Abstract

We study electromagnetically induced transparency (EIT) in a heated potassium vapor cell, using a simple optical setup with a single free-running diode laser and an acousto-optic modulator. Despite the fact that the Doppler width is comparable to the ground state hyperfine splitting, transparency windows with deeply sub-natural line widths and large group indices are obtained. A longitudinal magnetic field is used to split the EIT feature and induce magneto-optical anisotropy. Using the beat note between co-propagating coupling and probe beams, we perform a heterodyne measurement of the circular dichroism (and therefore birefringence) of the EIT medium. The observed spectra reveal that lin‖lin polarizations lead to greater anisotropy than lin⊥lin. A simplified ‖analytical model encompassing sixteen Zeeman states and eighteen Λ subsytems reproduces the experimental observations.

© 2016 Optical Society of America

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Corrections

11 January 2017: A correction was made to Ref. 30.


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References

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  4. D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153 (2002).
    [Crossref]
  5. J. Vanier, “Atomic clocks based on coherent population trapping: a review,” Appl. Phys. B 81, 421 (2005).
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  6. S. Gozzini, S. Cartaleva, A. Lucchesini, C. Marinelli, L. Marmugi, D. Slavov, and T. Karaulanov, “Coherent population trapping and strong electromagnetically induced transparency resonances on the D1 line of potassium,” Eur. Phys. J. D. 53, 153–161 (2009).
    [Crossref]
  7. K. Nasyrov, S. Gozzini, A. Lucchesini, C. Marinelli, S. Gateva, S. Cartaleva, and L. Marmugi, “Antirelaxation coatings in coherent spectroscopy: theoretical investigation and experimental test,” Phys. Rev. A 92, 043803 (2015).
    [Crossref]
  8. S. Gu, J. A. Behr, M. N. Groves, and D. Dhat, “Coherent population trapping states with cold atoms in a magnetic field,” Opt. Commun. 220, 365–370 (2003).
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  9. A. Sargsyan, P. A. Petrov, T. A. Vartanyan, and D. Sarkisyan, “Electromagnetically induced transparency in potassium vapors: features and restrictions,” Opt. Spectrosc. 120, 339–344 (2015).
    [Crossref]
  10. E. Haller, J. Hudson, A. Kelly, D. A. Cotta, B. Peaudecerf, G. D. Bruce, and S. Kuhr, “Single-atom imaging of fermions in a quantum-gas microscope,” Nat. Phys. 11, 738–742 (2015).
    [Crossref]
  11. G. J. A. Edge, R. Anderson, D. Jervis, D. C. McKay, R. Day, S. Trotzky, and J. H. Thywissen, “Imaging and addressing of individual fermionic atoms in an optical lattice,” Phys. Rev. A 92, 063406 (2015).
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    [Crossref]
  14. K. A. Whittaker, J. Keaveney, I. G. Hughes, and C. S. Adams, “Hilbert transform: applications to atomic spectra,” Phys. Rev. A 91, 032513 (2015).
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    [Crossref]
  19. S. M. Iftiquar and V. Natarajan, “Line narrowing of electromagnetically induced transparency in Rb with a longitudinal magnetic field,” Phys. Rev. A 79, 013808 (2009).
    [Crossref]
  20. S. Franke-Arnold, M. Arndt, and A. Zeilinger, “Magneto-optical effects with cold lithium atoms,” J. Phys. B: At. Mol. Opt. Phys. 342527 (2001).
    [Crossref]
  21. J. M. Choi, J. M. Kim, Q.-H. Park, and D. Cho, “Optically induced Faraday effect in a Λ configuration of spin-polarized cold cesium atoms,” Phys. Rev. A 75, 013815 (2007).
    [Crossref]
  22. A. Wojciechowski, E. Corsini, J. Zachorowski, and W. Gawlik, “Nonlinear Faraday rotation and detection of superposition states in cold atoms,” Phys. Rev. A 81, 053420 (2010).
    [Crossref]
  23. B. Wang, S. Li, J. Ma, H. Wang, K. C. Peng, and M. Xiao, “Controlling the polarization rotation of an optical field via asymmetry in electromagnetically induced transparency,” Phys. Rev. A 73, 051801 (2006)
    [Crossref]
  24. N. Hombo, S. Taniguchi, S. Sugimura, K. Fujita, and M. Mitsunaga, “Electromagnetically induced polarization rotation in Na vapor,” J. Opt. Soc. Am. B 29, 1717–1721 (2012).
    [Crossref]
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  26. Trade names and part numbers are used for identification purposes only, and do not constitute endorsements. Other products may perform similarly or better.
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    [Crossref]
  28. K. Li, L. Deng, and M. G. Payne, “Realization of a single and closed Λ-system in a room-temperature three-level coherently prepared resonant medium with narrow D1 hyperfine splittings,” Appl. Phys. Lett. 95, 221103 (2009).
    [Crossref]
  29. O. S. Mishina, M. Scherman, P. Lombardi, J. Ortalo, D. Felinto, A. S. Sheremet, A. Bramati, D. V. Kupriyanov, J. Laurat, and E. Giacobino, “Electromagnetically induced transparency in an inhomogeneously broadened Λ transition with multiple excited levels,” Phys. Rev. A 83, 053809 (2011).
    [Crossref]
  30. R. K. Hanley, P. D. Gregory, I. G. Hughes, and S. L. Cornish, “Absolute absorption on the potassium D lines: theory and experiment,” J. Phys. B: At. Mol. Opt. Phys. 48, 195004 (2015).
    [Crossref]
  31. H. Wang, D. J. Goorskey, W. H. Burkett, and M. Xiao, “Cavity-linewidth narrowing by means of electromagnetically induced transparency,” Opt. Lett. 23, 1732–1734 (2000).
    [Crossref]
  32. G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett. 99, 133601 (2007).
    [Crossref] [PubMed]
  33. T. Lauprêtre, C. Proux, R. Ghosh, S. Schwartz, F. Goldfarb, and F. Bretenaker, “Photon lifetime in a cavity containing a slow-light medium,” Opt. Lett. 9, 1551–1553 (2011).
    [Crossref]
  34. T. Lauprêtre, S. Schwartz, R. Ghosh, I. Carusotto, F. Goldfarb, and F. Bretenaker, “Anomalous ring-down effects and breakdown of the decay rate concept in optical cavities with negative group delay,” New J. Phys. 14043012 (2012).
    [Crossref]
  35. J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 78–81 (2012).
    [Crossref] [PubMed]
  36. J. M. Weiner, K. C. Cox, J. G. Bohnet, Z. Chen, and J. K. Thompson, “Superradiant Raman laser magnetometer,” Appl. Phys. Lett. 101, 261107 (2012).
    [Crossref]
  37. M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75, 053807 (2007).
    [Crossref]
  38. http://epapers.bham.ac.uk/2130/

2016 (1)

W. Xu and B. DeMarco, “Velocity-selective electromagnetically-induced-transparency measurements of potassium Rydberg states,” Phys. Rev. A 93, 011801 (2016).
[Crossref]

2015 (6)

K. A. Whittaker, J. Keaveney, I. G. Hughes, and C. S. Adams, “Hilbert transform: applications to atomic spectra,” Phys. Rev. A 91, 032513 (2015).
[Crossref]

K. Nasyrov, S. Gozzini, A. Lucchesini, C. Marinelli, S. Gateva, S. Cartaleva, and L. Marmugi, “Antirelaxation coatings in coherent spectroscopy: theoretical investigation and experimental test,” Phys. Rev. A 92, 043803 (2015).
[Crossref]

A. Sargsyan, P. A. Petrov, T. A. Vartanyan, and D. Sarkisyan, “Electromagnetically induced transparency in potassium vapors: features and restrictions,” Opt. Spectrosc. 120, 339–344 (2015).
[Crossref]

