Abstract

Detailed analysis on the tunable reflection based on electromagnetically induced transparency is presented. We adopt the configuration of a four-level atom driven by a bichromatic standing wave. The Maxwell–Liouville equations for the steady state are employed to describe the mechanics of the system and numerically solved using the parameters of Rb87 in a magneto-optical trap. The analytic solutions are also obtained, which lead to the conditions for getting the higher reflectivity. Theoretically, under such conditions, the reflectivity could be arranged as high as 90% with the coherence decay rate already considered. The controllability of the reflectivity provided by adjusting the intensities and detunings of the coupling fields (the two components of the bichromatic standing wave) is investigated as well. The result shows that the two coupling fields can impact the reflectivity differently. Such a feature allows us to control the reflectivity more flexibly.

© 2013 Optical Society of America

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  1. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
    [CrossRef]
  2. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
    [CrossRef]
  3. M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
    [CrossRef]
  4. M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
    [CrossRef]
  5. C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
    [CrossRef]
  6. D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
    [CrossRef]
  7. A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602 (2001).
    [CrossRef]
  8. J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, “Stopped light with storage times greater than one second using electromagnetically induced transparency in a solid,” Phys. Rev. Lett. 95, 063601 (2005).
    [CrossRef]
  9. C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
    [CrossRef]
  10. Z.-B. Wang, K. P. Marzlin, and B. C. Sanders, “Large cross-phase modulation between slow copropagating weak pulses in Rb87,” Phys. Rev. Lett. 97, 063901 (2006).
    [CrossRef]
  11. S. Li, X. Yang, X. Cao, C. Zhang, C. Xie, and H. Wang, “Enhanced cross-phase modulation based on a double electromagnetically induced transparency in a four-level tripod atomic system,” Phys. Rev. Lett. 101, 073602 (2008).
    [CrossRef]
  12. Y. Wu, J. Saldana, and Y. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electromagnetically induced transparency,” Phys. Rev. A 67, 013811 (2003).
    [CrossRef]
  13. M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Stationary pulses of light in an atomic medium,” Nature 426, 638–641 (2003).
    [CrossRef]
  14. K. R. Hansen and K. Mølmer, “Trapping of light pulses in ensembles of stationary Λ atoms,” Phys. Rev. A 75, 053802 (2007).
    [CrossRef]
  15. Y.-W. Lin, W.-T. Liao, T. Peters, H.-C. Chou, J.-S. Wang, H.-W. Cho, P.-C. Kuan, and I. A. Yu, “Stationary light pulses in cold atomic media and without Bragg gratings,” Phys. Rev. Lett. 102, 213601 (2009).
    [CrossRef]
  16. G. Nikoghosyan and M. Fleischhauer, “Stationary light in cold-atomic gases,” Phys. Rev. A 80, 013818 (2009).
    [CrossRef]
  17. J. Otterbach, R. G. Unanyan, and M. Fleischhauer, “Confining stationary light: Dirac dynamics and Klein tunneling,” Phys. Rev. Lett. 102, 063602 (2009).
    [CrossRef]
  18. J. Otterbach, J. Ruseckas, R. G. Unanyan, G. Juzeliūnas, and M. Fleischhauer, “Effective magnetic fields for stationary light,” Phys. Rev. Lett. 104, 033903 (2010).
    [CrossRef]
  19. T. Peters, Y.-H. Chen, J. S. Wang, Y.-W. Lin, and I. A. Yu, “Observation of phase variation within stationary light pulses inside a cold atomic medium,” Opt. Lett. 35, 151–153 (2010).
    [CrossRef]
  20. X.-J. Zhang, H.-H. Wang, L. Wang, R.-G. Wan, J. Kou, Y.-F. Fan, B. Zhang, and J.-Y. Gao, “Stationary light pulse in solids with long-lived spin coherence,” Phys. Rev. A 83, 063804 (2011).
    [CrossRef]
  21. X.-J. Zhang, H.-H. Wang, C.-Z. Liu, X.-W. Han, C.-B. Fan, J.-H. Wu, and J.-Y. Gao, “Direct conversion of slow light into a stationary light pulse,” Phys. Rev. A 86, 023821 (2012).
    [CrossRef]
  22. T. Peters, S.-W. Su, Y.-H. Chen, J. S. Wang, S.-C. Gou, and I. A. Yu, “Formation of stationary light in a medium of nonstationary atoms,” Phys. Rev. A 85, 023838 (2012).
    [CrossRef]
  23. 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]
  24. J. Wang, C. Hang, and G. X. Huang, “Weak-light gap solitons in a resonant three-level system,” Phys. Lett. A 366, 528–533 (2007).
    [CrossRef]
  25. J.-H. Wu, M. Artoni, and G. C. La Rocca, “Controlling the photonic band structure of optically driven cold atoms,” J. Opt. Soc. Am. B 25, 1840–1849 (2008).
    [CrossRef]
  26. J.-H. Wu, M. Artoni, and G. C. La Rocca, “All-optical light confinement in dynamic cavities in cold atoms,” Phys. Rev. Lett. 103, 133601 (2009).
    [CrossRef]
  27. A. André and M. D. Lukin, “Manipulating light pulses via dynamically controlled photonic band gap,” Phys. Rev. Lett. 89, 143602 (2002).
    [CrossRef]
  28. X. M. Su and B. S. Ham, “Dynamic control of the photonic band gap using quantum coherence,” Phys. Rev. A 71, 013821 (2005).
    [CrossRef]
  29. M. Artoni and G. C. La Rocca, “Optically tunable photonic stop bands in homogeneous absorbing media,” Phys. Rev. Lett. 96, 073905 (2006).
    [CrossRef]
  30. D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
    [CrossRef]
  31. S. A. Moiseev and B. S. Ham, “Quantum control and manipulation of multi-color light fields,” Opt. Spectrosc. 103, 210–218 (2007).
    [CrossRef]
  32. F. E. Zimmer, A. André, M. D. Lukin, and M. Fleischhauer, “Coherent control of stationary light pulses,” Opt. Commun. 264, 441–453 (2006).
    [CrossRef]
  33. H.-T. Zhou, D.-W. Wang, D. Wang, J.-X. Zhang, and S.-Y. Zhu, “Efficient reflection via four-wave mixing in a Doppler-free electromagnetically-induced-transparency gas system,” Phys. Rev. A 84, 053835 (2011).
    [CrossRef]
  34. Y.-W. Lin, H.-C. Chou, P. P. Dwivedi, Y.-C. Chen, and I. A. Yu, “Using a pair of rectangular coils in the MOT for the production of cold atom clouds with large optical density,” Opt. Express 16, 3753–3761 (2008).
    [CrossRef]
  35. S. A. Moiseev and B. S. Ham, “Quantum manipulation of two-color stationary light: quantum wavelength conversion,” Phys. Rev. A 73, 033812 (2006).
    [CrossRef]

