Abstract

We report an experimental study of quantum interference between two-photon Raman transitions and demonstration of the phase control of light attenuation/transmission in cold Rb atoms. By varying the phase and frequency of a weak control laser, either constructive interference or destructive interference between the two-photon Raman transitions in a three-level Λ system can be manipulated. The interference enables absorptive switching of one field by another field at low light levels.

© 2008 Optical Society of America

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  1. R. W. Boyd, D. J. Gauthier, M. S. Malcuit, and K. Rzazewski, "Competition between amplified spontaneous emission and the 4-wave-mixing process," Phys. Rev. A 35, 1648-1658 (1987).
    [CrossRef] [PubMed]
  2. C. Chen, Y. Y. Yin, and D. S. Elliott, "Interference between optical-transitions," Phys. Rev. Lett. 64, 507-510 (1990).
    [CrossRef] [PubMed]
  3. D. J. Gauthier, "Alternate schemes for the coherent laser control of chemical-reactions," J. Chem. Phys. 99, 1618-1622 (1993).
    [CrossRef]
  4. N. Georgiades, E. S. Polzik, and H. J. Kimble, "Frequency metrology by use of quantum interference," Opt. Lett. 21, 1688-1690 (1996).
    [CrossRef] [PubMed]
  5. M. Yan, E. Rickey, and Y. Zhu, "Suppression of two-photon absorption by quantum interference," Phys. Rev. A 64, 043807(1-4) (2001).
    [CrossRef]
  6. M. W. Hamilton and D. S. Elliott, "Second order interference in two photon absorption," J. Mod. Opt. 43, 1765-1771 (1996).
    [CrossRef]
  7. L. Zhu, V. Kleinman, X. Li, S. P. Lu, K. Trentelman, and R. J. Gordon, "Coherent laser control of the product distribution obtained in the photoexcitation of hi," Science 270, 77-80 (1995).
    [CrossRef]
  8. A. Shnitman, I. Sofer, I. Golub, A. Yogev, M. Shapiro, Z. Chen, and P. Brumer, "Experimental observation of laser control: Electronic branching in the photodissociation of Na-2," Phys. Rev. Lett. 76, 2886-2889 (1996).
    [CrossRef] [PubMed]
  9. D. Petrosyan, and P. Lambropoulos, "Phase control of resonantly enhanced photoionization in an optically dense medium," Phys. Rev. A 63 043417(1-8) (2001).
    [CrossRef]
  10. F. Wang, C. Chen C, and D. S. Elliott, "Product state control through interfering excitation routes," Phys. Rev. Lett. 77, 2416-2419 (1996).
    [CrossRef] [PubMed]
  11. S. E. Harris and Y. Yamamoto, "Photon switching by quantum interference," Phys. Rev. Lett. 81, 3611-3614 (1998)
    [CrossRef]
  12. B. S. Ham and P. R. Hemmer, "Coherence switching in a four-level system: Quantum switching," Phys. Rev. Lett. 84, 4080-4083 (2000).
    [CrossRef] [PubMed]
  13. K. J. Resch, J. S. Lundeen, and A. M. Steinberg, "Nonlinear optics with less than one photon," Phys. Rev. Lett. 87, 123603-123606 (2001).
    [CrossRef] [PubMed]
  14. J. Resch, J. S. Lundeen, A. M. Steinberg, "Conditional-phase switch at the single-photon level," Phys. Rev. Lett. 89, 037904(1-4) (2002).
    [CrossRef]
  15. H. Schmidt and R. J. Ram, "All-optical wavelength converter and switch based on electromagnetically induced transparency," Appl. Phys. Lett. 76, 3173-3175 (2000).
    [CrossRef]
  16. M. Yan, E. Rickey, and Y. Zhu, "Observation of absorptive photon switching by quantum interference," Phys. Rev. A 64, 041801(1-4) (2001).
    [CrossRef]
  17. D. A. Braje, V. Balic, G. Y. Yin, and S. E. Harris, "Low-light-level nonlinear optics with slow light," Phy. Rev. A 68, 041801(1-4) (2003).
    [CrossRef]
  18. Y. F. Chen, Z. H. Tsai, Y. C. Liu, and I. A. Yu, "Low-light-level photon switching by quantum iterference," Opt. Lett. 30, 3207-3209 (2005).
    [CrossRef] [PubMed]
  19. C. Y. Wang, Y. F. Chen, S. C. Lin, W. H. Lin, P. C. Kuan, and I. A. Yu, "Low-light-level all-optical switching," Opt. Lett. 31, 2350-2352 (2006).
    [CrossRef] [PubMed]
  20. H. Wang, D. Goorskey, and M. Xiao, "Controlling light by light with three-level atoms inside an optical cavity," Opt. Lett. 27, 1354-1356 (2002).
    [CrossRef]
  21. A. Dawes, L. Illing, S. M. Clark, D. J. Gauthier, "All-optical switching in rubidium vapor," Science 29, 672-674 (2005).
    [CrossRef]
  22. A. M. C. Dawes, L. Illing, J. A. Greenberg, and D. J. Gauthier, "All-optical switching with transverse optical patterns," Phys. Rev. A 77, 013833(1-8) (2008).
    [CrossRef]
  23. J. Zhang, G. Hernandez, and Y. Zhu, "All optical switching at ultralow light levels, " Opt. Lett. 32, 1317-1319 (2007).
    [CrossRef] [PubMed]
  24. E. Arimondo, in Progress in Optics, edited by E. Wolf (Elsevier Science, Amsterdam, 1996), p. 257.
  25. J. Zhang, J. Xu, G. Hernandez, X. Hu, and Y. Zhu, "Polychromatic-field induced transparency and absorption in a three-level Λ system," Phys. Rev. A 75, 0438109 (1-4) (2007).
  26. X. X. Li, X. M. Hu, W. X. Shi, Q. Xu, H. J. Guo, and J. Y. Li, "Phase Control of Spontaneous Emission of a Three-Level Atom in Two Bichromatic Fields,"  23, 340-343 (2006).

