  We have developed a microscopic many-body theory of two-dimensional coherent
spectroscopy (2DCS) for a model of polarons in one-dimensional (1D) materials.
Our theory accounts for contributions from all three processes: excited-state
emission (ESE), ground-state bleaching (GSB), and excited-state absorption
(ESA). While the ESE and GSB contributions can be accurately described using a
Chevy's ansatz with one particle-hole excitation, the ESA process requires
information about the many-body eigenstates involving two impurities. To
calculate these double polaron states, we have extended the Chevy's ansatz with
one particle-hole excitation. The validity of this ansatz was verified by
comparing our results with an exact calculation using Bethe's ansatz. Our
numerical results reveal that in the weak interaction limit, the ESA
contribution cancels out the total ESE and GSB contributions, resulting in less
significant spectral features. However, for strong interactions, the features
of the ESA contribution and the combined ESE and GSB contributions remain
observable in the 2DCS spectra. These features provide valuable information
about the interactions between polarons. Additionally, we have investigated the
mixing time dynamics, which characterize the quantum coherences of the polaron
resonances. Overall, our theory provides a comprehensive framework for
understanding and interpreting the 2DCS spectra of polarons in 1D materials,
shedding light on their interactions and coherent dynamics.
