Coherent control and four wave-mixing of Fermi edge singularities in doped quantum wells

We discuss Fermi-edge singularities in the linear and nonlinear transient response of a doped quantum well at finite temperatures. In the linear response, we compute the coherent control of the energy absorption. A phase-shift appears in the coherent control oscillations. For the nonlinear response, we show that four wave-mixing experiments with varying energy presents a Fermi-edge singularity.