2007 (1)

2006 (1)

2005 (2)

Y. F. Chen, Z. H. Tsai, Y. C. Liu, and I. A. Yu, "Low-light-level photon switching by quantum iterference," Opt. Lett. 30, 3207-3209 (2005).
[CrossRef] [PubMed]

A. Dawes, L. Illing, S. M. Clark, D. J. Gauthier, "All-optical switching in rubidium vapor," Science 29, 672-674 (2005).
[CrossRef]

2002 (1)

2001 (1)

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, "Nonlinear optics with less than one photon," Phys. Rev. Lett. 87, 123603-123606 (2001).
[CrossRef] [PubMed]

2000 (2)

H. Schmidt and R. J. Ram, "All-optical wavelength converter and switch based on electromagnetically induced transparency," Appl. Phys. Lett. 76, 3173-3175 (2000).
[CrossRef]

B. S. Ham and P. R. Hemmer, "Coherence switching in a four-level system: Quantum switching," Phys. Rev. Lett. 84, 4080-4083 (2000).
[CrossRef] [PubMed]

1998 (1)

S. E. Harris and Y. Yamamoto, "Photon switching by quantum interference," Phys. Rev. Lett. 81, 3611-3614 (1998)
[CrossRef]

1996 (4)

M. W. Hamilton and D. S. Elliott, "Second order interference in two photon absorption," J. Mod. Opt. 43, 1765-1771 (1996).
[CrossRef]

A. Shnitman, I. Sofer, I. Golub, A. Yogev, M. Shapiro, Z. Chen, and P. Brumer, "Experimental observation of laser control: Electronic branching in the photodissociation of Na-2," Phys. Rev. Lett. 76, 2886-2889 (1996).
[CrossRef] [PubMed]

F. Wang, C. Chen C, and D. S. Elliott, "Product state control through interfering excitation routes," Phys. Rev. Lett. 77, 2416-2419 (1996).
[CrossRef] [PubMed]

N. Georgiades, E. S. Polzik, and H. J. Kimble, "Frequency metrology by use of quantum interference," Opt. Lett. 21, 1688-1690 (1996).
[CrossRef] [PubMed]

1995 (1)

L. Zhu, V. Kleinman, X. Li, S. P. Lu, K. Trentelman, and R. J. Gordon, "Coherent laser control of the product distribution obtained in the photoexcitation of hi," Science 270, 77-80 (1995).
[CrossRef]

1993 (1)

D. J. Gauthier, "Alternate schemes for the coherent laser control of chemical-reactions," J. Chem. Phys. 99, 1618-1622 (1993).
[CrossRef]

1990 (1)

C. Chen, Y. Y. Yin, and D. S. Elliott, "Interference between optical-transitions," Phys. Rev. Lett. 64, 507-510 (1990).
[CrossRef] [PubMed]

1987 (1)

R. W. Boyd, D. J. Gauthier, M. S. Malcuit, and K. Rzazewski, "Competition between amplified spontaneous emission and the 4-wave-mixing process," Phys. Rev. A 35, 1648-1658 (1987).
[CrossRef] [PubMed]

Boyd, R. W.

