Abstract

We show that application of self-induced transparency (SIT) solitons as a driving field in V-type electromagnetically induced transparency (EIT) leads to “mixed induced transparency” (MIT) that nicely combines the best features of both SIT and EIT.

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  1. S. L. McCall and E. L. Hahn, "Self induced transparency by pulsed coherent light," Phys. Rev. Lett. 18, 908 (1967).
    [CrossRef]
  2. S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183 457 (1969).
    [CrossRef]
  3. M. J. Konopnicki and J. H. Eberly, "Simultaneous propagation of short different-wavelength optical pulses," Phys. Rev. A 24, 2567 (1981).
    [CrossRef]
  4. J. Oreg, F. T. Hioe, and J. H. Eberly, "Adiabatic following in multilevel systems," Phys. Rev. A 29, 690 (1984).
    [CrossRef]
  5. R. Grobe, F. T. Hioe, and J. H. Eberly, "Formation of shape-preserving pulses in a nonlinear adiabatically integrable system," Phys. Rev. Lett. 73, 3183 (1994).
    [CrossRef] [PubMed]
  6. S. E. Harris, "Electromagnetically induced tranparency with matched pulses," Phys. Rev. Lett. 71, 552 (1993).
    [CrossRef]
  7. S. E. Harris, "Normal-modes of electromagnetically induced transparency," Phys. Rev. Lett. 72, 52 (1994).
    [CrossRef] [PubMed]
  8. J. H. Eberly, M. L. Pons, H. R. Haq, "Dressed-state pulses in an absorbing medium," Phys. Rev. Lett. 72, 56 (1994).
    [CrossRef] [PubMed]
  9. W. E. Lamb, Jr., and R. C. Retherford, "Fine structure of the hydrogen atom. Part II," Phys. Rev. 81, 222 (1951).
    [CrossRef]
  10. A. Javan, "Theory of three-level maser," Phys. Rev. 107, 1579 (1957).
    [CrossRef]
  11. M. S. Feld and A. Javan, "Laser-induced line-narrowing effects in coupled Doppler-broadened transitions," Phys. Rev. 177, 540 (1969).
    [CrossRef]
  12. I. M. Beterov and V. P. Chebotaev, "Three-level gas laser," Pis'ma Zh. Eksp. Teor. Fiz. 9, 216 (1969) [Sov. Phys. JETP Lett. 9, 127 (1969)].
  13. T. H�nch and P. Toschek, "Theory of three-level gas laser amplifier," Z. Phys. 236, 213 (1970).
    [CrossRef]
  14. O. Kocharovskaya, "Amplificaton and lasing without inversion," Phys. Rep. 219, 175 (1992).
    [CrossRef]
  15. M. O. Scully, "From lasers and masers to phaseonium and phasers," Phys. Rep. 219, 191 (1992).
    [CrossRef]
  16. E. Arimondo, "Coherent population trapping in laser spectroscopy" in Progress in Optics edited by E. Wolf, Vol. XXXV, p.257 (Elsevier Science, Amsterdam, 1996).
    [CrossRef]
  17. S. E. Harris, "Electromagnetically induced transparency," Phys. Today p. 36, June (1997).
    [CrossRef]
  18. J. P. Marangos, "Electromagnetically induced transparency," J. Mod. Opt. 45, 471 (1998).
    [CrossRef]
  19. J. Mompart and R. Corbalan, "Lasing without inversion," Quantum Semiclass. Opt. 2, R7 (2000).
    [CrossRef]
  20. S. E. Harris, J. E. Field, and A. Imamoglu, "Non-linear optical processes using electromagnetically induced transparency," Phys. Rev. Lett. 64, 1107 (1990).
    [CrossRef] [PubMed]
  21. K. Hakuta, L. Marmet, and B. P. Stoicheff, "Electric-field-induced second harmonic generation with reduced absorption," Phys. Rev. Lett. 66, 596 (1991).
    [CrossRef] [PubMed]
  22. P. Hemmer, D. P. Katz, J. Donoghue, M. Cronin-Golomb, M. Shahriar, and P. Kumar, "Efficient low-intensity optical phase conjugation based on coherent population trapping in sodium," Opt. Lett. 20, 982 (1995).
    [CrossRef] [PubMed]
  23. M. Jain, M. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, "Efficient nonlinear frequency conversion with maximum atomic coherence," Phys. Rev. Lett. 77, 4326 (1996).
    [CrossRef] [PubMed]
  24. 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, 4049 (1999).
    [CrossRef]
  25. A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, "Raman generation by phased and antiphased molecular states," Phys. Rev. Lett. 85, 562 (2000).
    [CrossRef] [PubMed]
  26. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).
  27. J. H. Eberly, "Optical pulse and pulse-train propagation in a resonant medium," Phys. Rev. Lett. 22, 760 (1969).
    [CrossRef]
  28. L. Matulic and J. H. Eberly, "Analytic study of pulse chirping in self-induced transparency," Phys. Rev. A 6, 822 and 1258E (1972).
    [CrossRef]
  29. G. L. Lamb Jr., "Analytical descriptions of ultrashort optical pulse propagation in a resonant medium," Rev. Mod. Phys. 43, 99 (1971).
    [CrossRef]
  30. A. I. Maimistov, A. M. Basharov, S. O. Elyutin, and Yu. M. Sklyarov, "Present state of self-induced transparency theory," Phys. Rep. 191, 1 (1990).
    [CrossRef]
  31. L. A. Bolshov and V. V. Likhanskii, "Coherent interaction between emission pulses and resonant multilevel media," Kvantovaya Elektronika 12, 1339 (1985) [Sov. J. Quantum Electron. 15, 889 (1985)].
  32. A. Rahman and J. H. Eberly, "Theory of shape-preserving short pulses in inhomogeneously broadened three-level media," Phys. Rev. A 58, R805 (1998).
    [CrossRef]
  33. A. Rahman and J. H. Eberly, "Numerical experiments with optical pulses in V -type media," Opt. Express 4, 133 (1999). http://www.opticsexpress.org/oearchive/source/8487.htm
    [CrossRef] [PubMed]
  34. G. S. Agarwal and J. H. Eberly, " Continuous-probe solutions for self-similar pulses in four-level systems," Phys. Rev. A 60, 013404 (2000).
  35. V. V. Kozlov, P. G. Polynkin, and M. O. Scully, "Resonant Raman amplification of ultrashort pulses in a V-type medium," Phys. Rev. A 59, 3060 (1999).
    [CrossRef]
  36. N. V. Denisova, V. S. Egorov, V. V. Kozlov, N. M. Reutova, P. Yu. Serdobintsev, and E. E. Fradkin, "Weak-pulse transparency enhancement in an optically dense three-level medium induced by a 2pi-pulse in a neighboring transition (V -scheme)," Zh. Eksp. Teor. Fiz. 113, 71 (1998) [Sov. Phys. JETP 86, 39 (1998)];
  37. V. V. Kozlov and E. E. Fradkin, "Coherent effects in ultrashort pulse propagation through an optically thick three-level medium," Pis'ma Zh. Eksp. Teor. Fiz. 68, 359 (1998) [Sov. Phys. JETP Lett. 68, 383 (1998)].
  38. V. V. Kozlov and J. H. Eberly, "Ultrashort pulses in phaseonium: the interplay between SIT and EIT," Opt. Commun. 179, 85 (2000).
    [CrossRef]
  39. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge Univ. Press UK, 1997).
  40. G. S. Agarwal, M. O. Scully and H. Walther, to be published.
  41. J. H. Eberly, "Area Theorem rederived," Opt. Express 2, 173 (1998) http://www.opticsexpress.org/oearchive/source/4295.htm
    [CrossRef] [PubMed]
  42. F. A. Hopf, G. L. Lamb, Jr., C. K. Rhodes, and M. O. Scully, "Some results on coherent radiative phenomena with 0 pi pulses," Phys. Rev. A 3, 758 (1971).
    [CrossRef]

