Copyright by Kirsten Viering 2006 - Raizen Lab - The University of ...

∆1 and ∆2 describe the detunings from the transition frequency,
and
∆1 = ω1 − ωIi
(5.15)
∆2 = ω2 − ωI f . (5.16)
Here we have neglected the decay rate Γ of the intermediate level which is justified
because of a negligible population due to large detunings. Furthermore the decay rate
is negligible compared to the Rabi frequencies, Ω1, Ω2 ≫ Γ. A sketch of the frequencies
and detuning involved in a stimulated Raman process in a three-level atom is shown
in fig. 5.4.
Figure 5.4: Schematic of the frequencies and detunings in a stimulated Raman process
in a three-level atom.
5.3.2 Adiabatic Reduction to a two-level system
Eq. 5.12 can be integrated directly by neglegting the time-dependance of the coefficients
ci and c f [28]. We can use the solution
cI = − Ω1
cie
2∆1
−i∆1t Ω2
− c f e
2∆2
−i∆2t
31
(5.17)