R. W. Boyd, D. J. Gauthier, M. S. Malcuit, and K. Rzazewski, "Competition between amplified spontaneous emission and the 4-wave-mixing process," Phys. Rev. A 35, 1648-1658 (1987).
[CrossRef] [PubMed]

Brumer, P.

A. Shnitman, I. Sofer, I. Golub, A. Yogev, M. Shapiro, Z. Chen, and P. Brumer, "Experimental observation of laser control: Electronic branching in the photodissociation of Na-2," Phys. Rev. Lett. 76, 2886-2889 (1996).
[CrossRef] [PubMed]

Chen, C.

C. Chen, Y. Y. Yin, and D. S. Elliott, "Interference between optical-transitions," Phys. Rev. Lett. 64, 507-510 (1990).
[CrossRef] [PubMed]

Chen, Y. F.

Chen, Z.

A. Shnitman, I. Sofer, I. Golub, A. Yogev, M. Shapiro, Z. Chen, and P. Brumer, "Experimental observation of laser control: Electronic branching in the photodissociation of Na-2," Phys. Rev. Lett. 76, 2886-2889 (1996).
[CrossRef] [PubMed]

Clark, S. M.

A. Dawes, L. Illing, S. M. Clark, D. J. Gauthier, "All-optical switching in rubidium vapor," Science 29, 672-674 (2005).
[CrossRef]

Dawes, A.

A. Dawes, L. Illing, S. M. Clark, D. J. Gauthier, "All-optical switching in rubidium vapor," Science 29, 672-674 (2005).
[CrossRef]

Elliott, D. S.

M. W. Hamilton and D. S. Elliott, "Second order interference in two photon absorption," J. Mod. Opt. 43, 1765-1771 (1996).
[CrossRef]

C. Chen, Y. Y. Yin, and D. S. Elliott, "Interference between optical-transitions," Phys. Rev. Lett. 64, 507-510 (1990).
[CrossRef] [PubMed]

Gauthier, D. J.

A. Dawes, L. Illing, S. M. Clark, D. J. Gauthier, "All-optical switching in rubidium vapor," Science 29, 672-674 (2005).
[CrossRef]

D. J. Gauthier, "Alternate schemes for the coherent laser control of chemical-reactions," J. Chem. Phys. 99, 1618-1622 (1993).
[CrossRef]

R. W. Boyd, D. J. Gauthier, M. S. Malcuit, and K. Rzazewski, "Competition between amplified spontaneous emission and the 4-wave-mixing process," Phys. Rev. A 35, 1648-1658 (1987).
[CrossRef] [PubMed]

Georgiades, N.

Golub, I.

A. Shnitman, I. Sofer, I. Golub, A. Yogev, M. Shapiro, Z. Chen, and P. Brumer, "Experimental observation of laser control: Electronic branching in the photodissociation of Na-2," Phys. Rev. Lett. 76, 2886-2889 (1996).
[CrossRef] [PubMed]

Goorskey, D.

Gordon, R. J.

L. Zhu, V. Kleinman, X. Li, S. P. Lu, K. Trentelman, and R. J. Gordon, "Coherent laser control of the product distribution obtained in the photoexcitation of hi," Science 270, 77-80 (1995).
[CrossRef]

Guo, H. J.

X. X. Li, X. M. Hu, W. X. Shi, Q. Xu, H. J. Guo, and J. Y. Li, "Phase Control of Spontaneous Emission of a Three-Level Atom in Two Bichromatic Fields,"  23, 340-343 (2006).

Ham, B. S.

B. S. Ham and P. R. Hemmer, "Coherence switching in a four-level system: Quantum switching," Phys. Rev. Lett. 84, 4080-4083 (2000).
[CrossRef] [PubMed]

Hamilton, M. W.

M. W. Hamilton and D. S. Elliott, "Second order interference in two photon absorption," J. Mod. Opt. 43, 1765-1771 (1996).
[CrossRef]

Harris, S. E.

S. E. Harris and Y. Yamamoto, "Photon switching by quantum interference," Phys. Rev. Lett. 81, 3611-3614 (1998)
[CrossRef]

Hemmer, P. R.

