Abstract

We study the spectral features and phase of four-wave mixing (FWM) light according to the relative phase-noise of the optical fields coupled to a double Λ-type atomic system of the 5S1/2–5P1/2 transition of 87Rb atoms. We observe that the spectral shape of the FWM spectrum is identical to that of the two-photon absorption (TPA) spectrum due to two-photon coherence and that it is independent of the relative phase-noise of the pump light. From these results, we clarify that the two-photon coherence plays a very important role in the FWM process. Furthermore, we measure the relative linewidth of the FWM signal to the probe and pump lasers by means of a beat interferometer. We confirmed that the phase of the FWM signal is strongly correlated with that of the pump laser under the condition of phase-locked probe and coupling lasers for two-photon coherence.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  18. R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009).
    [Crossref]
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    [Crossref] [PubMed]
  20. L. Zhao, X. Guo, Y. Sun, Y. Su, M. M. T. Loy, and S. Du, “Shaping the biphoton temporal waveform with spatial light modulation,” Phys. Rev. Lett. 115(19), 193601 (2015).
    [Crossref] [PubMed]
  21. P. Qian, Z. Gu, R. Cao, R. Wen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Temporal purity and quantum interference of single photons from two independent cold atomic ensembles,” Phys. Rev. Lett. 117(1), 013602 (2016).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  24. I.-H. Bae, H. J. Lee, and H. S. Moon, “Electromagnetically induced transparency with variable fluctuation time of photon number of pseudothermal probe light,” J. Opt. Soc. Am. B 28(6), 1578–1582 (2011).
    [Crossref]
  25. Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009).
    [Crossref] [PubMed]
  26. N. B. Phillips, A. V. Gorshkov, and I. Novikova, “Light storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four wave mixing,” Phys. Rev. A 83(6), 063823 (2011).
    [Crossref]
  27. Y.-F. Hsiao, P.-J. Tsai, C.-C. Lin, Y.-F. Chen, I. A. Yu, and Y.-C. Chen, “Coherence properties of amplified slow light by four-wave mixing,” Opt. Lett. 39(12), 3394–3397 (2014).
    [Crossref] [PubMed]
  28. A. M. Akulshin, R. J. McLean, A. I. Sidorov, and P. Hannaford, “Probing degenerate two-level atomic media by coherent optical heterodyning,” J. Phys. At. Mol. Opt. Phys. 44(17), 175502 (2011).
    [Crossref]
  29. A. M. Akulshin and R. J. McLean, “Distinguishing coherent atomic processes using wave mixing,” Phys. Rev. A 85(6), 065802 (2012).
    [Crossref]
  30. Y.-S. Lee and H. S. Moon, “Atomic coherence effects in four-wave mixing process of a ladder-type atomic system,” Opt. Express 24(10), 10723–10732 (2016).
    [Crossref] [PubMed]
  31. D. J. Whiting, E. Bimbard, J. Keaveney, M. A. Zentile, C. S. Adams, and I. G. Hughes, “Electromagnetically induced absorption in a nondegenerate three-level ladder system,” Opt. Lett. 40(18), 4289–4292 (2015).
    [Crossref] [PubMed]
  32. D. J. Whiting, J. Keaveney, C. S. Adams, and I. G. Hughes, “Direct measurement of excited-state dipole matrix elements using electromagnetically induced transparency in the hyperfine Paschen-Back regime,” Phys. Rev. A 93(4), 043854 (2016).
    [Crossref]
  33. H. R. Noh and H. S. Moon, “Analytical solutions of the susceptibility for Doppler-broadened three-level atomic system,” J. Phys. At. Mol. Opt. Phys. 45(24), 245002 (2012).
    [Crossref]
  34. M. D. Rotondaro and G. P. Perram, “Collisional broadening and shift of the Rubidium D1 and D2 lines (52S1/2®52P1/2, 52P3/2) by rare gases, H2, D2, N2, CH4, and CF4,” J. Quant. Spectrosc. Radiat. Transf. 57(4), 497–507 (1997).
    [Crossref]
  35. H. S. Moon and H.-R. Noh, “Atomic coherences of on-resonant and off-resonant two-photon absorptions in a ladder-type,” J. Opt. Soc. Am. B 31(5), 1217–1222 (2014).
    [Crossref]

2016 (4)

P. Qian, Z. Gu, R. Cao, R. Wen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Temporal purity and quantum interference of single photons from two independent cold atomic ensembles,” Phys. Rev. Lett. 117(1), 013602 (2016).
[Crossref] [PubMed]

D. J. Whiting, J. Keaveney, C. S. Adams, and I. G. Hughes, “Direct measurement of excited-state dipole matrix elements using electromagnetically induced transparency in the hyperfine Paschen-Back regime,” Phys. Rev. A 93(4), 043854 (2016).
[Crossref]

C.-Y. Lee, B.-H. Wu, G. Wang, Y.-F. Chen, Y.-C. Chen, and I. A. Yu, “High conversion efficiency in resonant four-wave mixing processes,” Opt. Express 24(2), 1008–1016 (2016).
[Crossref] [PubMed]

Y.-S. Lee and H. S. Moon, “Atomic coherence effects in four-wave mixing process of a ladder-type atomic system,” Opt. Express 24(10), 10723–10732 (2016).
[Crossref] [PubMed]

