Rev. A 58, 4886–4891 (1998).
    [CrossRef]
  23. A. K. Patnaik and G. S. Agarwal, “Cavity-induced coherence effects in spontaneous emissions from preselection of polarization,” Phys. Rev. A 59, 3015–3020 (1999).
    [CrossRef]
  24. M. O. Scully and S.-Y. Zhu, “Ultra-large index of refraction via quantum interference,” Opt. Commun. 87, 134–138 (1992).
    [CrossRef]
  25. M. Fleischhauer, C. H. Keitel, M. O. Scully, C. Su, B. T. Ulrich, and S.-Y. Zhu, “Resonantly enhanced refractive index without absorption via atomic coherence,” Phys. Rev. A 46, 1468–1487 (1992).
    [CrossRef] [PubMed]

2002 (2)

J. Evers, D. Bullock, and C. H. Keitel, “Dark state suppression and narrow fluorescent feature in a laser-driven Λ atom,” Opt. Commun. 209, 173–179 (2002).
[CrossRef]

J.-H. Wu and J.-Y. Gao, “Phase control of light amplification without inversion in a Λ system with spontaneously generated coherence,” Phys. Rev. A 65, 063807 (2002).
[CrossRef]

2001 (1)

G. S. Agarwal and S. Menon, “Quantum interferences and the question of thermodynamic equilibrium,” Phys. Rev. A 63, 023818 (2001).
[CrossRef]

2000 (2)

X.-M. Hu and J.-S. Peng, “Quantum interference from spontaneous decay in Λ systems: realization in the dressed-state picture,” J. Phys. B 33, 921–931 (2000).
[CrossRef]

E. Paspalakis and P. L. Knight, “Spontaneous emission properties of a quasi-continuum,” Opt. Commun. 179, 257–265 (2000).
[CrossRef]

1999 (4)

S. Menon and G. S. Agarwal, “Gain components in the Autler-Townes doublet from quantum interferences in decay channels,” Phys. Rev. A 61, 013807 (1999).
[CrossRef]

F.-L. Li and S.-Y. Zhu, “Effects of quantum interference on coherent population trapping states of a four-level atom interacting with coherent fields,” Opt. Commun. 162, 155–161 (1999).
[CrossRef]

E. Paspalakis, N. J. Kylstra, and P. L. Knight, “Transparency induced via decay interference,” Phys. Rev. Lett. 82, 2079–2082 (1999).
[CrossRef]

A. K. Patnaik and G. S. Agarwal, “Cavity-induced coherence effects in spontaneous emissions from preselection of polarization,” Phys. Rev. A 59, 3015–3020 (1999).
[CrossRef]

1998 (4)

E. Paspalakis and P. L. Knight, “Phase control of spontaneous emission,” Phys. Rev. Lett. 81, 293–296 (1998).
[CrossRef]

P. R. Berman, “Analysis of dynamical suppression of spontaneous emission,” Phys. Rev. A 58, 4886–4891 (1998).
[CrossRef]

S. Menon and G. S. Agarwal, “Effects of spontaneously generated coherence on the pump-probe response of a Λ system,” Phys. Rev. A 57, 4014–4018 (1998).
[CrossRef]

E. Paspalakis, S. Q. Gong, and P. L. Knight, “Spontaneous emission-induced coherent effects in absorption and dispersion of a V-type three-level atom,” Opt. Commun. 152, 293–298 (1998).
[CrossRef]

1997 (3)

P. Zhou and S. Swain, “Quantum interference in probe absorption: narrow resonances, transparency, and gain without population inversion,” Phys. Rev. Lett. 78, 832–835 (1997).
[CrossRef]

P. Zhou and S. Swain, “Quantum interference in resonance fluorescence for a driven V atom,” Phys. Rev. A 56, 3011–3021 (1997).
[CrossRef]

H. Lee, P. Polynkin, M. O. Scully, and S.-Y. Zhu, “Quenchingof spontaneous emission via quantum interference,” Phys. Rev. A 55, 4454–4465 (1997).
[CrossRef]

