Abstract

We systematically investigate the electromagnetically induced transparency (EIT) and slow light properties in ultracold Bose and Fermi gases. It shows a very different property from the classical theory, which assumes frozen atomic motion. For example, the speed of light inside the atomic gases can be changed significantly near the Bose–Einstein condensation temperature, while the presence of the Fermi sea can destroy the EIT effect even at zero temperature. From an experimental point of view, such quantum EIT property is mostly manifested in the counterpropagating excitation schemes in either the low-lying Rydberg transition with a narrow linewidth or in the D2 transitions with a weak coupling field. We further investigate the interaction effects on the EIT for a weakly interacting Bose–Einstein condensate, showing an inhomogeneous broadening of the EIT profile and nontrivial change of the light speed due to the quantum depletion other than mean-field energy shifts.

© 2013 Optical Society of America

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    [CrossRef]
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  3. K. Hamerer, A. S. Sørensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041–1093 (2010).
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    [CrossRef]
  6. S.-W. Su, Y.-H. Chen, S.-C. Gou, T.-L. Horng, and I. A. Yu, “Dynamics of slow light and light storage in a Doppler-broadened electromagnetically-induced-transparency medium: a numerical approach,” Phys. Rev. A 83, 013827 (2011).
    [CrossRef]
  7. Z. Dutton and L. Vestergaard Hau, “Storing and processing optical information with ultraslow light in Bose–Einstein condensates,” Phys. Rev. A 70, 053831 (2004).
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    [CrossRef]
  9. G. Morigi and G. S. Agarwal, “Temperature variation of ultraslow light in a cold gas,” Phys. Rev. A 62, 013801 (2000).
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  14. O. Kocharovskaya, Y. Rostovtsev, and M. O. Scully, “Stopping light via hot atoms,” Phys. Rev. Lett. 86, 628–631 (2001).
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    [CrossRef]
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    [CrossRef]
  23. K. Singer, J. Stanojevic, M. Weidemüller, and R. Côté, “Long-range interactions between alkali Rydberg atom pairs correlated to the ns-ns, np-np and nd-nd asymptotes,” J. Phys. B 38, S295–S307 (2005).
    [CrossRef]
  24. R. Löw, H. Weimer, U. Krohn, R. Heidemann, V. Bendkowsky, B. Butscher, H. P. Büchler, and T. Pfau, “Universal scaling in a strongly interacting Rydberg gas,” Phys. Rev. A 80, 033422 (2009).
    [CrossRef]
  25. R. Heidemann, U. Raitzsch, V. Bendkowsky, B. Butscher, R. Löw, L. Santos, and T. Pfau, “Evidence for coherent collective Rydberg excitation in the strong blockade regime,” Phys. Rev. Lett. 99, 163601 (2007).
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    [CrossRef]
  28. E. Caliebe and K. Niemax, “Oscillator strengths of the principal series lines of Rb,” J. Phys. B 12, L45–L51 (1979).
    [CrossRef]
  29. D. Hofsaess, “Photoabsorption of alkali and alkaline earth elements calculated by the scaled Thomas Fermi method,” Z. Phys. A 281, 1–13 (1977).
    [CrossRef]
  30. B. Kaltenhäuser, H. Kübler, A. Chromik, J. Stuhler, T. Pfau, and A. Imamoglu, “Narrow bandwidth electromagnetically induced transparency in optically trapped atoms,” J. Phys. B 40, 1907–1915 (2007).
    [CrossRef]
  31. 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]
  32. M. Albert, A. Dantan, and M. Drewsen, “Cavity electromagnetically induced transparency and all-optical switching using ion Coulomb crystals,” Nat. Photonics 5, 633–636 (2011).
    [CrossRef]
  33. L. Zhou, K. Zhang, B. Zhu, Y. Li, and W. Zhang, “Phase detection in an ultracold polarized Fermi gas via electromagnetically induced transparency,” Phys. Lett. A 376, 919–924 (2012).
    [CrossRef]
  34. S. M. Farooqi, D. Tong, S. Krishnan, J. Stanojevic, Y. P. Zhang, J. R. Ensher, A. S. Estrin, C. Boisseau, R. Côté, E. E. Eyler, and P. L. Gould, “Long-range molecular resonances in a cold Rydberg gas,” Phys. Rev. Lett. 91, 183002 (2003).
    [CrossRef]
  35. R. Zhang, S. R. Garner, and L. V. Hau, “Creation of long-term coherent optical memory via controlled nonlinear interactions in Bose-Einstein condensates,” Phys. Rev. Lett. 103, 233602 (2009).
    [CrossRef]
  36. Y.-J. Lin, R. L. Compton, K.-J. Garcia, J. V. Porto, and I. B. Spielman, “Synthetic magnetic fields for ultracold neutral atoms,” Nature 462, 628–632 (2009).
    [CrossRef]
  37. Y.-J. Lin, K.-J. Garcia, and I. B. Spielman, “Spin-orbit-coupled Bose–Einstein condensates,” Nature 471, 83–86 (2011).
    [CrossRef]

2013 (1)

H. H. Jen and D.-W. Wang, “Theory of electromagnetically induced transparency in strongly correlated quantum gases,” Phys. Rev. A 87, 061802(R) (2013).
[CrossRef]

2012 (1)

L. Zhou, K. Zhang, B. Zhu, Y. Li, and W. Zhang, “Phase detection in an ultracold polarized Fermi gas via electromagnetically induced transparency,” Phys. Lett. A 376, 919–924 (2012).
[CrossRef]

2011 (4)

M. Albert, A. Dantan, and M. Drewsen, “Cavity electromagnetically induced transparency and all-optical switching using ion Coulomb crystals,” Nat. Photonics 5, 633–636 (2011).
[CrossRef]

Y.-J. Lin, K.-J. Garcia, and I. B. Spielman, “Spin-orbit-coupled Bose–Einstein condensates,” Nature 471, 83–86 (2011).
[CrossRef]

S.-W. Su, Y.-H. Chen, S.-C. Gou, and I. A. Yu, “An effective thermal-parametrization theory for the slow-light dynamics in a Doppler-broadened electromagnetically induced transparency medium,” J. Phys. B 44, 165504 (2011).
[CrossRef]

S.-W. Su, Y.-H. Chen, S.-C. Gou, T.-L. Horng, and I. A. Yu, “Dynamics of slow light and light storage in a Doppler-broadened electromagnetically-induced-transparency medium: a numerical approach,” Phys. Rev. A 83, 013827 (2011).
[CrossRef]

2010 (2)

K. Hamerer, A. S. Sørensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041–1093 (2010).
[CrossRef]

M. Saffman and T. G. Waller, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010).
[CrossRef]

2009 (4)

