Abstract

We theoretically study the transmission and reflection of the probe travelling wave in an electromagnetically induced absorption grating (EIG), which is created in a three-level Λ-type atomic system when the coupling field is a standing wave. Using the system, we show that a photonic stop band can exist on one side away from the resonance point in ultracold atomic gas, while there is an enhanced absorption at resonance and small reflection around it in the thermal atomic gas. Because our method can deal with such two cases, it is helpful to further understand the effects of the Doppler effect on atomic coherence and interference.

© 2008 Optical Society of America

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  1. H. Y. Ling, Y. Q. Li, and M. Xiao, "Electromagnetically induced grating: Homogeneously broadened medium," Phys. Rev. A 57, 1338-1344 (1998).
    [CrossRef]
  2. M. Mitsunaga and N. Imoto, "Observation of an electromagnetically induced grating in cold sodium atoms," Phys. Rev. A 59, 4773-4776 (1999).
    [CrossRef]
  3. M. Artoni and G. C. La Rocca, "Optically tunable photonic stop bands in homogeneous absorbing media," Phys. Rev. Lett. 96, 073905 (2006).
    [CrossRef] [PubMed]
  4. A. W. Brown and M. Xiao, "All-optical switching and routing based on an electromagnetically induced absorption grating," Opt. Lett. 30, 699-701 (2005).
    [CrossRef] [PubMed]
  5. A.W. Brown and M. Xiao, "Frequency detuning and power depedence of reflection from an electromagnetically induced absorption grating," J. Mod. Opt. 52, 2365-2371 (2003).
    [CrossRef]
  6. M. Bajcsy, A. S. Zibrov, and M. D. Lukin, "Stationary pulses of light in an atomic medium," Nature 426, 638-641 (2003).
    [CrossRef] [PubMed]
  7. M. Fleischhauer and M. D. Lukin, "Dark-State polaritons in Electromagnetically induced transparency," Phys. Rev. Lett. 84, 5094-5097 (2000).
    [CrossRef] [PubMed]
  8. M. Fleischhauer and M. D. Lukin, "Quantum memory for photons: Dark-state polaritons," Phys. Rev. A 65, 022314 (2002).
    [CrossRef]
  9. F. E. Zimmer, A. Andre, M. D. Lukin, and M. Fleischhauer, "Coherent control of stationary light pulses," Opt. Commun. 264, 441-453 (2006).
    [CrossRef]
  10. K. R. Hansen and K. Mølmer, "Trapping of light pulses in ensembles of stationary ??? atoms," Phys. Rev. A 75, 053802 (2007).
    [CrossRef]
  11. K. R. Hansen and K. Mølmer, "Stationary light pulses in ultra cold gases," Phys. Rev. A 75, 065804 (2007).
    [CrossRef]
  12. A. Andre and M. D. Lukin, "Manipulating light pulses via dynamically controlled photonic band gap," Phys. Rev. Lett. 89, 143602 (2002).
    [CrossRef] [PubMed]
  13. X. M. Su and B. S. Ham, "Dynamic control of the photonic band gap using quantum coherence," Phys. Rev. A 71, 013821 (2005).
    [CrossRef]
  14. F. Silva, J. Mompart, V. Ahufinger, and R. Corbalan, "Electromagnetically induced transparency in Dopplerbroadened three-level systems with resonant standing-wave drive," Europhys. Lett. 51, 286-292 (2000).
    [CrossRef]
  15. F. Silva, J. Mompart, V. Ahufinger, and R. Corbalan, "Electromagnetically induced transparency with a standingwave drive in the frequency up-conversion regime," Phys. Rev. A 64, 033802 (2001).
    [CrossRef]
  16. S. A. Babin, D. V. Churkin, E. V. Podivilov, V. V. Potapov, and D. A. Shapiro, "Splitting of the peak of electromagnetically induced transparency by the higher-order spatial harmonics of the atomic coherence," Phys. Rev. A 67, 043808 (2003).
    [CrossRef]
  17. E. Kyrola and R. Salomaa, "Probe spectroscopy in an inhomogeneously broadened three-level system saturated by an intense standing wave," Phys. Rev. A 23, 1874-1892 (1981).
    [CrossRef]
  18. B. J. Feldman and M. S. Feld, "Laser-induced line-narrowing effects in coupled Doppler-broadened transitions. II. Standing-wave features," Phys. Rev. A 5, 899-918 (1972).
    [CrossRef]
  19. M. Artoni, G. C. La Rocca, and F. Bassani, "Resonantly absorbing one-dimensional photonic crystals," Phys. Rev. E 72, 046604 (2005).
    [CrossRef]
  20. J. D. Jackson, Classical Electrodynamics, 2nd ed (Wiley, New York, 1975), pp. 306-312.
  21. S. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36-42 (1997).
    [CrossRef]
  22. J. Wang, Y. F. Zhu, K. J. Jiang, and M. S. Zhan, "Bichromatic electromagnitically induced transparency in cold rubidium atoms," Phys. Rev. A 68, 063810 (2003).
    [CrossRef]
  23. Y. F. Zhu, Q. L. Wu, A. Lezama, D. J. Gauthier, and T. W. Mossberg, "Resonance fluorescence of two-level atoms under strong bichromatic excitation," Phys. Rev. A 41, 6574-6576 (1990).
    [CrossRef] [PubMed]
  24. Z. Ficek and H. S. Freedhoff, "Resonance-fluorescence and absorption spectra of two-level atom driven by a strong bichromatic field," Phys. Rev. A 48, 3092-3104 (1993).
    [CrossRef] [PubMed]
  25. P. R. S. Carvalho, L. E. E. de Araujo and J. W. R. Tabosa, "Angular dependence of an electromagnetically induced transparency resonance in a Doppler-broadened atomic vapor," Phys. Rev. A 70, 063818 (2004).
    [CrossRef]
  26. M. Born and E. Wolf, Principles of Optics, 7th ed (Cambridge University Press, Cambridge, UK, 1999), pp. 64-74.
  27. H. Wang, D. Goorskey, and M. Xiao, "Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system," Phys. Rev. Lett. 87, 073601 (2001).
    [CrossRef] [PubMed]
  28. H. Wang, D. Goorskey, and M. Xiao, "Atomic coherence induced Kerr nonlinearity enhancement in Rb vapour," J. Mod. Opt. 49, 335-347 (2002).
    [CrossRef]

