Abstract

The improved density-functional theory is employed to obtain the eigenstates of electrons in an asymmetric quantum well. On the basis of calculated eigenstates, the semiconductor Bloch equations are used to calculate the transient density matrix when a pulsed intersubband laser coupling is applied to the system. The new dynamics of the individual absorption peaks is analyzed for the first time by use of a self-consistent-field theory. Based on this, the time-averaged optical spectrum is calculated to show the coherent-transition-induced quantum interference in the system. The new phenomena of probe-field amplification is observed, and the threshold laser intensity for observing it is given.

© 1998 Optical Society of America

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References

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  1. B. R. Mollow, Phys. Rev. A 5, 2217 (1972).
    [CrossRef]
  2. F. Y. Wu, S. Ezekiel, M. Ducloy, and B. R. Mollow, Phys. Rev. Lett. 38, 1077 (1977).
    [CrossRef]
  3. D. A. Cardimona, M. G. Raymer, and C. R. Stroud, Jr., J. Phys. B 15, 55 (1982).
    [CrossRef]
  4. S. E. Harris, J. E. Field, and A. Imamogğlu, Phys. Rev. Lett. 64, 1107 (1990).
    [CrossRef] [PubMed]
  5. H. Fearn, C. Keitel, M. O. Scully, and S.-Y. Zhu, Opt. Commun. 87, 323 (1992).
    [CrossRef]
  6. A. Imamogğlu, J. E. Field, and S. E. Harris, Phys. Rev. Lett. 66, 1154 (1991).
    [CrossRef]
  7. Y. Zhao, D. Huang, and C. Wu, Opt. Lett. 19, 816 (1994); D. Huang, C. Wu, and Y. Zhao, J. Opt. Soc. Am. B 11, 2258 (1994); S. M. Sadeghi, J. F. Young, and J. Meyer, Phys. Rev. B PRBMDO 51, 13349 (1995); D. S. Lee and K. J. Malloy, Phys. Rev. B PRBMDO 53, 15749 (1996).
    [CrossRef] [PubMed]
  8. S. Schmitt-Rink and D. S. Chemla, Phys. Rev. Lett. 57, 2752 (1986); Y. Zhao, D. Huang, and C. Wu, Quantum Opt. 6, 327 (1994); D. Huang and Y. Zhao, Phys. Rev. A PLRAAN 51, 1617 (1995).
    [CrossRef] [PubMed]
  9. A. Imamogğlu and R. J. Ram, Opt. Lett. 19, 1744 (1994).
    [CrossRef]
  10. Y. Zhao, D. Huang, and C. Wu, J. Opt. Soc. Am. B 13, 1614 (1996).
    [CrossRef]
  11. D. A. Cardimona, M. P. Sharma, and M. A. Ortega, J. Phys. B 22, 4029 (1989); D. A. Cardimona, Phys. Rev. A 41, 5016 (1990).
    [CrossRef] [PubMed]
  12. M. Lindberg and S. W. Koch, Phys. Rev. B 38, 3342 (1988).
    [CrossRef]
  13. D. H. Huang and M. O. Manasreh, Phys. Rev. B 54, 5620 (1996).
    [CrossRef]
  14. W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
    [CrossRef]
  15. L. Hedin and B. I. Lundqvist, J. Phys. C 4, 2064 (1971).
    [CrossRef]
  16. S. Adachi, J. Appl. Phys. 53, R1 (1985).
    [CrossRef]
  17. A. Tomita, Phys. Rev. B 54, 5609 (1996).
    [CrossRef]

1996 (3)

D. H. Huang and M. O. Manasreh, Phys. Rev. B 54, 5620 (1996).
[CrossRef]

A. Tomita, Phys. Rev. B 54, 5609 (1996).
[CrossRef]

Y. Zhao, D. Huang, and C. Wu, J. Opt. Soc. Am. B 13, 1614 (1996).
[CrossRef]

1994 (1)

1992 (1)

H. Fearn, C. Keitel, M. O. Scully, and S.-Y. Zhu, Opt. Commun. 87, 323 (1992).
[CrossRef]

1991 (1)

A. Imamogğlu, J. E. Field, and S. E. Harris, Phys. Rev. Lett. 66, 1154 (1991).
[CrossRef]

1990 (1)

S. E. Harris, J. E. Field, and A. Imamogğlu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef] [PubMed]

1988 (1)

M. Lindberg and S. W. Koch, Phys. Rev. B 38, 3342 (1988).
[CrossRef]

1985 (1)

S. Adachi, J. Appl. Phys. 53, R1 (1985).
[CrossRef]

1982 (1)

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

1977 (1)

F. Y. Wu, S. Ezekiel, M. Ducloy, and B. R. Mollow, Phys. Rev. Lett. 38, 1077 (1977).
[CrossRef]

1972 (1)

B. R. Mollow, Phys. Rev. A 5, 2217 (1972).
[CrossRef]

1971 (1)

L. Hedin and B. I. Lundqvist, J. Phys. C 4, 2064 (1971).
[CrossRef]

1965 (1)

W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
[CrossRef]

Adachi, S.