E. Haller, J. Hudson, A. Kelly, D. A. Cotta, B. Peaudecerf, G. D. Bruce, and S. Kuhr, “Single-atom imaging of fermions in a quantum-gas microscope,” Nat. Phys. 11, 738–742 (2015).
[Crossref]

G. J. A. Edge, R. Anderson, D. Jervis, D. C. McKay, R. Day, S. Trotzky, and J. H. Thywissen, “Imaging and addressing of individual fermionic atoms in an optical lattice,” Phys. Rev. A 92, 063406 (2015).
[Crossref]

R. K. Hanley, P. D. Gregory, I. G. Hughes, and S. L. Cornish, “Absolute absorption on the potassium D lines: theory and experiment,” J. Phys. B: At. Mol. Opt. Phys. 48, 195004 (2015).
[Crossref]

2012 (4)

T. Lauprêtre, S. Schwartz, R. Ghosh, I. Carusotto, F. Goldfarb, and F. Bretenaker, “Anomalous ring-down effects and breakdown of the decay rate concept in optical cavities with negative group delay,” New J. Phys. 14043012 (2012).
[Crossref]

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 78–81 (2012).
[Crossref] [PubMed]

J. M. Weiner, K. C. Cox, J. G. Bohnet, Z. Chen, and J. K. Thompson, “Superradiant Raman laser magnetometer,” Appl. Phys. Lett. 101, 261107 (2012).
[Crossref]

N. Hombo, S. Taniguchi, S. Sugimura, K. Fujita, and M. Mitsunaga, “Electromagnetically induced polarization rotation in Na vapor,” J. Opt. Soc. Am. B 29, 1717–1721 (2012).
[Crossref]

2011 (2)

O. S. Mishina, M. Scherman, P. Lombardi, J. Ortalo, D. Felinto, A. S. Sheremet, A. Bramati, D. V. Kupriyanov, J. Laurat, and E. Giacobino, “Electromagnetically induced transparency in an inhomogeneously broadened Λ transition with multiple excited levels,” Phys. Rev. A 83, 053809 (2011).
[Crossref]

T. Lauprêtre, C. Proux, R. Ghosh, S. Schwartz, F. Goldfarb, and F. Bretenaker, “Photon lifetime in a cavity containing a slow-light medium,” Opt. Lett. 9, 1551–1553 (2011).
[Crossref]

2010 (1)

A. Wojciechowski, E. Corsini, J. Zachorowski, and W. Gawlik, “Nonlinear Faraday rotation and detection of superposition states in cold atoms,” Phys. Rev. A 81, 053420 (2010).
[Crossref]

2009 (3)

K. Li, L. Deng, and M. G. Payne, “Realization of a single and closed Λ-system in a room-temperature three-level coherently prepared resonant medium with narrow D1 hyperfine splittings,” Appl. Phys. Lett. 95, 221103 (2009).
[Crossref]

S. Gozzini, S. Cartaleva, A. Lucchesini, C. Marinelli, L. Marmugi, D. Slavov, and T. Karaulanov, “Coherent population trapping and strong electromagnetically induced transparency resonances on the D1 line of potassium,” Eur. Phys. J. D. 53, 153–161 (2009).
[Crossref]

S. M. Iftiquar and V. Natarajan, “Line narrowing of electromagnetically induced transparency in Rb with a longitudinal magnetic field,” Phys. Rev. A 79, 013808 (2009).
[Crossref]

2007 (3)

J. M. Choi, J. M. Kim, Q.-H. Park, and D. Cho, “Optically induced Faraday effect in a Λ configuration of spin-polarized cold cesium atoms,” Phys. Rev. A 75, 013815 (2007).
[Crossref]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett. 99, 133601 (2007).
[Crossref] [PubMed]

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75, 053807 (2007).
[Crossref]

2006 (2)

B. Wang, S. Li, J. Ma, H. Wang, K. C. Peng, and M. Xiao, “Controlling the polarization rotation of an optical field via asymmetry in electromagnetically induced transparency,” Phys. Rev. A 73, 051801 (2006)
[Crossref]

S. Falke, E. Tiemann, C. Lisdat, H. Schnatz, and G. Grosche, “Transition frequencies of the D lines of 39K, 40K, and 41K measured with a femtosecond laser frequency comb,” Phys. Rev. A 74, 032503 (2006).
[Crossref]

2005 (3)

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

J. Vanier, “Atomic clocks based on coherent population trapping: a review,” Appl. Phys. B 81, 421 (2005).
[Crossref]

X. Wei, J. Wu, G. Sun, Z. Shao, Z. Kang, Y. Jiang, and J. Gao, “Splitting of an electromagnetically induced transparency window of rubidium atoms in a static magnetic field,” Phys. Rev. A 72, 023806 (2005).
[Crossref]

2003 (2)

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

S. Gu, J. A. Behr, M. N. Groves, and D. Dhat, “Coherent population trapping states with cold atoms in a magnetic field,” Opt. Commun. 220, 365–370 (2003).
[Crossref]

2002 (1)

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153 (2002).
[Crossref]

2001 (1)

S. Franke-Arnold, M. Arndt, and A. Zeilinger, “Magneto-optical effects with cold lithium atoms,” J. Phys. B: At. Mol. Opt. Phys. 342527 (2001).
[Crossref]

2000 (2)

Y.-C. Chen, C.-W. Lin, and I. A. Yu, “Roles of degenerate Zeeman levels in electromagnetically induced transparency,” Phys. Rev. A 61, 053805 (2000).
[Crossref]

H. Wang, D. J. Goorskey, W. H. Burkett, and M. Xiao, “Cavity-linewidth narrowing by means of electromagnetically induced transparency,” Opt. Lett. 23, 1732–1734 (2000).
[Crossref]

1998 (1)

R. Wynands, A. Nagel, S. Brandt, D. Meschede, and A. Weis, “Selection rules and line strengths of Zeeman-split dark resonances,” Phys. Rev. A 58, 196 (1998).
[Crossref]

1997 (1)

H. Wang, P. L. Gould, and W. C. Stwalley, “Long-range interaction of the 39K(4s)+39K(4p) asymptote by photoassociative spectroscopy. I. The 0g− pure long-range state and the long-range potential constants,” J. Chem. Phys. 106, 7899 (1997).
[Crossref]

1996 (1)

O. Schmidt, R. Wynands, Z. Hussein, and D. Meschede, “Steep dispersion and group velocity below c/ 3000 in coherent population trapping,” Phys. Rev. A 53, R27 (1996).
[Crossref]

1991 (1)

K-J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[Crossref] [PubMed]

Adams, C. S.

K. A. Whittaker, J. Keaveney, I. G. Hughes, and C. S. Adams, “Hilbert transform: applications to atomic spectra,” Phys. Rev. A 91, 032513 (2015).
[Crossref]

Anderson, R.

G. J. A. Edge, R. Anderson, D. Jervis, D. C. McKay, R. Day, S. Trotzky, and J. H. Thywissen, “Imaging and addressing of individual fermionic atoms in an optical lattice,” Phys. Rev. A 92, 063406 (2015).
[Crossref]

Arndt, M.

S. Franke-Arnold, M. Arndt, and A. Zeilinger, “Magneto-optical effects with cold lithium atoms,” J. Phys. B: At. Mol. Opt. Phys. 342527 (2001).
[Crossref]

Behr, J. A.

S. Gu, J. A. Behr, M. N. Groves, and D. Dhat, “Coherent population trapping states with cold atoms in a magnetic field,” Opt. Commun. 220, 365–370 (2003).
[Crossref]

Bohnet, J. G.

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 78–81 (2012).
[Crossref] [PubMed]

J. M. Weiner, K. C. Cox, J. G. Bohnet, Z. Chen, and J. K. Thompson, “Superradiant Raman laser magnetometer,” Appl. Phys. Lett. 101, 261107 (2012).
[Crossref]

Boller, K-J.

