Abstract

We investigate the effects of collisional dephasing and Doppler broadening on the quantum beats, narrow resonances, and probe transparency induced by quantum interference in a Vee-type atom consisting of an excited doublet coupled to a single ground level by the vacuum. We show that the amplitudes of the quantum-beat oscillations are greatly reduced, and the narrow resonances are substantially suppressed and broadened, for even very small dephasing rates and Doppler broadening. Fluorescence quenching and the previously reported probe transparency can never occur in the presence of dephasing collisions and Doppler broadening.

© 1998 Optical Society of America

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  1. D. A. Cardimona, M. G. Raymer, and C. R. Stroud Jr., J. Phys. B 15, 55 (1982).
    [CrossRef]
  2. S. Y. Zhu, R. C. F. Chan, and C. P. Lee, Phys. Rev. A 52, 710 (1995); S. Y. Zhu and M. O. Scully, Phys. Rev. Lett. 76, 388 (1996); H. R. Xia, C. Y. Ye, and S. Y. Zhu, Phys. Rev. Lett. PRLTAO 77, 1032 (1996).
    [CrossRef] [PubMed]
  3. P. Zhou and S. Swain, Phys. Rev. Lett. 77, 3995 (1996); 78, 832 (1997); Phys. Rev. A 56, 3011 (1997).
    [CrossRef] [PubMed]
  4. S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989); S. E. Harris and J. J. Macklin, Phys. Rev. A 40, R4135 (1989); A. Imamoglu, Phys. Rev. A PLRAAN 40, R2835 (1989).
    [CrossRef] [PubMed]
  5. M. O. Scully, S. Y. Zhu, and A. Gavrielides, Phys. Rev. Lett. 62, 2813 (1989).
    [CrossRef] [PubMed]
  6. K. J. Boller, A. Imamoglu, and S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991); M. Fleischauer, C. H. Keitel, L. M. Narducci, M. O. Scully, S. Y. Zhu, and M. S. Zubairy, Opt. Commun. 94, 599 (1992); G. C. Hegerfeld and M. B. Plenio, Z. Phys. B ZPCMDN 96, 533 (1995); Y. Li and M. Xiao, Phys. Rev. A PLRAAN 51, 4959 (1995); S. Y. Zhu, L. M. Narducci, and M. O. Scully, Phys. Rev. A PLRAAN 52, 4791 (1995); G. S. Agarwal, Phys. Rev. A PLRAAN 54, R3734 (1996).
    [CrossRef] [PubMed]
  7. J. E. Field, K. H. Hahn, and S. E. Harris, Phys. Rev. Lett. 67, 3062 (1991).
    [CrossRef] [PubMed]
  8. S. E. Harris, J. E. Field, and A. Imamoglu, Phys. Rev. Lett. 64, 1107 (1990); P. A. Lakshmi and S. Swain, J. Mod. Opt. 38, 2031 (1991); A. Karawajczyk and J. Zakrzewski, Phys. Rev. A PLRAAN 51, 830 (1995); G. Vemuri and G. S. Agarwal, Phys. Rev. A PLRAAN 53, 1060 (1996).
    [CrossRef] [PubMed]
  9. T. Hellmuth, H. Walther, A. Zajonc, and W. Schleich, Phys. Rev. A 35, 2532 (1987); G. C. Hegerfeldt and M. B. Plenio, Quantum Opt. 6, 15 (1994); B. M. Garraway and P. L. Knight, Phys. Rev. A PLRAAN 54, 3592 (1996).
    [CrossRef] [PubMed]
  10. G. S. Agarwal, Quantum Optics, Vol. 70 of Springer Tracts in Modern Physics (Springer, Berlin, 1974).
  11. M. Sargent III, M. O. Scully, and W. E. Lamb, Jr., Laser Physics (Addison-Wesley, London, 1974), Chap. 10.

1991 (1)

J. E. Field, K. H. Hahn, and S. E. Harris, Phys. Rev. Lett. 67, 3062 (1991).
[CrossRef] [PubMed]

1989 (1)

M. O. Scully, S. Y. Zhu, and A. Gavrielides, Phys. Rev. Lett. 62, 2813 (1989).
[CrossRef] [PubMed]

1982 (1)

D. A. Cardimona, M. G. Raymer, and C. R. Stroud Jr., J. Phys. B 15, 55 (1982).
[CrossRef]

Cardimona, D. A.

D. A. Cardimona, M. G. Raymer, and C. R. Stroud Jr., J. Phys. B 15, 55 (1982).
[CrossRef]

Field, J. E.

J. E. Field, K. H. Hahn, and S. E. Harris, Phys. Rev. Lett. 67, 3062 (1991).
[CrossRef] [PubMed]

Gavrielides, A.

M. O. Scully, S. Y. Zhu, and A. Gavrielides, Phys. Rev. Lett. 62, 2813 (1989).
[CrossRef] [PubMed]

Hahn, K. H.