S. Adachi, J. Appl. Phys. 53, R1 (1985).
[CrossRef]

Cardimona, D. A.

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

Ducloy, M.

F. Y. Wu, S. Ezekiel, M. Ducloy, and B. R. Mollow, Phys. Rev. Lett. 38, 1077 (1977).
[CrossRef]

Ezekiel, S.

F. Y. Wu, S. Ezekiel, M. Ducloy, and B. R. Mollow, Phys. Rev. Lett. 38, 1077 (1977).
[CrossRef]

Fearn, H.

H. Fearn, C. Keitel, M. O. Scully, and S.-Y. Zhu, Opt. Commun. 87, 323 (1992).
[CrossRef]

Field, J. E.

A. Imamogğlu, J. E. Field, and S. E. Harris, Phys. Rev. Lett. 66, 1154 (1991).
[CrossRef]

S. E. Harris, J. E. Field, and A. Imamogğlu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef] [PubMed]

Harris, S. E.

A. Imamogğlu, J. E. Field, and S. E. Harris, Phys. Rev. Lett. 66, 1154 (1991).
[CrossRef]

S. E. Harris, J. E. Field, and A. Imamogğlu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef] [PubMed]

Hedin, L.

L. Hedin and B. I. Lundqvist, J. Phys. C 4, 2064 (1971).
[CrossRef]

Huang, D.

Huang, D. H.

D. H. Huang and M. O. Manasreh, Phys. Rev. B 54, 5620 (1996).
[CrossRef]

Imamogglu, A.

A. Imamogğlu and R. J. Ram, Opt. Lett. 19, 1744 (1994).
[CrossRef]

A. Imamogğlu, J. E. Field, and S. E. Harris, Phys. Rev. Lett. 66, 1154 (1991).
[CrossRef]

S. E. Harris, J. E. Field, and A. Imamogğlu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef] [PubMed]

Keitel, C.

H. Fearn, C. Keitel, M. O. Scully, and S.-Y. Zhu, Opt. Commun. 87, 323 (1992).
[CrossRef]

Koch, S. W.

M. Lindberg and S. W. Koch, Phys. Rev. B 38, 3342 (1988).
[CrossRef]

Kohn, W.

W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
[CrossRef]

Lindberg, M.

M. Lindberg and S. W. Koch, Phys. Rev. B 38, 3342 (1988).
[CrossRef]

Lundqvist, B. I.

L. Hedin and B. I. Lundqvist, J. Phys. C 4, 2064 (1971).
[CrossRef]

Manasreh, M. O.

D. H. Huang and M. O. Manasreh, Phys. Rev. B 54, 5620 (1996).
[CrossRef]

Mollow, B. R.

F. Y. Wu, S. Ezekiel, M. Ducloy, and B. R. Mollow, Phys. Rev. Lett. 38, 1077 (1977).
[CrossRef]

B. R. Mollow, Phys. Rev. A 5, 2217 (1972).
[CrossRef]

Ram, R. J.

Raymer, M. G.

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

Scully, M. O.

H. Fearn, C. Keitel, M. O. Scully, and S.-Y. Zhu, Opt. Commun. 87, 323 (1992).
[CrossRef]

Sham, L. J.

W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
[CrossRef]

Stroud Jr., C. R.

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

Tomita, A.

A. Tomita, Phys. Rev. B 54, 5609 (1996).
[CrossRef]

Wu, C.

Wu, F. Y.

F. Y. Wu, S. Ezekiel, M. Ducloy, and B. R. Mollow, Phys. Rev. Lett. 38, 1077 (1977).
[CrossRef]

Zhao, Y.

Zhu, S.-Y.

H. Fearn, C. Keitel, M. O. Scully, and S.-Y. Zhu, Opt. Commun. 87, 323 (1992).
[CrossRef]

J. Appl. Phys. (1)

S. Adachi, J. Appl. Phys. 53, R1 (1985).
[CrossRef]

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

J. Phys. B (1)

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

J. Phys. C (1)

L. Hedin and B. I. Lundqvist, J. Phys. C 4, 2064 (1971).
[CrossRef]

Opt. Commun. (1)

H. Fearn, C. Keitel, M. O. Scully, and S.-Y. Zhu, Opt. Commun. 87, 323 (1992).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
[CrossRef]

Phys. Rev. A (1)

B. R. Mollow, Phys. Rev. A 5, 2217 (1972).
[CrossRef]

Phys. Rev. B (3)