2013

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[CrossRef]

2012

X.-J. Zhang, H.-H. Wang, C.-Z. Liu, X.-W. Han, C.-B. Fan, J.-H. Wu, and J.-Y. Gao, “Direct conversion of slow light into a stationary light pulse,” Phys. Rev. A 86, 023821 (2012).
[CrossRef]

T. Peters, S.-W. Su, Y.-H. Chen, J. S. Wang, S.-C. Gou, and I. A. Yu, “Formation of stationary light in a medium of nonstationary atoms,” Phys. Rev. A 85, 023838 (2012).
[CrossRef]

2011

H.-T. Zhou, D.-W. Wang, D. Wang, J.-X. Zhang, and S.-Y. Zhu, “Efficient reflection via four-wave mixing in a Doppler-free electromagnetically-induced-transparency gas system,” Phys. Rev. A 84, 053835 (2011).
[CrossRef]

X.-J. Zhang, H.-H. Wang, L. Wang, R.-G. Wan, J. Kou, Y.-F. Fan, B. Zhang, and J.-Y. Gao, “Stationary light pulse in solids with long-lived spin coherence,” Phys. Rev. A 83, 063804 (2011).
[CrossRef]

2010

T. Peters, Y.-H. Chen, J. S. Wang, Y.-W. Lin, and I. A. Yu, “Observation of phase variation within stationary light pulses inside a cold atomic medium,” Opt. Lett. 35, 151–153 (2010).
[CrossRef]

J. Otterbach, J. Ruseckas, R. G. Unanyan, G. Juzeliūnas, and M. Fleischhauer, “Effective magnetic fields for stationary light,” Phys. Rev. Lett. 104, 033903 (2010).
[CrossRef]

2009

J.-H. Wu, M. Artoni, and G. C. La Rocca, “All-optical light confinement in dynamic cavities in cold atoms,” Phys. Rev. Lett. 103, 133601 (2009).
[CrossRef]

Y.-W. Lin, W.-T. Liao, T. Peters, H.-C. Chou, J.-S. Wang, H.-W. Cho, P.-C. Kuan, and I. A. Yu, “Stationary light pulses in cold atomic media and without Bragg gratings,” Phys. Rev. Lett. 102, 213601 (2009).
[CrossRef]

G. Nikoghosyan and M. Fleischhauer, “Stationary light in cold-atomic gases,” Phys. Rev. A 80, 013818 (2009).
[CrossRef]

J. Otterbach, R. G. Unanyan, and M. Fleischhauer, “Confining stationary light: Dirac dynamics and Klein tunneling,” Phys. Rev. Lett. 102, 063602 (2009).
[CrossRef]

2008

2007

J. Wang, C. Hang, and G. X. Huang, “Weak-light gap solitons in a resonant three-level system,” Phys. Lett. A 366, 528–533 (2007).
[CrossRef]

S. A. Moiseev and B. S. Ham, “Quantum control and manipulation of multi-color light fields,” Opt. Spectrosc. 103, 210–218 (2007).
[CrossRef]

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

2006

Z.-B. Wang, K. P. Marzlin, and B. C. Sanders, “Large cross-phase modulation between slow copropagating weak pulses in Rb87,” Phys. Rev. Lett. 97, 063901 (2006).
[CrossRef]

F. E. Zimmer, A. André, 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]

S. A. Moiseev and B. S. Ham, “Quantum manipulation of two-color stationary light: quantum wavelength conversion,” Phys. Rev. A 73, 033812 (2006).
[CrossRef]

2005

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]

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

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, “Stopped light with storage times greater than one second using electromagnetically induced transparency in a solid,” Phys. Rev. Lett. 95, 063601 (2005).
[CrossRef]

2003

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef]

Y. Wu, J. Saldana, and Y. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electromagnetically induced transparency,” Phys. Rev. A 67, 013811 (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]

2002

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

2001

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef]

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602 (2001).
[CrossRef]

2000

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
[CrossRef]

1999

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

1997

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

André, A.