K-J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[Crossref] [PubMed]

Bramati, A.

O. S. Mishina, M. Scherman, P. Lombardi, J. Ortalo, D. Felinto, A. S. Sheremet, A. Bramati, D. V. Kupriyanov, J. Laurat, and E. Giacobino, “Electromagnetically induced transparency in an inhomogeneously broadened Λ transition with multiple excited levels,” Phys. Rev. A 83, 053809 (2011).
[Crossref]

Brandt, S.

R. Wynands, A. Nagel, S. Brandt, D. Meschede, and A. Weis, “Selection rules and line strengths of Zeeman-split dark resonances,” Phys. Rev. A 58, 196 (1998).
[Crossref]

Bretenaker, F.

T. Lauprêtre, S. Schwartz, R. Ghosh, I. Carusotto, F. Goldfarb, and F. Bretenaker, “Anomalous ring-down effects and breakdown of the decay rate concept in optical cavities with negative group delay,” New J. Phys. 14043012 (2012).
[Crossref]

T. Lauprêtre, C. Proux, R. Ghosh, S. Schwartz, F. Goldfarb, and F. Bretenaker, “Photon lifetime in a cavity containing a slow-light medium,” Opt. Lett. 9, 1551–1553 (2011).
[Crossref]

Bruce, G. D.

E. Haller, J. Hudson, A. Kelly, D. A. Cotta, B. Peaudecerf, G. D. Bruce, and S. Kuhr, “Single-atom imaging of fermions in a quantum-gas microscope,” Nat. Phys. 11, 738–742 (2015).
[Crossref]

Budker, D.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153 (2002).
[Crossref]

Burkett, W. H.

H. Wang, D. J. Goorskey, W. H. Burkett, and M. Xiao, “Cavity-linewidth narrowing by means of electromagnetically induced transparency,” Opt. Lett. 23, 1732–1734 (2000).
[Crossref]

Cartaleva, S.

K. Nasyrov, S. Gozzini, A. Lucchesini, C. Marinelli, S. Gateva, S. Cartaleva, and L. Marmugi, “Antirelaxation coatings in coherent spectroscopy: theoretical investigation and experimental test,” Phys. Rev. A 92, 043803 (2015).
[Crossref]

S. Gozzini, S. Cartaleva, A. Lucchesini, C. Marinelli, L. Marmugi, D. Slavov, and T. Karaulanov, “Coherent population trapping and strong electromagnetically induced transparency resonances on the D1 line of potassium,” Eur. Phys. J. D. 53, 153–161 (2009).
[Crossref]

Carusotto, I.

T. Lauprêtre, S. Schwartz, R. Ghosh, I. Carusotto, F. Goldfarb, and F. Bretenaker, “Anomalous ring-down effects and breakdown of the decay rate concept in optical cavities with negative group delay,” New J. Phys. 14043012 (2012).
[Crossref]

Chen, Y.-C.

Y.-C. Chen, C.-W. Lin, and I. A. Yu, “Roles of degenerate Zeeman levels in electromagnetically induced transparency,” Phys. Rev. A 61, 053805 (2000).
[Crossref]

Chen, Z.

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 78–81 (2012).
[Crossref] [PubMed]

J. M. Weiner, K. C. Cox, J. G. Bohnet, Z. Chen, and J. K. Thompson, “Superradiant Raman laser magnetometer,” Appl. Phys. Lett. 101, 261107 (2012).
[Crossref]

Cho, D.

J. M. Choi, J. M. Kim, Q.-H. Park, and D. Cho, “Optically induced Faraday effect in a Λ configuration of spin-polarized cold cesium atoms,” Phys. Rev. A 75, 013815 (2007).
[Crossref]

Choi, J. M.

J. M. Choi, J. M. Kim, Q.-H. Park, and D. Cho, “Optically induced Faraday effect in a Λ configuration of spin-polarized cold cesium atoms,” Phys. Rev. A 75, 013815 (2007).
[Crossref]

Cornish, S. L.

R. K. Hanley, P. D. Gregory, I. G. Hughes, and S. L. Cornish, “Absolute absorption on the potassium D lines: theory and experiment,” J. Phys. B: At. Mol. Opt. Phys. 48, 195004 (2015).
[Crossref]

Corsini, E.

A. Wojciechowski, E. Corsini, J. Zachorowski, and W. Gawlik, “Nonlinear Faraday rotation and detection of superposition states in cold atoms,” Phys. Rev. A 81, 053420 (2010).
[Crossref]

Cotta, D. A.

E. Haller, J. Hudson, A. Kelly, D. A. Cotta, B. Peaudecerf, G. D. Bruce, and S. Kuhr, “Single-atom imaging of fermions in a quantum-gas microscope,” Nat. Phys. 11, 738–742 (2015).
[Crossref]

Cox, K. C.

J. M. Weiner, K. C. Cox, J. G. Bohnet, Z. Chen, and J. K. Thompson, “Superradiant Raman laser magnetometer,” Appl. Phys. Lett. 101, 261107 (2012).
[Crossref]

Day, R.

G. J. A. Edge, R. Anderson, D. Jervis, D. C. McKay, R. Day, S. Trotzky, and J. H. Thywissen, “Imaging and addressing of individual fermionic atoms in an optical lattice,” Phys. Rev. A 92, 063406 (2015).
[Crossref]

DeMarco, B.

W. Xu and B. DeMarco, “Velocity-selective electromagnetically-induced-transparency measurements of potassium Rydberg states,” Phys. Rev. A 93, 011801 (2016).
[Crossref]

Deng, L.

K. Li, L. Deng, and M. G. Payne, “Realization of a single and closed Λ-system in a room-temperature three-level coherently prepared resonant medium with narrow D1 hyperfine splittings,” Appl. Phys. Lett. 95, 221103 (2009).
[Crossref]

Dhat, D.

S. Gu, J. A. Behr, M. N. Groves, and D. Dhat, “Coherent population trapping states with cold atoms in a magnetic field,” Opt. Commun. 220, 365–370 (2003).
[Crossref]

Edge, G. J. A.

G. J. A. Edge, R. Anderson, D. Jervis, D. C. McKay, R. Day, S. Trotzky, and J. H. Thywissen, “Imaging and addressing of individual fermionic atoms in an optical lattice,” Phys. Rev. A 92, 063406 (2015).
[Crossref]

Falke, S.

S. Falke, E. Tiemann, C. Lisdat, H. Schnatz, and G. Grosche, “Transition frequencies of the D lines of 39K, 40K, and 41K measured with a femtosecond laser frequency comb,” Phys. Rev. A 74, 032503 (2006).
[Crossref]

Felinto, D.

O. S. Mishina, M. Scherman, P. Lombardi, J. Ortalo, D. Felinto, A. S. Sheremet, A. Bramati, D. V. Kupriyanov, J. Laurat, and E. Giacobino, “Electromagnetically induced transparency in an inhomogeneously broadened Λ transition with multiple excited levels,” Phys. Rev. A 83, 053809 (2011).
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K. Nasyrov, S. Gozzini, A. Lucchesini, C. Marinelli, S. Gateva, S. Cartaleva, and L. Marmugi, “Antirelaxation coatings in coherent spectroscopy: theoretical investigation and experimental test,” Phys. Rev. A 92, 043803 (2015).
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T. Lauprêtre, S. Schwartz, R. Ghosh, I. Carusotto, F. Goldfarb, and F. Bretenaker, “Anomalous ring-down effects and breakdown of the decay rate concept in optical cavities with negative group delay,” New J. Phys. 14043012 (2012).
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T. Lauprêtre, C. Proux, R. Ghosh, S. Schwartz, F. Goldfarb, and F. Bretenaker, “Photon lifetime in a cavity containing a slow-light medium,” Opt. Lett. 9, 1551–1553 (2011).
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Giacobino, E.