B. S. Ham and P. R. Hemmer, "Coherence switching in a four-level system: Quantum switching," Phys. Rev. Lett. 84, 4080-4083 (2000).
[CrossRef] [PubMed]

Hernandez, G.

Hu, X. M.

X. X. Li, X. M. Hu, W. X. Shi, Q. Xu, H. J. Guo, and J. Y. Li, "Phase Control of Spontaneous Emission of a Three-Level Atom in Two Bichromatic Fields,"  23, 340-343 (2006).

Illing, L.

A. Dawes, L. Illing, S. M. Clark, D. J. Gauthier, "All-optical switching in rubidium vapor," Science 29, 672-674 (2005).
[CrossRef]

Kimble, H. J.

Kleinman, V.

L. Zhu, V. Kleinman, X. Li, S. P. Lu, K. Trentelman, and R. J. Gordon, "Coherent laser control of the product distribution obtained in the photoexcitation of hi," Science 270, 77-80 (1995).
[CrossRef]

Kuan, P. C.

Li, J. Y.

X. X. Li, X. M. Hu, W. X. Shi, Q. Xu, H. J. Guo, and J. Y. Li, "Phase Control of Spontaneous Emission of a Three-Level Atom in Two Bichromatic Fields,"  23, 340-343 (2006).

Li, X.

L. Zhu, V. Kleinman, X. Li, S. P. Lu, K. Trentelman, and R. J. Gordon, "Coherent laser control of the product distribution obtained in the photoexcitation of hi," Science 270, 77-80 (1995).
[CrossRef]

Li, X. X.

X. X. Li, X. M. Hu, W. X. Shi, Q. Xu, H. J. Guo, and J. Y. Li, "Phase Control of Spontaneous Emission of a Three-Level Atom in Two Bichromatic Fields,"  23, 340-343 (2006).

Lin, S. C.

Lin, W. H.

Liu, Y. C.

Lu, S. P.

L. Zhu, V. Kleinman, X. Li, S. P. Lu, K. Trentelman, and R. J. Gordon, "Coherent laser control of the product distribution obtained in the photoexcitation of hi," Science 270, 77-80 (1995).
[CrossRef]

Lundeen, J. S.

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, "Nonlinear optics with less than one photon," Phys. Rev. Lett. 87, 123603-123606 (2001).
[CrossRef] [PubMed]

Malcuit, M. S.

R. W. Boyd, D. J. Gauthier, M. S. Malcuit, and K. Rzazewski, "Competition between amplified spontaneous emission and the 4-wave-mixing process," Phys. Rev. A 35, 1648-1658 (1987).
[CrossRef] [PubMed]

Polzik, E. S.

Ram, R. J.

H. Schmidt and R. J. Ram, "All-optical wavelength converter and switch based on electromagnetically induced transparency," Appl. Phys. Lett. 76, 3173-3175 (2000).
[CrossRef]

Resch, K. J.

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, "Nonlinear optics with less than one photon," Phys. Rev. Lett. 87, 123603-123606 (2001).
[CrossRef] [PubMed]

Rzazewski, K.

R. W. Boyd, D. J. Gauthier, M. S. Malcuit, and K. Rzazewski, "Competition between amplified spontaneous emission and the 4-wave-mixing process," Phys. Rev. A 35, 1648-1658 (1987).
[CrossRef] [PubMed]

Schmidt, H.

H. Schmidt and R. J. Ram, "All-optical wavelength converter and switch based on electromagnetically induced transparency," Appl. Phys. Lett. 76, 3173-3175 (2000).
[CrossRef]

Shapiro, M.

A. Shnitman, I. Sofer, I. Golub, A. Yogev, M. Shapiro, Z. Chen, and P. Brumer, "Experimental observation of laser control: Electronic branching in the photodissociation of Na-2," Phys. Rev. Lett. 76, 2886-2889 (1996).
[CrossRef] [PubMed]

Shi, W. X.

X. X. Li, X. M. Hu, W. X. Shi, Q. Xu, H. J. Guo, and J. Y. Li, "Phase Control of Spontaneous Emission of a Three-Level Atom in Two Bichromatic Fields,"  23, 340-343 (2006).

Shnitman, A.

A. Shnitman, I. Sofer, I. Golub, A. Yogev, M. Shapiro, Z. Chen, and P. Brumer, "Experimental observation of laser control: Electronic branching in the photodissociation of Na-2," Phys. Rev. Lett. 76, 2886-2889 (1996).
[CrossRef] [PubMed]

Sofer, I.

