Abstract

A coherent mechanism of robust population inversion in atomic and molecular systems by a chirped field is presented. It is demonstrated that a field of sufficiently high chirp rate imposes a certain relative phase between a ground and excited state wavefunction of a two-level system. The value of the relative phase angle is thus restricted to be negative and close to 0 or -π for positive and negative chirp, respectively. This explains the unidirectionality of the population transfer from the ground to the excited state. In a molecular system composed of a ground and excited potential energy surface the symmetry between the action of a pulse with a large positive and negative chirp is broken. The same framwork of the coherent mechanism can explain the symmetry breaking and the population inversion due to a positive chirped field.

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References

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  1. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms, (Dover Publications, Inc., New York, 1987).
  2. Denise Sawicki and J. H. Eberly "Perfect following in the diabatic limit," Opt. Express, 4 217-222 (1999), http://www.opticsexpress.org/oearchive/source/9096.htm
    [CrossRef] [PubMed]
  3. Y. B. Band and O. Magnes, "Chirped adiabatic passage with temporally delayed pulses," Phys. Rev. A 50, 584-594 (1994).
    [CrossRef] [PubMed]
  4. J. Cao, C. J. Bardeen and K. R. Wilson, "Molecular pi Pulse for Total Inversion of Electronic State Population," Phys. Rev. Lett. 80, 1406-1409 (1998).
    [CrossRef]
  5. J. Cao, C. J. Bardeen and K. R. Wilson, "Molecular pi pulses: Population inversion with positively chirped short pulses," J. Chem. Phys. 113, 1898-1909 (2000).
    [CrossRef]
  6. R. Kosloff, A. D. Hammerich and D. Tannor, "Excitation without demolition: Radiative excitation of ground-surface vibration by impulsive stimulated Raman scattering with damage control," Phys. Rev. Lett. 69, 2172-2175 (1992).
    [CrossRef] [PubMed]
  7. S. A. Rice and M. Zhao, Optical Control of Molecular Dynamics, (John Wiley and Sons, New York 2000).
  8. R. Kosloff, Propagation Methods for Quantum Molecular Dynamics, Annu. Rev. Phys. Chem. 45, 145-178 (1994).
    [CrossRef]
  9. R. Kosloff, Quantum Molecular Dynamics on Grids., in R. E. Wyatt and J. Z. Zhang, editor, Dynamics of Molecules and Chemical Reactions, pages 185-230, Marcel Dekker, (1996).
  10. J. Vala, O. Dulieu, F. Masnou-Seeuws, P. Pillet and R. Kosloff, "Coherent control of cold-molecule formation through photoassociation using a chirped-pulsed-laser field," Phys. Rev. A 63, 013412 (2001).
    [CrossRef]
  11. G. Ashkenazi, U. Banin, A. Bartana, R. Kosloff and S. Ruhman, "Quantum Description of the Impulsive Photodissociation Dynamics of I 3 in Solution," Adv. Chem Phys. 100, 229-315 (1997).
    [CrossRef]

Other (11)

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms, (Dover Publications, Inc., New York, 1987).

Denise Sawicki and J. H. Eberly "Perfect following in the diabatic limit," Opt. Express, 4 217-222 (1999), http://www.opticsexpress.org/oearchive/source/9096.htm
[CrossRef] [PubMed]

Y. B. Band and O. Magnes, "Chirped adiabatic passage with temporally delayed pulses," Phys. Rev. A 50, 584-594 (1994).
[CrossRef] [PubMed]

J. Cao, C. J. Bardeen and K. R. Wilson, "Molecular pi Pulse for Total Inversion of Electronic State Population," Phys. Rev. Lett. 80, 1406-1409 (1998).
[CrossRef]

J. Cao, C. J. Bardeen and K. R. Wilson, "Molecular pi pulses: Population inversion with positively chirped short pulses," J. Chem. Phys. 113, 1898-1909 (2000).
[CrossRef]

R. Kosloff, A. D. Hammerich and D. Tannor, "Excitation without demolition: Radiative excitation of ground-surface vibration by impulsive stimulated Raman scattering with damage control," Phys. Rev. Lett. 69, 2172-2175 (1992).
[CrossRef] [PubMed]

S. A. Rice and M. Zhao, Optical Control of Molecular Dynamics, (John Wiley and Sons, New York 2000).

R. Kosloff, Propagation Methods for Quantum Molecular Dynamics, Annu. Rev. Phys. Chem. 45, 145-178 (1994).
[CrossRef]

R. Kosloff, Quantum Molecular Dynamics on Grids., in R. E. Wyatt and J. Z. Zhang, editor, Dynamics of Molecules and Chemical Reactions, pages 185-230, Marcel Dekker, (1996).

J. Vala, O. Dulieu, F. Masnou-Seeuws, P. Pillet and R. Kosloff, "Coherent control of cold-molecule formation through photoassociation using a chirped-pulsed-laser field," Phys. Rev. A 63, 013412 (2001).
[CrossRef]

G. Ashkenazi, U. Banin, A. Bartana, R. Kosloff and S. Ruhman, "Quantum Description of the Impulsive Photodissociation Dynamics of I 3 in Solution," Adv. Chem Phys. 100, 229-315 (1997).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

The evolution of the ground state population Ng (t) (left) and the imaginary part of the transition dipole moment multiplied by the field amplitude (right). The normalized time is defined as tr =t/(6τ χ ′=0.f) and (dNg/dt)r=(6τχ ′=0.f)dNg /dt is the rate of change in the normalized time units. τχ′=0 is the pulse duration for a transform-limited pulse (χ′=0) and f is the ratio of pulse duration between the chirped and unchirped cases. The numbers indicate the value of the chirp rate.

Fig. 2.
Fig. 2.

Trajectories of the transition dipole moment, renormalized by its maximal amplitude, for excitation by the transform limited (on the imaginary axis) and chirped pulsed field of positive and negative chirp rates.

Fig. 3.
Fig. 3.

Chirped field population transfer for χ′=20 in a two-potential system Vg (r)=0. and Ve (r)=-2.r. The positive chirp rate results in robust population inversion (invariant with variation of field and system parameters in a certain extent). On the other hand, the negative chirp rate leads to the break-down of robust population transfer efficiency and can give any possible result in dependence on the parameters (here the zero transfer is apparently accidental). The relative quantities are defined in Fig. 1, the intensity is stronger by the factor of five.

Tables (1)

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Table 1. The typical values of the propagation parameters. The grid parameters are related only to a TPS.

Equations (7)

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d N g dt = 2 ψ e μ ̂ ψ g E ( t ) sin ( ϕ μ + ϕ E )
E ˜ ( ω ) = E ˜ ( ω 0 ) exp [ ( ω ω 0 ) 2 2 Γ 2 i χ ( ω ω 0 ) 2 2 ] ,
E ( t ) = E 0 exp [ t 2 2 τ 2 i ω 0 t i χ t 2 2 + i ϕ E ] ,
i t ( ψ e ψ g ) = ( H ̂ e μ E ( t ) μ E ( t ) * H ̂ g ) ( ψ e ψ g )
ψ e ( t ) = i 0 t d τ e i H ̂ e ( t τ ) μ ̂ E ( τ ) ψ g ( τ )
d N g dt = 2 Im [ i 0 t d τ ψ g ( t ) μ ̂ e i H ̂ e ( t τ ) μ ̂ ψ g ( τ ) E * ( t ) E ( τ ) ]
d N g dt = 2 ψ g ( 0 ) μ ̂ 2 ψ g ( 0 ) E 0 sin ( 2 Ω t )

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