2015 (2)

D. J. Whiting, E. Bimbard, J. Keaveney, M. A. Zentile, C. S. Adams, and I. G. Hughes, “Electromagnetically induced absorption in a nondegenerate three-level ladder system,” Opt. Lett. 40(18), 4289–4292 (2015).
[Crossref] [PubMed]

L. Zhao, X. Guo, Y. Sun, Y. Su, M. M. T. Loy, and S. Du, “Shaping the biphoton temporal waveform with spatial light modulation,” Phys. Rev. Lett. 115(19), 193601 (2015).
[Crossref] [PubMed]

2014 (4)

Y.-W. Cho, K.-K. Park, J.-C. Lee, and Y.-H. Kim, “Engineering frequency-time quantum correlation of narrow-band biphotons from cold atoms,” Phys. Rev. Lett. 113(6), 063602 (2014).
[Crossref] [PubMed]

F. Wen, H. Zheng, X. Xue, H. Chen, J. Song, and Y. Zhang, “Electromagnetically induced transparency-assisted four-wave mixing process in the diamond-type four-level atomic system,” Opt. Mater. 37, 724–726 (2014).
[Crossref]

H. S. Moon and H.-R. Noh, “Atomic coherences of on-resonant and off-resonant two-photon absorptions in a ladder-type,” J. Opt. Soc. Am. B 31(5), 1217–1222 (2014).
[Crossref]

Y.-F. Hsiao, P.-J. Tsai, C.-C. Lin, Y.-F. Chen, I. A. Yu, and Y.-C. Chen, “Coherence properties of amplified slow light by four-wave mixing,” Opt. Lett. 39(12), 3394–3397 (2014).
[Crossref] [PubMed]

2012 (4)

U. Khadka, H. Zheng, and M. Xiao, “Four-wave-mixing between the upper excited states in a ladder-type atomic configuration,” Opt. Express 20(6), 6204–6214 (2012).
[Crossref] [PubMed]

A. M. Akulshin and R. J. McLean, “Distinguishing coherent atomic processes using wave mixing,” Phys. Rev. A 85(6), 065802 (2012).
[Crossref]

H. R. Noh and H. S. Moon, “Analytical solutions of the susceptibility for Doppler-broadened three-level atomic system,” J. Phys. At. Mol. Opt. Phys. 45(24), 245002 (2012).
[Crossref]

Q. Glorieux, J. B. Clark, N. V. Corzo, and P. D. Lett, “Generation of pulsed bipartite entanglement using four-wave mixing,” New J. Phys. 14(12), 123024 (2012).
[Crossref]

2011 (3)

N. B. Phillips, A. V. Gorshkov, and I. Novikova, “Light storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four wave mixing,” Phys. Rev. A 83(6), 063823 (2011).
[Crossref]

A. M. Akulshin, R. J. McLean, A. I. Sidorov, and P. Hannaford, “Probing degenerate two-level atomic media by coherent optical heterodyning,” J. Phys. At. Mol. Opt. Phys. 44(17), 175502 (2011).
[Crossref]

I.-H. Bae, H. J. Lee, and H. S. Moon, “Electromagnetically induced transparency with variable fluctuation time of photon number of pseudothermal probe light,” J. Opt. Soc. Am. B 28(6), 1578–1582 (2011).
[Crossref]

2010 (1)

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[Crossref]

2009 (3)

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009).
[Crossref] [PubMed]

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Four-wave mixing in the diamond configuration in an atomic vapor,” Phys. Rev. A 79(3), 033814 (2009).
[Crossref]

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009).
[Crossref]

2008 (2)

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100(18), 183603 (2008).
[Crossref] [PubMed]

F. E. Becerra, R. T. Willis, S. L. Rolston, and L. A. Orozco, “Nondegenerate four-wave mixing in rubidium vapor: the diamond configuration,” Phys. Rev. A 78(1), 013834 (2008).
[Crossref]

2006 (1)

E. E. Mikhailov, V. A. Sautenkov, Y. V. Rostovtsev, A. Zhang, M. S. Zubairy, M. O. Scully, and G. R. Welch, “Spectral narrowing via quantum coherence,” Phys. Rev. A 74(1), 013807 (2006).
[Crossref]

2005 (1)

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94(18), 183601 (2005).
[Crossref] [PubMed]

1999 (1)

A. S. Zibrov, M. D. Lukin, and M. O. Scully, “Nondegenerate parametric self-oscillation via multiwave mixing in coherent atomic media,” Phys. Rev. Lett. 83(20), 4049–4052 (1999).
[Crossref]

1997 (2)

B. Lü, W. H. Burkett, and M. Xiao, “Electromagnetically induced transparency with variable coupling-laser linewidth,” Phys. Rev. A 56(1), 976–979 (1997).
[Crossref]

M. D. Rotondaro and G. P. Perram, “Collisional broadening and shift of the Rubidium D1 and D2 lines (52S1/2®52P1/2, 52P3/2) by rare gases, H2, D2, N2, CH4, and CF4,” J. Quant. Spectrosc. Radiat. Transf. 57(4), 497–507 (1997).
[Crossref]

1996 (2)

Y.-Q. Li and M. Xiao, “Enhancement of nondegenerate four-wave mixing based on electromagnetically induced transparency in rubidium atoms,” Opt. Lett. 21(14), 1064–1066 (1996).
[Crossref] [PubMed]

J. C. Petch, C. H. Keitel, P. L. Knight, and J. P. Marangos, “Role of electromagnetically induced transparency in resonant four-wave-mixing schemes,” Phys. Rev. A 53(1), 543–561 (1996).
[Crossref] [PubMed]

1995 (1)

1993 (1)

1991 (1)

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref] [PubMed]

1990 (1)

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref] [PubMed]

1977 (1)

Adams, C. S.