1996 (2)

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]

H. R. Xia, C. Y. Ye, and S. Y. Zhu, “Experimental observation of spontaneous emission cancellation,” Phys. Rev. Lett. 77, 1032–1037 (1996).
[CrossRef] [PubMed]

1995 (1)

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

1992 (4)

J. Javanainen, “Effect of state superpositions created by spontaneous emission on laser-driven transitions,” Europhys. Lett. 17, 407–412 (1992).
[CrossRef]

K. Hakuta, L. Marmet, and B. P. Stoicheff, “Nonlinear optical generation with reduced absorption using electric-field coupling in atomic hydrogen,” Phys. Rev. A 45, 5152–5159 (1992).
[CrossRef] [PubMed]

M. O. Scully and S.-Y. Zhu, “Ultra-large index of refraction via quantum interference,” Opt. Commun. 87, 134–138 (1992).
[CrossRef]

M. Fleischhauer, C. H. Keitel, M. O. Scully, C. Su, B. T. Ulrich, and S.-Y. Zhu, “Resonantly enhanced refractive index without absorption via atomic coherence,” Phys. Rev. A 46, 1468–1487 (1992).
[CrossRef] [PubMed]

1991 (1)

K. Hakuta, L. Marmet, and B. P. Stoicheff, “Electric-field-induced second-harmonic generation with reduced absorption in atomic hydrogen,” Phys. Rev. Lett. 66, 596–599 (1991).
[CrossRef] [PubMed]

Agarwal, G. S.

G. S. Agarwal and S. Menon, “Quantum interferences and the question of thermodynamic equilibrium,” Phys. Rev. A 63, 023818 (2001).
[CrossRef]

S. Menon and G. S. Agarwal, “Gain components in the Autler-Townes doublet from quantum interferences in decay channels,” Phys. Rev. A 61, 013807 (1999).
[CrossRef]

A. K. Patnaik and G. S. Agarwal, “Cavity-induced coherence effects in spontaneous emissions from preselection of polarization,” Phys. Rev. A 59, 3015–3020 (1999).
[CrossRef]

S. Menon and G. S. Agarwal, “Effects of spontaneously generated coherence on the pump-probe response of a Λ system,” Phys. Rev. A 57, 4014–4018 (1998).
[CrossRef]

Berman, P. R.

P. R. Berman, “Analysis of dynamical suppression of spontaneous emission,” Phys. Rev. A 58, 4886–4891 (1998).
[CrossRef]

Bullock, D.

J. Evers, D. Bullock, and C. H. Keitel, “Dark state suppression and narrow fluorescent feature in a laser-driven Λ atom,” Opt. Commun. 209, 173–179 (2002).
[CrossRef]

Chan, R. C. F.

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

Evers, J.

J. Evers, D. Bullock, and C. H. Keitel, “Dark state suppression and narrow fluorescent feature in a laser-driven Λ atom,” Opt. Commun. 209, 173–179 (2002).
[CrossRef]

Fleischhauer, M.

M. Fleischhauer, C. H. Keitel, M. O. Scully, C. Su, B. T. Ulrich, and S.-Y. Zhu, “Resonantly enhanced refractive index without absorption via atomic coherence,” Phys. Rev. A 46, 1468–1487 (1992).
[CrossRef] [PubMed]

Gao, J.-Y.

J.-H. Wu and J.-Y. Gao, “Phase control of light amplification without inversion in a Λ system with spontaneously generated coherence,” Phys. Rev. A 65, 063807 (2002).
[CrossRef]

Gong, S. Q.

E. Paspalakis, S. Q. Gong, and P. L. Knight, “Spontaneous emission-induced coherent effects in absorption and dispersion of a V-type three-level atom,” Opt. Commun. 152, 293–298 (1998).
[CrossRef]

Hakuta, K.

