Resonant excitation of a two-level system free from relaxation

4 Resonant excitation of a two-level system free from relaxation 

The laser control of atoms and molecules is most effective when the particles are isolated from external influences. The necessary degree of isolation differs widely between different laser control methods. For coherent control techniques, even an accidental displacement of the phase of the wave function must be excluded. For incoherent laser control techniques, it is sufficient to exclude relaxation of the quantum-state populations of the atomic particles. One should therefore consider first the interaction of an isolated simple (two-level) quantum system with a coherent light field (Fig. 2.4(a)). 

The state of a quantum system with two energy levels Ei and E2 in an external laser-light held is fully described by the wave function F, governed by the Schrodinger equation 

In the case of an electric dipole interaction between the light field and the particle, the interaction operator V has the form 

According to the superposition principle, the wave function of the two-level quantum system interacting with the field may be written in a general form as 

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