L. Jiang, H. Pu, W. Zhang, and H. Y. Ling, “Detection of Fermi pairing via electromagnetically induced transparency,” Phys. Rev. A 80, 033606 (2009).
[CrossRef]

R. Zhang, S. R. Garner, and L. V. Hau, “Creation of long-term coherent optical memory via controlled nonlinear interactions in Bose-Einstein condensates,” Phys. Rev. Lett. 103, 233602 (2009).
[CrossRef]

Y.-J. Lin, R. L. Compton, K.-J. Garcia, J. V. Porto, and I. B. Spielman, “Synthetic magnetic fields for ultracold neutral atoms,” Nature 462, 628–632 (2009).
[CrossRef]

R. Löw, H. Weimer, U. Krohn, R. Heidemann, V. Bendkowsky, B. Butscher, H. P. Büchler, and T. Pfau, “Universal scaling in a strongly interacting Rydberg gas,” Phys. Rev. A 80, 033422 (2009).
[CrossRef]

2007 (2)

R. Heidemann, U. Raitzsch, V. Bendkowsky, B. Butscher, R. Löw, L. Santos, and T. Pfau, “Evidence for coherent collective Rydberg excitation in the strong blockade regime,” Phys. Rev. Lett. 99, 163601 (2007).
[CrossRef]

B. Kaltenhäuser, H. Kübler, A. Chromik, J. Stuhler, T. Pfau, and A. Imamoglu, “Narrow bandwidth electromagnetically induced transparency in optically trapped atoms,” J. Phys. B 40, 1907–1915 (2007).
[CrossRef]

2005 (3)

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]

K. Singer, J. Stanojevic, M. Weidemüller, and R. Côté, “Long-range interactions between alkali Rydberg atom pairs correlated to the ns-ns, np-np and nd-nd asymptotes,” J. Phys. B 38, S295–S307 (2005).
[CrossRef]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

2004 (3)

Z. Dutton and L. Vestergaard Hau, “Storing and processing optical information with ultraslow light in Bose–Einstein condensates,” Phys. Rev. A 70, 053831 (2004).
[CrossRef]

F. Zimmer and M. Fleischhauer, “Sagnac interferometry based on ultraslow polaritons in cold atomic vapors,” Phys. Rev. Lett. 92, 253201 (2004).
[CrossRef]

D. Tong, S. M. Farooqi, J. Stanojevic, S. Krishnan, Y. P. Zhang, R. Côté, E. E. Eyler, and P. L. Gould, “Local blockade of Rydberg excitation in an ultracold gas,” Phys. Rev. Lett. 93, 063001 (2004).
[CrossRef]

2003 (2)

S. M. Farooqi, D. Tong, S. Krishnan, J. Stanojevic, Y. P. Zhang, J. R. Ensher, A. S. Estrin, C. Boisseau, R. Côté, E. E. Eyler, and P. L. Gould, “Long-range molecular resonances in a cold Rydberg gas,” Phys. Rev. Lett. 91, 183002 (2003).
[CrossRef]

M. D. Lukin, “Colloquium: trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. 75, 457–472 (2003).
[CrossRef]

2002 (2)

V. Ahufinger, R. Corbalán, F. Cataliotti, S. Burger, F. Minardi, and C. Fort, “Electromagnetically induced transparency in a Bose–Einstein condensate,” Opt. Commun. 211, 159–165 (2002).
[CrossRef]

E. Cerboneschi, F. Renzoni, and E. Arimondo, “Relaxation processes in slow light: the role of the atomic momentum,” Opt. Commun. 204, 211–217 (2002).
[CrossRef]

2001 (2)

Ö. Ë. Müstecaplioglu and L. You, “Propagation of Raman-matched laser pulses through a Bose–Einstein condensate,” Opt. Commun. 193, 301–312 (2001).
[CrossRef]

O. Kocharovskaya, Y. Rostovtsev, and M. O. Scully, “Stopping light via hot atoms,” Phys. Rev. Lett. 86, 628–631 (2001).
[CrossRef]

2000 (2)

I. Carusotto, M. Artoni, and G. C. La Rocca, “Atomic recoil effects in slow light propagation,” JETP Lett. 72, 289–293 (2000).
[CrossRef]

G. Morigi and G. S. Agarwal, “Temperature variation of ultraslow light in a cold gas,” Phys. Rev. A 62, 013801 (2000).
[CrossRef]

1999 (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]

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]

1979 (2)

F. Gounand, “Calculation of radial matrix elements and radiative lifetimes for highly excited states of alkali atoms using Coulomb approximation,” J. Phys. 40, 457–460 (1979).
[CrossRef]

E. Caliebe and K. Niemax, “Oscillator strengths of the principal series lines of Rb,” J. Phys. B 12, L45–L51 (1979).
[CrossRef]

1977 (1)

D. Hofsaess, “Photoabsorption of alkali and alkaline earth elements calculated by the scaled Thomas Fermi method,” Z. Phys. A 281, 1–13 (1977).
[CrossRef]

1968 (1)

G. V. Marr and D. M. Creek, “The absorption oscillator strengths in alkali metal vapours,” Proc. R. Soc. Edin. Sect. A 304, 245–254 (1968).
[CrossRef]

Agarwal, G. S.

G. Morigi and G. S. Agarwal, “Temperature variation of ultraslow light in a cold gas,” Phys. Rev. A 62, 013801 (2000).
[CrossRef]

Ahufinger, V.

V. Ahufinger, R. Corbalán, F. Cataliotti, S. Burger, F. Minardi, and C. Fort, “Electromagnetically induced transparency in a Bose–Einstein condensate,” Opt. Commun. 211, 159–165 (2002).
[CrossRef]

Albert, M.

M. Albert, A. Dantan, and M. Drewsen, “Cavity electromagnetically induced transparency and all-optical switching using ion Coulomb crystals,” Nat. Photonics 5, 633–636 (2011).
[CrossRef]

Arimondo, E.

E. Cerboneschi, F. Renzoni, and E. Arimondo, “Relaxation processes in slow light: the role of the atomic momentum,” Opt. Commun. 204, 211–217 (2002).
[CrossRef]

Artoni, M.

I. Carusotto, M. Artoni, and G. C. La Rocca, “Atomic recoil effects in slow light propagation,” JETP Lett. 72, 289–293 (2000).
[CrossRef]

Behroozi, C. H.

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]

Bendkowsky, V.

