Photon echo polarimetry of excitons and biexcitons in a CH$_3$NH$_3$PbI$_3$ perovskite single crystal

Lead halide perovskites show remarkable performance when used in photovoltaic and optoelectronic devices. However, the peculiarities of light-matter interactions in these materials in general are far from being fully explored experimentally and theoretically. Here we specifically address the energy level order of optical transitions and demonstrate photon echos in a methylammonium lead triiodide single crystal, thereby determining the optical coherence times $T_2$ for excitons and biexcitons at cryogenic temperature to be 0.79 ps and 0.67 ps, respectively. Most importantly, we have developed an experimental photon-echo polarimetry method that not only identifies the contributions from exciton and biexciton complexes, but also allows accurate determination of the biexciton binding energy of 2.4 meV, even though the period of quantum beats between excitons and biexcitons is much longer than the coherence times of the resonances. Our experimental and theoretical analysis methods contribute to the understanding of the complex mechanism of quasiparticle interactions at moderate pump density and show that even in high-quality perovskite crystals and at very low temperatures, inhomogeneous broadening of excitonic transitions due to local crystal potential fluctuations is a source of optical dephasing.