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We analyze the thermalization of a photoexcited charge carrier coupled to asingle branch of quantum phonons within the Holstein model. To this end, wecalculate the far-from-equilibrium time evolution of a pure many-body state andcompare it with predictions of the thermal Gibbs ensemble. We show that atstrong enough carrier excitation, the nonequilibrium system evolves towards athermal steady state. Our analysis is based on two classes of observables.First, the occupations of fermionic momenta, which are the eigenvalues of theone-particle density matrix, match in the steady state the values in thecorresponding Gibbs ensemble. This indicates thermalization of static fermioniccorrelations on the entire lattice. Second, the dynamic current-currentcorrelations, including the time-resolved optical conductivity, also take theform of their thermal counterparts. Remarkably, both static and dynamicfermionic correlations thermalize with identical temperatures. Our resultssuggest that the subsequent relaxation processes, observed in time-resolvedultrafast spectroscopy, may be efficiently described by applying quasithermalapproaches, e.g., multi-temperature models.

Thermalization after photoexcitation from the perspective of optical spectroscopy