Other

S. L. McCall and E. L. Hahn, "Self induced transparency by pulsed coherent light," Phys. Rev. Lett. 18, 908 (1967).
[CrossRef]

S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183 457 (1969).
[CrossRef]

M. J. Konopnicki and J. H. Eberly, "Simultaneous propagation of short different-wavelength optical pulses," Phys. Rev. A 24, 2567 (1981).
[CrossRef]

J. Oreg, F. T. Hioe, and J. H. Eberly, "Adiabatic following in multilevel systems," Phys. Rev. A 29, 690 (1984).
[CrossRef]

R. Grobe, F. T. Hioe, and J. H. Eberly, "Formation of shape-preserving pulses in a nonlinear adiabatically integrable system," Phys. Rev. Lett. 73, 3183 (1994).
[CrossRef] [PubMed]

S. E. Harris, "Electromagnetically induced tranparency with matched pulses," Phys. Rev. Lett. 71, 552 (1993).
[CrossRef]

S. E. Harris, "Normal-modes of electromagnetically induced transparency," Phys. Rev. Lett. 72, 52 (1994).
[CrossRef] [PubMed]

J. H. Eberly, M. L. Pons, H. R. Haq, "Dressed-state pulses in an absorbing medium," Phys. Rev. Lett. 72, 56 (1994).
[CrossRef] [PubMed]

W. E. Lamb, Jr., and R. C. Retherford, "Fine structure of the hydrogen atom. Part II," Phys. Rev. 81, 222 (1951).
[CrossRef]

A. Javan, "Theory of three-level maser," Phys. Rev. 107, 1579 (1957).
[CrossRef]

M. S. Feld and A. Javan, "Laser-induced line-narrowing effects in coupled Doppler-broadened transitions," Phys. Rev. 177, 540 (1969).
[CrossRef]

I. M. Beterov and V. P. Chebotaev, "Three-level gas laser," Pis'ma Zh. Eksp. Teor. Fiz. 9, 216 (1969) [Sov. Phys. JETP Lett. 9, 127 (1969)].

