Abstract

The spatiotemporal dynamics of pulse-pair propagation in prepared media is investigated under two-photon resonance. A vector model is presented for the observation of the phase regulation of the temporal evolution of the coherent pulses. The results show how the phase and amplitude of one pulse are altered with the use of another pulse at the input of the detuning medium.

© 1999 Optical Society of America

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References

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  1. S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
    [Crossref] [PubMed]
  2. G. S. Agarwal, “Origin of gain in systems without inversion in bare or dressed states,” Phys. Rev. A 44, R28–R30 (1991); J. P. Dowling and C. M. Bowden, “Near dipole–dipole effects in lasing without inversion: an enhancement of gain and absorptionless index of refraction,” Phys. Rev. Lett. 70, 1421–1424 (1993).
    [Crossref] [PubMed]
  3. Lin Fu-Cheng, “Coherent control of a simple quantum system,” Chin. Phys. Lett. 14, 417–420 (1997).
    [Crossref]
  4. M. O. Scully, “Correlated spontaneous-emission lasers: quenching of quantum fluctuations in the relative phase angle,” Phys. Rev. Lett. 55, 2802–2805 (1985); M. O. Scully, “Enhancement of the index of refraction via quantum coherence,” Phys. Rev. Lett. 67, 1885–1888 (1991).
    [Crossref] [PubMed]
  5. M. Fleischhauer, C. H. Keitel, and M. O. Scully, “Resonantly enhanced refractive index without absorption via atomic coherence,” Phys. Rev. A 46, 1468–1687 (1992).
    [Crossref] [PubMed]
  6. S. E. Harris, “Normal modes for electromagnetically induced transparency,” Phys. Rev. Lett. 72, 52–55 (1994).
    [Crossref] [PubMed]
  7. J. H. Eberly, M. L. Pons, and H. R. Haq, “Dressed-field pulses in an absorbing medium,” Phys. Rev. Lett. 72, 56–59 (1994).
    [Crossref] [PubMed]
  8. J. H. Eberly, A. Rahman, and R. Grobe, “Index of refraction for an optical medium with clamped quantum phase,” Phys. Rev. Lett. 76, 3687–3690 (1996).
    [Crossref] [PubMed]
  9. N. Wang and H. Rabitz, “Optical control of optical pulse propagation in a medium of three-level systems,” Phys. Rev. A 52, R17–R20 (1995).
    [Crossref]
  10. G. Vemuri and K. V. Vasavada, “Pulse propagation in coherently prepared media,” Opt. Commun. 129, 379–386 (1996); G. Vemuri, K. V. Vasavada, G. S. Agarwal, and Q. Zhang, “Coherence-induced effects in pulse-pair propagation through absorbing media,” Phys. Rev. A 54, 3394–3399 (1996).
    [Crossref] [PubMed]
  11. P. Meystre and M. Sargent, Elements of Quantum Optics (Springer-Verlag, New York, 1990).

1997 (1)

Lin Fu-Cheng, “Coherent control of a simple quantum system,” Chin. Phys. Lett. 14, 417–420 (1997).
[Crossref]

1996 (2)

J. H. Eberly, A. Rahman, and R. Grobe, “Index of refraction for an optical medium with clamped quantum phase,” Phys. Rev. Lett. 76, 3687–3690 (1996).
[Crossref] [PubMed]

G. Vemuri and K. V. Vasavada, “Pulse propagation in coherently prepared media,” Opt. Commun. 129, 379–386 (1996); G. Vemuri, K. V. Vasavada, G. S. Agarwal, and Q. Zhang, “Coherence-induced effects in pulse-pair propagation through absorbing media,” Phys. Rev. A 54, 3394–3399 (1996).
[Crossref] [PubMed]

1995 (1)

N. Wang and H. Rabitz, “Optical control of optical pulse propagation in a medium of three-level systems,” Phys. Rev. A 52, R17–R20 (1995).
[Crossref]

1994 (2)

S. E. Harris, “Normal modes for electromagnetically induced transparency,” Phys. Rev. Lett. 72, 52–55 (1994).
[Crossref] [PubMed]

J. H. Eberly, M. L. Pons, and H. R. Haq, “Dressed-field pulses in an absorbing medium,” Phys. Rev. Lett. 72, 56–59 (1994).
[Crossref] [PubMed]

1992 (1)

M. Fleischhauer, C. H. Keitel, and M. O. Scully, “Resonantly enhanced refractive index without absorption via atomic coherence,” Phys. Rev. A 46, 1468–1687 (1992).
[Crossref] [PubMed]

1991 (1)

G. S. Agarwal, “Origin of gain in systems without inversion in bare or dressed states,” Phys. Rev. A 44, R28–R30 (1991); J. P. Dowling and C. M. Bowden, “Near dipole–dipole effects in lasing without inversion: an enhancement of gain and absorptionless index of refraction,” Phys. Rev. Lett. 70, 1421–1424 (1993).
[Crossref] [PubMed]

1990 (1)

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

1985 (1)

M. O. Scully, “Correlated spontaneous-emission lasers: quenching of quantum fluctuations in the relative phase angle,” Phys. Rev. Lett. 55, 2802–2805 (1985); M. O. Scully, “Enhancement of the index of refraction via quantum coherence,” Phys. Rev. Lett. 67, 1885–1888 (1991).
[Crossref] [PubMed]

Agarwal, G. S.