M. Lindberg and S. W. Koch, Phys. Rev. B 38, 3342 (1988).
[CrossRef]

D. H. Huang and M. O. Manasreh, Phys. Rev. B 54, 5620 (1996).
[CrossRef]

A. Tomita, Phys. Rev. B 54, 5609 (1996).
[CrossRef]

Phys. Rev. Lett. (3)

F. Y. Wu, S. Ezekiel, M. Ducloy, and B. R. Mollow, Phys. Rev. Lett. 38, 1077 (1977).
[CrossRef]

S. E. Harris, J. E. Field, and A. Imamogğlu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef] [PubMed]

A. Imamogğlu, J. E. Field, and S. E. Harris, Phys. Rev. Lett. 66, 1154 (1991).
[CrossRef]

Other (3)

Y. Zhao, D. Huang, and C. Wu, Opt. Lett. 19, 816 (1994); D. Huang, C. Wu, and Y. Zhao, J. Opt. Soc. Am. B 11, 2258 (1994); S. M. Sadeghi, J. F. Young, and J. Meyer, Phys. Rev. B PRBMDO 51, 13349 (1995); D. S. Lee and K. J. Malloy, Phys. Rev. B PRBMDO 53, 15749 (1996).
[CrossRef] [PubMed]

S. Schmitt-Rink and D. S. Chemla, Phys. Rev. Lett. 57, 2752 (1986); Y. Zhao, D. Huang, and C. Wu, Quantum Opt. 6, 327 (1994); D. Huang and Y. Zhao, Phys. Rev. A PLRAAN 51, 1617 (1995).
[CrossRef] [PubMed]

D. A. Cardimona, M. P. Sharma, and M. A. Ortega, J. Phys. B 22, 4029 (1989); D. A. Cardimona, Phys. Rev. A 41, 5016 (1990).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Sketch of the three-level Al0.25Ga0.75As/GaAs/ Al0.4Ga0.6As asymmetry quantum-well structure. The three energy levels are labeled by Ej with j=1,2,3; EF is the Fermi energy, and the double-head thick arrow stands for the intersubband laser coupling applied to the system. Here, the second energy level is slightly populated.

Fig. 2
Fig. 2

Plots of the diagonal density-matrix elements ρ22(k;t) (solid curve) and ρ33(k;t) (dashed curve) at k=0 in an intersubband laser coupled three-level asymmetric Al0.25Ga0.75As/ GaAs/Al0.4Ga0.6As quantum-well system, where T=4 K, LW =150 Å, n2D=1.5×1012 cm-2 (doping in the well), Ec =200 kV/cm, ωc=E3(0)-E2(0), τ23(k;t)=28 fs, τjrel(k;t) =45 fs for j=1, 2, 3, and the square coupling laser pulse duration is 350 fs.

Fig. 3
Fig. 3

Sketch of the two possible processes of quantum interference in the coupled asymmetric quantum well, where the thick arrow represents the coherent transition and the thin arrows represent the probe-field-induced indirect transitions.

Fig. 4
Fig. 4

Plots of (a) the dynamics of one negative absorption peak with ωp=30 meV and Tpulse=612 fs and (b) the time-averaged absorption coefficient with (solid curve) or without (dashed curve) quantum interference for square probe pulse duration Tpulse=200 fs in the same system as described in Fig. 2. Here, we have taken τ12(k;t)=132 fs, τ13(k;t)=36 fs, and tD =0.

Fig. 5
Fig. 5

Plots of (a) the time-averaged optical spectrum with different coupling laser strengths Ec = 100, 200, 300, 400 kV/cm, and (b) the time-averaged optical spectrum with various detunings Δ(ωc)=-20, -10, 0, 10, 20 meV in the same system as described in Fig. 2. Here, we have taken τ12(k;t)=132 fs, τ13(k;t)=36 fs, Tpulse=200 fs, and tD=0.

Equations (42)