T. H�nch and P. Toschek, "Theory of three-level gas laser amplifier," Z. Phys. 236, 213 (1970).
[CrossRef]

O. Kocharovskaya, "Amplificaton and lasing without inversion," Phys. Rep. 219, 175 (1992).
[CrossRef]

M. O. Scully, "From lasers and masers to phaseonium and phasers," Phys. Rep. 219, 191 (1992).
[CrossRef]

E. Arimondo, "Coherent population trapping in laser spectroscopy" in Progress in Optics edited by E. Wolf, Vol. XXXV, p.257 (Elsevier Science, Amsterdam, 1996).
[CrossRef]

S. E. Harris, "Electromagnetically induced transparency," Phys. Today p. 36, June (1997).
[CrossRef]

J. P. Marangos, "Electromagnetically induced transparency," J. Mod. Opt. 45, 471 (1998).
[CrossRef]

J. Mompart and R. Corbalan, "Lasing without inversion," Quantum Semiclass. Opt. 2, R7 (2000).
[CrossRef]

S. E. Harris, J. E. Field, and A. Imamoglu, "Non-linear optical processes using electromagnetically induced transparency," Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef] [PubMed]

K. Hakuta, L. Marmet, and B. P. Stoicheff, "Electric-field-induced second harmonic generation with reduced absorption," Phys. Rev. Lett. 66, 596 (1991).
[CrossRef] [PubMed]

P. Hemmer, D. P. Katz, J. Donoghue, M. Cronin-Golomb, M. Shahriar, and P. Kumar, "Efficient low-intensity optical phase conjugation based on coherent population trapping in sodium," Opt. Lett. 20, 982 (1995).
[CrossRef] [PubMed]

M. Jain, M. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, "Efficient nonlinear frequency conversion with maximum atomic coherence," Phys. Rev. Lett. 77, 4326 (1996).
[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, 4049 (1999).
[CrossRef]

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, "Raman generation by phased and antiphased molecular states," Phys. Rev. Lett. 85, 562 (2000).
[CrossRef] [PubMed]

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).

J. H. Eberly, "Optical pulse and pulse-train propagation in a resonant medium," Phys. Rev. Lett. 22, 760 (1969).
[CrossRef]

L. Matulic and J. H. Eberly, "Analytic study of pulse chirping in self-induced transparency," Phys. Rev. A 6, 822 and 1258E (1972).
[CrossRef]

G. L. Lamb Jr., "Analytical descriptions of ultrashort optical pulse propagation in a resonant medium," Rev. Mod. Phys. 43, 99 (1971).
[CrossRef]

A. I. Maimistov, A. M. Basharov, S. O. Elyutin, and Yu. M. Sklyarov, "Present state of self-induced transparency theory," Phys. Rep. 191, 1 (1990).
[CrossRef]

L. A. Bolshov and V. V. Likhanskii, "Coherent interaction between emission pulses and resonant multilevel media," Kvantovaya Elektronika 12, 1339 (1985) [Sov. J. Quantum Electron. 15, 889 (1985)].

A. Rahman and J. H. Eberly, "Theory of shape-preserving short pulses in inhomogeneously broadened three-level media," Phys. Rev. A 58, R805 (1998).
[CrossRef]

A. Rahman and J. H. Eberly, "Numerical experiments with optical pulses in V -type media," Opt. Express 4, 133 (1999). http://www.opticsexpress.org/oearchive/source/8487.htm
[CrossRef] [PubMed]

G. S. Agarwal and J. H. Eberly, " Continuous-probe solutions for self-similar pulses in four-level systems," Phys. Rev. A 60, 013404 (2000).