2007 (2)

K. R. Hansen and K. Mølmer, "Trapping of light pulses in ensembles of stationary ??? atoms," Phys. Rev. A 75, 053802 (2007).
[CrossRef]

K. R. Hansen and K. Mølmer, "Stationary light pulses in ultra cold gases," Phys. Rev. A 75, 065804 (2007).
[CrossRef]

2006 (2)

F. E. Zimmer, A. Andre, M. D. Lukin, and M. Fleischhauer, "Coherent control of stationary light pulses," Opt. Commun. 264, 441-453 (2006).
[CrossRef]

M. Artoni and G. C. La Rocca, "Optically tunable photonic stop bands in homogeneous absorbing media," Phys. Rev. Lett. 96, 073905 (2006).
[CrossRef] [PubMed]

2005 (3)

A. W. Brown and M. Xiao, "All-optical switching and routing based on an electromagnetically induced absorption grating," Opt. Lett. 30, 699-701 (2005).
[CrossRef] [PubMed]

X. M. Su and B. S. Ham, "Dynamic control of the photonic band gap using quantum coherence," Phys. Rev. A 71, 013821 (2005).
[CrossRef]

M. Artoni, G. C. La Rocca, and F. Bassani, "Resonantly absorbing one-dimensional photonic crystals," Phys. Rev. E 72, 046604 (2005).
[CrossRef]

2004 (1)

P. R. S. Carvalho, L. E. E. de Araujo and J. W. R. Tabosa, "Angular dependence of an electromagnetically induced transparency resonance in a Doppler-broadened atomic vapor," Phys. Rev. A 70, 063818 (2004).
[CrossRef]

2003 (4)

S. A. Babin, D. V. Churkin, E. V. Podivilov, V. V. Potapov, and D. A. Shapiro, "Splitting of the peak of electromagnetically induced transparency by the higher-order spatial harmonics of the atomic coherence," Phys. Rev. A 67, 043808 (2003).
[CrossRef]

J. Wang, Y. F. Zhu, K. J. Jiang, and M. S. Zhan, "Bichromatic electromagnitically induced transparency in cold rubidium atoms," Phys. Rev. A 68, 063810 (2003).
[CrossRef]

A.W. Brown and M. Xiao, "Frequency detuning and power depedence of reflection from an electromagnetically induced absorption grating," J. Mod. Opt. 52, 2365-2371 (2003).
[CrossRef]