O. S. Mishina, M. Scherman, P. Lombardi, J. Ortalo, D. Felinto, A. S. Sheremet, A. Bramati, D. V. Kupriyanov, J. Laurat, and E. Giacobino, “Electromagnetically induced transparency in an inhomogeneously broadened Λ transition with multiple excited levels,” Phys. Rev. A 83, 053809 (2011).
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Goldfarb, F.

T. Lauprêtre, S. Schwartz, R. Ghosh, I. Carusotto, F. Goldfarb, and F. Bretenaker, “Anomalous ring-down effects and breakdown of the decay rate concept in optical cavities with negative group delay,” New J. Phys. 14043012 (2012).
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T. Lauprêtre, C. Proux, R. Ghosh, S. Schwartz, F. Goldfarb, and F. Bretenaker, “Photon lifetime in a cavity containing a slow-light medium,” Opt. Lett. 9, 1551–1553 (2011).
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H. Wang, D. J. Goorskey, W. H. Burkett, and M. Xiao, “Cavity-linewidth narrowing by means of electromagnetically induced transparency,” Opt. Lett. 23, 1732–1734 (2000).
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M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75, 053807 (2007).
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H. Wang, P. L. Gould, and W. C. Stwalley, “Long-range interaction of the 39K(4s)+39K(4p) asymptote by photoassociative spectroscopy. I. The 0g− pure long-range state and the long-range potential constants,” J. Chem. Phys. 106, 7899 (1997).
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K. Nasyrov, S. Gozzini, A. Lucchesini, C. Marinelli, S. Gateva, S. Cartaleva, and L. Marmugi, “Antirelaxation coatings in coherent spectroscopy: theoretical investigation and experimental test,” Phys. Rev. A 92, 043803 (2015).
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S. Gozzini, S. Cartaleva, A. Lucchesini, C. Marinelli, L. Marmugi, D. Slavov, and T. Karaulanov, “Coherent population trapping and strong electromagnetically induced transparency resonances on the D1 line of potassium,” Eur. Phys. J. D. 53, 153–161 (2009).
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S. Falke, E. Tiemann, C. Lisdat, H. Schnatz, and G. Grosche, “Transition frequencies of the D lines of 39K, 40K, and 41K measured with a femtosecond laser frequency comb,” Phys. Rev. A 74, 032503 (2006).
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S. Gu, J. A. Behr, M. N. Groves, and D. Dhat, “Coherent population trapping states with cold atoms in a magnetic field,” Opt. Commun. 220, 365–370 (2003).
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Haller, E.

E. Haller, J. Hudson, A. Kelly, D. A. Cotta, B. Peaudecerf, G. D. Bruce, and S. Kuhr, “Single-atom imaging of fermions in a quantum-gas microscope,” Nat. Phys. 11, 738–742 (2015).
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R. K. Hanley, P. D. Gregory, I. G. Hughes, and S. L. Cornish, “Absolute absorption on the potassium D lines: theory and experiment,” J. Phys. B: At. Mol. Opt. Phys. 48, 195004 (2015).
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K-J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
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Holland, M. J.

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 78–81 (2012).
[Crossref] [PubMed]

Hombo, N.

Hudson, J.

E. Haller, J. Hudson, A. Kelly, D. A. Cotta, B. Peaudecerf, G. D. Bruce, and S. Kuhr, “Single-atom imaging of fermions in a quantum-gas microscope,” Nat. Phys. 11, 738–742 (2015).
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K. A. Whittaker, J. Keaveney, I. G. Hughes, and C. S. Adams, “Hilbert transform: applications to atomic spectra,” Phys. Rev. A 91, 032513 (2015).
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R. K. Hanley, P. D. Gregory, I. G. Hughes, and S. L. Cornish, “Absolute absorption on the potassium D lines: theory and experiment,” J. Phys. B: At. Mol. Opt. Phys. 48, 195004 (2015).
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Hussein, Z.

O. Schmidt, R. Wynands, Z. Hussein, and D. Meschede, “Steep dispersion and group velocity below c/ 3000 in coherent population trapping,” Phys. Rev. A 53, R27 (1996).
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Iftiquar, S. M.

S. M. Iftiquar and V. Natarajan, “Line narrowing of electromagnetically induced transparency in Rb with a longitudinal magnetic field,” Phys. Rev. A 79, 013808 (2009).
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Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633 (2005).
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K-J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
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Jervis, D.

G. J. A. Edge, R. Anderson, D. Jervis, D. C. McKay, R. Day, S. Trotzky, and J. H. Thywissen, “Imaging and addressing of individual fermionic atoms in an optical lattice,” Phys. Rev. A 92, 063406 (2015).
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Jiang, Y.

X. Wei, J. Wu, G. Sun, Z. Shao, Z. Kang, Y. Jiang, and J. Gao, “Splitting of an electromagnetically induced transparency window of rubidium atoms in a static magnetic field,” Phys. Rev. A 72, 023806 (2005).
[Crossref]

Kang, Z.

X. Wei, J. Wu, G. Sun, Z. Shao, Z. Kang, Y. Jiang, and J. Gao, “Splitting of an electromagnetically induced transparency window of rubidium atoms in a static magnetic field,” Phys. Rev. A 72, 023806 (2005).
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Karaulanov, T.

S. Gozzini, S. Cartaleva, A. Lucchesini, C. Marinelli, L. Marmugi, D. Slavov, and T. Karaulanov, “Coherent population trapping and strong electromagnetically induced transparency resonances on the D1 line of potassium,” Eur. Phys. J. D. 53, 153–161 (2009).
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K. A. Whittaker, J. Keaveney, I. G. Hughes, and C. S. Adams, “Hilbert transform: applications to atomic spectra,” Phys. Rev. A 91, 032513 (2015).
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Kelly, A.

E. Haller, J. Hudson, A. Kelly, D. A. Cotta, B. Peaudecerf, G. D. Bruce, and S. Kuhr, “Single-atom imaging of fermions in a quantum-gas microscope,” Nat. Phys. 11, 738–742 (2015).
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Kim, J. M.

J. M. Choi, J. M. Kim, Q.-H. Park, and D. Cho, “Optically induced Faraday effect in a Λ configuration of spin-polarized cold cesium atoms,” Phys. Rev. A 75, 013815 (2007).
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Kimball, D. F.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153 (2002).
[Crossref]

Kuhr, S.

E. Haller, J. Hudson, A. Kelly, D. A. Cotta, B. Peaudecerf, G. D. Bruce, and S. Kuhr, “Single-atom imaging of fermions in a quantum-gas microscope,” Nat. Phys. 11, 738–742 (2015).
[Crossref]

Kupriyanov, D. V.

O. S. Mishina, M. Scherman, P. Lombardi, J. Ortalo, D. Felinto, A. S. Sheremet, A. Bramati, D. V. Kupriyanov, J. Laurat, and E. Giacobino, “Electromagnetically induced transparency in an inhomogeneously broadened Λ transition with multiple excited levels,” Phys. Rev. A 83, 053809 (2011).
[Crossref]

Lauprêtre, T.

T. Lauprêtre, S. Schwartz, R. Ghosh, I. Carusotto, F. Goldfarb, and F. Bretenaker, “Anomalous ring-down effects and breakdown of the decay rate concept in optical cavities with negative group delay,” New J. Phys. 14043012 (2012).
[Crossref]

T. Lauprêtre, C. Proux, R. Ghosh, S. Schwartz, F. Goldfarb, and F. Bretenaker, “Photon lifetime in a cavity containing a slow-light medium,” Opt. Lett. 9, 1551–1553 (2011).
[Crossref]

Laurat, J.