V. V. Kozlov, P. G. Polynkin, and M. O. Scully, "Resonant Raman amplification of ultrashort pulses in a V-type medium," Phys. Rev. A 59, 3060 (1999).
[CrossRef]

N. V. Denisova, V. S. Egorov, V. V. Kozlov, N. M. Reutova, P. Yu. Serdobintsev, and E. E. Fradkin, "Weak-pulse transparency enhancement in an optically dense three-level medium induced by a 2pi-pulse in a neighboring transition (V -scheme)," Zh. Eksp. Teor. Fiz. 113, 71 (1998) [Sov. Phys. JETP 86, 39 (1998)];

V. V. Kozlov and E. E. Fradkin, "Coherent effects in ultrashort pulse propagation through an optically thick three-level medium," Pis'ma Zh. Eksp. Teor. Fiz. 68, 359 (1998) [Sov. Phys. JETP Lett. 68, 383 (1998)].

V. V. Kozlov and J. H. Eberly, "Ultrashort pulses in phaseonium: the interplay between SIT and EIT," Opt. Commun. 179, 85 (2000).
[CrossRef]

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge Univ. Press UK, 1997).

G. S. Agarwal, M. O. Scully and H. Walther, to be published.

J. H. Eberly, "Area Theorem rederived," Opt. Express 2, 173 (1998) http://www.opticsexpress.org/oearchive/source/4295.htm
[CrossRef] [PubMed]

F. A. Hopf, G. L. Lamb, Jr., C. K. Rhodes, and M. O. Scully, "Some results on coherent radiative phenomena with 0 pi pulses," Phys. Rev. A 3, 758 (1971).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Pictorial illustration of MIT via a V -type atom under the action of a sequence of 2π-pulses (Ω) and a continuous probe field (α). The overall effect of a 2π-pulse applied to cb transition is in flipping the sign of the wave function of the ground state.

Fig. 2.
Fig. 2.

Time dependent plots of intensity of the probe pulse showing the effect of propagation over 2 Beer’s lengths in V-type system driven by a sequence of eleven 2π-pulses (shown in the inset). In all plots local time (t-z/v)/τp (with ν as phase velocity of light in the medium) is measured in units of the strong pulse duration τp and distance in Beer’s lengths, defined here as β≡i(k π τp )-1. For Rabi frequencies of the strong field, Ω, and the weak probe, α, we define intensity as |Ωτp2 and |ατp|2, correspondingly. Initially, the weak pulse has a super-Gaussian shape α=0.01 exp[-(t/80τp )8], see the snapshot at βL=0, and the strong pulses are identical 2π-solitons of self-induced transparency separated by 10 their own durations from each other: Ω=n=55 sech[(t+10p )/τp ], see inset.

Fig. 3.
Fig. 3.

Time dependent plots of population of the jai state at the input and after propagating 0.5, 1, 1.5, and 2 Beer’s lengths. Inset shows time evolution of ρaa at the entrance plane (βL=0) in absence of driving pulses on the |c〉↔|b〉 transition.

Fig. 4.
Fig. 4.

Energy and Area versus distance for the weak pulse: (1) with no driving field; (2) with driving field in the form of 2π-pulses, see figure caption for Fig. 2. Energy is normalized to its initial value.

Equations (17)

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V = α ( t ) 2 ( α b e i Δ t + adj . ) ,
a ˙ = i 2 α e i Δ t b ,
b ˙ = i 2 α e i Δ t a ,
c ˙ = 0 .
U α ( t ) = A a a + B b b + c c + ( C a b adj . ) .
A ( t ) = ( cos α ˜ 2 t i Δ α ˜ cos α ˜ 2 t ) exp [ i Δ 2 t ]
B ( t ) = ( cos α ˜ 2 t i Δ α ˜ cos α ˜ 2 t ) exp [ i Δ 2 t ]
C ( t ) = i α α ˜ sin α ˜ 2 t exp [ i Δ 2 t ]
U α ( t ) = cos [ α 2 t ] ( α α + b b ) i sin [ α 2 t ] σ x ( a , b ) + c c
U α ( t ) = exp [ i α 2 t σ x ] + c c = n = 0 N exp [ i α 2 τ σ x ] + c c ,
U θ ( t ) = cos [ θ ( t ) 2 ] ( b b + c c ) + a a i sin [ θ ( t ) 2 ] ( b c + c b ) ,
U 2 π ( t ) = a a ( b b + c c ) .
U ( t ) = U 2 π ( N ) U α ( τ ) U 2 π ( N 1 ) U 2 π ( 2 ) U α ( τ ) U 2 π ( 1 ) U α ( τ ) .
U 2 π U α ( τ ) U 2 π U α ( τ ) = exp ( i α 2 σ x τ ) exp ( i α 2 σ x τ ) = 1 .
[ z + n Ω c t ] Ω ( t , z ) = ik Ω ρ cb ,
[ z + n α c t ] α ( t , z ) = ik α ρ ab ,
κ Ω = k Ω cb 2 N 0 n Ω and κ α = k α ab 2 N 0 n α .

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