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

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

Artoni, M.

J.-H. Wu, M. Artoni, and G. C. La Rocca, “All-optical light confinement in dynamic cavities in cold atoms,” Phys. Rev. Lett. 103, 133601 (2009).
[CrossRef]

J.-H. Wu, M. Artoni, and G. C. La Rocca, “Controlling the photonic band structure of optically driven cold atoms,” J. Opt. Soc. Am. B 25, 1840–1849 (2008).
[CrossRef]

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

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (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]

Behroozi, C. H.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Brown, A. W.

Cao, X.

S. Li, X. Yang, X. Cao, C. Zhang, C. Xie, and H. Wang, “Enhanced cross-phase modulation based on a double electromagnetically induced transparency in a four-level tripod atomic system,” Phys. Rev. Lett. 101, 073602 (2008).
[CrossRef]

Cataliotti, F.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef]

Chen, Y.-C.

Chen, Y.-H.

T. Peters, S.-W. Su, Y.-H. Chen, J. S. Wang, S.-C. Gou, and I. A. Yu, “Formation of stationary light in a medium of nonstationary atoms,” Phys. Rev. A 85, 023838 (2012).
[CrossRef]

T. Peters, Y.-H. Chen, J. S. Wang, Y.-W. Lin, and I. A. Yu, “Observation of phase variation within stationary light pulses inside a cold atomic medium,” Opt. Lett. 35, 151–153 (2010).
[CrossRef]

Cho, H.-W.

Y.-W. Lin, W.-T. Liao, T. Peters, H.-C. Chou, J.-S. Wang, H.-W. Cho, P.-C. Kuan, and I. A. Yu, “Stationary light pulses in cold atomic media and without Bragg gratings,” Phys. Rev. Lett. 102, 213601 (2009).
[CrossRef]

Chou, H.-C.

Y.-W. Lin, W.-T. Liao, T. Peters, H.-C. Chou, J.-S. Wang, H.-W. Cho, P.-C. Kuan, and I. A. Yu, “Stationary light pulses in cold atomic media and without Bragg gratings,” Phys. Rev. Lett. 102, 213601 (2009).
[CrossRef]

Y.-W. Lin, H.-C. Chou, P. P. Dwivedi, Y.-C. Chen, and I. A. Yu, “Using a pair of rectangular coils in the MOT for the production of cold atom clouds with large optical density,” Opt. Express 16, 3753–3761 (2008).
[CrossRef]

Dutton, Z.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Dwivedi, P. P.

Evers, J.

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[CrossRef]

Fan, C.-B.

X.-J. Zhang, H.-H. Wang, C.-Z. Liu, X.-W. Han, C.-B. Fan, J.-H. Wu, and J.-Y. Gao, “Direct conversion of slow light into a stationary light pulse,” Phys. Rev. A 86, 023821 (2012).
[CrossRef]

Fan, Y.-F.

X.-J. Zhang, H.-H. Wang, L. Wang, R.-G. Wan, J. Kou, Y.-F. Fan, B. Zhang, and J.-Y. Gao, “Stationary light pulse in solids with long-lived spin coherence,” Phys. Rev. A 83, 063804 (2011).
[CrossRef]

Fleischhauer, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef]

Fleischhauer, M.

J. Otterbach, J. Ruseckas, R. G. Unanyan, G. Juzeliūnas, and M. Fleischhauer, “Effective magnetic fields for stationary light,” Phys. Rev. Lett. 104, 033903 (2010).
[CrossRef]

J. Otterbach, R. G. Unanyan, and M. Fleischhauer, “Confining stationary light: Dirac dynamics and Klein tunneling,” Phys. Rev. Lett. 102, 063602 (2009).
[CrossRef]

G. Nikoghosyan and M. Fleischhauer, “Stationary light in cold-atomic gases,” Phys. Rev. A 80, 013818 (2009).
[CrossRef]

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

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
[CrossRef]

Fraval, E.

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, “Stopped light with storage times greater than one second using electromagnetically induced transparency in a solid,” Phys. Rev. Lett. 95, 063601 (2005).
[CrossRef]

Fry, E. S.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Gao, J.-Y.

X.-J. Zhang, H.-H. Wang, C.-Z. Liu, X.-W. Han, C.-B. Fan, J.-H. Wu, and J.-Y. Gao, “Direct conversion of slow light into a stationary light pulse,” Phys. Rev. A 86, 023821 (2012).
[CrossRef]

X.-J. Zhang, H.-H. Wang, L. Wang, R.-G. Wan, J. Kou, Y.-F. Fan, B. Zhang, and J.-Y. Gao, “Stationary light pulse in solids with long-lived spin coherence,” Phys. Rev. A 83, 063804 (2011).
[CrossRef]

Gou, S.-C.

T. Peters, S.-W. Su, Y.-H. Chen, J. S. Wang, S.-C. Gou, and I. A. Yu, “Formation of stationary light in a medium of nonstationary atoms,” Phys. Rev. A 85, 023838 (2012).
[CrossRef]

Guo, M.-J.

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[CrossRef]

Ham, B. S.