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-22 ddz 1m*(z) dϕj(z)dz+{VQW(z)+VH(z)
+Vxc[n(z)]}ϕj(z)=Ejϕj(z)
VQW(z)=0.57×1.247x(eV)leftbarrier00<z<LW0.57×1.247y(eV)rightbarrier,
n(z)=1π j=1N0+kdkfj(k)ϕj2(z).
ddz b(z) ddz VH(z)=e20 [ND(z)-n(z)],
Vxc[n(z)]=-e28π0b(z)a0*(z)× 1+0.7734rs(z)21 ln1+21rs(z)×2παrs(z).
α=49π1/3,
fj(k)=expEj(k)-EFkBT+1-1,
a0*(z)=4π0b(z)2m*(z)e2
rs(z)={(4/3)π[a0*(z)]3n(z)}-1/3
Ej(k)=Ej+2k22mj*(k),
1mj*(k)=1-PjWmB*(k)+PjWmW*(k),
PjW=wellregionsϕj2(z)dz
memα*(k)=1+Epα3 2Egα+2k2/2mα*+1Egα+Δ0α+2k2/2mα*
δΣjc(k)=--+dzϕj2(z)Vxc[n(z)]-i,kfi(k)e220b(|k-k|+qiTF)×-+dz-+dzϕj(z)ϕi(z)×exp(-|k-k||z-z|)ϕi(z)ϕj(z),
qiTF=e28π0bkBT 0+dk k cosh-2Ei(k)-EF2kBT.
ρ11(k;t)t=-Δρ11(k;t)τ1rel(k;t),
t ρ22(k;t)=-Δρ22(k;t)τ2rel(k;t)-2 Imρ¯23(k;t)Δ¯c(t)+U32,32kρ¯23*(k;t)+2j=13U32,jjkΔρjj(k;t)exp(iωct)+U32,23kρ¯23(k;t)exp(i2ωct),
[ρ22(k;t)+ρ33(k;t)]t
=-Δρ22(k;t)τ2rel(k;t)-Δρ33(k;t)τ3rel(k;t).
i t ρ¯23(k;t)
=ρ¯23(k;t)ωc-iτ23(k;t)-Ω32(k)+2j=13(U22,jj-U33,jj)kΔρjj(k;t)+2 Re(U22,23-U33,23)kρ¯23(k;t)exp(iωct)+[ρ33(k;t)-ρ22(k;t)]Δ¯c(t)+U23,23kρ¯23(k;t)+2j=13U23,jjkΔρjj(k;t)exp(-iωct)+U23,32kρ¯23*(k;t)exp(-i2ωct).
Δ¯c(t)=-eEc(t)-+ϕ2(z)zϕ3(z)dz,
Uii,jj=-e220b -+dz-+dzϕi(z)×ϕi(z)|z-z|ϕj(z)ϕj(z)+-+dzϕi(z)ϕi(z) Vxc[n(z)]n(z) ϕj(z)ϕj(z)
i t ρ¯12(k;t)
=ρ¯12(k;t)ωp-iτ12(k;t)-Ω21(k)+2j=13(U11,jj-U22,jj)kΔρjj(k;t)
+2 Re(U11,23-U22,23)kρ¯23(k;t)exp(iωct)+[ρ22(k;t)-ρ11(k;t)]Δ¯12(tD;t)+U12,12kχ12ωp(k;t)+U12,13kχ13ωp(k;t)+ρ¯23*(k;t)Δ¯13(tD;t)+U13,12kχ12ωp(k;t)+U13,13kχ13ωp(k;t)exp(-iωct)+ρ¯13(k;t)×Δ¯c(t)exp(-iωct)+2 ReU32,32kρ¯23*(k;t)×exp(-iωct)+2j=13U32,jjkΔρjj(k;t),
i t ρ¯13(k;t)
=ρ¯13(k;t)ωp-iτ13(k;t)-Ω31(k)+2j=13(U11,jj-U33,jj)kΔρjj(k;t)+2 Re(U11,23-U33,23)kρ¯23(k;t)exp(iωct)+[ρ33(k;t)-ρ11(k;t)]Δ¯13(tD;t)+U13,12kχ12ωp(k;t)+U13,13kχ13ωp(k;t)+ρ¯23(k;t)Δ¯12(tD;t)+U12,12kχ12ωp(k;t)+U12,13kχ13ωp(k;t)exp(iωct)+ρ¯12(k;t)×Δ¯c(t)exp(iωct)+2 ReU23,23kρ¯23(k;t)×exp(iωct)+2j=13U23,jjkΔρjj(k;t),
χijωp(k;t)=ρ¯ij(k;j)ωp+ρ¯ji(k;t)-ωp,
Δ¯1j(tD;t)=-eEp(t)θ(t-tD)-+ϕ1(z)zϕj(z)dz
βabs[ωp, tD; t]=ωpbcn[ωp, tD; t] 11-exp(-ωp/kBT)×Im αL[ωp, tD; t],
αL[ωp, tD; t]=1π0bLWEp2(t) 0+kdk[χ12ωp(k; t)×Δ¯12(tD; t)+χ13ωp(k; t)Δ¯13(tD; t)].
n[ωp, tD; t]
=12 {1+Re αL[ωp, tD; t]
+(1+Re αL[ωp,tD;t])2+(Im αL[ωp,tD;t])2}1/2.
β¯abs[ωp,tD]=1Tpulse tDtD+Tpulsesdtβabs[ωp,tD;t].
ΩR=[E3(0)-E2(0)-ωc]2+[Δc(0)]2.
ρ31(k;t)ωpρ12(k;t)ωpρ23*(k;t),
ρ21(k;t)ωpρ13(k;t)ωpρ23(k;t).
ωp±=(ΩRωc)/2±Ω32±δcoul±,
-1Δc>Ω32+2δcoul-

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