O. S. Mishina, M. Scherman, P. Lombardi, J. Ortalo, D. Felinto, A. S. Sheremet, A. Bramati, D. V. Kupriyanov, J. Laurat, and E. Giacobino, “Electromagnetically induced transparency in an inhomogeneously broadened Λ transition with multiple excited levels,” Phys. Rev. A 83, 053809 (2011).
[Crossref]

Li, K.

K. Li, L. Deng, and M. G. Payne, “Realization of a single and closed Λ-system in a room-temperature three-level coherently prepared resonant medium with narrow D1 hyperfine splittings,” Appl. Phys. Lett. 95, 221103 (2009).
[Crossref]

Li, S.

B. Wang, S. Li, J. Ma, H. Wang, K. C. Peng, and M. Xiao, “Controlling the polarization rotation of an optical field via asymmetry in electromagnetically induced transparency,” Phys. Rev. A 73, 051801 (2006)
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Y.-C. Chen, C.-W. Lin, and I. A. Yu, “Roles of degenerate Zeeman levels in electromagnetically induced transparency,” Phys. Rev. A 61, 053805 (2000).
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Lisdat, C.

S. Falke, E. Tiemann, C. Lisdat, H. Schnatz, and G. Grosche, “Transition frequencies of the D lines of 39K, 40K, and 41K measured with a femtosecond laser frequency comb,” Phys. Rev. A 74, 032503 (2006).
[Crossref]

Lombardi, P.

O. S. Mishina, M. Scherman, P. Lombardi, J. Ortalo, D. Felinto, A. S. Sheremet, A. Bramati, D. V. Kupriyanov, J. Laurat, and E. Giacobino, “Electromagnetically induced transparency in an inhomogeneously broadened Λ transition with multiple excited levels,” Phys. Rev. A 83, 053809 (2011).
[Crossref]

Lucchesini, A.

K. Nasyrov, S. Gozzini, A. Lucchesini, C. Marinelli, S. Gateva, S. Cartaleva, and L. Marmugi, “Antirelaxation coatings in coherent spectroscopy: theoretical investigation and experimental test,” Phys. Rev. A 92, 043803 (2015).
[Crossref]

S. Gozzini, S. Cartaleva, A. Lucchesini, C. Marinelli, L. Marmugi, D. Slavov, and T. Karaulanov, “Coherent population trapping and strong electromagnetically induced transparency resonances on the D1 line of potassium,” Eur. Phys. J. D. 53, 153–161 (2009).
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M. D. Lukin, “Colloquium: trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. 75, 457 (2003).
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Ma, J.

B. Wang, S. Li, J. Ma, H. Wang, K. C. Peng, and M. Xiao, “Controlling the polarization rotation of an optical field via asymmetry in electromagnetically induced transparency,” Phys. Rev. A 73, 051801 (2006)
[Crossref]

Marangos, J. P.

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

Marinelli, C.

K. Nasyrov, S. Gozzini, A. Lucchesini, C. Marinelli, S. Gateva, S. Cartaleva, and L. Marmugi, “Antirelaxation coatings in coherent spectroscopy: theoretical investigation and experimental test,” Phys. Rev. A 92, 043803 (2015).
[Crossref]

S. Gozzini, S. Cartaleva, A. Lucchesini, C. Marinelli, L. Marmugi, D. Slavov, and T. Karaulanov, “Coherent population trapping and strong electromagnetically induced transparency resonances on the D1 line of potassium,” Eur. Phys. J. D. 53, 153–161 (2009).
[Crossref]

Marmugi, L.

K. Nasyrov, S. Gozzini, A. Lucchesini, C. Marinelli, S. Gateva, S. Cartaleva, and L. Marmugi, “Antirelaxation coatings in coherent spectroscopy: theoretical investigation and experimental test,” Phys. Rev. A 92, 043803 (2015).
[Crossref]

S. Gozzini, S. Cartaleva, A. Lucchesini, C. Marinelli, L. Marmugi, D. Slavov, and T. Karaulanov, “Coherent population trapping and strong electromagnetically induced transparency resonances on the D1 line of potassium,” Eur. Phys. J. D. 53, 153–161 (2009).
[Crossref]

McKay, D. C.

G. J. A. Edge, R. Anderson, D. Jervis, D. C. McKay, R. Day, S. Trotzky, and J. H. Thywissen, “Imaging and addressing of individual fermionic atoms in an optical lattice,” Phys. Rev. A 92, 063406 (2015).
[Crossref]

Meiser, D.

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 78–81 (2012).
[Crossref] [PubMed]

Meschede, D.

R. Wynands, A. Nagel, S. Brandt, D. Meschede, and A. Weis, “Selection rules and line strengths of Zeeman-split dark resonances,” Phys. Rev. A 58, 196 (1998).
[Crossref]

O. Schmidt, R. Wynands, Z. Hussein, and D. Meschede, “Steep dispersion and group velocity below c/ 3000 in coherent population trapping,” Phys. Rev. A 53, R27 (1996).
[Crossref]

Messall, M.

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75, 053807 (2007).
[Crossref]

Mishina, O. S.

O. S. Mishina, M. Scherman, P. Lombardi, J. Ortalo, D. Felinto, A. S. Sheremet, A. Bramati, D. V. Kupriyanov, J. Laurat, and E. Giacobino, “Electromagnetically induced transparency in an inhomogeneously broadened Λ transition with multiple excited levels,” Phys. Rev. A 83, 053809 (2011).
[Crossref]

Mitsunaga, M.

Nagel, A.

R. Wynands, A. Nagel, S. Brandt, D. Meschede, and A. Weis, “Selection rules and line strengths of Zeeman-split dark resonances,” Phys. Rev. A 58, 196 (1998).
[Crossref]

Nasyrov, K.

K. Nasyrov, S. Gozzini, A. Lucchesini, C. Marinelli, S. Gateva, S. Cartaleva, and L. Marmugi, “Antirelaxation coatings in coherent spectroscopy: theoretical investigation and experimental test,” Phys. Rev. A 92, 043803 (2015).
[Crossref]

Natarajan, V.

S. M. Iftiquar and V. Natarajan, “Line narrowing of electromagnetically induced transparency in Rb with a longitudinal magnetic field,” Phys. Rev. A 79, 013808 (2009).
[Crossref]

Ortalo, J.

O. S. Mishina, M. Scherman, P. Lombardi, J. Ortalo, D. Felinto, A. S. Sheremet, A. Bramati, D. V. Kupriyanov, J. Laurat, and E. Giacobino, “Electromagnetically induced transparency in an inhomogeneously broadened Λ transition with multiple excited levels,” Phys. Rev. A 83, 053809 (2011).
[Crossref]

Park, Q.-H.

J. M. Choi, J. M. Kim, Q.-H. Park, and D. Cho, “Optically induced Faraday effect in a Λ configuration of spin-polarized cold cesium atoms,” Phys. Rev. A 75, 013815 (2007).
[Crossref]

Pati, G. S.

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett. 99, 133601 (2007).
[Crossref] [PubMed]

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75, 053807 (2007).
[Crossref]

Payne, M. G.

K. Li, L. Deng, and M. G. Payne, “Realization of a single and closed Λ-system in a room-temperature three-level coherently prepared resonant medium with narrow D1 hyperfine splittings,” Appl. Phys. Lett. 95, 221103 (2009).
[Crossref]

Peaudecerf, B.

E. Haller, J. Hudson, A. Kelly, D. A. Cotta, B. Peaudecerf, G. D. Bruce, and S. Kuhr, “Single-atom imaging of fermions in a quantum-gas microscope,” Nat. Phys. 11, 738–742 (2015).
[Crossref]

Peng, K. C.

B. Wang, S. Li, J. Ma, H. Wang, K. C. Peng, and M. Xiao, “Controlling the polarization rotation of an optical field via asymmetry in electromagnetically induced transparency,” Phys. Rev. A 73, 051801 (2006)
[Crossref]

Petrov, P. A.