K. Hakuta, L. Marmet, and B. P. Stoicheff, “Nonlinear optical generation with reduced absorption using electric-field coupling in atomic hydrogen,” Phys. Rev. A 45, 5152–5159 (1992).
[CrossRef] [PubMed]

K. Hakuta, L. Marmet, and B. P. Stoicheff, “Electric-field-induced second-harmonic generation with reduced absorption in atomic hydrogen,” Phys. Rev. Lett. 66, 596–599 (1991).
[CrossRef] [PubMed]

Hu, X.-M.

X.-M. Hu and J.-S. Peng, “Quantum interference from spontaneous decay in Λ systems: realization in the dressed-state picture,” J. Phys. B 33, 921–931 (2000).
[CrossRef]

Javanainen, J.

J. Javanainen, “Effect of state superpositions created by spontaneous emission on laser-driven transitions,” Europhys. Lett. 17, 407–412 (1992).
[CrossRef]

Keitel, C. H.

J. Evers, D. Bullock, and C. H. Keitel, “Dark state suppression and narrow fluorescent feature in a laser-driven Λ atom,” Opt. Commun. 209, 173–179 (2002).
[CrossRef]

M. Fleischhauer, C. H. Keitel, M. O. Scully, C. Su, B. T. Ulrich, and S.-Y. Zhu, “Resonantly enhanced refractive index without absorption via atomic coherence,” Phys. Rev. A 46, 1468–1487 (1992).
[CrossRef] [PubMed]

Knight, P. L.

E. Paspalakis and P. L. Knight, “Spontaneous emission properties of a quasi-continuum,” Opt. Commun. 179, 257–265 (2000).
[CrossRef]

E. Paspalakis, N. J. Kylstra, and P. L. Knight, “Transparency induced via decay interference,” Phys. Rev. Lett. 82, 2079–2082 (1999).
[CrossRef]

E. Paspalakis, S. Q. Gong, and P. L. Knight, “Spontaneous emission-induced coherent effects in absorption and dispersion of a V-type three-level atom,” Opt. Commun. 152, 293–298 (1998).
[CrossRef]

E. Paspalakis and P. L. Knight, “Phase control of spontaneous emission,” Phys. Rev. Lett. 81, 293–296 (1998).
[CrossRef]

Kylstra, N. J.

E. Paspalakis, N. J. Kylstra, and P. L. Knight, “Transparency induced via decay interference,” Phys. Rev. Lett. 82, 2079–2082 (1999).
[CrossRef]

Lee, C. P.

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

Lee, H.

H. Lee, P. Polynkin, M. O. Scully, and S.-Y. Zhu, “Quenchingof spontaneous emission via quantum interference,” Phys. Rev. A 55, 4454–4465 (1997).
[CrossRef]

Li, F.-L.

F.-L. Li and S.-Y. Zhu, “Effects of quantum interference on coherent population trapping states of a four-level atom interacting with coherent fields,” Opt. Commun. 162, 155–161 (1999).
[CrossRef]

Marmet, L.

K. Hakuta, L. Marmet, and B. P. Stoicheff, “Nonlinear optical generation with reduced absorption using electric-field coupling in atomic hydrogen,” Phys. Rev. A 45, 5152–5159 (1992).
[CrossRef] [PubMed]

K. Hakuta, L. Marmet, and B. P. Stoicheff, “Electric-field-induced second-harmonic generation with reduced absorption in atomic hydrogen,” Phys. Rev. Lett. 66, 596–599 (1991).
[CrossRef] [PubMed]

Menon, S.

G. S. Agarwal and S. Menon, “Quantum interferences and the question of thermodynamic equilibrium,” Phys. Rev. A 63, 023818 (2001).
[CrossRef]

S. Menon and G. S. Agarwal, “Gain components in the Autler-Townes doublet from quantum interferences in decay channels,” Phys. Rev. A 61, 013807 (1999).
[CrossRef]

S. Menon and G. S. Agarwal, “Effects of spontaneously generated coherence on the pump-probe response of a Λ system,” Phys. Rev. A 57, 4014–4018 (1998).
[CrossRef]

Paspalakis, E.