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, "Stationary pulses of light in an atomic medium," Nature 426, 638-641 (2003).
[CrossRef] [PubMed]

2002 (3)

M. Fleischhauer and M. D. Lukin, "Quantum memory for photons: Dark-state polaritons," Phys. Rev. A 65, 022314 (2002).
[CrossRef]

A. Andre and M. D. Lukin, "Manipulating light pulses via dynamically controlled photonic band gap," Phys. Rev. Lett. 89, 143602 (2002).
[CrossRef] [PubMed]

H. Wang, D. Goorskey, and M. Xiao, "Atomic coherence induced Kerr nonlinearity enhancement in Rb vapour," J. Mod. Opt. 49, 335-347 (2002).
[CrossRef]

2001 (2)

H. Wang, D. Goorskey, and M. Xiao, "Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system," Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef] [PubMed]

F. Silva, J. Mompart, V. Ahufinger, and R. Corbalan, "Electromagnetically induced transparency with a standingwave drive in the frequency up-conversion regime," Phys. Rev. A 64, 033802 (2001).
[CrossRef]

2000 (2)

F. Silva, J. Mompart, V. Ahufinger, and R. Corbalan, "Electromagnetically induced transparency in Dopplerbroadened three-level systems with resonant standing-wave drive," Europhys. Lett. 51, 286-292 (2000).
[CrossRef]

M. Fleischhauer and M. D. Lukin, "Dark-State polaritons in Electromagnetically induced transparency," Phys. Rev. Lett. 84, 5094-5097 (2000).
[CrossRef] [PubMed]

1999 (1)

M. Mitsunaga and N. Imoto, "Observation of an electromagnetically induced grating in cold sodium atoms," Phys. Rev. A 59, 4773-4776 (1999).
[CrossRef]

1998 (1)

H. Y. Ling, Y. Q. Li, and M. Xiao, "Electromagnetically induced grating: Homogeneously broadened medium," Phys. Rev. A 57, 1338-1344 (1998).
[CrossRef]

1997 (1)

S. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36-42 (1997).
[CrossRef]

1993 (1)

Z. Ficek and H. S. Freedhoff, "Resonance-fluorescence and absorption spectra of two-level atom driven by a strong bichromatic field," Phys. Rev. A 48, 3092-3104 (1993).
[CrossRef] [PubMed]

1990 (1)

Y. F. Zhu, Q. L. Wu, A. Lezama, D. J. Gauthier, and T. W. Mossberg, "Resonance fluorescence of two-level atoms under strong bichromatic excitation," Phys. Rev. A 41, 6574-6576 (1990).
[CrossRef] [PubMed]

1981 (1)

E. Kyrola and R. Salomaa, "Probe spectroscopy in an inhomogeneously broadened three-level system saturated by an intense standing wave," Phys. Rev. A 23, 1874-1892 (1981).
[CrossRef]

1972 (1)

B. J. Feldman and M. S. Feld, "Laser-induced line-narrowing effects in coupled Doppler-broadened transitions. II. Standing-wave features," Phys. Rev. A 5, 899-918 (1972).
[CrossRef]

Ahufinger, V.

F. Silva, J. Mompart, V. Ahufinger, and R. Corbalan, "Electromagnetically induced transparency with a standingwave drive in the frequency up-conversion regime," Phys. Rev. A 64, 033802 (2001).
[CrossRef]

F. Silva, J. Mompart, V. Ahufinger, and R. Corbalan, "Electromagnetically induced transparency in Dopplerbroadened three-level systems with resonant standing-wave drive," Europhys. Lett. 51, 286-292 (2000).
[CrossRef]

Artoni, M.

M. Artoni and G. C. La Rocca, "Optically tunable photonic stop bands in homogeneous absorbing media," Phys. Rev. Lett. 96, 073905 (2006).
[CrossRef] [PubMed]

M. Artoni, G. C. La Rocca, and F. Bassani, "Resonantly absorbing one-dimensional photonic crystals," Phys. Rev. E 72, 046604 (2005).
[CrossRef]

Babin, S. A.

S. A. Babin, D. V. Churkin, E. V. Podivilov, V. V. Potapov, and D. A. Shapiro, "Splitting of the peak of electromagnetically induced transparency by the higher-order spatial harmonics of the atomic coherence," Phys. Rev. A 67, 043808 (2003).
[CrossRef]

Bajcsy, M.