S. A. Moiseev and B. S. Ham, “Quantum control and manipulation of multi-color light fields,” Opt. Spectrosc. 103, 210–218 (2007).
[CrossRef]

S. A. Moiseev and B. S. Ham, “Quantum manipulation of two-color stationary light: quantum wavelength conversion,” Phys. Rev. A 73, 033812 (2006).
[CrossRef]

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

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602 (2001).
[CrossRef]

Han, X.-W.

X.-J. Zhang, H.-H. Wang, C.-Z. Liu, X.-W. Han, C.-B. Fan, J.-H. Wu, and J.-Y. Gao, “Direct conversion of slow light into a stationary light pulse,” Phys. Rev. A 86, 023821 (2012).
[CrossRef]

Hang, C.

J. Wang, C. Hang, and G. X. Huang, “Weak-light gap solitons in a resonant three-level system,” Phys. Lett. A 366, 528–533 (2007).
[CrossRef]

Hansen, K. R.

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

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

Hau, L. V.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Hemmer, P. R.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602 (2001).
[CrossRef]

Hollberg, L.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Huang, G. X.

J. Wang, C. Hang, and G. X. Huang, “Weak-light gap solitons in a resonant three-level system,” Phys. Lett. A 366, 528–533 (2007).
[CrossRef]

Juzeliunas, G.

J. Otterbach, J. Ruseckas, R. G. Unanyan, G. Juzeliūnas, and M. Fleischhauer, “Effective magnetic fields for stationary light,” Phys. Rev. Lett. 104, 033903 (2010).
[CrossRef]

Kash, M. M.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Kou, J.

X.-J. Zhang, H.-H. Wang, L. Wang, R.-G. Wan, J. Kou, Y.-F. Fan, B. Zhang, and J.-Y. Gao, “Stationary light pulse in solids with long-lived spin coherence,” Phys. Rev. A 83, 063804 (2011).
[CrossRef]

Kuan, P.-C.

Y.-W. Lin, W.-T. Liao, T. Peters, H.-C. Chou, J.-S. Wang, H.-W. Cho, P.-C. Kuan, and I. A. Yu, “Stationary light pulses in cold atomic media and without Bragg gratings,” Phys. Rev. Lett. 102, 213601 (2009).
[CrossRef]

La Rocca, G. C.

J.-H. Wu, M. Artoni, and G. C. La Rocca, “All-optical light confinement in dynamic cavities in cold atoms,” Phys. Rev. Lett. 103, 133601 (2009).
[CrossRef]

J.-H. Wu, M. Artoni, and G. C. La Rocca, “Controlling the photonic band structure of optically driven cold atoms,” J. Opt. Soc. Am. B 25, 1840–1849 (2008).
[CrossRef]

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

Li, S.

S. Li, X. Yang, X. Cao, C. Zhang, C. Xie, and H. Wang, “Enhanced cross-phase modulation based on a double electromagnetically induced transparency in a four-level tripod atomic system,” Phys. Rev. Lett. 101, 073602 (2008).
[CrossRef]

Liao, W.-T.

Y.-W. Lin, W.-T. Liao, T. Peters, H.-C. Chou, J.-S. Wang, H.-W. Cho, P.-C. Kuan, and I. A. Yu, “Stationary light pulses in cold atomic media and without Bragg gratings,” Phys. Rev. Lett. 102, 213601 (2009).
[CrossRef]

Lin, Y.-W.

Liu, C.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef]

Liu, C.-Z.

X.-J. Zhang, H.-H. Wang, C.-Z. Liu, X.-W. Han, C.-B. Fan, J.-H. Wu, and J.-Y. Gao, “Direct conversion of slow light into a stationary light pulse,” Phys. Rev. A 86, 023821 (2012).
[CrossRef]

Longdell, J. J.

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, “Stopped light with storage times greater than one second using electromagnetically induced transparency in a solid,” Phys. Rev. Lett. 95, 063601 (2005).
[CrossRef]

Lukin, M. D.

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

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

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

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef]

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
[CrossRef]

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Mair, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef]

Manson, N. B.

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, “Stopped light with storage times greater than one second using electromagnetically induced transparency in a solid,” Phys. Rev. Lett. 95, 063601 (2005).
[CrossRef]

Marzlin, K. P.

Z.-B. Wang, K. P. Marzlin, and B. C. Sanders, “Large cross-phase modulation between slow copropagating weak pulses in Rb87,” Phys. Rev. Lett. 97, 063901 (2006).
[CrossRef]

Moiseev, S. A.

S. A. Moiseev and B. S. Ham, “Quantum control and manipulation of multi-color light fields,” Opt. Spectrosc. 103, 210–218 (2007).
[CrossRef]

S. A. Moiseev and B. S. Ham, “Quantum manipulation of two-color stationary light: quantum wavelength conversion,” Phys. Rev. A 73, 033812 (2006).
[CrossRef]

Mølmer, K.

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

Musser, J. A.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602 (2001).
[CrossRef]

Nikoghosyan, G.

G. Nikoghosyan and M. Fleischhauer, “Stationary light in cold-atomic gases,” Phys. Rev. A 80, 013818 (2009).
[CrossRef]

Ottaviani, C.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef]

Otterbach, J.

J. Otterbach, J. Ruseckas, R. G. Unanyan, G. Juzeliūnas, and M. Fleischhauer, “Effective magnetic fields for stationary light,” Phys. Rev. Lett. 104, 033903 (2010).
[CrossRef]

J. Otterbach, R. G. Unanyan, and M. Fleischhauer, “Confining stationary light: Dirac dynamics and Klein tunneling,” Phys. Rev. Lett. 102, 063602 (2009).
[CrossRef]

Peters, T.