E. Paspalakis and P. L. Knight, “Spontaneous emission properties of a quasi-continuum,” Opt. Commun. 179, 257–265 (2000).
[CrossRef]

E. Paspalakis, N. J. Kylstra, and P. L. Knight, “Transparency induced via decay interference,” Phys. Rev. Lett. 82, 2079–2082 (1999).
[CrossRef]

E. Paspalakis, S. Q. Gong, and P. L. Knight, “Spontaneous emission-induced coherent effects in absorption and dispersion of a V-type three-level atom,” Opt. Commun. 152, 293–298 (1998).
[CrossRef]

E. Paspalakis and P. L. Knight, “Phase control of spontaneous emission,” Phys. Rev. Lett. 81, 293–296 (1998).
[CrossRef]

Patnaik, A. K.

A. K. Patnaik and G. S. Agarwal, “Cavity-induced coherence effects in spontaneous emissions from preselection of polarization,” Phys. Rev. A 59, 3015–3020 (1999).
[CrossRef]

Peng, J.-S.

X.-M. Hu and J.-S. Peng, “Quantum interference from spontaneous decay in Λ systems: realization in the dressed-state picture,” J. Phys. B 33, 921–931 (2000).
[CrossRef]

Polynkin, P.

H. Lee, P. Polynkin, M. O. Scully, and S.-Y. Zhu, “Quenchingof spontaneous emission via quantum interference,” Phys. Rev. A 55, 4454–4465 (1997).
[CrossRef]

Scully, M. O.

H. Lee, P. Polynkin, M. O. Scully, and S.-Y. Zhu, “Quenchingof spontaneous emission via quantum interference,” Phys. Rev. A 55, 4454–4465 (1997).
[CrossRef]

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. Fleischhauer, C. H. Keitel, M. O. Scully, C. Su, B. T. Ulrich, and S.-Y. Zhu, “Resonantly enhanced refractive index without absorption via atomic coherence,” Phys. Rev. A 46, 1468–1487 (1992).
[CrossRef] [PubMed]

M. O. Scully and S.-Y. Zhu, “Ultra-large index of refraction via quantum interference,” Opt. Commun. 87, 134–138 (1992).
[CrossRef]

Stoicheff, B. P.

K. Hakuta, L. Marmet, and B. P. Stoicheff, “Nonlinear optical generation with reduced absorption using electric-field coupling in atomic hydrogen,” Phys. Rev. A 45, 5152–5159 (1992).
[CrossRef] [PubMed]

K. Hakuta, L. Marmet, and B. P. Stoicheff, “Electric-field-induced second-harmonic generation with reduced absorption in atomic hydrogen,” Phys. Rev. Lett. 66, 596–599 (1991).
[CrossRef] [PubMed]

Su, C.

M. Fleischhauer, C. H. Keitel, M. O. Scully, C. Su, B. T. Ulrich, and S.-Y. Zhu, “Resonantly enhanced refractive index without absorption via atomic coherence,” Phys. Rev. A 46, 1468–1487 (1992).
[CrossRef] [PubMed]

Swain, S.

P. Zhou and S. Swain, “Quantum interference in probe absorption: narrow resonances, transparency, and gain without population inversion,” Phys. Rev. Lett. 78, 832–835 (1997).
[CrossRef]

P. Zhou and S. Swain, “Quantum interference in resonance fluorescence for a driven V atom,” Phys. Rev. A 56, 3011–3021 (1997).
[CrossRef]

Ulrich, B. T.

M. Fleischhauer, C. H. Keitel, M. O. Scully, C. Su, B. T. Ulrich, and S.-Y. Zhu, “Resonantly enhanced refractive index without absorption via atomic coherence,” Phys. Rev. A 46, 1468–1487 (1992).
[CrossRef] [PubMed]

Wu, J.-H.

J.-H. Wu and J.-Y. Gao, “Phase control of light amplification without inversion in a Λ system with spontaneously generated coherence,” Phys. Rev. A 65, 063807 (2002).
[CrossRef]

Xia, H. R.

H. R. Xia, C. Y. Ye, and S. Y. Zhu, “Experimental observation of spontaneous emission cancellation,” Phys. Rev. Lett. 77, 1032–1037 (1996).
[CrossRef] [PubMed]

Ye, C. Y.

