Time-dependence of quasi-energy states and dynamical fractional stark ladders in semiconductor superlattice

The ladder structure of the quasi-energy states of a one-dimensional semiconductor superlattice under combined dc-ac fields has been studied by calculating the absorption spectrum based on the semiconductor Bloch equations. In particular, we investigated the periodic motion of the carriers in a band under an ac field or a dc field. Under ac field with the frequency of ω_L, we found periodic motion of ω_L, which was very similar to the Bloch oscillation under the a dc field. The ladder structure of quasi-energy states with a ladder spacing ℏω_L under an ac field were shown to be the counterparts of the frequency domain of periodic motion. Under combined ac-dc fields, we found the absorption peaks corresponding to the so-called dynamical fractional Stark ladders with energies ∈_o + mℏω_B + m′ℏω_L, where m and m′ are integers and ω_B is the Bloch oscillation frequency.