Semiconductor Bloch Equations

In this chapter we derive the semi-classical semiconductor Bloch equations which describe in a consistent way linear and nonlinear as well as coherent phenomena in semiconductors. We will start with the dynamics of coherent superpositions of the states in two-level systems and introduce Rabi oscillations for different approaches. These are the wave-function description, the formalism using complex polarisation and inversion as parameters as well as the pseudo-spin analogy. We illustrate some basic coherent processes like (detuned) Rabi oscillation, dephasing or coherent manipulation in the Bloch sphere representation. Then we outline the optical Bloch equations for the case of two-band semiconductors and generalize them by including Coulomb interaction and many-particle effects. As an example we derive the effects of excitonic states on the optical susceptibility of a typical semiconductor.