From microsecond spin echo to femtosecond photon echo

For more than 70 years spin and photon echo excited by micro- and nanosecond pulses have been the subject of research by various scientific groups. Bloch equations are the mathematical basis in these studies. However, Bloch equations cannot describe echo signals if excitation of the electron-vibrational system is realized by short femtosecond pulses. Only theory for density matrix, which is more general than the Bloch equation approach, is able to describe femtosecond relaxation of polarization and decay of femtosecond echo signals. This work gives an overview of the resent results obtained in developing such a general theoretical formalism. (paper)