Coherent control for a two-level system coupled to phonons

The interband polarization induced by two phase-locked pulses in a semiconductor shows strong interference effects depending on the time, τ₁, separating the pulses. The four-wave mixing signal diffracted from a third pulse delayed by τ is coherently controlled by tuning τ₁. The four-wave mixing response is evaluated exactly for a two-level system coupled to a single LO phonon. In the weak coupling regime it shows oscillations with the phonon frequency which turn into sharp peaks at multiples of the phonon period for a larger coupling strength. Destructive interferences between the two phase-locked pulses produce a splitting of the phonon peaks into a doublet. For fixed τ but varying τ₁, the signal shows rapid oscillations at the interband transition frequency, whose amplitude exhibits bursts at multiples of the phonon period.