Exactly solvable spin dynamics of an electron coupled to a large number of nuclei; the electron-nuclear spin echo in a quantum dot

The model used to describe the spin dynamics in quantum dots after optical excitation is considered. Problems of the electron-spin polarization decay and the dependence of the steady-state polarization on magnetic field are solved on the basis of exact diagonalization of the model Hamiltonian. An important role of the nuclear state is shown and methods of its calculation for different regimes of optical excitation are proposed. The effect of spin echo generation after application of a π pulse of a magnetic field is predicted for the system under consideration.