A. Sargsyan, P. A. Petrov, T. A. Vartanyan, and D. Sarkisyan, “Electromagnetically induced transparency in potassium vapors: features and restrictions,” Opt. Spectrosc. 120, 339–344 (2015).
[Crossref]

Proux, C.

T. Lauprêtre, C. Proux, R. Ghosh, S. Schwartz, F. Goldfarb, and F. Bretenaker, “Photon lifetime in a cavity containing a slow-light medium,” Opt. Lett. 9, 1551–1553 (2011).
[Crossref]

Rochester, S. M.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153 (2002).
[Crossref]

Salit, K.

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett. 99, 133601 (2007).
[Crossref] [PubMed]

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75, 053807 (2007).
[Crossref]

Salit, M.

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett. 99, 133601 (2007).
[Crossref] [PubMed]

Sargsyan, A.

A. Sargsyan, P. A. Petrov, T. A. Vartanyan, and D. Sarkisyan, “Electromagnetically induced transparency in potassium vapors: features and restrictions,” Opt. Spectrosc. 120, 339–344 (2015).
[Crossref]

Sarkisyan, D.

A. Sargsyan, P. A. Petrov, T. A. Vartanyan, and D. Sarkisyan, “Electromagnetically induced transparency in potassium vapors: features and restrictions,” Opt. Spectrosc. 120, 339–344 (2015).
[Crossref]

Scherman, M.

O. S. Mishina, M. Scherman, P. Lombardi, J. Ortalo, D. Felinto, A. S. Sheremet, A. Bramati, D. V. Kupriyanov, J. Laurat, and E. Giacobino, “Electromagnetically induced transparency in an inhomogeneously broadened Λ transition with multiple excited levels,” Phys. Rev. A 83, 053809 (2011).
[Crossref]

Schmidt, O.

O. Schmidt, R. Wynands, Z. Hussein, and D. Meschede, “Steep dispersion and group velocity below c/ 3000 in coherent population trapping,” Phys. Rev. A 53, R27 (1996).
[Crossref]

Schnatz, H.

S. Falke, E. Tiemann, C. Lisdat, H. Schnatz, and G. Grosche, “Transition frequencies of the D lines of 39K, 40K, and 41K measured with a femtosecond laser frequency comb,” Phys. Rev. A 74, 032503 (2006).
[Crossref]

Schwartz, S.

T. Lauprêtre, S. Schwartz, R. Ghosh, I. Carusotto, F. Goldfarb, and F. Bretenaker, “Anomalous ring-down effects and breakdown of the decay rate concept in optical cavities with negative group delay,” New J. Phys. 14043012 (2012).
[Crossref]

T. Lauprêtre, C. Proux, R. Ghosh, S. Schwartz, F. Goldfarb, and F. Bretenaker, “Photon lifetime in a cavity containing a slow-light medium,” Opt. Lett. 9, 1551–1553 (2011).
[Crossref]

Shahriar, M. S.

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett. 99, 133601 (2007).
[Crossref] [PubMed]

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75, 053807 (2007).
[Crossref]

Shao, Z.

X. Wei, J. Wu, G. Sun, Z. Shao, Z. Kang, Y. Jiang, and J. Gao, “Splitting of an electromagnetically induced transparency window of rubidium atoms in a static magnetic field,” Phys. Rev. A 72, 023806 (2005).
[Crossref]

Sheremet, A. S.

O. S. Mishina, M. Scherman, P. Lombardi, J. Ortalo, D. Felinto, A. S. Sheremet, A. Bramati, D. V. Kupriyanov, J. Laurat, and E. Giacobino, “Electromagnetically induced transparency in an inhomogeneously broadened Λ transition with multiple excited levels,” Phys. Rev. A 83, 053809 (2011).
[Crossref]

Slavov, D.

S. Gozzini, S. Cartaleva, A. Lucchesini, C. Marinelli, L. Marmugi, D. Slavov, and T. Karaulanov, “Coherent population trapping and strong electromagnetically induced transparency resonances on the D1 line of potassium,” Eur. Phys. J. D. 53, 153–161 (2009).
[Crossref]

Stwalley, W. C.

H. Wang, P. L. Gould, and W. C. Stwalley, “Long-range interaction of the 39K(4s)+39K(4p) asymptote by photoassociative spectroscopy. I. The 0g− pure long-range state and the long-range potential constants,” J. Chem. Phys. 106, 7899 (1997).
[Crossref]

Sugimura, S.

Sun, G.

X. Wei, J. Wu, G. Sun, Z. Shao, Z. Kang, Y. Jiang, and J. Gao, “Splitting of an electromagnetically induced transparency window of rubidium atoms in a static magnetic field,” Phys. Rev. A 72, 023806 (2005).
[Crossref]

Taniguchi, S.

Thompson, J. K.

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 78–81 (2012).
[Crossref] [PubMed]

J. M. Weiner, K. C. Cox, J. G. Bohnet, Z. Chen, and J. K. Thompson, “Superradiant Raman laser magnetometer,” Appl. Phys. Lett. 101, 261107 (2012).
[Crossref]

Thywissen, J. H.

G. J. A. Edge, R. Anderson, D. Jervis, D. C. McKay, R. Day, S. Trotzky, and J. H. Thywissen, “Imaging and addressing of individual fermionic atoms in an optical lattice,” Phys. Rev. A 92, 063406 (2015).
[Crossref]

Tiemann, E.

S. Falke, E. Tiemann, C. Lisdat, H. Schnatz, and G. Grosche, “Transition frequencies of the D lines of 39K, 40K, and 41K measured with a femtosecond laser frequency comb,” Phys. Rev. A 74, 032503 (2006).
[Crossref]

Tripathi, R.

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75, 053807 (2007).
[Crossref]

Trotzky, S.

G. J. A. Edge, R. Anderson, D. Jervis, D. C. McKay, R. Day, S. Trotzky, and J. H. Thywissen, “Imaging and addressing of individual fermionic atoms in an optical lattice,” Phys. Rev. A 92, 063406 (2015).
[Crossref]

Vanier, J.

J. Vanier, “Atomic clocks based on coherent population trapping: a review,” Appl. Phys. B 81, 421 (2005).
[Crossref]

Vartanyan, T. A.

A. Sargsyan, P. A. Petrov, T. A. Vartanyan, and D. Sarkisyan, “Electromagnetically induced transparency in potassium vapors: features and restrictions,” Opt. Spectrosc. 120, 339–344 (2015).
[Crossref]

Wang, B.

B. Wang, S. Li, J. Ma, H. Wang, K. C. Peng, and M. Xiao, “Controlling the polarization rotation of an optical field via asymmetry in electromagnetically induced transparency,” Phys. Rev. A 73, 051801 (2006)
[Crossref]

Wang, H.

B. Wang, S. Li, J. Ma, H. Wang, K. C. Peng, and M. Xiao, “Controlling the polarization rotation of an optical field via asymmetry in electromagnetically induced transparency,” Phys. Rev. A 73, 051801 (2006)
[Crossref]

H. Wang, D. J. Goorskey, W. H. Burkett, and M. Xiao, “Cavity-linewidth narrowing by means of electromagnetically induced transparency,” Opt. Lett. 23, 1732–1734 (2000).
[Crossref]

H. Wang, P. L. Gould, and W. C. Stwalley, “Long-range interaction of the 39K(4s)+39K(4p) asymptote by photoassociative spectroscopy. I. The 0g− pure long-range state and the long-range potential constants,” J. Chem. Phys. 106, 7899 (1997).
[Crossref]

Wei, X.

X. Wei, J. Wu, G. Sun, Z. Shao, Z. Kang, Y. Jiang, and J. Gao, “Splitting of an electromagnetically induced transparency window of rubidium atoms in a static magnetic field,” Phys. Rev. A 72, 023806 (2005).
[Crossref]

Weiner, J. M.