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, "Stationary pulses of light in an atomic medium," Nature 426, 638-641 (2003).
[CrossRef] [PubMed]

Bassani, F.

M. Artoni, G. C. La Rocca, and F. Bassani, "Resonantly absorbing one-dimensional photonic crystals," Phys. Rev. E 72, 046604 (2005).
[CrossRef]

Brown, A. W.

Brown, A.W.

A.W. Brown and M. Xiao, "Frequency detuning and power depedence of reflection from an electromagnetically induced absorption grating," J. Mod. Opt. 52, 2365-2371 (2003).
[CrossRef]

Carvalho, P. R. S.

P. R. S. Carvalho, L. E. E. de Araujo and J. W. R. Tabosa, "Angular dependence of an electromagnetically induced transparency resonance in a Doppler-broadened atomic vapor," Phys. Rev. A 70, 063818 (2004).
[CrossRef]

Churkin, D. V.

S. A. Babin, D. V. Churkin, E. V. Podivilov, V. V. Potapov, and D. A. Shapiro, "Splitting of the peak of electromagnetically induced transparency by the higher-order spatial harmonics of the atomic coherence," Phys. Rev. A 67, 043808 (2003).
[CrossRef]

Corbalan, R.

F. Silva, J. Mompart, V. Ahufinger, and R. Corbalan, "Electromagnetically induced transparency with a standingwave drive in the frequency up-conversion regime," Phys. Rev. A 64, 033802 (2001).
[CrossRef]

F. Silva, J. Mompart, V. Ahufinger, and R. Corbalan, "Electromagnetically induced transparency in Dopplerbroadened three-level systems with resonant standing-wave drive," Europhys. Lett. 51, 286-292 (2000).
[CrossRef]

de Araujo, L. E. E.

P. R. S. Carvalho, L. E. E. de Araujo and J. W. R. Tabosa, "Angular dependence of an electromagnetically induced transparency resonance in a Doppler-broadened atomic vapor," Phys. Rev. A 70, 063818 (2004).
[CrossRef]

Feld, M. S.

B. J. Feldman and M. S. Feld, "Laser-induced line-narrowing effects in coupled Doppler-broadened transitions. II. Standing-wave features," Phys. Rev. A 5, 899-918 (1972).
[CrossRef]

Feldman, B. J.

B. J. Feldman and M. S. Feld, "Laser-induced line-narrowing effects in coupled Doppler-broadened transitions. II. Standing-wave features," Phys. Rev. A 5, 899-918 (1972).
[CrossRef]

Ficek, Z.

Z. Ficek and H. S. Freedhoff, "Resonance-fluorescence and absorption spectra of two-level atom driven by a strong bichromatic field," Phys. Rev. A 48, 3092-3104 (1993).
[CrossRef] [PubMed]

Fleischhauer, M.

M. Fleischhauer and M. D. Lukin, "Quantum memory for photons: Dark-state polaritons," Phys. Rev. A 65, 022314 (2002).
[CrossRef]

M. Fleischhauer and M. D. Lukin, "Dark-State polaritons in Electromagnetically induced transparency," Phys. Rev. Lett. 84, 5094-5097 (2000).
[CrossRef] [PubMed]

Freedhoff, H. S.

Z. Ficek and H. S. Freedhoff, "Resonance-fluorescence and absorption spectra of two-level atom driven by a strong bichromatic field," Phys. Rev. A 48, 3092-3104 (1993).
[CrossRef] [PubMed]

Gauthier, D. J.

Y. F. Zhu, Q. L. Wu, A. Lezama, D. J. Gauthier, and T. W. Mossberg, "Resonance fluorescence of two-level atoms under strong bichromatic excitation," Phys. Rev. A 41, 6574-6576 (1990).
[CrossRef] [PubMed]

Goorskey, D.

H. Wang, D. Goorskey, and M. Xiao, "Atomic coherence induced Kerr nonlinearity enhancement in Rb vapour," J. Mod. Opt. 49, 335-347 (2002).
[CrossRef]

H. Wang, D. Goorskey, and M. Xiao, "Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system," Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef] [PubMed]

Ham, B. S.

X. M. Su and B. S. Ham, "Dynamic control of the photonic band gap using quantum coherence," Phys. Rev. A 71, 013821 (2005).
[CrossRef]

Hansen, K. R.