D. J. Whiting, J. Keaveney, C. S. Adams, and I. G. Hughes, “Direct measurement of excited-state dipole matrix elements using electromagnetically induced transparency in the hyperfine Paschen-Back regime,” Phys. Rev. A 93(4), 043854 (2016).
[Crossref]

D. J. Whiting, E. Bimbard, J. Keaveney, M. A. Zentile, C. S. Adams, and I. G. Hughes, “Electromagnetically induced absorption in a nondegenerate three-level ladder system,” Opt. Lett. 40(18), 4289–4292 (2015).
[Crossref] [PubMed]

Akulshin, A. M.

A. M. Akulshin and R. J. McLean, “Distinguishing coherent atomic processes using wave mixing,” Phys. Rev. A 85(6), 065802 (2012).
[Crossref]

A. M. Akulshin, R. J. McLean, A. I. Sidorov, and P. Hannaford, “Probing degenerate two-level atomic media by coherent optical heterodyning,” J. Phys. At. Mol. Opt. Phys. 44(17), 175502 (2011).
[Crossref]

Anderson, B.

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009).
[Crossref] [PubMed]

Arimondo, E.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[Crossref]

Bae, I.-H.

Balic, V.

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94(18), 183601 (2005).
[Crossref] [PubMed]

Becerra, F. E.

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Four-wave mixing in the diamond configuration in an atomic vapor,” Phys. Rev. A 79(3), 033814 (2009).
[Crossref]

F. E. Becerra, R. T. Willis, S. L. Rolston, and L. A. Orozco, “Nondegenerate four-wave mixing in rubidium vapor: the diamond configuration,” Phys. Rev. A 78(1), 013834 (2008).
[Crossref]

Belthangady, C.

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100(18), 183603 (2008).
[Crossref] [PubMed]

Bimbard, E.

Boller, K.-J.

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref] [PubMed]

Braje, D. A.

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94(18), 183601 (2005).
[Crossref] [PubMed]

Burkett, W. H.

B. Lü, W. H. Burkett, and M. Xiao, “Electromagnetically induced transparency with variable coupling-laser linewidth,” Phys. Rev. A 56(1), 976–979 (1997).
[Crossref]

Camacho, R. M.

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009).
[Crossref]

Cao, R.

P. Qian, Z. Gu, R. Cao, R. Wen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Temporal purity and quantum interference of single photons from two independent cold atomic ensembles,” Phys. Rev. Lett. 117(1), 013602 (2016).
[Crossref] [PubMed]

Chen, H.

F. Wen, H. Zheng, X. Xue, H. Chen, J. Song, and Y. Zhang, “Electromagnetically induced transparency-assisted four-wave mixing process in the diamond-type four-level atomic system,” Opt. Mater. 37, 724–726 (2014).
[Crossref]

Chen, J. F.

P. Qian, Z. Gu, R. Cao, R. Wen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Temporal purity and quantum interference of single photons from two independent cold atomic ensembles,” Phys. Rev. Lett. 117(1), 013602 (2016).
[Crossref] [PubMed]

Chen, Y.-C.

Chen, Y.-F.

Cho, Y.-W.

Y.-W. Cho, K.-K. Park, J.-C. Lee, and Y.-H. Kim, “Engineering frequency-time quantum correlation of narrow-band biphotons from cold atoms,” Phys. Rev. Lett. 113(6), 063602 (2014).
[Crossref] [PubMed]

Clark, J. B.

Q. Glorieux, J. B. Clark, N. V. Corzo, and P. D. Lett, “Generation of pulsed bipartite entanglement using four-wave mixing,” New J. Phys. 14(12), 123024 (2012).
[Crossref]

Corzo, N. V.

Q. Glorieux, J. B. Clark, N. V. Corzo, and P. D. Lett, “Generation of pulsed bipartite entanglement using four-wave mixing,” New J. Phys. 14(12), 123024 (2012).
[Crossref]

Coudreau, T.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[Crossref]

Cronin-Golomb, M.

Donoghue, J.

Du, S.

L. Zhao, X. Guo, Y. Sun, Y. Su, M. M. T. Loy, and S. Du, “Shaping the biphoton temporal waveform with spatial light modulation,” Phys. Rev. Lett. 115(19), 193601 (2015).
[Crossref] [PubMed]

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100(18), 183603 (2008).
[Crossref] [PubMed]

Dubessy, R.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[Crossref]

Field, J. E.

M. Jain, G. Y. Yin, J. E. Field, and S. E. Harris, “Observation of electromagnetically induced phase matching,” Opt. Lett. 18(12), 998–1000 (1993).
[Crossref] [PubMed]

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref] [PubMed]

Glorieux, Q.