J. E. Field, K. H. Hahn, and S. E. Harris, Phys. Rev. Lett. 67, 3062 (1991).
[CrossRef] [PubMed]

Harris, S. E.

J. E. Field, K. H. Hahn, and S. E. Harris, Phys. Rev. Lett. 67, 3062 (1991).
[CrossRef] [PubMed]

Raymer, M. G.

D. A. Cardimona, M. G. Raymer, and C. R. Stroud Jr., J. Phys. B 15, 55 (1982).
[CrossRef]

Scully, M. O.

M. O. Scully, S. Y. Zhu, and A. Gavrielides, Phys. Rev. Lett. 62, 2813 (1989).
[CrossRef] [PubMed]

Stroud Jr., C. R.

D. A. Cardimona, M. G. Raymer, and C. R. Stroud Jr., J. Phys. B 15, 55 (1982).
[CrossRef]

Zhu, S. Y.

M. O. Scully, S. Y. Zhu, and A. Gavrielides, Phys. Rev. Lett. 62, 2813 (1989).
[CrossRef] [PubMed]

J. Phys. B (1)

D. A. Cardimona, M. G. Raymer, and C. R. Stroud Jr., J. Phys. B 15, 55 (1982).
[CrossRef]

Phys. Rev. Lett. (2)

J. E. Field, K. H. Hahn, and S. E. Harris, Phys. Rev. Lett. 67, 3062 (1991).
[CrossRef] [PubMed]

M. O. Scully, S. Y. Zhu, and A. Gavrielides, Phys. Rev. Lett. 62, 2813 (1989).
[CrossRef] [PubMed]

Other (8)

K. J. Boller, A. Imamoglu, and S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991); M. Fleischauer, C. H. Keitel, L. M. Narducci, M. O. Scully, S. Y. Zhu, and M. S. Zubairy, Opt. Commun. 94, 599 (1992); G. C. Hegerfeld and M. B. Plenio, Z. Phys. B ZPCMDN 96, 533 (1995); Y. Li and M. Xiao, Phys. Rev. A PLRAAN 51, 4959 (1995); S. Y. Zhu, L. M. Narducci, and M. O. Scully, Phys. Rev. A PLRAAN 52, 4791 (1995); G. S. Agarwal, Phys. Rev. A PLRAAN 54, R3734 (1996).
[CrossRef] [PubMed]

S. E. Harris, J. E. Field, and A. Imamoglu, Phys. Rev. Lett. 64, 1107 (1990); P. A. Lakshmi and S. Swain, J. Mod. Opt. 38, 2031 (1991); A. Karawajczyk and J. Zakrzewski, Phys. Rev. A PLRAAN 51, 830 (1995); G. Vemuri and G. S. Agarwal, Phys. Rev. A PLRAAN 53, 1060 (1996).
[CrossRef] [PubMed]

T. Hellmuth, H. Walther, A. Zajonc, and W. Schleich, Phys. Rev. A 35, 2532 (1987); G. C. Hegerfeldt and M. B. Plenio, Quantum Opt. 6, 15 (1994); B. M. Garraway and P. L. Knight, Phys. Rev. A PLRAAN 54, 3592 (1996).
[CrossRef] [PubMed]

G. S. Agarwal, Quantum Optics, Vol. 70 of Springer Tracts in Modern Physics (Springer, Berlin, 1974).

M. Sargent III, M. O. Scully, and W. E. Lamb, Jr., Laser Physics (Addison-Wesley, London, 1974), Chap. 10.

S. Y. Zhu, R. C. F. Chan, and C. P. Lee, Phys. Rev. A 52, 710 (1995); S. Y. Zhu and M. O. Scully, Phys. Rev. Lett. 76, 388 (1996); H. R. Xia, C. Y. Ye, and S. Y. Zhu, Phys. Rev. Lett. PRLTAO 77, 1032 (1996).
[CrossRef] [PubMed]

P. Zhou and S. Swain, Phys. Rev. Lett. 77, 3995 (1996); 78, 832 (1997); Phys. Rev. A 56, 3011 (1997).
[CrossRef] [PubMed]

S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989); S. E. Harris and J. J. Macklin, Phys. Rev. A 40, R4135 (1989); A. Imamoglu, Phys. Rev. A PLRAAN 40, R2835 (1989).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Fluorescence intensity against τ=γ2t/π, with ω21=5γ2 and various initial conditions: |Ψ(0)=|s (solid curve), |a (dashed curve), and |1〉 (dot-dashed curve). We set γ1=γ2, γ12=γM, and Γ21=0.

Fig. 2
Fig. 2

Same as Fig. 1 but with ω21=3γ2, |Ψ(0)=|a, and different dephasing rates: Γ21=0 (solid curve), 0.1γ2 (dashed curve), and 0.5γ2 (dot-dashed curve).