G. S. Agarwal, “Origin of gain in systems without inversion in bare or dressed states,” Phys. Rev. A 44, R28–R30 (1991); J. P. Dowling and C. M. Bowden, “Near dipole–dipole effects in lasing without inversion: an enhancement of gain and absorptionless index of refraction,” Phys. Rev. Lett. 70, 1421–1424 (1993).
[Crossref] [PubMed]

Eberly, J. H.

J. H. Eberly, A. Rahman, and R. Grobe, “Index of refraction for an optical medium with clamped quantum phase,” Phys. Rev. Lett. 76, 3687–3690 (1996).
[Crossref] [PubMed]

J. H. Eberly, M. L. Pons, and H. R. Haq, “Dressed-field pulses in an absorbing medium,” Phys. Rev. Lett. 72, 56–59 (1994).
[Crossref] [PubMed]

Field, J. E.

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

Fleischhauer, M.

M. Fleischhauer, C. H. Keitel, and M. O. Scully, “Resonantly enhanced refractive index without absorption via atomic coherence,” Phys. Rev. A 46, 1468–1687 (1992).
[Crossref] [PubMed]

Fu-Cheng, Lin

Lin Fu-Cheng, “Coherent control of a simple quantum system,” Chin. Phys. Lett. 14, 417–420 (1997).
[Crossref]

Grobe, R.

J. H. Eberly, A. Rahman, and R. Grobe, “Index of refraction for an optical medium with clamped quantum phase,” Phys. Rev. Lett. 76, 3687–3690 (1996).
[Crossref] [PubMed]

Haq, H. R.

J. H. Eberly, M. L. Pons, and H. R. Haq, “Dressed-field pulses in an absorbing medium,” Phys. Rev. Lett. 72, 56–59 (1994).
[Crossref] [PubMed]

Harris, S. E.

S. E. Harris, “Normal modes for electromagnetically induced transparency,” Phys. Rev. Lett. 72, 52–55 (1994).
[Crossref] [PubMed]

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

Imamoglu, A.

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

Keitel, C. H.

M. Fleischhauer, C. H. Keitel, and M. O. Scully, “Resonantly enhanced refractive index without absorption via atomic coherence,” Phys. Rev. A 46, 1468–1687 (1992).
[Crossref] [PubMed]

Meystre, P.

P. Meystre and M. Sargent, Elements of Quantum Optics (Springer-Verlag, New York, 1990).

Pons, M. L.

J. H. Eberly, M. L. Pons, and H. R. Haq, “Dressed-field pulses in an absorbing medium,” Phys. Rev. Lett. 72, 56–59 (1994).
[Crossref] [PubMed]

Rabitz, H.

N. Wang and H. Rabitz, “Optical control of optical pulse propagation in a medium of three-level systems,” Phys. Rev. A 52, R17–R20 (1995).
[Crossref]

Rahman, A.

J. H. Eberly, A. Rahman, and R. Grobe, “Index of refraction for an optical medium with clamped quantum phase,” Phys. Rev. Lett. 76, 3687–3690 (1996).
[Crossref] [PubMed]

Sargent, M.

P. Meystre and M. Sargent, Elements of Quantum Optics (Springer-Verlag, New York, 1990).

Scully, M. O.

M. Fleischhauer, C. H. Keitel, and M. O. Scully, “Resonantly enhanced refractive index without absorption via atomic coherence,” Phys. Rev. A 46, 1468–1687 (1992).
[Crossref] [PubMed]

M. O. Scully, “Correlated spontaneous-emission lasers: quenching of quantum fluctuations in the relative phase angle,” Phys. Rev. Lett. 55, 2802–2805 (1985); M. O. Scully, “Enhancement of the index of refraction via quantum coherence,” Phys. Rev. Lett. 67, 1885–1888 (1991).
[Crossref] [PubMed]

Vasavada, K. V.

G. Vemuri and K. V. Vasavada, “Pulse propagation in coherently prepared media,” Opt. Commun. 129, 379–386 (1996); G. Vemuri, K. V. Vasavada, G. S. Agarwal, and Q. Zhang, “Coherence-induced effects in pulse-pair propagation through absorbing media,” Phys. Rev. A 54, 3394–3399 (1996).
[Crossref] [PubMed]

Vemuri, G.