T. Peters, S.-W. Su, Y.-H. Chen, J. S. Wang, S.-C. Gou, and I. A. Yu, “Formation of stationary light in a medium of nonstationary atoms,” Phys. Rev. A 85, 023838 (2012).
[CrossRef]

T. Peters, Y.-H. Chen, J. S. Wang, Y.-W. Lin, and I. A. Yu, “Observation of phase variation within stationary light pulses inside a cold atomic medium,” Opt. Lett. 35, 151–153 (2010).
[CrossRef]

Y.-W. Lin, W.-T. Liao, T. Peters, H.-C. Chou, J.-S. Wang, H.-W. Cho, P.-C. Kuan, and I. A. Yu, “Stationary light pulses in cold atomic media and without Bragg gratings,” Phys. Rev. Lett. 102, 213601 (2009).
[CrossRef]

Phillips, D. F.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef]

Rostovtsev, Y.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Ruseckas, J.

J. Otterbach, J. Ruseckas, R. G. Unanyan, G. Juzeliūnas, and M. Fleischhauer, “Effective magnetic fields for stationary light,” Phys. Rev. Lett. 104, 033903 (2010).
[CrossRef]

Saldana, J.

Y. Wu, J. Saldana, and Y. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electromagnetically induced transparency,” Phys. Rev. A 67, 013811 (2003).
[CrossRef]

Sanders, B. C.

Z.-B. Wang, K. P. Marzlin, and B. C. Sanders, “Large cross-phase modulation between slow copropagating weak pulses in Rb87,” Phys. Rev. Lett. 97, 063901 (2006).
[CrossRef]

Sautenkov, V. A.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Scully, M. O.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Sellars, M. J.

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, “Stopped light with storage times greater than one second using electromagnetically induced transparency in a solid,” Phys. Rev. Lett. 95, 063601 (2005).
[CrossRef]

Shahriar, M. S.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602 (2001).
[CrossRef]

Su, S.-W.

T. Peters, S.-W. Su, Y.-H. Chen, J. S. Wang, S.-C. Gou, and I. A. Yu, “Formation of stationary light in a medium of nonstationary atoms,” Phys. Rev. A 85, 023838 (2012).
[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]

Sudarshanam, V. S.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602 (2001).
[CrossRef]

Tombesi, P.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef]

Turukhin, A. V.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602 (2001).
[CrossRef]

Unanyan, R. G.

J. Otterbach, J. Ruseckas, R. G. Unanyan, G. Juzeliūnas, and M. Fleischhauer, “Effective magnetic fields for stationary light,” Phys. Rev. Lett. 104, 033903 (2010).
[CrossRef]

J. Otterbach, R. G. Unanyan, and M. Fleischhauer, “Confining stationary light: Dirac dynamics and Klein tunneling,” Phys. Rev. Lett. 102, 063602 (2009).
[CrossRef]

Vitali, D.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef]

Walsworth, R. L.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef]

Wan, R.-G.

X.-J. Zhang, H.-H. Wang, L. Wang, R.-G. Wan, J. Kou, Y.-F. Fan, B. Zhang, and J.-Y. Gao, “Stationary light pulse in solids with long-lived spin coherence,” Phys. Rev. A 83, 063804 (2011).
[CrossRef]

Wang, D.

H.-T. Zhou, D.-W. Wang, D. Wang, J.-X. Zhang, and S.-Y. Zhu, “Efficient reflection via four-wave mixing in a Doppler-free electromagnetically-induced-transparency gas system,” Phys. Rev. A 84, 053835 (2011).
[CrossRef]

Wang, D.-W.

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[CrossRef]

H.-T. Zhou, D.-W. Wang, D. Wang, J.-X. Zhang, and S.-Y. Zhu, “Efficient reflection via four-wave mixing in a Doppler-free electromagnetically-induced-transparency gas system,” Phys. Rev. A 84, 053835 (2011).
[CrossRef]

Wang, H.

S. Li, X. Yang, X. Cao, C. Zhang, C. Xie, and H. Wang, “Enhanced cross-phase modulation based on a double electromagnetically induced transparency in a four-level tripod atomic system,” Phys. Rev. Lett. 101, 073602 (2008).
[CrossRef]

Wang, H.-H.

X.-J. Zhang, H.-H. Wang, C.-Z. Liu, X.-W. Han, C.-B. Fan, J.-H. Wu, and J.-Y. Gao, “Direct conversion of slow light into a stationary light pulse,” Phys. Rev. A 86, 023821 (2012).
[CrossRef]

X.-J. Zhang, H.-H. Wang, L. Wang, R.-G. Wan, J. Kou, Y.-F. Fan, B. Zhang, and J.-Y. Gao, “Stationary light pulse in solids with long-lived spin coherence,” Phys. Rev. A 83, 063804 (2011).
[CrossRef]

Wang, J.

J. Wang, C. Hang, and G. X. Huang, “Weak-light gap solitons in a resonant three-level system,” Phys. Lett. A 366, 528–533 (2007).
[CrossRef]

Wang, J. S.

