Ultrafast phase dynamics of coherent emission from excitons in GaAs quantum wells

We investigate the temporal evolution of the instantaneous frequency of ultrashort-pulse four-wave mixing in GaAs/${\mathrm{Ga}}_{\mathit{x}}$ ${\mathrm{Al}}_{1\mathrm{-}\mathit{x}}$As quantum-well structures. We find that the coherent light emitted by excitons exhibits a complex phase behavior which depends critically on the density of excitons and the central frequency of the exciting pulses. Depending on the excitation conditions, we observe nonlinear shifts of the instantaneous frequency within one ultrashort pulsed emission or quantum beats. In the latter case we determine that the beat π-phase shift is very fast, only 40% above the fundamental quantum limit. We also present elaborate numerical simulations of the experiments based on a six-band generalization of the semiconductor Bloch equations. This formalism takes into account Coulomb many-body interactions and Pauli exclusion. It reproduces the salient features of the experimental data. It fails to account for important details revealed by the very sensitive phase measurements. The discrepancies can be traced back to two approximations in the theory: the statical treatment of screening, and the Lorentzian description of dephasing. In both cases, this indicates the need for theoretical refinements requiring a microscopic description of Coulomb scattering and dephasing processes in a non-Markovian theory.