A Appendix The picket fence model

Neither the bright nor the dark states are stationary in the sense that they are not sharp energy eigenstates of the Hamiltonian. To determine the eigenstates we need to allow for the weak residual coupling between the bright and dark states. We take the coupling to be weak because if it were not we would not be able to prepare the optically prepared state as it would couple to other states while our laser pulse was still on. 

The picket fence model as carried out in Problem F requires that the coupling between the bright and dark states does not vary too much between one dark state and another nearby so that the actual coupling can be replaced by its mean 

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