R. Löw, H. Weimer, U. Krohn, R. Heidemann, V. Bendkowsky, B. Butscher, H. P. Büchler, and T. Pfau, “Universal scaling in a strongly interacting Rydberg gas,” Phys. Rev. A 80, 033422 (2009).
[CrossRef]

R. Heidemann, U. Raitzsch, V. Bendkowsky, B. Butscher, R. Löw, L. Santos, and T. Pfau, “Evidence for coherent collective Rydberg excitation in the strong blockade regime,” Phys. Rev. Lett. 99, 163601 (2007).
[CrossRef]

Boisseau, C.

S. M. Farooqi, D. Tong, S. Krishnan, J. Stanojevic, Y. P. Zhang, J. R. Ensher, A. S. Estrin, C. Boisseau, R. Côté, E. E. Eyler, and P. L. Gould, “Long-range molecular resonances in a cold Rydberg gas,” Phys. Rev. Lett. 91, 183002 (2003).
[CrossRef]

Büchler, H. P.

R. Löw, H. Weimer, U. Krohn, R. Heidemann, V. Bendkowsky, B. Butscher, H. P. Büchler, and T. Pfau, “Universal scaling in a strongly interacting Rydberg gas,” Phys. Rev. A 80, 033422 (2009).
[CrossRef]

Burger, S.

V. Ahufinger, R. Corbalán, F. Cataliotti, S. Burger, F. Minardi, and C. Fort, “Electromagnetically induced transparency in a Bose–Einstein condensate,” Opt. Commun. 211, 159–165 (2002).
[CrossRef]

Butscher, B.

R. Löw, H. Weimer, U. Krohn, R. Heidemann, V. Bendkowsky, B. Butscher, H. P. Büchler, and T. Pfau, “Universal scaling in a strongly interacting Rydberg gas,” Phys. Rev. A 80, 033422 (2009).
[CrossRef]

R. Heidemann, U. Raitzsch, V. Bendkowsky, B. Butscher, R. Löw, L. Santos, and T. Pfau, “Evidence for coherent collective Rydberg excitation in the strong blockade regime,” Phys. Rev. Lett. 99, 163601 (2007).
[CrossRef]

Caliebe, E.

E. Caliebe and K. Niemax, “Oscillator strengths of the principal series lines of Rb,” J. Phys. B 12, L45–L51 (1979).
[CrossRef]

Carusotto, I.

I. Carusotto, M. Artoni, and G. C. La Rocca, “Atomic recoil effects in slow light propagation,” JETP Lett. 72, 289–293 (2000).
[CrossRef]

Cataliotti, F.

V. Ahufinger, R. Corbalán, F. Cataliotti, S. Burger, F. Minardi, and C. Fort, “Electromagnetically induced transparency in a Bose–Einstein condensate,” Opt. Commun. 211, 159–165 (2002).
[CrossRef]

Cerboneschi, E.

E. Cerboneschi, F. Renzoni, and E. Arimondo, “Relaxation processes in slow light: the role of the atomic momentum,” Opt. Commun. 204, 211–217 (2002).
[CrossRef]

Chen, Y.-H.

S.-W. Su, Y.-H. Chen, S.-C. Gou, and I. A. Yu, “An effective thermal-parametrization theory for the slow-light dynamics in a Doppler-broadened electromagnetically induced transparency medium,” J. Phys. B 44, 165504 (2011).
[CrossRef]

S.-W. Su, Y.-H. Chen, S.-C. Gou, T.-L. Horng, and I. A. Yu, “Dynamics of slow light and light storage in a Doppler-broadened electromagnetically-induced-transparency medium: a numerical approach,” Phys. Rev. A 83, 013827 (2011).
[CrossRef]

Chromik, A.

B. Kaltenhäuser, H. Kübler, A. Chromik, J. Stuhler, T. Pfau, and A. Imamoglu, “Narrow bandwidth electromagnetically induced transparency in optically trapped atoms,” J. Phys. B 40, 1907–1915 (2007).
[CrossRef]

Compton, R. L.

Y.-J. Lin, R. L. Compton, K.-J. Garcia, J. V. Porto, and I. B. Spielman, “Synthetic magnetic fields for ultracold neutral atoms,” Nature 462, 628–632 (2009).
[CrossRef]

Corbalán, R.

V. Ahufinger, R. Corbalán, F. Cataliotti, S. Burger, F. Minardi, and C. Fort, “Electromagnetically induced transparency in a Bose–Einstein condensate,” Opt. Commun. 211, 159–165 (2002).
[CrossRef]

Côté, R.

K. Singer, J. Stanojevic, M. Weidemüller, and R. Côté, “Long-range interactions between alkali Rydberg atom pairs correlated to the ns-ns, np-np and nd-nd asymptotes,” J. Phys. B 38, S295–S307 (2005).
[CrossRef]

D. Tong, S. M. Farooqi, J. Stanojevic, S. Krishnan, Y. P. Zhang, R. Côté, E. E. Eyler, and P. L. Gould, “Local blockade of Rydberg excitation in an ultracold gas,” Phys. Rev. Lett. 93, 063001 (2004).
[CrossRef]

S. M. Farooqi, D. Tong, S. Krishnan, J. Stanojevic, Y. P. Zhang, J. R. Ensher, A. S. Estrin, C. Boisseau, R. Côté, E. E. Eyler, and P. L. Gould, “Long-range molecular resonances in a cold Rydberg gas,” Phys. Rev. Lett. 91, 183002 (2003).
[CrossRef]

Creek, D. M.

G. V. Marr and D. M. Creek, “The absorption oscillator strengths in alkali metal vapours,” Proc. R. Soc. Edin. Sect. A 304, 245–254 (1968).
[CrossRef]

Dantan, A.

M. Albert, A. Dantan, and M. Drewsen, “Cavity electromagnetically induced transparency and all-optical switching using ion Coulomb crystals,” Nat. Photonics 5, 633–636 (2011).
[CrossRef]

Drewsen, M.

M. Albert, A. Dantan, and M. Drewsen, “Cavity electromagnetically induced transparency and all-optical switching using ion Coulomb crystals,” Nat. Photonics 5, 633–636 (2011).
[CrossRef]

Dutton, Z.

Z. Dutton and L. Vestergaard Hau, “Storing and processing optical information with ultraslow light in Bose–Einstein condensates,” Phys. Rev. A 70, 053831 (2004).
[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]

Ensher, J. R.

S. M. Farooqi, D. Tong, S. Krishnan, J. Stanojevic, Y. P. Zhang, J. R. Ensher, A. S. Estrin, C. Boisseau, R. Côté, E. E. Eyler, and P. L. Gould, “Long-range molecular resonances in a cold Rydberg gas,” Phys. Rev. Lett. 91, 183002 (2003).
[CrossRef]

Estrin, A. S.

