  A combined experimental and computational methodology for interrogating the
phonon contribution to polaron formation in real materials is developed. Using
LiF as an example, we show that the recent ab-initio theory of Sio et. al [PRL
122, 246403 (2019)] makes predictions of the momentum- and branch dependent
phonon amplitides in polaron quasiparticles that are testable using ultrafast
electron diffuse scattering (UEDS) and related techniques. The large electron
polaron in LiF has UEDS signatures that are qualitatively similar to those
expected from a simple point-defect model, but the small hole polaron exhibits
a profoundly anisotropic UEDS pattern that is in poor agreement with a
point-defect model. We also show that these polaron diffuse scattering
signatures are directly emblematic of the underlying polaron wavefunction. The
combination of new time and momentum resolved experimental probes of
nonequilibrium phonons with novel computational methods promises to complement
the qualitative results obtained via model Hamiltonians with a first
principles, material-specific quantiative understanding of polarons and their
properties.