G. Vemuri and K. V. Vasavada, “Pulse propagation in coherently prepared media,” Opt. Commun. 129, 379–386 (1996); G. Vemuri, K. V. Vasavada, G. S. Agarwal, and Q. Zhang, “Coherence-induced effects in pulse-pair propagation through absorbing media,” Phys. Rev. A 54, 3394–3399 (1996).
[Crossref] [PubMed]

Wang, N.

N. Wang and H. Rabitz, “Optical control of optical pulse propagation in a medium of three-level systems,” Phys. Rev. A 52, R17–R20 (1995).
[Crossref]

Chin. Phys. Lett. (1)

Lin Fu-Cheng, “Coherent control of a simple quantum system,” Chin. Phys. Lett. 14, 417–420 (1997).
[Crossref]

Opt. Commun. (1)

G. Vemuri and K. V. Vasavada, “Pulse propagation in coherently prepared media,” Opt. Commun. 129, 379–386 (1996); G. Vemuri, K. V. Vasavada, G. S. Agarwal, and Q. Zhang, “Coherence-induced effects in pulse-pair propagation through absorbing media,” Phys. Rev. A 54, 3394–3399 (1996).
[Crossref] [PubMed]

Phys. Rev. A (3)

N. Wang and H. Rabitz, “Optical control of optical pulse propagation in a medium of three-level systems,” Phys. Rev. A 52, R17–R20 (1995).
[Crossref]

G. S. Agarwal, “Origin of gain in systems without inversion in bare or dressed states,” Phys. Rev. A 44, R28–R30 (1991); J. P. Dowling and C. M. Bowden, “Near dipole–dipole effects in lasing without inversion: an enhancement of gain and absorptionless index of refraction,” Phys. Rev. Lett. 70, 1421–1424 (1993).
[Crossref] [PubMed]

M. Fleischhauer, C. H. Keitel, and M. O. Scully, “Resonantly enhanced refractive index without absorption via atomic coherence,” Phys. Rev. A 46, 1468–1687 (1992).
[Crossref] [PubMed]

Phys. Rev. Lett. (5)

S. E. Harris, “Normal modes for electromagnetically induced transparency,” Phys. Rev. Lett. 72, 52–55 (1994).
[Crossref] [PubMed]

J. H. Eberly, M. L. Pons, and H. R. Haq, “Dressed-field pulses in an absorbing medium,” Phys. Rev. Lett. 72, 56–59 (1994).
[Crossref] [PubMed]

J. H. Eberly, A. Rahman, and R. Grobe, “Index of refraction for an optical medium with clamped quantum phase,” Phys. Rev. Lett. 76, 3687–3690 (1996).
[Crossref] [PubMed]

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

M. O. Scully, “Correlated spontaneous-emission lasers: quenching of quantum fluctuations in the relative phase angle,” Phys. Rev. Lett. 55, 2802–2805 (1985); M. O. Scully, “Enhancement of the index of refraction via quantum coherence,” Phys. Rev. Lett. 67, 1885–1888 (1991).
[Crossref] [PubMed]

Other (1)

P. Meystre and M. Sargent, Elements of Quantum Optics (Springer-Verlag, New York, 1990).

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Figures (4)

Fig. 1
Fig. 1

Sketch of atomic levels. Ωp and Ωs are the Rabi frequency of control and of secondary pulse, respectively, and γ is the decay rate of |3〉 to other states.

Fig. 2
Fig. 2

Illustration of the rotation model. OA is the control vector and θp is the corresponding argument; OB is the secondary vector and θs is the corresponding argument. When OA changes in space, so does the secondary pulse. The relative amplitudes and the argument are shown. Medium coherent angle: (a) 0<ϕ<π/2, when ϕ>π/4 and |OA| is less than |OB|; (b) π/2<ϕ<π, when ϕ>3π/4 and |OA| is less than |OB|.

Fig. 3
Fig. 3

(a) Pulse amplitudes, (b) pulse phases in different conditions after propagation when ϕ=π/3. A, Control pulse; B, secondary pulse.

Fig. 4
Fig. 4

(a) Pulse amplitudes after propagation, (b) phase of the pulse in different conditions after propagation when ϕ=5π/6. A, Control pulse; B, secondary pulse.

Equations (13)

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c1t=i2(-Δc1+Ωp*c3),
c2t=i2(-Δc2+Ωs*c3),
c3t+γ2c3=i2[2Δc3+Ωpc1+Ωsc2],
z+ctΩp=2iαaγc3c1*,
z+ctΩs=2iαbγc3c2*,
|ψ=cos φ|1+sin φ|2,
c1τ=i2Ωp*c3,
c2τ=i2Ωs*c3,
(ic3)τ=-γ2+3i2Δ(ic3)-12[Ωpc1+Ωsc2],
Ωp(αξ)=2iγc3c1*,
Ωs(αξ)=2iγc3c2*.
|c1|2+|c2|2=1αξ 1γdτ(|Ωp|2+|Ωs|2).
|Ωs|exp(iθs)=-c1c2|Ωp|exp(iθp),

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