Q. Glorieux, J. B. Clark, N. V. Corzo, and P. D. Lett, “Generation of pulsed bipartite entanglement using four-wave mixing,” New J. Phys. 14(12), 123024 (2012).
[Crossref]

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[Crossref]

Gorshkov, A. V.

N. B. Phillips, A. V. Gorshkov, and I. Novikova, “Light storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four wave mixing,” Phys. Rev. A 83(6), 063823 (2011).
[Crossref]

Gu, Z.

P. Qian, Z. Gu, R. Cao, R. Wen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Temporal purity and quantum interference of single photons from two independent cold atomic ensembles,” Phys. Rev. Lett. 117(1), 013602 (2016).
[Crossref] [PubMed]

Guibal, S.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[Crossref]

Guidoni, L.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[Crossref]

Guo, X.

L. Zhao, X. Guo, Y. Sun, Y. Su, M. M. T. Loy, and S. Du, “Shaping the biphoton temporal waveform with spatial light modulation,” Phys. Rev. Lett. 115(19), 193601 (2015).
[Crossref] [PubMed]

Hannaford, P.

A. M. Akulshin, R. J. McLean, A. I. Sidorov, and P. Hannaford, “Probing degenerate two-level atomic media by coherent optical heterodyning,” J. Phys. At. Mol. Opt. Phys. 44(17), 175502 (2011).
[Crossref]

Harris, S. E.

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100(18), 183603 (2008).
[Crossref] [PubMed]

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94(18), 183601 (2005).
[Crossref] [PubMed]

M. Jain, G. Y. Yin, J. E. Field, and S. E. Harris, “Observation of electromagnetically induced phase matching,” Opt. Lett. 18(12), 998–1000 (1993).
[Crossref] [PubMed]

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref] [PubMed]

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref] [PubMed]

Hemmer, P. R.

Howell, J. C.

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009).
[Crossref]

Hsiao, Y.-F.

Hughes, I. G.

D. J. Whiting, J. Keaveney, C. S. Adams, and I. G. Hughes, “Direct measurement of excited-state dipole matrix elements using electromagnetically induced transparency in the hyperfine Paschen-Back regime,” Phys. Rev. A 93(4), 043854 (2016).
[Crossref]

D. J. Whiting, E. Bimbard, J. Keaveney, M. A. Zentile, C. S. Adams, and I. G. Hughes, “Electromagnetically induced absorption in a nondegenerate three-level ladder system,” Opt. Lett. 40(18), 4289–4292 (2015).
[Crossref] [PubMed]

Imamoglu, A.

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref] [PubMed]

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref] [PubMed]

Jain, M.

Katz, D. P.

Keaveney, J.

D. J. Whiting, J. Keaveney, C. S. Adams, and I. G. Hughes, “Direct measurement of excited-state dipole matrix elements using electromagnetically induced transparency in the hyperfine Paschen-Back regime,” Phys. Rev. A 93(4), 043854 (2016).
[Crossref]

D. J. Whiting, E. Bimbard, J. Keaveney, M. A. Zentile, C. S. Adams, and I. G. Hughes, “Electromagnetically induced absorption in a nondegenerate three-level ladder system,” Opt. Lett. 40(18), 4289–4292 (2015).
[Crossref] [PubMed]

Keitel, C. H.

J. C. Petch, C. H. Keitel, P. L. Knight, and J. P. Marangos, “Role of electromagnetically induced transparency in resonant four-wave-mixing schemes,” Phys. Rev. A 53(1), 543–561 (1996).
[Crossref] [PubMed]

Khadka, U.

U. Khadka, H. Zheng, and M. Xiao, “Four-wave-mixing between the upper excited states in a ladder-type atomic configuration,” Opt. Express 20(6), 6204–6214 (2012).
[Crossref] [PubMed]

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009).
[Crossref] [PubMed]

Kim, Y.-H.

Y.-W. Cho, K.-K. Park, J.-C. Lee, and Y.-H. Kim, “Engineering frequency-time quantum correlation of narrow-band biphotons from cold atoms,” Phys. Rev. Lett. 113(6), 063602 (2014).
[Crossref] [PubMed]

Knight, P. L.

J. C. Petch, C. H. Keitel, P. L. Knight, and J. P. Marangos, “Role of electromagnetically induced transparency in resonant four-wave-mixing schemes,” Phys. Rev. A 53(1), 543–561 (1996).
[Crossref] [PubMed]

Kolchin, P.

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100(18), 183603 (2008).
[Crossref] [PubMed]

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94(18), 183601 (2005).
[Crossref] [PubMed]

Kumar, P.

Lee, C.-Y.

Lee, H. J.

Lee, J.-C.

Y.-W. Cho, K.-K. Park, J.-C. Lee, and Y.-H. Kim, “Engineering frequency-time quantum correlation of narrow-band biphotons from cold atoms,” Phys. Rev. Lett. 113(6), 063602 (2014).
[Crossref] [PubMed]

Lee, Y.-S.

Lett, P. D.

Q. Glorieux, J. B. Clark, N. V. Corzo, and P. D. Lett, “Generation of pulsed bipartite entanglement using four-wave mixing,” New J. Phys. 14(12), 123024 (2012).
[Crossref]

Li, Y.-Q.