T. Peters, S.-W. Su, Y.-H. Chen, J. S. Wang, S.-C. Gou, and I. A. Yu, “Formation of stationary light in a medium of nonstationary atoms,” Phys. Rev. A 85, 023838 (2012).
[CrossRef]

T. Peters, Y.-H. Chen, J. S. Wang, Y.-W. Lin, and I. A. Yu, “Observation of phase variation within stationary light pulses inside a cold atomic medium,” Opt. Lett. 35, 151–153 (2010).
[CrossRef]

Wang, J.-S.

Y.-W. Lin, W.-T. Liao, T. Peters, H.-C. Chou, J.-S. Wang, H.-W. Cho, P.-C. Kuan, and I. A. Yu, “Stationary light pulses in cold atomic media and without Bragg gratings,” Phys. Rev. Lett. 102, 213601 (2009).
[CrossRef]

Wang, L.

X.-J. Zhang, H.-H. Wang, L. Wang, R.-G. Wan, J. Kou, Y.-F. Fan, B. Zhang, and J.-Y. Gao, “Stationary light pulse in solids with long-lived spin coherence,” Phys. Rev. A 83, 063804 (2011).
[CrossRef]

Wang, Z.-B.

Z.-B. Wang, K. P. Marzlin, and B. C. Sanders, “Large cross-phase modulation between slow copropagating weak pulses in Rb87,” Phys. Rev. Lett. 97, 063901 (2006).
[CrossRef]

Welch, G. R.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Wu, J.-H.

X.-J. Zhang, H.-H. Wang, C.-Z. Liu, X.-W. Han, C.-B. Fan, J.-H. Wu, and J.-Y. Gao, “Direct conversion of slow light into a stationary light pulse,” Phys. Rev. A 86, 023821 (2012).
[CrossRef]

J.-H. Wu, M. Artoni, and G. C. La Rocca, “All-optical light confinement in dynamic cavities in cold atoms,” Phys. Rev. Lett. 103, 133601 (2009).
[CrossRef]

J.-H. Wu, M. Artoni, and G. C. La Rocca, “Controlling the photonic band structure of optically driven cold atoms,” J. Opt. Soc. Am. B 25, 1840–1849 (2008).
[CrossRef]

Wu, Y.

Y. Wu, J. Saldana, and Y. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electromagnetically induced transparency,” Phys. Rev. A 67, 013811 (2003).
[CrossRef]

Xiao, M.

Xie, C.

S. Li, X. Yang, X. Cao, C. Zhang, C. Xie, and H. Wang, “Enhanced cross-phase modulation based on a double electromagnetically induced transparency in a four-level tripod atomic system,” Phys. Rev. Lett. 101, 073602 (2008).
[CrossRef]

Yang, X.

S. Li, X. Yang, X. Cao, C. Zhang, C. Xie, and H. Wang, “Enhanced cross-phase modulation based on a double electromagnetically induced transparency in a four-level tripod atomic system,” Phys. Rev. Lett. 101, 073602 (2008).
[CrossRef]

Yu, I. A.

T. Peters, S.-W. Su, Y.-H. Chen, J. S. Wang, S.-C. Gou, and I. A. Yu, “Formation of stationary light in a medium of nonstationary atoms,” Phys. Rev. A 85, 023838 (2012).
[CrossRef]

T. Peters, Y.-H. Chen, J. S. Wang, Y.-W. Lin, and I. A. Yu, “Observation of phase variation within stationary light pulses inside a cold atomic medium,” Opt. Lett. 35, 151–153 (2010).
[CrossRef]

Y.-W. Lin, W.-T. Liao, T. Peters, H.-C. Chou, J.-S. Wang, H.-W. Cho, P.-C. Kuan, and I. A. Yu, “Stationary light pulses in cold atomic media and without Bragg gratings,” Phys. Rev. Lett. 102, 213601 (2009).
[CrossRef]

Y.-W. Lin, H.-C. Chou, P. P. Dwivedi, Y.-C. Chen, and I. A. Yu, “Using a pair of rectangular coils in the MOT for the production of cold atom clouds with large optical density,” Opt. Express 16, 3753–3761 (2008).
[CrossRef]

Zhang, B.

X.-J. Zhang, H.-H. Wang, L. Wang, R.-G. Wan, J. Kou, Y.-F. Fan, B. Zhang, and J.-Y. Gao, “Stationary light pulse in solids with long-lived spin coherence,” Phys. Rev. A 83, 063804 (2011).
[CrossRef]

Zhang, C.

S. Li, X. Yang, X. Cao, C. Zhang, C. Xie, and H. Wang, “Enhanced cross-phase modulation based on a double electromagnetically induced transparency in a four-level tripod atomic system,” Phys. Rev. Lett. 101, 073602 (2008).
[CrossRef]

Zhang, J.-X.

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[CrossRef]

H.-T. Zhou, D.-W. Wang, D. Wang, J.-X. Zhang, and S.-Y. Zhu, “Efficient reflection via four-wave mixing in a Doppler-free electromagnetically-induced-transparency gas system,” Phys. Rev. A 84, 053835 (2011).
[CrossRef]

Zhang, X.-J.

X.-J. Zhang, H.-H. Wang, C.-Z. Liu, X.-W. Han, C.-B. Fan, J.-H. Wu, and J.-Y. Gao, “Direct conversion of slow light into a stationary light pulse,” Phys. Rev. A 86, 023821 (2012).
[CrossRef]

X.-J. Zhang, H.-H. Wang, L. Wang, R.-G. Wan, J. Kou, Y.-F. Fan, B. Zhang, and J.-Y. Gao, “Stationary light pulse in solids with long-lived spin coherence,” Phys. Rev. A 83, 063804 (2011).
[CrossRef]

Zhou, H.-T.

