Real-Time Formation of a Landau Polaron

Polarons are electronic excitations dressed by a self-consistent lattice distortion, yet their formation has not been directly resolved in real time. We develop a microscopic lineshape framework that connects the growth of a collective lattice polarization to the population-time evolution of the anti-diagonal linewidth in coherent multidimensional spectroscopy. Within this formalism, the anti-diagonal linewidth directly tracks the decay of lattice frequency-frequency correlations. Underdamped phonon environments produce oscillatory linewidth modulation, whereas overdamped collective polarization dynamics generate monotonic exponential broadening. Applying this framework to multidimensional measurements on perovskite quantum dots, we show that the observed approximately 150 femtosecond exponential anti-diagonal broadening reflects the decay of a collective polarization order parameter. These results establish anti-diagonal linewidth dynamics as a direct real-time signature of Landau polaron formation.