K. R. Hansen and K. Mølmer, "Stationary light pulses in ultra cold gases," Phys. Rev. A 75, 065804 (2007).
[CrossRef]

K. R. Hansen and K. Mølmer, "Trapping of light pulses in ensembles of stationary ??? atoms," Phys. Rev. A 75, 053802 (2007).
[CrossRef]

Harris, S.

S. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36-42 (1997).
[CrossRef]

Imoto, N.

M. Mitsunaga and N. Imoto, "Observation of an electromagnetically induced grating in cold sodium atoms," Phys. Rev. A 59, 4773-4776 (1999).
[CrossRef]

Jiang, K. J.

J. Wang, Y. F. Zhu, K. J. Jiang, and M. S. Zhan, "Bichromatic electromagnitically induced transparency in cold rubidium atoms," Phys. Rev. A 68, 063810 (2003).
[CrossRef]

Kyrola, E.

E. Kyrola and R. Salomaa, "Probe spectroscopy in an inhomogeneously broadened three-level system saturated by an intense standing wave," Phys. Rev. A 23, 1874-1892 (1981).
[CrossRef]

La Rocca, G. C.

M. Artoni and G. C. La Rocca, "Optically tunable photonic stop bands in homogeneous absorbing media," Phys. Rev. Lett. 96, 073905 (2006).
[CrossRef] [PubMed]

M. Artoni, G. C. La Rocca, and F. Bassani, "Resonantly absorbing one-dimensional photonic crystals," Phys. Rev. E 72, 046604 (2005).
[CrossRef]

Lezama, A.

Y. F. Zhu, Q. L. Wu, A. Lezama, D. J. Gauthier, and T. W. Mossberg, "Resonance fluorescence of two-level atoms under strong bichromatic excitation," Phys. Rev. A 41, 6574-6576 (1990).
[CrossRef] [PubMed]

Li, Y. Q.

H. Y. Ling, Y. Q. Li, and M. Xiao, "Electromagnetically induced grating: Homogeneously broadened medium," Phys. Rev. A 57, 1338-1344 (1998).
[CrossRef]

Ling, H. Y.

H. Y. Ling, Y. Q. Li, and M. Xiao, "Electromagnetically induced grating: Homogeneously broadened medium," Phys. Rev. A 57, 1338-1344 (1998).
[CrossRef]

Lukin, M. D.

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, "Stationary pulses of light in an atomic medium," Nature 426, 638-641 (2003).
[CrossRef] [PubMed]

M. Fleischhauer and M. D. Lukin, "Quantum memory for photons: Dark-state polaritons," Phys. Rev. A 65, 022314 (2002).
[CrossRef]

M. Fleischhauer and M. D. Lukin, "Dark-State polaritons in Electromagnetically induced transparency," Phys. Rev. Lett. 84, 5094-5097 (2000).
[CrossRef] [PubMed]

Mitsunaga, M.

M. Mitsunaga and N. Imoto, "Observation of an electromagnetically induced grating in cold sodium atoms," Phys. Rev. A 59, 4773-4776 (1999).
[CrossRef]

Mølmer, K.

K. R. Hansen and K. Mølmer, "Stationary light pulses in ultra cold gases," Phys. Rev. A 75, 065804 (2007).
[CrossRef]

K. R. Hansen and K. Mølmer, "Trapping of light pulses in ensembles of stationary ??? atoms," Phys. Rev. A 75, 053802 (2007).
[CrossRef]

Mompart, J.

F. Silva, J. Mompart, V. Ahufinger, and R. Corbalan, "Electromagnetically induced transparency with a standingwave drive in the frequency up-conversion regime," Phys. Rev. A 64, 033802 (2001).
[CrossRef]

F. Silva, J. Mompart, V. Ahufinger, and R. Corbalan, "Electromagnetically induced transparency in Dopplerbroadened three-level systems with resonant standing-wave drive," Europhys. Lett. 51, 286-292 (2000).
[CrossRef]

Mossberg, T. W.

Y. F. Zhu, Q. L. Wu, A. Lezama, D. J. Gauthier, and T. W. Mossberg, "Resonance fluorescence of two-level atoms under strong bichromatic excitation," Phys. Rev. A 41, 6574-6576 (1990).
[CrossRef] [PubMed]

Podivilov, E. V.