H. R. Xia, C. Y. Ye, and S. Y. Zhu, “Experimental observation of spontaneous emission cancellation,” Phys. Rev. Lett. 77, 1032–1037 (1996).
[CrossRef] [PubMed]

Zhou, P.

P. Zhou and S. Swain, “Quantum interference in probe absorption: narrow resonances, transparency, and gain without population inversion,” Phys. Rev. Lett. 78, 832–835 (1997).
[CrossRef]

P. Zhou and S. Swain, “Quantum interference in resonance fluorescence for a driven V atom,” Phys. Rev. A 56, 3011–3021 (1997).
[CrossRef]

Zhu, S. Y.

H. R. Xia, C. Y. Ye, and S. Y. Zhu, “Experimental observation of spontaneous emission cancellation,” Phys. Rev. Lett. 77, 1032–1037 (1996).
[CrossRef] [PubMed]

Zhu, S.-Y.

F.-L. Li and S.-Y. Zhu, “Effects of quantum interference on coherent population trapping states of a four-level atom interacting with coherent fields,” Opt. Commun. 162, 155–161 (1999).
[CrossRef]

H. Lee, P. Polynkin, M. O. Scully, and S.-Y. Zhu, “Quenchingof spontaneous emission via quantum interference,” Phys. Rev. A 55, 4454–4465 (1997).
[CrossRef]

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. C. 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, “Ultra-large index of refraction via quantum interference,” Opt. Commun. 87, 134–138 (1992).
[CrossRef]

M. Fleischhauer, C. H. Keitel, M. O. Scully, C. Su, B. T. Ulrich, and S.-Y. Zhu, “Resonantly enhanced refractive index without absorption via atomic coherence,” Phys. Rev. A 46, 1468–1487 (1992).
[CrossRef] [PubMed]

Europhys. Lett. (1)

J. Javanainen, “Effect of state superpositions created by spontaneous emission on laser-driven transitions,” Europhys. Lett. 17, 407–412 (1992).
[CrossRef]

J. Phys. B (1)

X.-M. Hu and J.-S. Peng, “Quantum interference from spontaneous decay in Λ systems: realization in the dressed-state picture,” J. Phys. B 33, 921–931 (2000).
[CrossRef]

Opt. Commun. (5)

E. Paspalakis and P. L. Knight, “Spontaneous emission properties of a quasi-continuum,” Opt. Commun. 179, 257–265 (2000).
[CrossRef]

J. Evers, D. Bullock, and C. H. Keitel, “Dark state suppression and narrow fluorescent feature in a laser-driven Λ atom,” Opt. Commun. 209, 173–179 (2002).
[CrossRef]

E. Paspalakis, S. Q. Gong, and P. L. Knight, “Spontaneous emission-induced coherent effects in absorption and dispersion of a V-type three-level atom,” Opt. Commun. 152, 293–298 (1998).
[CrossRef]

F.-L. Li and S.-Y. Zhu, “Effects of quantum interference on coherent population trapping states of a four-level atom interacting with coherent fields,” Opt. Commun. 162, 155–161 (1999).
[CrossRef]

M. O. Scully and S.-Y. Zhu, “Ultra-large index of refraction via quantum interference,” Opt. Commun. 87, 134–138 (1992).
[CrossRef]

Phys. Rev. A (11)

M. Fleischhauer, C. H. Keitel, M. O. Scully, C. Su, B. T. Ulrich, and S.-Y. Zhu, “Resonantly enhanced refractive index without absorption via atomic coherence,” Phys. Rev. A 46, 1468–1487 (1992).
[CrossRef] [PubMed]

K. Hakuta, L. Marmet, and B. P. Stoicheff, “Nonlinear optical generation with reduced absorption using electric-field coupling in atomic hydrogen,” Phys. Rev. A 45, 5152–5159 (1992).
[CrossRef] [PubMed]

