Theoretical analysis and simulations of two-dimensional Fourier transform spectroscopy performed on exciton-polaritons of a quantum-well microcavity system

We analyze four-wave-mixing experiments with three incident laser pulses performed on a semiconductor quantum well embedded in a microcavity. The coupling of the intracavity field and the exciton transition leads to exciton polaritons. The many-body hierarchy problem that arises due to the Coulomb interaction is treated by the dynamics-controlled truncation scheme, which leads to a set of Bloch equations that contain optical nonlinearities including biexcitonic many-body correlations and contributions beyond the coherent limit, which have not been thoroughly explored for a microcavity yet. A numerical solution of these Bloch equations is performed by projecting onto the 1s-exciton and biexciton states. We present the two-dimensional Fourier transform of the four-wave-mixing signal for different polarization directions of the incident pulses, which allows us to investigate the absorption and emission of the system and the couplings among the different resonances from the lower polariton, the upper polariton, and the biexciton. The numerical results are compared with measurements, in which a GaAs quantum well sample enclosed in distributed Bragg reflectors is investigated for four different polarization configurations, and we find a good agreement.