S. M. Farooqi, D. Tong, S. Krishnan, J. Stanojevic, Y. P. Zhang, J. R. Ensher, A. S. Estrin, C. Boisseau, R. Côté, E. E. Eyler, and P. L. Gould, “Long-range molecular resonances in a cold Rydberg gas,” Phys. Rev. Lett. 91, 183002 (2003).
[CrossRef]

Eyler, E. E.

D. Tong, S. M. Farooqi, J. Stanojevic, S. Krishnan, Y. P. Zhang, R. Côté, E. E. Eyler, and P. L. Gould, “Local blockade of Rydberg excitation in an ultracold gas,” Phys. Rev. Lett. 93, 063001 (2004).
[CrossRef]

S. M. Farooqi, D. Tong, S. Krishnan, J. Stanojevic, Y. P. Zhang, J. R. Ensher, A. S. Estrin, C. Boisseau, R. Côté, E. E. Eyler, and P. L. Gould, “Long-range molecular resonances in a cold Rydberg gas,” Phys. Rev. Lett. 91, 183002 (2003).
[CrossRef]

Farooqi, S. M.

D. Tong, S. M. Farooqi, J. Stanojevic, S. Krishnan, Y. P. Zhang, R. Côté, E. E. Eyler, and P. L. Gould, “Local blockade of Rydberg excitation in an ultracold gas,” Phys. Rev. Lett. 93, 063001 (2004).
[CrossRef]

S. M. Farooqi, D. Tong, S. Krishnan, J. Stanojevic, Y. P. Zhang, J. R. Ensher, A. S. Estrin, C. Boisseau, R. Côté, E. E. Eyler, and P. L. Gould, “Long-range molecular resonances in a cold Rydberg gas,” Phys. Rev. Lett. 91, 183002 (2003).
[CrossRef]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

F. Zimmer and M. Fleischhauer, “Sagnac interferometry based on ultraslow polaritons in cold atomic vapors,” Phys. Rev. Lett. 92, 253201 (2004).
[CrossRef]

Fort, C.

V. Ahufinger, R. Corbalán, F. Cataliotti, S. Burger, F. Minardi, and C. Fort, “Electromagnetically induced transparency in a Bose–Einstein condensate,” Opt. Commun. 211, 159–165 (2002).
[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]

Gallagher, T. F.

T. F. Gallagher, Rydberg Atoms (Cambridge University, 1994).

Garcia, K.-J.

Y.-J. Lin, K.-J. Garcia, and I. B. Spielman, “Spin-orbit-coupled Bose–Einstein condensates,” Nature 471, 83–86 (2011).
[CrossRef]

Y.-J. Lin, R. L. Compton, K.-J. Garcia, J. V. Porto, and I. B. Spielman, “Synthetic magnetic fields for ultracold neutral atoms,” Nature 462, 628–632 (2009).
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R. Zhang, S. R. Garner, and L. V. Hau, “Creation of long-term coherent optical memory via controlled nonlinear interactions in Bose-Einstein condensates,” Phys. Rev. Lett. 103, 233602 (2009).
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S.-W. Su, Y.-H. Chen, S.-C. Gou, and I. A. Yu, “An effective thermal-parametrization theory for the slow-light dynamics in a Doppler-broadened electromagnetically induced transparency medium,” J. Phys. B 44, 165504 (2011).
[CrossRef]

S.-W. Su, Y.-H. Chen, S.-C. Gou, T.-L. Horng, and I. A. Yu, “Dynamics of slow light and light storage in a Doppler-broadened electromagnetically-induced-transparency medium: a numerical approach,” Phys. Rev. A 83, 013827 (2011).
[CrossRef]

Gould, P. L.

D. Tong, S. M. Farooqi, J. Stanojevic, S. Krishnan, Y. P. Zhang, R. Côté, E. E. Eyler, and P. L. Gould, “Local blockade of Rydberg excitation in an ultracold gas,” Phys. Rev. Lett. 93, 063001 (2004).
[CrossRef]

S. M. Farooqi, D. Tong, S. Krishnan, J. Stanojevic, Y. P. Zhang, J. R. Ensher, A. S. Estrin, C. Boisseau, R. Côté, E. E. Eyler, and P. L. Gould, “Long-range molecular resonances in a cold Rydberg gas,” Phys. Rev. Lett. 91, 183002 (2003).
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Gounand, F.

F. Gounand, “Calculation of radial matrix elements and radiative lifetimes for highly excited states of alkali atoms using Coulomb approximation,” J. Phys. 40, 457–460 (1979).
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K. Hamerer, A. S. Sørensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041–1093 (2010).
[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]

Hau, L. V.

R. Zhang, S. R. Garner, and L. V. Hau, “Creation of long-term coherent optical memory via controlled nonlinear interactions in Bose-Einstein condensates,” Phys. Rev. Lett. 103, 233602 (2009).
[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]

Heidemann, R.

R. Löw, H. Weimer, U. Krohn, R. Heidemann, V. Bendkowsky, B. Butscher, H. P. Büchler, and T. Pfau, “Universal scaling in a strongly interacting Rydberg gas,” Phys. Rev. A 80, 033422 (2009).
[CrossRef]

R. Heidemann, U. Raitzsch, V. Bendkowsky, B. Butscher, R. Löw, L. Santos, and T. Pfau, “Evidence for coherent collective Rydberg excitation in the strong blockade regime,” Phys. Rev. Lett. 99, 163601 (2007).
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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]

Horng, T.-L.

S.-W. Su, Y.-H. Chen, S.-C. Gou, T.-L. Horng, and I. A. Yu, “Dynamics of slow light and light storage in a Doppler-broadened electromagnetically-induced-transparency medium: a numerical approach,” Phys. Rev. A 83, 013827 (2011).
[CrossRef]

Imamoglu, A.

B. Kaltenhäuser, H. Kübler, A. Chromik, J. Stuhler, T. Pfau, and A. Imamoglu, “Narrow bandwidth electromagnetically induced transparency in optically trapped atoms,” J. Phys. B 40, 1907–1915 (2007).
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M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
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Jen, H. H.

H. H. Jen and D.-W. Wang, “Theory of electromagnetically induced transparency in strongly correlated quantum gases,” Phys. Rev. A 87, 061802(R) (2013).
[CrossRef]

Jiang, L.

L. Jiang, H. Pu, W. Zhang, and H. Y. Ling, “Detection of Fermi pairing via electromagnetically induced transparency,” Phys. Rev. A 80, 033606 (2009).
[CrossRef]

Kaltenhäuser, B.

B. Kaltenhäuser, H. Kübler, A. Chromik, J. Stuhler, T. Pfau, and A. Imamoglu, “Narrow bandwidth electromagnetically induced transparency in optically trapped atoms,” J. Phys. B 40, 1907–1915 (2007).
[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).
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Kocharovskaya, O.

