Propagation processing of short pulses in Rydberg exciton medium under blockade conditions

Propagation of short pulses through Cu$_2$O crystal containing Rydberg excitons is studied with the use of density matrix formalism and FDTD method. Saturation effects related to the so-called Rydberg blockade are studied extensively, exploring not only reduction of absorption (bleaching) but also power-dependent changes of the dispersive properties of the medium. The role of exciton lifetime and coherent population oscillations in the dynamics of the system is investigated. A pump-probe setup with two pulses is also studied, showing good agreement with recent experimental studies.