J. M. Weiner, K. C. Cox, J. G. Bohnet, Z. Chen, and J. K. Thompson, “Superradiant Raman laser magnetometer,” Appl. Phys. Lett. 101, 261107 (2012).
[Crossref]

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 78–81 (2012).
[Crossref] [PubMed]

Weis, A.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153 (2002).
[Crossref]

R. Wynands, A. Nagel, S. Brandt, D. Meschede, and A. Weis, “Selection rules and line strengths of Zeeman-split dark resonances,” Phys. Rev. A 58, 196 (1998).
[Crossref]

Whittaker, K. A.

K. A. Whittaker, J. Keaveney, I. G. Hughes, and C. S. Adams, “Hilbert transform: applications to atomic spectra,” Phys. Rev. A 91, 032513 (2015).
[Crossref]

Wojciechowski, A.

A. Wojciechowski, E. Corsini, J. Zachorowski, and W. Gawlik, “Nonlinear Faraday rotation and detection of superposition states in cold atoms,” Phys. Rev. A 81, 053420 (2010).
[Crossref]

Wu, J.

X. Wei, J. Wu, G. Sun, Z. Shao, Z. Kang, Y. Jiang, and J. Gao, “Splitting of an electromagnetically induced transparency window of rubidium atoms in a static magnetic field,” Phys. Rev. A 72, 023806 (2005).
[Crossref]

Wynands, R.

R. Wynands, A. Nagel, S. Brandt, D. Meschede, and A. Weis, “Selection rules and line strengths of Zeeman-split dark resonances,” Phys. Rev. A 58, 196 (1998).
[Crossref]

O. Schmidt, R. Wynands, Z. Hussein, and D. Meschede, “Steep dispersion and group velocity below c/ 3000 in coherent population trapping,” Phys. Rev. A 53, R27 (1996).
[Crossref]

Xiao, M.

B. Wang, S. Li, J. Ma, H. Wang, K. C. Peng, and M. Xiao, “Controlling the polarization rotation of an optical field via asymmetry in electromagnetically induced transparency,” Phys. Rev. A 73, 051801 (2006)
[Crossref]

H. Wang, D. J. Goorskey, W. H. Burkett, and M. Xiao, “Cavity-linewidth narrowing by means of electromagnetically induced transparency,” Opt. Lett. 23, 1732–1734 (2000).
[Crossref]

Xu, W.

W. Xu and B. DeMarco, “Velocity-selective electromagnetically-induced-transparency measurements of potassium Rydberg states,” Phys. Rev. A 93, 011801 (2016).
[Crossref]

Yashchuk, V. V.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153 (2002).
[Crossref]

Yu, I. A.

Y.-C. Chen, C.-W. Lin, and I. A. Yu, “Roles of degenerate Zeeman levels in electromagnetically induced transparency,” Phys. Rev. A 61, 053805 (2000).
[Crossref]

Zachorowski, J.

A. Wojciechowski, E. Corsini, J. Zachorowski, and W. Gawlik, “Nonlinear Faraday rotation and detection of superposition states in cold atoms,” Phys. Rev. A 81, 053420 (2010).
[Crossref]

Zeilinger, A.

S. Franke-Arnold, M. Arndt, and A. Zeilinger, “Magneto-optical effects with cold lithium atoms,” J. Phys. B: At. Mol. Opt. Phys. 342527 (2001).
[Crossref]

Appl. Phys. B (1)

J. Vanier, “Atomic clocks based on coherent population trapping: a review,” Appl. Phys. B 81, 421 (2005).
[Crossref]

Appl. Phys. Lett. (2)

K. Li, L. Deng, and M. G. Payne, “Realization of a single and closed Λ-system in a room-temperature three-level coherently prepared resonant medium with narrow D1 hyperfine splittings,” Appl. Phys. Lett. 95, 221103 (2009).
[Crossref]

J. M. Weiner, K. C. Cox, J. G. Bohnet, Z. Chen, and J. K. Thompson, “Superradiant Raman laser magnetometer,” Appl. Phys. Lett. 101, 261107 (2012).
[Crossref]

Eur. Phys. J. D. (1)

S. Gozzini, S. Cartaleva, A. Lucchesini, C. Marinelli, L. Marmugi, D. Slavov, and T. Karaulanov, “Coherent population trapping and strong electromagnetically induced transparency resonances on the D1 line of potassium,” Eur. Phys. J. D. 53, 153–161 (2009).
[Crossref]

J. Chem. Phys. (1)

H. Wang, P. L. Gould, and W. C. Stwalley, “Long-range interaction of the 39K(4s)+39K(4p) asymptote by photoassociative spectroscopy. I. The 0g− pure long-range state and the long-range potential constants,” J. Chem. Phys. 106, 7899 (1997).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. B: At. Mol. Opt. Phys. (2)

R. K. Hanley, P. D. Gregory, I. G. Hughes, and S. L. Cornish, “Absolute absorption on the potassium D lines: theory and experiment,” J. Phys. B: At. Mol. Opt. Phys. 48, 195004 (2015).
[Crossref]

S. Franke-Arnold, M. Arndt, and A. Zeilinger, “Magneto-optical effects with cold lithium atoms,” J. Phys. B: At. Mol. Opt. Phys. 342527 (2001).
[Crossref]

Nat. Phys. (1)

E. Haller, J. Hudson, A. Kelly, D. A. Cotta, B. Peaudecerf, G. D. Bruce, and S. Kuhr, “Single-atom imaging of fermions in a quantum-gas microscope,” Nat. Phys. 11, 738–742 (2015).
[Crossref]

Nature (1)

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 78–81 (2012).
[Crossref] [PubMed]

New J. Phys. (1)

T. Lauprêtre, S. Schwartz, R. Ghosh, I. Carusotto, F. Goldfarb, and F. Bretenaker, “Anomalous ring-down effects and breakdown of the decay rate concept in optical cavities with negative group delay,” New J. Phys. 14043012 (2012).
[Crossref]

Opt. Commun. (1)

S. Gu, J. A. Behr, M. N. Groves, and D. Dhat, “Coherent population trapping states with cold atoms in a magnetic field,” Opt. Commun. 220, 365–370 (2003).
[Crossref]

Opt. Lett. (2)

T. Lauprêtre, C. Proux, R. Ghosh, S. Schwartz, F. Goldfarb, and F. Bretenaker, “Photon lifetime in a cavity containing a slow-light medium,” Opt. Lett. 9, 1551–1553 (2011).
[Crossref]

H. Wang, D. J. Goorskey, W. H. Burkett, and M. Xiao, “Cavity-linewidth narrowing by means of electromagnetically induced transparency,” Opt. Lett. 23, 1732–1734 (2000).
[Crossref]

Opt. Spectrosc. (1)

A. Sargsyan, P. A. Petrov, T. A. Vartanyan, and D. Sarkisyan, “Electromagnetically induced transparency in potassium vapors: features and restrictions,” Opt. Spectrosc. 120, 339–344 (2015).
[Crossref]

Phys. Rev. A (15)

K. Nasyrov, S. Gozzini, A. Lucchesini, C. Marinelli, S. Gateva, S. Cartaleva, and L. Marmugi, “Antirelaxation coatings in coherent spectroscopy: theoretical investigation and experimental test,” Phys. Rev. A 92, 043803 (2015).
[Crossref]

G. J. A. Edge, R. Anderson, D. Jervis, D. C. McKay, R. Day, S. Trotzky, and J. H. Thywissen, “Imaging and addressing of individual fermionic atoms in an optical lattice,” Phys. Rev. A 92, 063406 (2015).
[Crossref]

W. Xu and B. DeMarco, “Velocity-selective electromagnetically-induced-transparency measurements of potassium Rydberg states,” Phys. Rev. A 93, 011801 (2016).
[Crossref]