O. Kocharovskaya, Y. Rostovtsev, and M. O. Scully, “Stopping light via hot atoms,” Phys. Rev. Lett. 86, 628–631 (2001).
[CrossRef]

Krishnan, S.

D. Tong, S. M. Farooqi, J. Stanojevic, S. Krishnan, Y. P. Zhang, R. Côté, E. E. Eyler, and P. L. Gould, “Local blockade of Rydberg excitation in an ultracold gas,” Phys. Rev. Lett. 93, 063001 (2004).
[CrossRef]

S. M. Farooqi, D. Tong, S. Krishnan, J. Stanojevic, Y. P. Zhang, J. R. Ensher, A. S. Estrin, C. Boisseau, R. Côté, E. E. Eyler, and P. L. Gould, “Long-range molecular resonances in a cold Rydberg gas,” Phys. Rev. Lett. 91, 183002 (2003).
[CrossRef]

Krohn, U.

R. Löw, H. Weimer, U. Krohn, R. Heidemann, V. Bendkowsky, B. Butscher, H. P. Büchler, and T. Pfau, “Universal scaling in a strongly interacting Rydberg gas,” Phys. Rev. A 80, 033422 (2009).
[CrossRef]

Kübler, H.

B. Kaltenhäuser, H. Kübler, A. Chromik, J. Stuhler, T. Pfau, and A. Imamoglu, “Narrow bandwidth electromagnetically induced transparency in optically trapped atoms,” J. Phys. B 40, 1907–1915 (2007).
[CrossRef]

La Rocca, G. C.

I. Carusotto, M. Artoni, and G. C. La Rocca, “Atomic recoil effects in slow light propagation,” JETP Lett. 72, 289–293 (2000).
[CrossRef]

Li, Y.

L. Zhou, K. Zhang, B. Zhu, Y. Li, and W. Zhang, “Phase detection in an ultracold polarized Fermi gas via electromagnetically induced transparency,” Phys. Lett. A 376, 919–924 (2012).
[CrossRef]

Lin, Y.-J.

Y.-J. Lin, K.-J. Garcia, and I. B. Spielman, “Spin-orbit-coupled Bose–Einstein condensates,” Nature 471, 83–86 (2011).
[CrossRef]

Y.-J. Lin, R. L. Compton, K.-J. Garcia, J. V. Porto, and I. B. Spielman, “Synthetic magnetic fields for ultracold neutral atoms,” Nature 462, 628–632 (2009).
[CrossRef]

Ling, H. Y.

L. Jiang, H. Pu, W. Zhang, and H. Y. Ling, “Detection of Fermi pairing via electromagnetically induced transparency,” Phys. Rev. A 80, 033606 (2009).
[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]

Löw, R.

R. Löw, H. Weimer, U. Krohn, R. Heidemann, V. Bendkowsky, B. Butscher, H. P. Büchler, and T. Pfau, “Universal scaling in a strongly interacting Rydberg gas,” Phys. Rev. A 80, 033422 (2009).
[CrossRef]

R. Heidemann, U. Raitzsch, V. Bendkowsky, B. Butscher, R. Löw, L. Santos, and T. Pfau, “Evidence for coherent collective Rydberg excitation in the strong blockade regime,” Phys. Rev. Lett. 99, 163601 (2007).
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M. D. Lukin, “Colloquium: trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. 75, 457–472 (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]

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]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

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G. V. Marr and D. M. Creek, “The absorption oscillator strengths in alkali metal vapours,” Proc. R. Soc. Edin. Sect. A 304, 245–254 (1968).
[CrossRef]

Minardi, F.

V. Ahufinger, R. Corbalán, F. Cataliotti, S. Burger, F. Minardi, and C. Fort, “Electromagnetically induced transparency in a Bose–Einstein condensate,” Opt. Commun. 211, 159–165 (2002).
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Morigi, G.

G. Morigi and G. S. Agarwal, “Temperature variation of ultraslow light in a cold gas,” Phys. Rev. A 62, 013801 (2000).
[CrossRef]

Müstecaplioglu, Ö. Ë.

Ö. Ë. Müstecaplioglu and L. You, “Propagation of Raman-matched laser pulses through a Bose–Einstein condensate,” Opt. Commun. 193, 301–312 (2001).
[CrossRef]

Niemax, K.

E. Caliebe and K. Niemax, “Oscillator strengths of the principal series lines of Rb,” J. Phys. B 12, L45–L51 (1979).
[CrossRef]

Pethick, C. J.

C. J. Pethick and H. Smith, Bose–Einstein Condensation in Dilute Gases (Cambridge University, 2002).

Pfau, T.

R. Löw, H. Weimer, U. Krohn, R. Heidemann, V. Bendkowsky, B. Butscher, H. P. Büchler, and T. Pfau, “Universal scaling in a strongly interacting Rydberg gas,” Phys. Rev. A 80, 033422 (2009).
[CrossRef]

R. Heidemann, U. Raitzsch, V. Bendkowsky, B. Butscher, R. Löw, L. Santos, and T. Pfau, “Evidence for coherent collective Rydberg excitation in the strong blockade regime,” Phys. Rev. Lett. 99, 163601 (2007).
[CrossRef]

B. Kaltenhäuser, H. Kübler, A. Chromik, J. Stuhler, T. Pfau, and A. Imamoglu, “Narrow bandwidth electromagnetically induced transparency in optically trapped atoms,” J. Phys. B 40, 1907–1915 (2007).
[CrossRef]

Polzik, E. S.

K. Hamerer, A. S. Sørensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041–1093 (2010).
[CrossRef]

Porto, J. V.

Y.-J. Lin, R. L. Compton, K.-J. Garcia, J. V. Porto, and I. B. Spielman, “Synthetic magnetic fields for ultracold neutral atoms,” Nature 462, 628–632 (2009).
[CrossRef]

Pu, H.

L. Jiang, H. Pu, W. Zhang, and H. Y. Ling, “Detection of Fermi pairing via electromagnetically induced transparency,” Phys. Rev. A 80, 033606 (2009).
[CrossRef]

Raitzsch, U.

R. Heidemann, U. Raitzsch, V. Bendkowsky, B. Butscher, R. Löw, L. Santos, and T. Pfau, “Evidence for coherent collective Rydberg excitation in the strong blockade regime,” Phys. Rev. Lett. 99, 163601 (2007).
[CrossRef]

Renzoni, F.

E. Cerboneschi, F. Renzoni, and E. Arimondo, “Relaxation processes in slow light: the role of the atomic momentum,” Opt. Commun. 204, 211–217 (2002).
[CrossRef]

Rostovtsev, Y.