S. A. Babin, D. V. Churkin, E. V. Podivilov, V. V. Potapov, and D. A. Shapiro, "Splitting of the peak of electromagnetically induced transparency by the higher-order spatial harmonics of the atomic coherence," Phys. Rev. A 67, 043808 (2003).
[CrossRef]

Potapov, V. V.

S. A. Babin, D. V. Churkin, E. V. Podivilov, V. V. Potapov, and D. A. Shapiro, "Splitting of the peak of electromagnetically induced transparency by the higher-order spatial harmonics of the atomic coherence," Phys. Rev. A 67, 043808 (2003).
[CrossRef]

Salomaa, R.

E. Kyrola and R. Salomaa, "Probe spectroscopy in an inhomogeneously broadened three-level system saturated by an intense standing wave," Phys. Rev. A 23, 1874-1892 (1981).
[CrossRef]

Shapiro, D. A.

S. A. Babin, D. V. Churkin, E. V. Podivilov, V. V. Potapov, and D. A. Shapiro, "Splitting of the peak of electromagnetically induced transparency by the higher-order spatial harmonics of the atomic coherence," Phys. Rev. A 67, 043808 (2003).
[CrossRef]

Silva, F.

F. Silva, J. Mompart, V. Ahufinger, and R. Corbalan, "Electromagnetically induced transparency with a standingwave drive in the frequency up-conversion regime," Phys. Rev. A 64, 033802 (2001).
[CrossRef]

F. Silva, J. Mompart, V. Ahufinger, and R. Corbalan, "Electromagnetically induced transparency in Dopplerbroadened three-level systems with resonant standing-wave drive," Europhys. Lett. 51, 286-292 (2000).
[CrossRef]

Su, X. M.

X. M. Su and B. S. Ham, "Dynamic control of the photonic band gap using quantum coherence," Phys. Rev. A 71, 013821 (2005).
[CrossRef]

Tabosa, J.W. R.

P. R. S. Carvalho, L. E. E. de Araujo and J. W. R. Tabosa, "Angular dependence of an electromagnetically induced transparency resonance in a Doppler-broadened atomic vapor," Phys. Rev. A 70, 063818 (2004).
[CrossRef]

Wang, H.

H. Wang, D. Goorskey, and M. Xiao, "Atomic coherence induced Kerr nonlinearity enhancement in Rb vapour," J. Mod. Opt. 49, 335-347 (2002).
[CrossRef]

H. Wang, D. Goorskey, and M. Xiao, "Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system," Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef] [PubMed]

Wang, J.

J. Wang, Y. F. Zhu, K. J. Jiang, and M. S. Zhan, "Bichromatic electromagnitically induced transparency in cold rubidium atoms," Phys. Rev. A 68, 063810 (2003).
[CrossRef]

Wu, Q. L.

Y. F. Zhu, Q. L. Wu, A. Lezama, D. J. Gauthier, and T. W. Mossberg, "Resonance fluorescence of two-level atoms under strong bichromatic excitation," Phys. Rev. A 41, 6574-6576 (1990).
[CrossRef] [PubMed]

Xiao, M.

A. W. Brown and M. Xiao, "All-optical switching and routing based on an electromagnetically induced absorption grating," Opt. Lett. 30, 699-701 (2005).
[CrossRef] [PubMed]

A.W. Brown and M. Xiao, "Frequency detuning and power depedence of reflection from an electromagnetically induced absorption grating," J. Mod. Opt. 52, 2365-2371 (2003).
[CrossRef]

H. Wang, D. Goorskey, and M. Xiao, "Atomic coherence induced Kerr nonlinearity enhancement in Rb vapour," J. Mod. Opt. 49, 335-347 (2002).
[CrossRef]

H. Wang, D. Goorskey, and M. Xiao, "Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system," Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef] [PubMed]

H. Y. Ling, Y. Q. Li, and M. Xiao, "Electromagnetically induced grating: Homogeneously broadened medium," Phys. Rev. A 57, 1338-1344 (1998).
[CrossRef]

Zhan, M. S.

J. Wang, Y. F. Zhu, K. J. Jiang, and M. S. Zhan, "Bichromatic electromagnitically induced transparency in cold rubidium atoms," Phys. Rev. A 68, 063810 (2003).
[CrossRef]

Zhu, Y. F.