S. Falke, E. Tiemann, C. Lisdat, H. Schnatz, and G. Grosche, “Transition frequencies of the D lines of 39K, 40K, and 41K measured with a femtosecond laser frequency comb,” Phys. Rev. A 74, 032503 (2006).
[Crossref]

K. A. Whittaker, J. Keaveney, I. G. Hughes, and C. S. Adams, “Hilbert transform: applications to atomic spectra,” Phys. Rev. A 91, 032513 (2015).
[Crossref]

O. Schmidt, R. Wynands, Z. Hussein, and D. Meschede, “Steep dispersion and group velocity below c/ 3000 in coherent population trapping,” Phys. Rev. A 53, R27 (1996).
[Crossref]

R. Wynands, A. Nagel, S. Brandt, D. Meschede, and A. Weis, “Selection rules and line strengths of Zeeman-split dark resonances,” Phys. Rev. A 58, 196 (1998).
[Crossref]

X. Wei, J. Wu, G. Sun, Z. Shao, Z. Kang, Y. Jiang, and J. Gao, “Splitting of an electromagnetically induced transparency window of rubidium atoms in a static magnetic field,” Phys. Rev. A 72, 023806 (2005).
[Crossref]

S. M. Iftiquar and V. Natarajan, “Line narrowing of electromagnetically induced transparency in Rb with a longitudinal magnetic field,” Phys. Rev. A 79, 013808 (2009).
[Crossref]

O. S. Mishina, M. Scherman, P. Lombardi, J. Ortalo, D. Felinto, A. S. Sheremet, A. Bramati, D. V. Kupriyanov, J. Laurat, and E. Giacobino, “Electromagnetically induced transparency in an inhomogeneously broadened Λ transition with multiple excited levels,” Phys. Rev. A 83, 053809 (2011).
[Crossref]

J. M. Choi, J. M. Kim, Q.-H. Park, and D. Cho, “Optically induced Faraday effect in a Λ configuration of spin-polarized cold cesium atoms,” Phys. Rev. A 75, 013815 (2007).
[Crossref]

A. Wojciechowski, E. Corsini, J. Zachorowski, and W. Gawlik, “Nonlinear Faraday rotation and detection of superposition states in cold atoms,” Phys. Rev. A 81, 053420 (2010).
[Crossref]

B. Wang, S. Li, J. Ma, H. Wang, K. C. Peng, and M. Xiao, “Controlling the polarization rotation of an optical field via asymmetry in electromagnetically induced transparency,” Phys. Rev. A 73, 051801 (2006)
[Crossref]

Y.-C. Chen, C.-W. Lin, and I. A. Yu, “Roles of degenerate Zeeman levels in electromagnetically induced transparency,” Phys. Rev. A 61, 053805 (2000).
[Crossref]

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75, 053807 (2007).
[Crossref]

Phys. Rev. Lett. (2)

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett. 99, 133601 (2007).
[Crossref] [PubMed]

K-J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
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Rev. Mod. Phys. (3)

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

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

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153 (2002).
[Crossref]

Other (3)

D. A. Steck, Classical and Modern Optics, available online at http://steck.us/teaching (revision 1.5.2, 28June2015).

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Figures (5)

Fig. 1
Fig. 1 (a) Simplified energy schematic of the D1 hyperfine transitions of 39K used in this work. The coupling beam field Ec (red) is detuned by ∆ from the excited state F′ = 2 manifold (F′ = 1 has been omitted for clarity), and the probe (Ep, blue) is detuned by δ from Raman resonance. The ground state hyperfine splitting is taken from [13]. (b) Saturated absorption spectrum with no coupling beam present, showing the transitions in (a) and the background Doppler profile. The partially resolved features include excited state crossover resonances, and the transmission dips between manifolds are due to ground state crossovers. (c) Experimental layout, as described in the text. ECDL: external cavity diode laser; M: mirror; HWP: half-wave plate; QWP: quarter-wave plate; PBS: polarizing beam splitter; AOM: acousto-optic modulator; BB: beam block; PMF: polarization-maintaining fiber; PD: photodiode.
Fig. 2
Fig. 2 Absorption and group index. (a) Fractional transmission spectra T(ωp) for coupling (probe) power of 300 (50) µW and a cell temperature of 84°C. The background absorption coefficient is varied by coarse tuning of the laser, as described in the text. The EIT linewidth is {2π × 96,98,72} kHz for trace {A,B,C}, and the amplitude is {16,3,8} %. (b) Effect of optical depth on the group index. For each cell temperature, the group index is measured for varying laser detuning ∆, leading to varying background probe absorption (i.e., just outside the EIT resonance). The upper branches correspond to probing on the blue side of the Doppler profile near the Fp → F′ transitions, and the bottom halves on the red side near Fc → F′. The solid line shows the linear dependence expected for simple EIT.
Fig. 3
Fig. 3 Simplified schematic for heterodyne measurements of optical anisotropy. The quarter-wave plate and PBS act together as a circularly polarizing beam splitter according to Eq. (3). The probe and coupling beam components interfere at the fast photodiodes A and B, and the resulting beat notes are used as inputs to a gain/phase detecting circuit (EVAL) as described in the text.
Fig. 4
Fig. 4 Heterodyne spectra of magneto-optically induced anisotropy. Red (blue) traces show the results for lin‖lin (lin⊥lin) polarizations; ∆α is the differential absorption coefficient, ∆ϕ is the phase difference (obtained by Hilbert transformation of ∆α), and ∆ng is the group index difference obtained by numerical differentiation of ∆ϕ after smoothing with a cubic Savitzky-Golay filter (implemented in Matlab using the sgolayfilt command).
Fig. 5
Fig. 5 Theoretical spectra, calculated using Eqs. (10)(13). Parameters are ∆ = 0, Ω c = 2π ×10 MHz, Γ = 2π ×0.18 MHz, and N = 1.5×1011 cm 3 (we expect 1.8×1011 cm 3 for our temperature [30]).

Equations (14)

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n g = n + ω p d n d ω p .
T ( ω p ) = exp [ α ( ω p ) L ] .
e r e l } QWP { e v e i π / 4 e h e i π / 4 ,
E p ( after cell ) = E p e i ω p t 2 ( e r e α r L / 2 e i ϕ r + e l e α l L / 2 e i ϕ l ) ,
E p ( after QWP ) = E p e i w p t 2 [ e v e α r L / 2 e i ( ϕ r π / 4 ) + e h e α l L / 2 e i ( ϕ r + π / 4 ) ]
E c ( after QWP ) = E c e i ω c t 2 [ e ν e α c L / 2 e i π / 4 + e h e α c L / 2 e ± i π / 4 ] ,
LHC ( h after PBS ) = E p E c e ( α l + α c ) L / 2 cos sin ( δ ω t ϕ l )
RHC ( v after PBS ) = ± E p E c e ( α r + α c ) L / 2 cos sin ( δ ω t ϕ r ) ,
amplitude ratio: V G = 0.9 V 0.6 V ( Δ α L 2 ln 10 )
phase difference: V φ = 0.9 V 1.8 V ( | Δ ϕ | π / 2 π ) .
χ = i N d p 2 ε 0 1 2 Γ i δ | 1 2 Ω c | 2 + ( 1 2 Γ i δ ) [ γ i ( δ + Δ ) ] .
δ δ + μ B B [ g F p m p g F c ( m p + q p q c ) ]
( δ + Δ ) ( δ + Δ ) + Δ F + μ B B [ g F p m p g F ( m p + q p ) ]
Δ χ = χ 1 χ + 1 = { ( χ 1 + 1 + χ 1 1 ) ( χ + 1 1 + χ + 1 + 1 ) , lin lin ( χ 1 + 1 χ 1 1 ) ( χ + 1 1 χ + 1 + 1 ) , lin lin .

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