O. Kocharovskaya, Y. Rostovtsev, and M. O. Scully, “Stopping light via hot atoms,” Phys. Rev. Lett. 86, 628–631 (2001).
[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]

Saffman, M.

M. Saffman and T. G. Waller, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010).
[CrossRef]

Santos, L.

R. Heidemann, U. Raitzsch, V. Bendkowsky, B. Butscher, R. Löw, L. Santos, and T. Pfau, “Evidence for coherent collective Rydberg excitation in the strong blockade regime,” Phys. Rev. Lett. 99, 163601 (2007).
[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.

O. Kocharovskaya, Y. Rostovtsev, and M. O. Scully, “Stopping light via hot atoms,” Phys. Rev. Lett. 86, 628–631 (2001).
[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]

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

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]

Singer, K.

K. Singer, J. Stanojevic, M. Weidemüller, and R. Côté, “Long-range interactions between alkali Rydberg atom pairs correlated to the ns-ns, np-np and nd-nd asymptotes,” J. Phys. B 38, S295–S307 (2005).
[CrossRef]

Smith, H.

C. J. Pethick and H. Smith, Bose–Einstein Condensation in Dilute Gases (Cambridge University, 2002).

Sørensen, A. S.

K. Hamerer, A. S. Sørensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041–1093 (2010).
[CrossRef]

Spielman, I. B.

Y.-J. Lin, K.-J. Garcia, and I. B. Spielman, “Spin-orbit-coupled Bose–Einstein condensates,” Nature 471, 83–86 (2011).
[CrossRef]

Y.-J. Lin, R. L. Compton, K.-J. Garcia, J. V. Porto, and I. B. Spielman, “Synthetic magnetic fields for ultracold neutral atoms,” Nature 462, 628–632 (2009).
[CrossRef]

Stanojevic, J.

K. Singer, J. Stanojevic, M. Weidemüller, and R. Côté, “Long-range interactions between alkali Rydberg atom pairs correlated to the ns-ns, np-np and nd-nd asymptotes,” J. Phys. B 38, S295–S307 (2005).
[CrossRef]

D. Tong, S. M. Farooqi, J. Stanojevic, S. Krishnan, Y. P. Zhang, R. Côté, E. E. Eyler, and P. L. Gould, “Local blockade of Rydberg excitation in an ultracold gas,” Phys. Rev. Lett. 93, 063001 (2004).
[CrossRef]

S. M. Farooqi, D. Tong, S. Krishnan, J. Stanojevic, Y. P. Zhang, J. R. Ensher, A. S. Estrin, C. Boisseau, R. Côté, E. E. Eyler, and P. L. Gould, “Long-range molecular resonances in a cold Rydberg gas,” Phys. Rev. Lett. 91, 183002 (2003).
[CrossRef]

Stuhler, J.

B. Kaltenhäuser, H. Kübler, A. Chromik, J. Stuhler, T. Pfau, and A. Imamoglu, “Narrow bandwidth electromagnetically induced transparency in optically trapped atoms,” J. Phys. B 40, 1907–1915 (2007).
[CrossRef]

Su, S.-W.

S.-W. Su, Y.-H. Chen, S.-C. Gou, and I. A. Yu, “An effective thermal-parametrization theory for the slow-light dynamics in a Doppler-broadened electromagnetically induced transparency medium,” J. Phys. B 44, 165504 (2011).
[CrossRef]

S.-W. Su, Y.-H. Chen, S.-C. Gou, T.-L. Horng, and I. A. Yu, “Dynamics of slow light and light storage in a Doppler-broadened electromagnetically-induced-transparency medium: a numerical approach,” Phys. Rev. A 83, 013827 (2011).
[CrossRef]

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D. Tong, S. M. Farooqi, J. Stanojevic, S. Krishnan, Y. P. Zhang, R. Côté, E. E. Eyler, and P. L. Gould, “Local blockade of Rydberg excitation in an ultracold gas,” Phys. Rev. Lett. 93, 063001 (2004).
[CrossRef]

S. M. Farooqi, D. Tong, S. Krishnan, J. Stanojevic, Y. P. Zhang, J. R. Ensher, A. S. Estrin, C. Boisseau, R. Côté, E. E. Eyler, and P. L. Gould, “Long-range molecular resonances in a cold Rydberg gas,” Phys. Rev. Lett. 91, 183002 (2003).
[CrossRef]

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Z. Dutton and L. Vestergaard Hau, “Storing and processing optical information with ultraslow light in Bose–Einstein condensates,” Phys. Rev. A 70, 053831 (2004).
[CrossRef]

Waller, T. G.

M. Saffman and T. G. Waller, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010).
[CrossRef]

Wang, D.-W.

H. H. Jen and D.-W. Wang, “Theory of electromagnetically induced transparency in strongly correlated quantum gases,” Phys. Rev. A 87, 061802(R) (2013).
[CrossRef]

Weidemüller, M.

K. Singer, J. Stanojevic, M. Weidemüller, and R. Côté, “Long-range interactions between alkali Rydberg atom pairs correlated to the ns-ns, np-np and nd-nd asymptotes,” J. Phys. B 38, S295–S307 (2005).
[CrossRef]

Weimer, H.

R. Löw, H. Weimer, U. Krohn, R. Heidemann, V. Bendkowsky, B. Butscher, H. P. Büchler, and T. Pfau, “Universal scaling in a strongly interacting Rydberg gas,” Phys. Rev. A 80, 033422 (2009).
[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]

You, L.

Ö. Ë. Müstecaplioglu and L. You, “Propagation of Raman-matched laser pulses through a Bose–Einstein condensate,” Opt. Commun. 193, 301–312 (2001).
[CrossRef]

Yu, I. A.

S.-W. Su, Y.-H. Chen, S.-C. Gou, and I. A. Yu, “An effective thermal-parametrization theory for the slow-light dynamics in a Doppler-broadened electromagnetically induced transparency medium,” J. Phys. B 44, 165504 (2011).
[CrossRef]

S.-W. Su, Y.-H. Chen, S.-C. Gou, T.-L. Horng, and I. A. Yu, “Dynamics of slow light and light storage in a Doppler-broadened electromagnetically-induced-transparency medium: a numerical approach,” Phys. Rev. A 83, 013827 (2011).
[CrossRef]

Zhang, K.

L. Zhou, K. Zhang, B. Zhu, Y. Li, and W. Zhang, “Phase detection in an ultracold polarized Fermi gas via electromagnetically induced transparency,” Phys. Lett. A 376, 919–924 (2012).
[CrossRef]

Zhang, R.

R. Zhang, S. R. Garner, and L. V. Hau, “Creation of long-term coherent optical memory via controlled nonlinear interactions in Bose-Einstein condensates,” Phys. Rev. Lett. 103, 233602 (2009).
[CrossRef]

Zhang, W.

