Coherent excitation of continuum states

If the excited state is not a bound, but a continuum state, then the situation is fundamentally different, because of photoionisation. Once an electron is excited into the continuum, it escapes rapidly from the influence of the laser field (except at the highest laser field strengths), so that cycling of the population can no longer occur. This process of escape is irreversible, so that Rabi nutation can no longer occur. The time dependence of the laser and ionisation amplitudes must then be considered. 

Suppose the ionisation probability per unit time of an atom is dP/dt. The number of atoms left in the ground state 0 after a time t is 

The rate at which population is transferred into the continuum by a coherent field is determined by the Rabi frequency ftQoe(t) = 0 V(t) e , where the time dependence must now be included explicitly. The exciting laser is a coherent source of light, so we suppose that the field V(t) = Vo(t) cos (u t + j (t)) where both Vo(t) and / (t) vary only slowly with time. We then have 

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