Likforman, J.-P.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[Crossref]

Lin, C.-C.

Loy, M. M. T.

L. Zhao, X. Guo, Y. Sun, Y. Su, M. M. T. Loy, and S. Du, “Shaping the biphoton temporal waveform with spatial light modulation,” Phys. Rev. Lett. 115(19), 193601 (2015).
[Crossref] [PubMed]

Lü, B.

B. Lü, W. H. Burkett, and M. Xiao, “Electromagnetically induced transparency with variable coupling-laser linewidth,” Phys. Rev. A 56(1), 976–979 (1997).
[Crossref]

Lukin, M. D.

A. S. Zibrov, M. D. Lukin, and M. O. Scully, “Nondegenerate parametric self-oscillation via multiwave mixing in coherent atomic media,” Phys. Rev. Lett. 83(20), 4049–4052 (1999).
[Crossref]

Marangos, J. P.

J. C. Petch, C. H. Keitel, P. L. Knight, and J. P. Marangos, “Role of electromagnetically induced transparency in resonant four-wave-mixing schemes,” Phys. Rev. A 53(1), 543–561 (1996).
[Crossref] [PubMed]

McLean, R. J.

A. M. Akulshin and R. J. McLean, “Distinguishing coherent atomic processes using wave mixing,” Phys. Rev. A 85(6), 065802 (2012).
[Crossref]

A. M. Akulshin, R. J. McLean, A. I. Sidorov, and P. Hannaford, “Probing degenerate two-level atomic media by coherent optical heterodyning,” J. Phys. At. Mol. Opt. Phys. 44(17), 175502 (2011).
[Crossref]

Mikhailov, E. E.

E. E. Mikhailov, V. A. Sautenkov, Y. V. Rostovtsev, A. Zhang, M. S. Zubairy, M. O. Scully, and G. R. Welch, “Spectral narrowing via quantum coherence,” Phys. Rev. A 74(1), 013807 (2006).
[Crossref]

Moon, H. S.

Noh, H. R.

H. R. Noh and H. S. Moon, “Analytical solutions of the susceptibility for Doppler-broadened three-level atomic system,” J. Phys. At. Mol. Opt. Phys. 45(24), 245002 (2012).
[Crossref]

Noh, H.-R.

Novikova, I.

N. B. Phillips, A. V. Gorshkov, and I. Novikova, “Light storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four wave mixing,” Phys. Rev. A 83(6), 063823 (2011).
[Crossref]

Orozco, L. A.

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Four-wave mixing in the diamond configuration in an atomic vapor,” Phys. Rev. A 79(3), 033814 (2009).
[Crossref]

F. E. Becerra, R. T. Willis, S. L. Rolston, and L. A. Orozco, “Nondegenerate four-wave mixing in rubidium vapor: the diamond configuration,” Phys. Rev. A 78(1), 013834 (2008).
[Crossref]

Ou, Z. Y.

P. Qian, Z. Gu, R. Cao, R. Wen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Temporal purity and quantum interference of single photons from two independent cold atomic ensembles,” Phys. Rev. Lett. 117(1), 013602 (2016).
[Crossref] [PubMed]

Park, K.-K.

Y.-W. Cho, K.-K. Park, J.-C. Lee, and Y.-H. Kim, “Engineering frequency-time quantum correlation of narrow-band biphotons from cold atoms,” Phys. Rev. Lett. 113(6), 063602 (2014).
[Crossref] [PubMed]

Pepper, D. M.

Perram, G. P.

M. D. Rotondaro and G. P. Perram, “Collisional broadening and shift of the Rubidium D1 and D2 lines (52S1/2®52P1/2, 52P3/2) by rare gases, H2, D2, N2, CH4, and CF4,” J. Quant. Spectrosc. Radiat. Transf. 57(4), 497–507 (1997).
[Crossref]

Petch, J. C.

J. C. Petch, C. H. Keitel, P. L. Knight, and J. P. Marangos, “Role of electromagnetically induced transparency in resonant four-wave-mixing schemes,” Phys. Rev. A 53(1), 543–561 (1996).
[Crossref] [PubMed]

Phillips, N. B.

N. B. Phillips, A. V. Gorshkov, and I. Novikova, “Light storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four wave mixing,” Phys. Rev. A 83(6), 063823 (2011).
[Crossref]

Qian, P.

P. Qian, Z. Gu, R. Cao, R. Wen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Temporal purity and quantum interference of single photons from two independent cold atomic ensembles,” Phys. Rev. Lett. 117(1), 013602 (2016).
[Crossref] [PubMed]

Rolston, S. L.

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Four-wave mixing in the diamond configuration in an atomic vapor,” Phys. Rev. A 79(3), 033814 (2009).
[Crossref]

F. E. Becerra, R. T. Willis, S. L. Rolston, and L. A. Orozco, “Nondegenerate four-wave mixing in rubidium vapor: the diamond configuration,” Phys. Rev. A 78(1), 013834 (2008).
[Crossref]

Rostovtsev, Y. V.