L. Zhou, K. Zhang, B. Zhu, Y. Li, and W. Zhang, “Phase detection in an ultracold polarized Fermi gas via electromagnetically induced transparency,” Phys. Lett. A 376, 919–924 (2012).
[CrossRef]

L. Jiang, H. Pu, W. Zhang, and H. Y. Ling, “Detection of Fermi pairing via electromagnetically induced transparency,” Phys. Rev. A 80, 033606 (2009).
[CrossRef]

Zhang, Y. P.

D. Tong, S. M. Farooqi, J. Stanojevic, S. Krishnan, Y. P. Zhang, R. Côté, E. E. Eyler, and P. L. Gould, “Local blockade of Rydberg excitation in an ultracold gas,” Phys. Rev. Lett. 93, 063001 (2004).
[CrossRef]

S. M. Farooqi, D. Tong, S. Krishnan, J. Stanojevic, Y. P. Zhang, J. R. Ensher, A. S. Estrin, C. Boisseau, R. Côté, E. E. Eyler, and P. L. Gould, “Long-range molecular resonances in a cold Rydberg gas,” Phys. Rev. Lett. 91, 183002 (2003).
[CrossRef]

Zhou, L.

L. Zhou, K. Zhang, B. Zhu, Y. Li, and W. Zhang, “Phase detection in an ultracold polarized Fermi gas via electromagnetically induced transparency,” Phys. Lett. A 376, 919–924 (2012).
[CrossRef]

Zhu, B.

L. Zhou, K. Zhang, B. Zhu, Y. Li, and W. Zhang, “Phase detection in an ultracold polarized Fermi gas via electromagnetically induced transparency,” Phys. Lett. A 376, 919–924 (2012).
[CrossRef]

Zibrov, A. 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]

Zimmer, F.

F. Zimmer and M. Fleischhauer, “Sagnac interferometry based on ultraslow polaritons in cold atomic vapors,” Phys. Rev. Lett. 92, 253201 (2004).
[CrossRef]

Zubairy, M. S.

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

J. Phys. (1)

F. Gounand, “Calculation of radial matrix elements and radiative lifetimes for highly excited states of alkali atoms using Coulomb approximation,” J. Phys. 40, 457–460 (1979).
[CrossRef]

J. Phys. B (4)

E. Caliebe and K. Niemax, “Oscillator strengths of the principal series lines of Rb,” J. Phys. B 12, L45–L51 (1979).
[CrossRef]

K. Singer, J. Stanojevic, M. Weidemüller, and R. Côté, “Long-range interactions between alkali Rydberg atom pairs correlated to the ns-ns, np-np and nd-nd asymptotes,” J. Phys. B 38, S295–S307 (2005).
[CrossRef]

B. Kaltenhäuser, H. Kübler, A. Chromik, J. Stuhler, T. Pfau, and A. Imamoglu, “Narrow bandwidth electromagnetically induced transparency in optically trapped atoms,” J. Phys. B 40, 1907–1915 (2007).
[CrossRef]

S.-W. Su, Y.-H. Chen, S.-C. Gou, and I. A. Yu, “An effective thermal-parametrization theory for the slow-light dynamics in a Doppler-broadened electromagnetically induced transparency medium,” J. Phys. B 44, 165504 (2011).
[CrossRef]

JETP Lett. (1)

I. Carusotto, M. Artoni, and G. C. La Rocca, “Atomic recoil effects in slow light propagation,” JETP Lett. 72, 289–293 (2000).
[CrossRef]

Nat. Photonics (1)

M. Albert, A. Dantan, and M. Drewsen, “Cavity electromagnetically induced transparency and all-optical switching using ion Coulomb crystals,” Nat. Photonics 5, 633–636 (2011).
[CrossRef]

Nature (3)

Y.-J. Lin, R. L. Compton, K.-J. Garcia, J. V. Porto, and I. B. Spielman, “Synthetic magnetic fields for ultracold neutral atoms,” Nature 462, 628–632 (2009).
[CrossRef]

Y.-J. Lin, K.-J. Garcia, and I. B. Spielman, “Spin-orbit-coupled Bose–Einstein condensates,” Nature 471, 83–86 (2011).
[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]

Opt. Commun. (3)

V. Ahufinger, R. Corbalán, F. Cataliotti, S. Burger, F. Minardi, and C. Fort, “Electromagnetically induced transparency in a Bose–Einstein condensate,” Opt. Commun. 211, 159–165 (2002).
[CrossRef]

Ö. Ë. Müstecaplioglu and L. You, “Propagation of Raman-matched laser pulses through a Bose–Einstein condensate,” Opt. Commun. 193, 301–312 (2001).
[CrossRef]

E. Cerboneschi, F. Renzoni, and E. Arimondo, “Relaxation processes in slow light: the role of the atomic momentum,” Opt. Commun. 204, 211–217 (2002).
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Phys. Lett. A (1)

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Figures (7)

Fig. 1.
Fig. 1.

Electromagnetically induced transparency (EIT) in Λ-type atoms. (a) The atoms are interacting with two laser fields either through a co- (dash) or counterpropagating (solid) scheme. (b) Control Ω2 and probe fields Ω1 couple two hyperfine ground states |a and |b with the excited state |e with detunings Δ2 and Δ1, respectively. Γ is the spontaneous emission rate of |e. (c) Linear susceptibility χ times i versus probe light detuning Δ1 in unit of Γ. Absorption (solid blue) and dispersion (red dash) profiles are plotted from the classical theory of EIT in resonance of the control field Δ2=0.

Fig. 2.
Fig. 2.

Counterpropagating excitation scheme for EIT in bosons using the Rydberg transition (Γ1=28.3μs) of Rb87. The control field is Ω2=1Γ with the detuning Δ2=0, which is used throughout the article if not specified. The OD is 12 for L=100μm and pr/m3×102ms1. Absorption (Re[iχ]) (solid blue) and dispersion (Im[iχ]) (dashed red) profiles are plotted at different temperatures (a) T=5; (b) 0.5; (c) 0.35; and (d) 0.1 μK where transition temperature Tc0.4μK [straight dotted line in (e)]. The dashed–dotted black line guides the eye to the zero of the plots. In (e), the group velocity vg is plotted for various control fields, Ω2/Γ=0.5(○), 1(□), 2(⋄), 4(+), and 10(•) over temperatures in log scale. The detuning is set as Δ2=pr2/(2m), so vg is calculated numerically at the transparency condition of Δ1=0. The solid lines guide the eyes for connecting data points.

Fig. 3.
Fig. 3.