A. Shnitman, I. Sofer, I. Golub, A. Yogev, M. Shapiro, Z. Chen, and P. Brumer, "Experimental observation of laser control: Electronic branching in the photodissociation of Na-2," Phys. Rev. Lett. 76, 2886-2889 (1996).
[CrossRef] [PubMed]

Steinberg, A. M.

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, "Nonlinear optics with less than one photon," Phys. Rev. Lett. 87, 123603-123606 (2001).
[CrossRef] [PubMed]

Trentelman, K.

L. Zhu, V. Kleinman, X. Li, S. P. Lu, K. Trentelman, and R. J. Gordon, "Coherent laser control of the product distribution obtained in the photoexcitation of hi," Science 270, 77-80 (1995).
[CrossRef]

Tsai, Z. H.

Wang, C. Y.

Wang, F.

F. Wang, C. Chen C, and D. S. Elliott, "Product state control through interfering excitation routes," Phys. Rev. Lett. 77, 2416-2419 (1996).
[CrossRef] [PubMed]

Wang, H.

Xiao, M.

Xu, Q.

X. X. Li, X. M. Hu, W. X. Shi, Q. Xu, H. J. Guo, and J. Y. Li, "Phase Control of Spontaneous Emission of a Three-Level Atom in Two Bichromatic Fields,"  23, 340-343 (2006).

Yamamoto, Y.

S. E. Harris and Y. Yamamoto, "Photon switching by quantum interference," Phys. Rev. Lett. 81, 3611-3614 (1998)
[CrossRef]

Yin, Y. Y.

C. Chen, Y. Y. Yin, and D. S. Elliott, "Interference between optical-transitions," Phys. Rev. Lett. 64, 507-510 (1990).
[CrossRef] [PubMed]

Yogev, A.

A. Shnitman, I. Sofer, I. Golub, A. Yogev, M. Shapiro, Z. Chen, and P. Brumer, "Experimental observation of laser control: Electronic branching in the photodissociation of Na-2," Phys. Rev. Lett. 76, 2886-2889 (1996).
[CrossRef] [PubMed]

Yu, I. A.

Zhang, J.

Zhu, L.

L. Zhu, V. Kleinman, X. Li, S. P. Lu, K. Trentelman, and R. J. Gordon, "Coherent laser control of the product distribution obtained in the photoexcitation of hi," Science 270, 77-80 (1995).
[CrossRef]

Zhu, Y.

Appl. Phys. Lett. (1)

H. Schmidt and R. J. Ram, "All-optical wavelength converter and switch based on electromagnetically induced transparency," Appl. Phys. Lett. 76, 3173-3175 (2000).
[CrossRef]

J. Chem. Phys. (1)

D. J. Gauthier, "Alternate schemes for the coherent laser control of chemical-reactions," J. Chem. Phys. 99, 1618-1622 (1993).
[CrossRef]

J. Mod. Opt. (1)

M. W. Hamilton and D. S. Elliott, "Second order interference in two photon absorption," J. Mod. Opt. 43, 1765-1771 (1996).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. A (1)

R. W. Boyd, D. J. Gauthier, M. S. Malcuit, and K. Rzazewski, "Competition between amplified spontaneous emission and the 4-wave-mixing process," Phys. Rev. A 35, 1648-1658 (1987).
[CrossRef] [PubMed]

Phys. Rev. Lett. (6)

C. Chen, Y. Y. Yin, and D. S. Elliott, "Interference between optical-transitions," Phys. Rev. Lett. 64, 507-510 (1990).
[CrossRef] [PubMed]

A. Shnitman, I. Sofer, I. Golub, A. Yogev, M. Shapiro, Z. Chen, and P. Brumer, "Experimental observation of laser control: Electronic branching in the photodissociation of Na-2," Phys. Rev. Lett. 76, 2886-2889 (1996).
[CrossRef] [PubMed]

F. Wang, C. Chen C, and D. S. Elliott, "Product state control through interfering excitation routes," Phys. Rev. Lett. 77, 2416-2419 (1996).
[CrossRef] [PubMed]

S. E. Harris and Y. Yamamoto, "Photon switching by quantum interference," Phys. Rev. Lett. 81, 3611-3614 (1998)
[CrossRef]

B. S. Ham and P. R. Hemmer, "Coherence switching in a four-level system: Quantum switching," Phys. Rev. Lett. 84, 4080-4083 (2000).
[CrossRef] [PubMed]