J. Wang, Y. F. Zhu, K. J. Jiang, and M. S. Zhan, "Bichromatic electromagnitically induced transparency in cold rubidium atoms," Phys. Rev. A 68, 063810 (2003).
[CrossRef]

Y. F. Zhu, Q. L. Wu, A. Lezama, D. J. Gauthier, and T. W. Mossberg, "Resonance fluorescence of two-level atoms under strong bichromatic excitation," Phys. Rev. A 41, 6574-6576 (1990).
[CrossRef] [PubMed]

Zibrov, A. S.

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic diagram of the three-level Λ-type atomic system driven by the strong standing wave and probed by the weak wave. (b) A block diagram of the case (i) or (ii). (c) A block diagram of the case (iii).

Fig. 2.
Fig. 2.

(a) (Color online) The reflectivity of the p robe wave and the transmissivity as inset in non-perfect standing wave configuration of case (i), Ω1=10γ21=0.8 and Δ c =0 (black solid line). The results of Artoni with the same parameters. (red dash line). (b) The transmissivity of the probe wave of case (ii) with only the co-propagating wave, Ω1=10 γ , Δ c =0 (dash line), and with perfect standing wave Ω12=10 γ , Δ c =0 (solid line). The inset shows the dressed state picture of the three-level Λ-type system coupled by a bichromatic wave and a weak probe wave, and δ is the half frequency between the two coupling waves.

Fig. 3.
Fig. 3.

(a) (Color online) The element Ψ31(0) for the responses of all atoms with different velocities. The insets show the elements σ31(0,υ)f(υ) for the response of the atoms with a certain velocity. The parameters are taken to be the same as in Fig. 2(b). (b) The refractive index of case (i) (dash line). Δ p =-0.1γ, other parameters are the same as in Fig. 2(a). And the refractive index of case (ii) (solid line). Δ p =7γ, other parameters are the same as in Fig. 2(b). For comparison, the value is multiplied by 100.

Fig. 4.
Fig. 4.

(a) The transmissivity of the probe wave in case (iii), Δ c =0. (b) (Color online) The reflectivity of the probe wave as a function of Δ p for different detunings Δ c of the standing wave in case (iii). Other parameters are taken to be the same as in Fig. 2(b).

Equations (16)

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H I = h ¯ ( Δ c Δ p ) 2 2 h ¯ Δ p 3 3 h ¯ [ ( Ω 1 e i k c z + Ω 2 e i k c z ) 3 2 + g e i k p z 3 1 + H . c . ]
( t + υ z ) ρ = i h ¯ [ H I , ρ ] + R ρ
( Γ 31 + υ z ) ρ 31 = i ( Ω 1 e i k c z + Ω 2 e i k c z ) ρ 21 + i g e i k p z
( Γ 21 + υ z ) ρ 21 = i ( Ω 1 e i k c z + Ω 2 e i k c z ) ρ 31
ρ 31 = e i k p z n = + σ 31 ( n ) e 2 n i k c z , ρ 21 = e i k p z n = + σ 21 ( n ) e ( 2 n 1 ) i k c z
a ( n ) σ 31 ( n ) + b ( n ) σ 31 ( n + 1 ) + c ( n ) σ 31 ( n 1 ) = i g
a ( n ) = L 31 1 ( n ) + Ω 1 2 L 21 ( n ) + Ω 2 2 L 21 ( n + 1 )
b ( n ) = Ω 1 Ω 2 L 21 ( n + 1 )
c ( n ) = Ω 1 Ω 2 L 21 ( n )
Φ 31 = n = + Ψ 31 ( n ) e 2 n i k c z = n = + + σ 31 ( n ) f ( υ ) d υ e 2 n i k c z
χ ( Δ p , z ) = 3 π N γ 31 Φ 31 ( Δ p , z ) g , ε ( Δ p , z ) = n 2 ( Δ p , z ) = 1 + χ ( Δ p , z )
( E + ( z + a ) E ( z + a ) ) = M ( Δ p ) ( E + ( z ) E ( z ) ) = ( e i κ a E + ( z ) e i κ a E ( z ) )
κ a = ± cos 1 [ T r [ M ( Δ p ) ] 2 ]
M ( N ) = sin ( N κ a ) sin ( κ a ) M [ ( N 1 ) κ a ] sin ( κ a ) I
R N = M N ( 12 ) M N ( 12 ) = M 12 sin ( N κ a ) M 22 sin ( N κ a ) sin [ ( N 1 ) κ a ]
T N = 1 M N ( 22 ) = sin ( κ a ) M 22 sin ( N κ a ) sin [ ( N 1 ) κ a ]

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