Excitonic Bloch equations for a two-dimensional system of interacting excitons

We derive the effective Bose Hamiltonian for a system of interacting excitons applying the Usui transformation. The fermionic nonlinearities are consistently included, leading to a density dependent correction to the kinetic Hamiltonian and to a saturation of the exciton oscillator strength. The exciton-exciton interaction potentials due to the Coulomb interaction are calculated, accounting for the spin dependence. Starting from the effective Hamiltonian, we obtain the excitonic Bloch equations. As a first application, we study the problem of excitonic Rabi oscillations in quantum wells.