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, "Nonlinear optics with less than one photon," Phys. Rev. Lett. 87, 123603-123606 (2001).
[CrossRef] [PubMed]

Science (2)

L. Zhu, V. Kleinman, X. Li, S. P. Lu, K. Trentelman, and R. J. Gordon, "Coherent laser control of the product distribution obtained in the photoexcitation of hi," Science 270, 77-80 (1995).
[CrossRef]

A. Dawes, L. Illing, S. M. Clark, D. J. Gauthier, "All-optical switching in rubidium vapor," Science 29, 672-674 (2005).
[CrossRef]

Other (9)

A. M. C. Dawes, L. Illing, J. A. Greenberg, and D. J. Gauthier, "All-optical switching with transverse optical patterns," Phys. Rev. A 77, 013833(1-8) (2008).
[CrossRef]

E. Arimondo, in Progress in Optics, edited by E. Wolf (Elsevier Science, Amsterdam, 1996), p. 257.

J. Zhang, J. Xu, G. Hernandez, X. Hu, and Y. Zhu, "Polychromatic-field induced transparency and absorption in a three-level Λ system," Phys. Rev. A 75, 0438109 (1-4) (2007).

X. X. Li, X. M. Hu, W. X. Shi, Q. Xu, H. J. Guo, and J. Y. Li, "Phase Control of Spontaneous Emission of a Three-Level Atom in Two Bichromatic Fields,"  23, 340-343 (2006).

M. Yan, E. Rickey, and Y. Zhu, "Observation of absorptive photon switching by quantum interference," Phys. Rev. A 64, 041801(1-4) (2001).
[CrossRef]

D. A. Braje, V. Balic, G. Y. Yin, and S. E. Harris, "Low-light-level nonlinear optics with slow light," Phy. Rev. A 68, 041801(1-4) (2003).
[CrossRef]

D. Petrosyan, and P. Lambropoulos, "Phase control of resonantly enhanced photoionization in an optically dense medium," Phys. Rev. A 63 043417(1-8) (2001).
[CrossRef]

J. Resch, J. S. Lundeen, A. M. Steinberg, "Conditional-phase switch at the single-photon level," Phys. Rev. Lett. 89, 037904(1-4) (2002).
[CrossRef]

M. Yan, E. Rickey, and Y. Zhu, "Suppression of two-photon absorption by quantum interference," Phys. Rev. A 64, 043807(1-4) (2001).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

(a). Coherently prepared three-level Λ-type system. γ 3 is the spontaneous decay rate. Interference occurs between two channels of resonant Raman transitions (b) and (c).

Fig. 2.
Fig. 2.

Calculated transmission of the signal field versus the normalized signal detuning Δs/γ 3. The relative phase difference of the control field and signal field is (a) ΔΦ=Φcs=0 and (b) ΔΦ=Φcs=π. At Δs=, the light absorption is suppressed by destructive interference (a) and enhanced by constructive interference (b). The parameters are Ω12=1.2γ 3, Ωsc=0.01γ 3, δ=3.5γ 3, Δcs+2δ. The optical depth of the medium is nσ13 =10.

Fig. 3.
Fig. 3.

(a). The coupled three-level Λ-type system formed with the 85Rb D1 transitions at 795 nm. (b) Simplified diagram of the experimental set up. The spontaneous decay rate γ 3=2πx5.6×106 s-1. AOM: acousto-optic modulator; EOM: electro-optic modulator; PMF: polarization maintaining fiber; λ/4: quarter-wave plate; DL1(2): extended-cavity diode laser; M: mirror; D: photodetector.

Fig. 4.
Fig. 4.

Measured light transmission versus the signal detuning Δs. Black (red) lines are experimental data (calculations). The experimental parameters are Ω1/(2π)≈Ω2/(2π)≈7 MHz, Ωc/(2π)≈Ωs/(2π)≈0.2 MHz and δ=20 MHz. The fitting parameters are γ 2 ≈0.02γ 3, Δcs+2δ, and nσ13 =6.

Fig. 5.
Fig. 5.

(a). The control phase Φc (proportional to the applied sinusoidal voltage) versus time. (b) Transmission of the combined signal and the control fields versus time. (c) The control phase Φc (proportional to the square-wave voltage) versus time. (d) Transmission of the combined signal and the control fields versus time. The measurements are taken with δ=20 MHz, Δs=-δ=-20 MHz, Δcs+2δ. The other parameters are the same as that in Fig. 4.

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