Isolation of a two level system

With the help of the AC Stark effect, a two-state system is to be isolated at the resonance of dysprosium at λ=657.973 nm using σ- polarised light. As criteria for a successful isolation we define an energy isolation of at least 30 kHz compared to other transitions and a lifetime of at least 1s, so that there is enough time to modify and investigate the two-state system. In order to be able to investigate the stability of this two-state system, we define a polarisation imperfection parameter x, which modifies the polarisation P=(1-x, -(1+x) i, 0).