P. R. Berman, “Analysis of dynamical suppression of spontaneous emission,” Phys. Rev. A 58, 4886–4891 (1998).
[CrossRef]

A. K. Patnaik and G. S. Agarwal, “Cavity-induced coherence effects in spontaneous emissions from preselection of polarization,” Phys. Rev. A 59, 3015–3020 (1999).
[CrossRef]

G. S. Agarwal and S. Menon, “Quantum interferences and the question of thermodynamic equilibrium,” Phys. Rev. A 63, 023818 (2001).
[CrossRef]

P. Zhou and S. Swain, “Quantum interference in resonance fluorescence for a driven V atom,” Phys. Rev. A 56, 3011–3021 (1997).
[CrossRef]

H. Lee, P. Polynkin, M. O. Scully, and S.-Y. Zhu, “Quenchingof spontaneous emission via quantum interference,” Phys. Rev. A 55, 4454–4465 (1997).
[CrossRef]

S. Menon and G. S. Agarwal, “Gain components in the Autler-Townes doublet from quantum interferences in decay channels,” Phys. Rev. A 61, 013807 (1999).
[CrossRef]

S. Menon and G. S. Agarwal, “Effects of spontaneously generated coherence on the pump-probe response of a Λ system,” Phys. Rev. A 57, 4014–4018 (1998).
[CrossRef]

J.-H. Wu and J.-Y. Gao, “Phase control of light amplification without inversion in a Λ system with spontaneously generated coherence,” Phys. Rev. A 65, 063807 (2002).
[CrossRef]

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

Phys. Rev. Lett. (6)

P. Zhou and S. Swain, “Quantum interference in probe absorption: narrow resonances, transparency, and gain without population inversion,” Phys. Rev. Lett. 78, 832–835 (1997).
[CrossRef]

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]

E. Paspalakis and P. L. Knight, “Phase control of spontaneous emission,” Phys. Rev. Lett. 81, 293–296 (1998).
[CrossRef]

E. Paspalakis, N. J. Kylstra, and P. L. Knight, “Transparency induced via decay interference,” Phys. Rev. Lett. 82, 2079–2082 (1999).
[CrossRef]

K. Hakuta, L. Marmet, and B. P. Stoicheff, “Electric-field-induced second-harmonic generation with reduced absorption in atomic hydrogen,” Phys. Rev. Lett. 66, 596–599 (1991).
[CrossRef] [PubMed]

H. R. Xia, C. Y. Ye, and S. Y. Zhu, “Experimental observation of spontaneous emission cancellation,” Phys. Rev. Lett. 77, 1032–1037 (1996).
[CrossRef] [PubMed]

Other (1)

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, 1997).

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic diagram of a four-level atomic system driven by two coherent fields. (b) The arrangement of field polarization required for a single field driving one transition if the dipoles are nonorthogonal.

Fig. 2
Fig. 2

Im(ρ41) (solid curves, which represent absorption) and Re(ρ41) (dashed curves, which represent index of refraction) versus probe detuning Δp for several values of Φ. The parameters are γ41=γ42=γ32=γ31, η1=η2=cos(π/4), Gc=3γ31 sin θ, Gp=0.1γ31 sin θ, and Λ=0.1γ31. (Parameters γ41, γ42, γ32, Gc, Gp, Λ, and Δp are given in units of γ31.)

Fig. 3
Fig. 3

Im(ρ41) (solid curves) and Re(ρ41) (dashed curves) versus relative phase Φ for several values of probe detuning Δp. The parameters are the same as those for Fig. 2.

