Abstract

The preparation of an optically dense ensemble of three-level systems in dark states of the interaction with coherent radiation is discussed. It is shown that methods involving spontaneous emissions of photons such as Raman optical pumping fail to work beyond a critical density due to multiple scattering and trapping of these photons and the associated decay of the dark state(s). In optically thick media coherent-state preparation is only possible by entirely coherent means such as stimulated Raman adiabatic passage (STIRAP). It is shown that STIRAP is the underlying physical mechanism for electromagnetically induced transparency (EIT).

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References

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  1. for a recent review on EIT see: S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36 (1997) and references therein.
  2. for a recent review see: E. Arimondo, "Coherent population trapping in laser spectroscopy," Prog. Opt. 35, 259 (1996).
  3. S. E. Harris and Zhen-Fei. Luo, "Preparation Energy for Electromagnetically Induced Transparency," Phys. Rev. A 52, R928 (1995).
    [CrossRef] [PubMed]
  4. for a recent review on STIRAP see: K. Bergmann, H. Theuer, and B. W. Shore, "Coherent Population Transfer Among Quantum States of Atoms and Molecules," Rev. Mod. Phys. 70, 1003 (1998).
    [CrossRef]
  5. T. Holstein, "Imprisonment of resonance radiation in gases," Phys. Rev. A 72, 1212 (1947).
  6. Michael Fleischhauer, "Optical pumping in dense atomic media: Limitations due to reabsorption of spontaneously emitted photons," http://xxx.lanl.gov/abs/quant-ph/9811017.
  7. Michael Fleischhauer and Aaron S. Manka, "Propagation of laser pulses and coherent population transfer in dissipative three-level systems: An adiabatic dressed-state picture," Phys. Rev. A. 54, 794 (1996).
    [CrossRef] [PubMed]
  8. Michael Fleischhauer and Susanne F. Yelin, "Radiative atom-atom interactions in optically dense media: Quantum corrections to the Lorentz-Lorenz formula," http://xxx.lanl.gov/abs/quant-ph/9809087.
  9. C. M. Bowden and J. Dowling, "Near-dipole-dipole effects in dense media: Generalized Maxwell- Bloch equations," Phys. Rev. A 47, 1247 (1993).
    [CrossRef] [PubMed]
  10. A. Rahman, R. Grobe, and J. H. Eberly, "Two-Photon Beers Law for Coherently Prepared Three-Level Media," Coherence and Quantum Optics VII p.449 (Plenum, New York, 1996).

Other (10)

for a recent review on EIT see: S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36 (1997) and references therein.

for a recent review see: E. Arimondo, "Coherent population trapping in laser spectroscopy," Prog. Opt. 35, 259 (1996).

S. E. Harris and Zhen-Fei. Luo, "Preparation Energy for Electromagnetically Induced Transparency," Phys. Rev. A 52, R928 (1995).
[CrossRef] [PubMed]

for a recent review on STIRAP see: K. Bergmann, H. Theuer, and B. W. Shore, "Coherent Population Transfer Among Quantum States of Atoms and Molecules," Rev. Mod. Phys. 70, 1003 (1998).
[CrossRef]

T. Holstein, "Imprisonment of resonance radiation in gases," Phys. Rev. A 72, 1212 (1947).

Michael Fleischhauer, "Optical pumping in dense atomic media: Limitations due to reabsorption of spontaneously emitted photons," http://xxx.lanl.gov/abs/quant-ph/9811017.

Michael Fleischhauer and Aaron S. Manka, "Propagation of laser pulses and coherent population transfer in dissipative three-level systems: An adiabatic dressed-state picture," Phys. Rev. A. 54, 794 (1996).
[CrossRef] [PubMed]

Michael Fleischhauer and Susanne F. Yelin, "Radiative atom-atom interactions in optically dense media: Quantum corrections to the Lorentz-Lorenz formula," http://xxx.lanl.gov/abs/quant-ph/9809087.

C. M. Bowden and J. Dowling, "Near-dipole-dipole effects in dense media: Generalized Maxwell- Bloch equations," Phys. Rev. A 47, 1247 (1993).
[CrossRef] [PubMed]

A. Rahman, R. Grobe, and J. H. Eberly, "Two-Photon Beers Law for Coherently Prepared Three-Level Media," Coherence and Quantum Optics VII p.449 (Plenum, New York, 1996).

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Figures (4)

Fig. 1:
Fig. 1:

Three level system driven by two coherent fields with real Rabi frequencies Ωl and Ω2 in (a) bare atomic basis and (b) basis of dark (∣ -⟩) and bright (∣+⟩) states.

Fig.2:
Fig.2:

Stationary population of the dark state, ρ --, as function of optical depth K 0 for different values of the de-phasing rate γ 0- The two fields have equal Rabi-frequencies and R = 100.

Fig.3:
Fig.3:

EIT for cw-fields. Plotted is the stationary pump rate, R(z), which is a measure for the average intensity of the fields as function of the propagation distance for different values of γ̄0 = γ 0K 0 = 10 and Ω1 = Ω2. The dashed lines correspond to the case when radiation trapping is ignored.

Fig.4:
Fig.4:

Absorption in arbitrary units and log-scale as function of time for simultaneous pulses (Ω1 = Ω2) (upper dashed curve) and for counterintuitive pulses (lower dashed and dashed-dotted curve). The upper half of the box shows corresponding Rabi-frequencies. Here R max/γ = 100 and K 0 = 10.

Equations (7)

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1 Ω ( t ) ( Ω 2 ( t ) c Ω 1 ( t ) b ) , + 1 Ω ( t ) ( Ω 2 ( t ) b Ω 1 ( t ) c ) .
( t + c z ) Ω z t = g 2 N Im [ ρ a + ]
Γ = γ 2 1 π d y e y 2 [ 1 exp { K e y 2 } ] 1 ρ 3 ρ 1
K = N λ 2 d γ 8 π Δ D 1 2 ( 3 ρ 1 ) = K 0 2 ( 3 ρ 1 ) .
ρ ˙ aa = ( 2 γ + Γ ) ρ aa + Γ ρ R ( ρ a a ρ + + ) ,
ρ ˙ + + = ( γ ̄ 0 + Γ ) ρ + + + ( γ ̄ 0 + Γ ) ρ + γ ρ aa + R ( ρ a a ρ + + )
d R ( ξ ) = ( ρ ̄ aa ρ ̄ + + ) R ( ξ ) .

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