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[CrossRef]

H.-T. Zhou, D.-W. Wang, D. Wang, J.-X. Zhang, and S.-Y. Zhu, “Efficient reflection via four-wave mixing in a Doppler-free electromagnetically-induced-transparency gas system,” Phys. Rev. A 84, 053835 (2011).
[CrossRef]

Zhu, S.-Y.

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[CrossRef]

H.-T. Zhou, D.-W. Wang, D. Wang, J.-X. Zhang, and S.-Y. Zhu, “Efficient reflection via four-wave mixing in a Doppler-free electromagnetically-induced-transparency gas system,” Phys. Rev. A 84, 053835 (2011).
[CrossRef]

Zhu, Y.

Y. Wu, J. Saldana, and Y. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electromagnetically induced transparency,” Phys. Rev. A 67, 013811 (2003).
[CrossRef]

Zibrov, A. S.

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

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Zimmer, F. E.

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

J. Opt. Soc. Am. B

Nature

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

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

Opt. Commun.

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

Opt. Express

Opt. Lett.

Opt. Spectrosc.

S. A. Moiseev and B. S. Ham, “Quantum control and manipulation of multi-color light fields,” Opt. Spectrosc. 103, 210–218 (2007).
[CrossRef]

Phys. Lett. A

J. Wang, C. Hang, and G. X. Huang, “Weak-light gap solitons in a resonant three-level system,” Phys. Lett. A 366, 528–533 (2007).
[CrossRef]

Phys. Rev. A

S. A. Moiseev and B. S. Ham, “Quantum manipulation of two-color stationary light: quantum wavelength conversion,” Phys. Rev. A 73, 033812 (2006).
[CrossRef]

H.-T. Zhou, D.-W. Wang, D. Wang, J.-X. Zhang, and S.-Y. Zhu, “Efficient reflection via four-wave mixing in a Doppler-free electromagnetically-induced-transparency gas system,” Phys. Rev. A 84, 053835 (2011).
[CrossRef]

X.-J. Zhang, H.-H. Wang, L. Wang, R.-G. Wan, J. Kou, Y.-F. Fan, B. Zhang, and J.-Y. Gao, “Stationary light pulse in solids with long-lived spin coherence,” Phys. Rev. A 83, 063804 (2011).
[CrossRef]

X.-J. Zhang, H.-H. Wang, C.-Z. Liu, X.-W. Han, C.-B. Fan, J.-H. Wu, and J.-Y. Gao, “Direct conversion of slow light into a stationary light pulse,” Phys. Rev. A 86, 023821 (2012).
[CrossRef]

T. Peters, S.-W. Su, Y.-H. Chen, J. S. Wang, S.-C. Gou, and I. A. Yu, “Formation of stationary light in a medium of nonstationary atoms,” Phys. Rev. A 85, 023838 (2012).
[CrossRef]

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

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

G. Nikoghosyan and M. Fleischhauer, “Stationary light in cold-atomic gases,” Phys. Rev. A 80, 013818 (2009).
[CrossRef]

Y. Wu, J. Saldana, and Y. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electromagnetically induced transparency,” Phys. Rev. A 67, 013811 (2003).
[CrossRef]

Phys. Rev. Lett.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
[CrossRef]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef]

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602 (2001).
[CrossRef]

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, “Stopped light with storage times greater than one second using electromagnetically induced transparency in a solid,” Phys. Rev. Lett. 95, 063601 (2005).
[CrossRef]

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef]

Z.-B. Wang, K. P. Marzlin, and B. C. Sanders, “Large cross-phase modulation between slow copropagating weak pulses in Rb87,” Phys. Rev. Lett. 97, 063901 (2006).
[CrossRef]

S. Li, X. Yang, X. Cao, C. Zhang, C. Xie, and H. Wang, “Enhanced cross-phase modulation based on a double electromagnetically induced transparency in a four-level tripod atomic system,” Phys. Rev. Lett. 101, 073602 (2008).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Energy level diagram for the atoms in a typical four-level double Λ configuration. The horizontal arrows represent the traveling directions of corresponding fields.

Fig. 2.
Fig. 2.

(a) Schematic of a double Λ system with large difference between α+ and α. Note that the level |3 is chosen as |5P1/2F=2. (b) Numerical solution with reflection amplitude r=0.8; all the fields resonate with the corresponding transitions. The peaks of the incident and reflected fields are of the same intensity at z=3.98mm. The inset shows the details around the crossing point, and the apparent increment of Ωr violates the exponential attenuation we mentioned before. (c) Situation with r=0.3, δi=δr=δc±=0. The peak of the reflected field falls to zero at the point z=0.43mm. The result is suitable for a medium with finite length, and the zero point corresponds to the end of the medium. (d) The reflection amplitude as a function of the incident detuning with δc±=0. The sample length is 0.43 mm. (e) The case with r=0.4914, δi=δr=δc±=0. The peaks of the incident and reflected fields decay along the z direction and never intersect with each other. The sample length is 10 mm. (f) The reflection amplitude as a function of the incident detuning with a sample length of 10 mm and resonant coupling fields. The relevant atomic parameters are γ21=2π×4kHz, γ41=γ31=2π×3MHz, N0=5.4×1010cm3, α+=9.970×1010m1s1, and α=4.907×1010m1s1. The Rabi frequencies of the coupling fields are both 30 MHz, and the boundary condition for the incident field is Ωi(0)=10MHz.

