Bayesian-recovered ultrafast dynamics in solids across four decades of time and energy

Ultrafast spectroscopy is a powerful method to capture excited-state dynamics, as well as a wealth of information about inter- and intra-molecular vibrations on the ground and excited states. In principle, coherent wave packets with energies across the entire bandwidth of the excitation light are accessible, but poor sensitivity, sample photodamage, low dynamic range, and limits of current analysis methods restrict accurate recovery to a limited spectral range. As a result, the information content of ultrafast spectroscopy remains far from reaching its full potential. These shortcomings are especially acute in the low frequency region below a few THz, which covers a diverse range of interactions that mediate interlayer coupling, buried interfaces, polarons, and solvent-solute interactions. Here, we present a method using ultrashort pulses that captures excited-state relaxation and inter- and intra-molecular vibrations over four decades in time and energy (0.1-2000 cm-1). We adopt Bayesian inference, demonstrating dramatically improved signal reconstruction in comparison with traditional Fourier analysis. Our approach facilities a comprehensive study of the electronic and vibrational landscapes within a probabilistic framework in multi-layer graphene and WSe2. In the latter, we demonstrate that Bayes not only provided accurate parameter estimation but also reduced sampling to less than 3% of the Nyquist-Shannon criteria. Layer-dependent studies on exfoliated flakes of WSe2 using correlated atomic force microscopy were also carried out. The results underscore the potential of this method in probing the complex dynamics of various chemical, biological, and materials systems, maximizing the information extracted from ultrafast spectroscopy.