E. E. Mikhailov, V. A. Sautenkov, Y. V. Rostovtsev, A. Zhang, M. S. Zubairy, M. O. Scully, and G. R. Welch, “Spectral narrowing via quantum coherence,” Phys. Rev. A 74(1), 013807 (2006).
[Crossref]

Rotondaro, M. D.

M. D. Rotondaro and G. P. Perram, “Collisional broadening and shift of the Rubidium D1 and D2 lines (52S1/2®52P1/2, 52P3/2) by rare gases, H2, D2, N2, CH4, and CF4,” J. Quant. Spectrosc. Radiat. Transf. 57(4), 497–507 (1997).
[Crossref]

Sautenkov, V. A.

E. E. Mikhailov, V. A. Sautenkov, Y. V. Rostovtsev, A. Zhang, M. S. Zubairy, M. O. Scully, and G. R. Welch, “Spectral narrowing via quantum coherence,” Phys. Rev. A 74(1), 013807 (2006).
[Crossref]

Scully, M. O.

E. E. Mikhailov, V. A. Sautenkov, Y. V. Rostovtsev, A. Zhang, M. S. Zubairy, M. O. Scully, and G. R. Welch, “Spectral narrowing via quantum coherence,” Phys. Rev. A 74(1), 013807 (2006).
[Crossref]

A. S. Zibrov, M. D. Lukin, and M. O. Scully, “Nondegenerate parametric self-oscillation via multiwave mixing in coherent atomic media,” Phys. Rev. Lett. 83(20), 4049–4052 (1999).
[Crossref]

Shahriar, M. S.

Sidorov, A. I.

A. M. Akulshin, R. J. McLean, A. I. Sidorov, and P. Hannaford, “Probing degenerate two-level atomic media by coherent optical heterodyning,” J. Phys. At. Mol. Opt. Phys. 44(17), 175502 (2011).
[Crossref]

Song, J.

F. Wen, H. Zheng, X. Xue, H. Chen, J. Song, and Y. Zhang, “Electromagnetically induced transparency-assisted four-wave mixing process in the diamond-type four-level atomic system,” Opt. Mater. 37, 724–726 (2014).
[Crossref]

Su, Y.

L. Zhao, X. Guo, Y. Sun, Y. Su, M. M. T. Loy, and S. Du, “Shaping the biphoton temporal waveform with spatial light modulation,” Phys. Rev. Lett. 115(19), 193601 (2015).
[Crossref] [PubMed]

Sun, Y.

L. Zhao, X. Guo, Y. Sun, Y. Su, M. M. T. Loy, and S. Du, “Shaping the biphoton temporal waveform with spatial light modulation,” Phys. Rev. Lett. 115(19), 193601 (2015).
[Crossref] [PubMed]

Tsai, P.-J.

Vudyasetu, P. K.

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009).
[Crossref]

Wang, G.

Welch, G. R.

E. E. Mikhailov, V. A. Sautenkov, Y. V. Rostovtsev, A. Zhang, M. S. Zubairy, M. O. Scully, and G. R. Welch, “Spectral narrowing via quantum coherence,” Phys. Rev. A 74(1), 013807 (2006).
[Crossref]

Wen, F.

F. Wen, H. Zheng, X. Xue, H. Chen, J. Song, and Y. Zhang, “Electromagnetically induced transparency-assisted four-wave mixing process in the diamond-type four-level atomic system,” Opt. Mater. 37, 724–726 (2014).
[Crossref]

Wen, R.

P. Qian, Z. Gu, R. Cao, R. Wen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Temporal purity and quantum interference of single photons from two independent cold atomic ensembles,” Phys. Rev. Lett. 117(1), 013602 (2016).
[Crossref] [PubMed]

Whiting, D. J.

D. J. Whiting, J. Keaveney, C. S. Adams, and I. G. Hughes, “Direct measurement of excited-state dipole matrix elements using electromagnetically induced transparency in the hyperfine Paschen-Back regime,” Phys. Rev. A 93(4), 043854 (2016).
[Crossref]

D. J. Whiting, E. Bimbard, J. Keaveney, M. A. Zentile, C. S. Adams, and I. G. Hughes, “Electromagnetically induced absorption in a nondegenerate three-level ladder system,” Opt. Lett. 40(18), 4289–4292 (2015).
[Crossref] [PubMed]

Willis, R. T.

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Four-wave mixing in the diamond configuration in an atomic vapor,” Phys. Rev. A 79(3), 033814 (2009).
[Crossref]

F. E. Becerra, R. T. Willis, S. L. Rolston, and L. A. Orozco, “Nondegenerate four-wave mixing in rubidium vapor: the diamond configuration,” Phys. Rev. A 78(1), 013834 (2008).
[Crossref]

Wu, B.-H.

Xiao, M.

U. Khadka, H. Zheng, and M. Xiao, “Four-wave-mixing between the upper excited states in a ladder-type atomic configuration,” Opt. Express 20(6), 6204–6214 (2012).
[Crossref] [PubMed]

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009).
[Crossref] [PubMed]

B. Lü, W. H. Burkett, and M. Xiao, “Electromagnetically induced transparency with variable coupling-laser linewidth,” Phys. Rev. A 56(1), 976–979 (1997).
[Crossref]

Y.-Q. Li and M. Xiao, “Enhancement of nondegenerate four-wave mixing based on electromagnetically induced transparency in rubidium atoms,” Opt. Lett. 21(14), 1064–1066 (1996).
[Crossref] [PubMed]

Xue, X.

