  The theory of linear and non-linear infrared response of vibrational Holstein
polarons in one-dimensional lattices is presented in order to identify the
spectral signatures of self-trapping phenomena. Using a canonical
transformation the optical response is computed from the small polaron point of
view which is valid in the anti-adiabatic limit. Two types of phonon baths are
considered: optical phonons and acoustical phonons, and simple expressions are
derived for the infrared response. It is shown that for the case of optical
phonons, the linear response can directly probe the polaron density of states.
The model is used to interpret the experimental spectrum of crystaline
actetanilide in the C=O range. For the case of acoustical phonons, it is shown
that two bound states can be observed in the two-dimensional infrared spectrum
at low temperature. At high temperature, analysis of the time-dependence of the
two-dimensional infrared spectrum indicates that bath mediated correlations
slow down spectral diffusion. The model is used to interpret the experimental
linear-spectroscopy of model alpha-helix and beta-sheet polypeptides. This work
shows that the Davydov Hamiltonian cannot explain the observations in the NH
stretching range.
