Bright-dark exciton splitting in lead halide perovskite crystals accessed via quantum beats in photon echoes
Understanding the fine structure of excitons is crucial for optoelectronic and quantum photonic applications of lead halide perovskites. It is demonstrated that polarization-sensitive photon echo spectroscopy in magnetic field provides a powerful method to access coherent exciton dynamics and reveal their energy level structure, which is hidden by inhomogeneous broadening. Exciton quantum beats observed in both Faraday and Voigt geometries offer a precise probe of the energy splittings among the four 1$s$ exciton states, enabling determination of the fine structure and bright-dark splittings. Application of this technique to bulk mixed halide perovskite crystals FA$_{0.9}$Cs$_{0.1}$PbI$_{2.8}$Br$_{0.2}$ reveals a bright-dark exciton splitting of $Δ_\mathrm{X}=0.46~$meV, along with electron and hole Landé $g$ factors $g_\mathrm{e}=3.38$ and $g_\mathrm{h}=-1.14$, respectively. The quantum beats persist on timescales of 20--50$~$ps, demonstrating remarkably robust spin and optical coherences at cryogenic temperature of 2$~$K. The decay of the quantum beats of the outer doublet is governed by dephasing due to dispersion of the bright-dark splitting of $\sim0.06~$meV caused by localization potential fluctuations, while dephasing in the bright exciton inner doublet originates from a small zero field splitting of $\sim0.035~$meV due to anisotropic potentials.