Counterpropagating excitation scheme for EIT in bosons using D2 transition (Γ1=26ns) of Rb87. The OD is 1450 for L=100μm and pr/m102ms1. Absorption (Re[iχ]) (solid blue) and dispersion (Im[iχ]) (dashed red) profiles are plotted as a comparison to Fig. 2 at the temperatures (a) T=5; (b) 0.5; (c) 0.35; and (d) 0.1 μK. The dash-dotted black line guides the eye to the zero of the plots, and Ω2=0.01Γ, Δ2=0. In (e), the group velocity vg is plotted for Ω2/Γ=0.003 (solid blue), 0.01 (dashed green), and 0.03 (dashed–dotted red) over temperatures in log scale across Tc (straight dotted line).

Fig. 4.
Fig. 4.

Counterpropagating excitation scheme for EIT in fermions. The OD is 1.2 for L=100μm and pr/m6×102ms1. (a) and (b) Absorption (solid blue) and dispersion (dashed red) profiles are plotted for K40 at temperatures of 5 and 0.5 μK (Fermi temperature Tf=1.98μK). (c) Two energy bands of free and shifted-recoil particles are shown as p2/(2m) and Δ1+(p+pr)2/(2m), respectively (Δ1 is chosen to be equal to recoil energy, for example). The energy difference between two energy bands is demonstrated for fermions where solid-red arrows represent different excitation paths from the Fermi surface. (d) The same energy bands of (c) are shown for bosons. The zero momentum (p=0) state (red-filled circle) match these two bands exactly for Bose–Einstein condensation.

Fig. 5.
Fig. 5.

Copropagating excitation scheme for EIT in bosons. The recoil velocity is pr/m107ms1. Absorption (solid blue) and dispersion (dashed red) profiles of Rb87 are shown in the same temperature conditions (a) to (d) as in Fig. 2. In (e), the group velocity vg is plotted for various control fields, Ω2/Γ=0.5(○), 1(□), 2(⋄) over temperatures from 0.01 to 10 μK in log scale, which shows significant reduction and saturates in the low T limit. High-temperature limit has more reduction due to the narrower transmission window. The solid lines are drawn to connect data points.

Fig. 6.
Fig. 6.

Copropagating excitation scheme for EIT in fermions. The recoil velocity is pr/m4×108ms1. Absorption (solid blue) and dispersion (dashed red) profiles of K40. The same temperature conditions are used as in Fig. 4. Group velocity vg is plotted for temperatures from 0.01 to 10 μK in log scale in (c) for various control fields, Ω2/Γ=0.5(○), 1(□), and 2(⋄). It saturates in the low T limit, and more reduction of velocity is observed due to the narrower transmission window at higher T. The solid lines are drawn to connect data points.

Fig. 7.
Fig. 7.

EIT property in a weakly interacting Rb87 condensate. Interacting dispersion (dashed red) and absorption (solid blue) profiles are shown in (a) counter- and (c) copropagating excitation schemes where noninteracting profiles (dashed–doted red and diamond blue) are included for comparisons. The respective group velocities (b) and (d) are calculated numerically at the transparency conditions and plotted over interaction strengths (as). The scattering length and temperature are chosen as as=7×106a0 and T=10nK in (a) and (c) where the insets are i(χQD+χTH) from Bogoliubov particles ρex0.1ρ. The coupling atomic levels and the atomic density ρ are the same as in Fig. 2, and the double arrows in (a) and (c) are the mean-field interaction energy shifts, ρcUaa. In (b) and (d), we draw the solid lines for eye-guiding.

Equations (15)

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E(z,t)z+1cE(z,t)t=ik12ϵ0P(z,t),
χ(ω1)=ρdae2Δ1Ω22(Δ1+iΓ)Δ1,vg=c1+N|g|2{(Ω22+Δ12)[(Ω22Δ12)2Δ12Γ2][(Ω22Δ12)2+Δ12Γ2]2}=c1+N|g|2/Ω22|Δ1=0,
HA=pp22m(a^pa^p+b^pb^p+e^pe^p)+Δ1pa^pa^p+Δ2pb^pb^p,HAL=Ω1pe^p+p1a^pΩ2pe^p+p2b^p+H.c.,
M^p=[Δ1+p22m0Ω10Δ2+(p+pr)22mΩ2Ω1Ω2(p+p1)22m].
β^p|0=[a^p+Ω1cosϕpsinϕp(1ϵD(p)ϵB+(p)1ϵD(p)ϵB(p))b^p+prΩ1(sin2ϕpϵD(p)ϵB+(p)+cos2ϕpϵD(p)ϵB(p))e^p+p1]|0,
ϵD(p)=Δ1+p22m,ϵB±(p)=Δ¯2+(p+p1)22m±[Δ¯2(p+p1)22m]2+4Ω222,
cosϕp=ϵB+(p)(p+p1)22mϵB+(p)ϵB(p).
χ(ω1)dae2Ω1Ad2rΨ^a(r)Ψ^e(r)eip1·r/,=ρdae2NΩ1p,pa^pe^p1Ad2rei(ppp1)·r/,=ρdae2NpFpnβp,
Fp=[sin2ϕpϵD(p)ϵB+(p)+cos2ϕpϵD(p)ϵB(p)],=Δ1Δ2+p22m(p+pr)22mΩ22[Δ1+p22m(p+p1)22m+iΓ][Δ1Δ2+p22m(p+pr)22m].
χ(ω1,T)=ρdae2[ρc(T)ρFp=0+1Np0Fpnβp],
HU=12Vp,p,q[Uaaa^p+qa^pqa^pa^p+Ubbb^p+qb^pqb^pb^p+Ueee^p+qe^pqe^pe^p]+12Vp,pq[2Uabb^p+qa^pqa^pb^p+2Uaee^p+qa^pqa^pe^p+2Ubee^p+qb^pqb^pe^p],Uaa2Vp,p,qa^p+qa^pqa^pa^p+ρcUabpb^pb^p+ρcUaepe^pe^p,
M^p=[Δ1+p22m0Ω10Δ2+(p+pr)22m+ρcUabΩ2Ω1Ω2(p+p1)22m+ρcUae],=ρcUaeI^+[Δ˜1+p22m0Ω10Δ˜2+(p+pr)22mΩ2Ω1Ω2(p+p1)22m],
HDμN^=EgμNc+q0ϵ(q)αqαq,
Eg=ϵ˜D(p=0)Nc+Uaa2V(Nc2+2Nex2)+NcNUaeV+q>0[ϵϵ1(q)],
χ(ω1)=χC(ω1)+χQD(ω1)+χTH(ω1),=ρdae2[ρcρF˜p=0+1Np0F˜psinh2θ+1Np0F˜pnbcosh2θ],

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