F. Wen, H. Zheng, X. Xue, H. Chen, J. Song, and Y. Zhang, “Electromagnetically induced transparency-assisted four-wave mixing process in the diamond-type four-level atomic system,” Opt. Mater. 37, 724–726 (2014).
[Crossref]

Yariv, A.

Yin, G. Y.

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100(18), 183603 (2008).
[Crossref] [PubMed]

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94(18), 183601 (2005).
[Crossref] [PubMed]

M. Jain, G. Y. Yin, J. E. Field, and S. E. Harris, “Observation of electromagnetically induced phase matching,” Opt. Lett. 18(12), 998–1000 (1993).
[Crossref] [PubMed]

Yu, I. A.

Zentile, M. A.

Zhang, A.

E. E. Mikhailov, V. A. Sautenkov, Y. V. Rostovtsev, A. Zhang, M. S. Zubairy, M. O. Scully, and G. R. Welch, “Spectral narrowing via quantum coherence,” Phys. Rev. A 74(1), 013807 (2006).
[Crossref]

Zhang, W.

P. Qian, Z. Gu, R. Cao, R. Wen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Temporal purity and quantum interference of single photons from two independent cold atomic ensembles,” Phys. Rev. Lett. 117(1), 013602 (2016).
[Crossref] [PubMed]

Zhang, Y.

F. Wen, H. Zheng, X. Xue, H. Chen, J. Song, and Y. Zhang, “Electromagnetically induced transparency-assisted four-wave mixing process in the diamond-type four-level atomic system,” Opt. Mater. 37, 724–726 (2014).
[Crossref]

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009).
[Crossref] [PubMed]

Zhao, L.

L. Zhao, X. Guo, Y. Sun, Y. Su, M. M. T. Loy, and S. Du, “Shaping the biphoton temporal waveform with spatial light modulation,” Phys. Rev. Lett. 115(19), 193601 (2015).
[Crossref] [PubMed]

Zheng, H.

F. Wen, H. Zheng, X. Xue, H. Chen, J. Song, and Y. Zhang, “Electromagnetically induced transparency-assisted four-wave mixing process in the diamond-type four-level atomic system,” Opt. Mater. 37, 724–726 (2014).
[Crossref]

U. Khadka, H. Zheng, and M. Xiao, “Four-wave-mixing between the upper excited states in a ladder-type atomic configuration,” Opt. Express 20(6), 6204–6214 (2012).
[Crossref] [PubMed]

Zibrov, A. S.

A. S. Zibrov, M. D. Lukin, and M. O. Scully, “Nondegenerate parametric self-oscillation via multiwave mixing in coherent atomic media,” Phys. Rev. Lett. 83(20), 4049–4052 (1999).
[Crossref]

Zubairy, M. S.

E. E. Mikhailov, V. A. Sautenkov, Y. V. Rostovtsev, A. Zhang, M. S. Zubairy, M. O. Scully, and G. R. Welch, “Spectral narrowing via quantum coherence,” Phys. Rev. A 74(1), 013807 (2006).
[Crossref]

J. Opt. Soc. Am. B (2)

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

H. R. Noh and H. S. Moon, “Analytical solutions of the susceptibility for Doppler-broadened three-level atomic system,” J. Phys. At. Mol. Opt. Phys. 45(24), 245002 (2012).
[Crossref]

A. M. Akulshin, R. J. McLean, A. I. Sidorov, and P. Hannaford, “Probing degenerate two-level atomic media by coherent optical heterodyning,” J. Phys. At. Mol. Opt. Phys. 44(17), 175502 (2011).
[Crossref]

J. Quant. Spectrosc. Radiat. Transf. (1)

M. D. Rotondaro and G. P. Perram, “Collisional broadening and shift of the Rubidium D1 and D2 lines (52S1/2®52P1/2, 52P3/2) by rare gases, H2, D2, N2, CH4, and CF4,” J. Quant. Spectrosc. Radiat. Transf. 57(4), 497–507 (1997).
[Crossref]

Nat. Photonics (1)

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009).
[Crossref]

New J. Phys. (1)

Q. Glorieux, J. B. Clark, N. V. Corzo, and P. D. Lett, “Generation of pulsed bipartite entanglement using four-wave mixing,” New J. Phys. 14(12), 123024 (2012).
[Crossref]

Opt. Express (3)

Opt. Lett. (6)

Opt. Mater. (1)

F. Wen, H. Zheng, X. Xue, H. Chen, J. Song, and Y. Zhang, “Electromagnetically induced transparency-assisted four-wave mixing process in the diamond-type four-level atomic system,” Opt. Mater. 37, 724–726 (2014).
[Crossref]

Phys. Rev. A (9)

J. C. Petch, C. H. Keitel, P. L. Knight, and J. P. Marangos, “Role of electromagnetically induced transparency in resonant four-wave-mixing schemes,” Phys. Rev. A 53(1), 543–561 (1996).
[Crossref] [PubMed]

F. E. Becerra, R. T. Willis, S. L. Rolston, and L. A. Orozco, “Nondegenerate four-wave mixing in rubidium vapor: the diamond configuration,” Phys. Rev. A 78(1), 013834 (2008).
[Crossref]