Fig. 3.
Fig. 3.

Reflectivity plotted as the function of incident detuning with the equal coupling Rabi frequencies, Ωc±=30MHz (dotted line), and the one (solid line) with coupling Rabi frequencies that satisfy Eq. (19): Ωc+=30MHz and Ωc+=21.0MHz. The other parameters are identical to those in Fig. 2(f).

Fig. 4.
Fig. 4.

Numerical result of the reflectivity as the function of Ωc+ and Ωc. The data is calculated from Eqs. (1)–(11). The lighter color corresponds to the higher reflectivity. The dash-dotted line indicates the points (Ωc+,Ωc) that satisfy Eq. (19). Other parameters are identical to that in Fig. 2(f).

Fig. 5.
Fig. 5.

(a) Candidate atomic configuration with nearly equal α± in Rb87. The level |3 is chosen as |5P3/2F=1. (b) Numerical solution of the reflectivity as a function of incident detuning δi. The result is calculated from Eqs. (1)–(11) using the atomic configuration shown in (a). The maximum reflectivity is 0.92 with equal coupling Rabi frequencies of 30 MHz. The other parameters are δc±=0, γ21=2π×4kHz, γ41=γ31=2π×3MHz, N0=5.4×1010cm3, α±=9.970×1010m1s1, and the length of the sample is 10 mm.

Fig. 6.
Fig. 6.

Controllability on the reflectivity provided by adjusting the coupling detunings. The data is calculated from Eqs. (1)–(11). Panel (a) corresponds to δc+=0, δc=10MHz. The maximum value of the reflectivity happens where the incident detuning is zero. For the given positive incident detuning and its opposite, the reflection that corresponds to the former is stronger. Panel (b) shows the result for δc+=10MHz, δc=0. The incident detuning corresponding to the maximum reflection is 10 MHz, which equals δc+. Panel (c) gives the results for δc=10MHz (solid line) and 10MHz (dotted line) with δc+=10MHz. Panel (d) shows the results for δc=10MHz (solid line) and 10MHz (dotted line) with δc+=10MHz. The other parameters are identical with those in Fig. 5.

Equations (21)

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tρ11=Γ31ρ33+Γ41ρ44+i(ρ41Ωp+*ρ13Ωp)i(ρ14Ωp++ρ31Ωp*),
tρ22=Γ32ρ33+Γ42ρ44+i(ρ42Ωc+*ρ24Ωc+)+i(ρ32Ωc*ρ23Ωc),
tρ33=Γ43ρ44Γ31ρ33Γ32ρ33+i(ρ13Ωp+ρ23Ωc)i(ρ32Ωc*ρ31Ωp*),
tρ41=(γ41+iδp+)ρ41iΩpρ43+i[Ωc+ρ21+Ωp+(ρ11ρ44)],
tρ31=(γ31+iδp)ρ31+i(Ωcρ21Ωpρ33+Ωpρ11)iΩp+ρ34,
ρ42=(γ42+iδc+)ρ42Ωcρ43+i[Ωp+ρ12+Ωc+(ρ22ρ44)],
tρ32=(γ32+iδc)ρ32+i(Ωpρ12+Ωcρ22Ωcρ33)iΩc+ρ34;
tρ21=(γ21+iδ)ρ21+(Ωpρ23+Ωc+*ρ41)(Ωp+ρ24Ωc*ρ31),
tρ43=[γ43+i(δp+δp)]ρ43+(Ωp+ρ13+Ωc+ρ23Ωp*ρ41Ωc*ρ42).
zΩi(z)=iα+ρ41,
zΩr(z)=iαρ31,
ρ41(δi+iγ41)+ρ21Ωc++Ωi(z)=0,
ρ31(δc++δc+δi+iγ31)ρ21Ωc+Ωr(z)=0,
ρ21(δc++δi+iγ21)+ρ41Ωc+*+ρ31Ωc*=0.
z[Ωi/α1Ωr/α2]=[Ω2Ωc+ΩcΩc+ΩcΩ+2][Ωi/aΩr/a].
Ωi(z)=exp[z(P+Δ)2A][Ωr(0)α+Ωc+ΩcΔ+Ωi(0)(12αΩ+2+α+Ω2Δ)]×exp[z(PΔ)2A][Ωr(0)α+Ωc+ΩcΔ+Ωi(0)(12+αΩ+2+α+Ω2Δ)];
Ωr(z)=exp[z(P+Δ)2A][Ωi(0)αΩc+ΩcΔ+Ωr(0)(12+αΩ+2+α+Ω2Δ)]×exp[z(PΔ)2A][Ωi(0)αΩc+ΩcΔ+Ωr(0)(12αΩ+2+α+Ω2Δ)].
r=Δα(Ω+22Ωc+Ωc)α+Ω2Δ+αΩ+2+α+(Ω22Ωc+Ωc).
Rα=RΩ2.
rmax=1/Rα=α/α+.
R={Ωc2/Ωc+2,ifΩc+>Ωc;Ωc+2/Ωc2,ifΩc>Ωc+.

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