Equations (30)

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σ˙44=(-γ42-γ41)σ44-1/2(η2γ42γ32+η1γ41γ31)[σ34×exp(iω43t)+σ43exp(-iω43t)],
σ˙33=(-γ32-γ31)σ33-1/2(η1γ41γ31+η2γ42γ32)×[σ34exp(iω43t)+σ43exp(-iω43t)],
σ˙22=γ42σ44+γ32σ33+η2γ42γ32[σ34exp(iω43t)+σ43exp(-iω43t)],
σ˙41=-Γ41σ41-1/2(η1γ41γ31+η2γ42γ32)×σ31exp(iω43t),
σ˙42=-Γ42σ42-1/2(η1γ41γ31+η2γ42γ32)×σ32exp(iω43t),
σ˙43=-Γ43σ43-1/2(η1γ41γ31+η2γ42γ32)×(σ44+σ33)exp(-iω43t),
σ˙31=-Γ31σ31-1/2(η1γ41γ31+η2γ42γ32)×σ41exp(-iω43t),
σ˙32=-Γ32σ32-1/2(η1γ41γ31+η2γ42γ32)×σ42exp(-iω43t),
σ˙21=-Γ21σ21,
HI=Δp|44|+Δc|33|+[Ωc|31|+Ωp|41|+H.c.].
σt=-i [HI, σ]+Λσ.
σ˙44=(-γ42-γ41)σ44+Λ(σ22-σ44)+iΩp*σ41-iΩpσ14-½(η2γ42γ32+η1γ41γ31)×(σ34+σ43),
σ˙33=(-γ32-γ31-Λ)σ33+Λσ22+iΩc*σ31-iΩcσ13-½(η1γ41γ31+η2γ42γ32)×(σ34+σ43),
σ˙22=(γ42+Λ)σ44+(γ32+Λ)σ33-2Λσ22+η2γ42γ32(σ34+σ43),
σ˙41=(-Γ41|-iΔp)σ41+iΩcσ43+iΩp(σ44-σ11)-½(η1γ41γ31+η2γ42γ32)σ31,
σ˙42=(-Γ42|-iΔp)σ42-iΩpσ12-½(η1γ41γ31+η2γ42γ32)σ32,
σ˙43=(-Γ43|-iΔp+iΔc)σ43+iΩc*σ41-iΩpσ13-½(η1γ41γ31+η2γ42γ32)(σ44+σ33),
σ˙31=(-Γ31|-iΔc)σ31+iΩc(σ33-σ11)+iΩpσ34-½(η1γ41γ31+η2γ42γ32)σ41,
σ˙32=(-Γ32|-iΔc)σ32-iΩcσ12-½(η1γ41γ31+η2γ42γ32)σ42,
σ˙21=-Γ21|σ21+iΩcσ23+iΩpσ24.
ρ˙44=(-γ42-γ41)ρ44+Λ(ρ22-ρ44)+iGp(ρ41-ρ14)-½(η2γ42γ32+η1γ41γ31)[exp(iΦ)ρ34+exp(-iΦ)ρ43],
ρ˙33=(-γ32-γ31-Λ)ρ33+Λρ22+iGc(ρ31-ρ13)-½(η1γ41γ31+η2γ42γ32)[exp(iΦ)ρ34+exp(-iΦ)ρ43],
ρ˙22=(γ42+Λ)ρ44+(γ32+Λ)ρ33-2Λρ22+η2γ42γ32[exp(iΦ)ρ34+exp(-iΦ)ρ43],
ρ˙41=(-Γ41|-iΔp)ρ41+iGcρ43+iGp(ρ44-ρ11)-½(η1γ41γ31+η2γ42γ32)exp(iΦ)ρ31,
ρ˙42=(-Γ42|-iΔp)ρ42-iGpρ12-½(η1γ41γ31+η2γ42γ32)exp(iΦ)ρ32,
ρ˙43=(-Γ43|-iΔp+iΔc)ρ43+iGcρ41-iGpσ13-½(η1γ41γ31+η2γ42γ32)exp(iΦ)(ρ44+ρ33),
ρ˙31=(-Γ31|-iΔc)ρ31+iGc(ρ33-ρ11)+iGpρ34-½(η1γ41γ31+η2γ42γ32)exp(-iΦ)ρ41,
ρ˙32=(-Γ32|-iΔc)ρ32-iGcρ12-½(η1γ41γ31+η2γ42γ32)exp(-iΦ)ρ42,
ρ˙21=-Γ21|ρ21+iGcρ23+iGpρ24.
ddΦRe(ρ41)-Im(ρ41).

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