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Four-wave mixing in the diamond configuration in an atomic vapor,” Phys. Rev. A 79(3), 033814 (2009).
[Crossref]

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[Crossref]

N. B. Phillips, A. V. Gorshkov, and I. Novikova, “Light storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four wave mixing,” Phys. Rev. A 83(6), 063823 (2011).
[Crossref]

B. Lü, W. H. Burkett, and M. Xiao, “Electromagnetically induced transparency with variable coupling-laser linewidth,” Phys. Rev. A 56(1), 976–979 (1997).
[Crossref]

E. E. Mikhailov, V. A. Sautenkov, Y. V. Rostovtsev, A. Zhang, M. S. Zubairy, M. O. Scully, and G. R. Welch, “Spectral narrowing via quantum coherence,” Phys. Rev. A 74(1), 013807 (2006).
[Crossref]

D. J. Whiting, J. Keaveney, C. S. Adams, and I. G. Hughes, “Direct measurement of excited-state dipole matrix elements using electromagnetically induced transparency in the hyperfine Paschen-Back regime,” Phys. Rev. A 93(4), 043854 (2016).
[Crossref]

A. M. Akulshin and R. J. McLean, “Distinguishing coherent atomic processes using wave mixing,” Phys. Rev. A 85(6), 065802 (2012).
[Crossref]

Phys. Rev. Lett. (9)

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94(18), 183601 (2005).
[Crossref] [PubMed]

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100(18), 183603 (2008).
[Crossref] [PubMed]

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009).
[Crossref] [PubMed]

A. S. Zibrov, M. D. Lukin, and M. O. Scully, “Nondegenerate parametric self-oscillation via multiwave mixing in coherent atomic media,” Phys. Rev. Lett. 83(20), 4049–4052 (1999).
[Crossref]

Y.-W. Cho, K.-K. Park, J.-C. Lee, and Y.-H. Kim, “Engineering frequency-time quantum correlation of narrow-band biphotons from cold atoms,” Phys. Rev. Lett. 113(6), 063602 (2014).
[Crossref] [PubMed]

L. Zhao, X. Guo, Y. Sun, Y. Su, M. M. T. Loy, and S. Du, “Shaping the biphoton temporal waveform with spatial light modulation,” Phys. Rev. Lett. 115(19), 193601 (2015).
[Crossref] [PubMed]

P. Qian, Z. Gu, R. Cao, R. Wen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Temporal purity and quantum interference of single photons from two independent cold atomic ensembles,” Phys. Rev. Lett. 117(1), 013602 (2016).
[Crossref] [PubMed]

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref] [PubMed]

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1 (a) Schematic of experimental setup for examining the characteristics of four-wave mixing (FWM) in the double-Λ-type atomic system of 87Rb with the use of 795-nm external cavity diode lasers (ECDLs) for probe (Ωpr), coupling (ΩC), and pump (ΩP) lasers (PD: photo-current detector; PBS: polarization beam splitter; BS: beam splitter; OI: optical isolator; HWP: half-wave plate; M: Mirror). (b) Energy-level diagram of the 5S1/2(F = 1 and 2)−5P1/2(F′ = 2) transition of 87Rb atoms.
Fig. 2
Fig. 2 Transmittances of probe laser (black), two-photon absorption (TPA, blue), and four-wave mixing (FWM, red) spectra as functions of the detuning δpr/2π of the Ωpr laser, where TPA is due to the pure two-photon coherence by the phase-locked Ωp and ΩC lasers. The inset shows the normalized FWM and TPA spectra.
Fig. 3
Fig. 3 (a) Relative linewidth measurements in cases of phase-unlocked ΩP (blue curve) and phase-locked ΩP (red curve); spectral density curves of beat signal between the ΩP and ΩC lasers at the center frequency of 8.0 GHz. (b) Comparison of four-wave mixing (FWM) spectra obtained with the phase-unlocked (blue curve) and phase-locked (red curve) ΩP laser.
Fig. 4
Fig. 4 Relative phase-noise measurement of ΩFWM with respect to those of ΩP or Ωpr for phase-unlocked ΩP: Spectral density of the beat signal between (a) Ωpr and ΩFWM and (b) ΩP and ΩFWM.
Fig. 5
Fig. 5 (a) Double Λ-type four-level atomic model for four-wave mixing (FWM) generation. (b) Numerically calculated Im(σ23) for two-photon absorption (TPA, black curve) and |σ14|2 for FWM (red curve) spectra in four-level atomic model.
Fig. 6
Fig. 6 Numerically calculated |σ14|2 for FWM signal according to relative phase noise γP of ΩP.

Equations (5)

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ρ ij t = i k [ H ik ρ kj ρ ik H kj ] Γ ij ρ ij ,
σ 12 = Ω pr Ω C Δ 13 Δ 12 Δ 13 Δ 14 | Ω P | 2
σ 14 = Ω pr Ω C Ω P Δ 13 Δ 12 Δ 13 Δ 14 | Ω P | 2 ,
σ 14 = Ω P Δ P σ 12 ,
ρ 14 = σ 14 e i[ ω FWM t+ φ FWM (t)] .

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