Fig. 3
Fig. 3

Probe absorption spectrum against ω=(ωp-ω0)/γ2 with different dephasing rates: Γ10=Γ20=0 (solid curve), 0.01γ2 (dashed curve), and 0.05γ2 (dot-dashed curve). (a) ω21=0, γ1=γ2, γ12=0.95γM; (b) ω21=0.5γ2, γ1=γ2, γ12=γM; and (c) ω21=0.5γ2, γ1=0.1γ2, γ12=γM.

Fig. 4
Fig. 4

Probe absorption spectrum for Γij=0, and different Doppler broadenings: σ=0 (solid curve), 0.1γ2 (dashed curve), 0.5γ2 (dash-dotted curve), and γ2 (dotted curve). (a) ω21=0, γ1=γ2, γ12=0.95γM; and (b) ω21=0.5γ2, γ1=γ2, γ12=γM.

Equations (35)

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ρ˙10=-12 γ1+Γ10-i 12 ω21ρ10-12 γ12ρ20,
ρ˙20=-12 γ2+Γ20+i 12 ω21ρ20-12 γ12ρ10,
ρ˙21=-12 (γ1+γ2)+Γ21+iω21ρ21-12 γ12(ρ22+ρ11),
ρ˙jj=-γjρjj-12 γ12(ρ12+ρ21)(j=1, 2),
j=02ρjj=1,ρlk=ρkl*,
I(t)-ρ˙11-ρ˙22
=γ1ρ11(t)+γ2ρ22(t)+γ12ρ12(t)+γ12ρ21(t).
I(t)=γ1ρ11(0)exp(-γ1t)+γ2ρ22(0)exp(-γ2t),
I(t)=-ω21A exp(-(γ+Γ21)t)+Λ-B exp(-Λ-t)+Λ+C exp(-Λ+t),
A=ω21γ[ρ11(0)+ρ22(0)]+iγ2[ρ21(0)-ρ12(0)]δ2,
B=γ2α+[ρ11(0)+ρ22(0)]-γ(δ-iα+ω21)ρ21(0)-γ(δ+iα+ω21)ρ12(0)2δ2,
C=γ2α-[ρ11(0)+ρ22(0)]+γ(δ+iα-ω21)ρ21(0)+γ(δ-iα-ω21)ρ12(0)2δ2,
Λ±=γ+γ2ω212 Γ21±δ,
α±=1±γ2Γ21ω212δ,
δ=γ2-ω212.
I(t)=γω21|δ|2(1-cos|δ|t)exp(-γt).
I(t)=2γ|δ|2 |δ|cos |δ|t2-γ sin |δ|t22 exp(-γt).
ρ(0)=|11|,|22|or1001,
I(t)=γ|δ|2 (ω212-γ2 cos|δ|t-γ|δ|sin|δ|t)exp(-γt),
I(t)=γω21|δ|2 exp[-(γ+Γ21)t]-γω21|δ|2 cos|δ|t+γ3Γ21ω212|δ|3 γ2-|δ|2+γ3Γ21ω212sin|δ|t×exp-γ+γ2Γ21ω212t.
I(t)=γω21|δ|2 exp[-(γ+Γ21)t]-γ1-γ2|δ|2cos|δ|t+2γ2|δ| 1+γΓ212|δ|2 1+γ3Γ21ω214sin|δ|t×exp-γ+γ2Γ21ω212t,
I(t)=γω21|δ|2 exp[-(γ+Γ21)t]-γ3|δ|2 cos|δ|t+γ2|δ| 1+γ3Γ21ω212|δ|2 1+γΓ21ω212sin|δ|t×exp-γ+γ2Γ21ω212t.
A(ωp)
=ReN(ωp)(12 γ1+Γ10-iω+)(12 γ2+Γ20-iω-)-14 γ122
N(ωp)=(12 κ-iγ1ω-+γ1Γ20)(ρ¯00-ρ¯11)+(12 κ-iγ2ω++γ2Γ10)(ρ¯00-ρ¯22)+γ12ρ¯21(iω+-Γ10)+γ12ρ¯12(iω--Γ20),
ρ¯21=-γ12(ρ¯11+ρ¯22)γ1+γ2+2Γ21+i2ω21,ρ¯12=ρ¯21*,
ωT=ω0+ω21(γ1-γ2)2(γ1+γ2).
ϱ(v)=1πμ exp(-v2/μ2),
A(ωp)=Re2ν--βiσ Z(ζ-)+2ν++βiσ Z(ζ+),
ν±=γ2 1±1-κ+ω212γ2,
β=ω212γ2-(κ+ω212),
Z(ζ±)iσν±-i(ωp-ω0),
A(ωp)=(2ν--β)ν-ν-2+(ωp-ω0)2+(2ν++β)ν+ν+2+(ωp-ω0)2,
Z(ζ±)exp-ωp-ω0σ2×iπ-20ωp-ω0σ exp(x2)dx,
A(ωp)2πγσ exp-ωp-ω0σ2.

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