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We review our recent quantum stochastic model for spectroscopic lineshapes in the presence of a coevolving and nonstationary background population of excitations. Starting from a field theory description for interacting bosonic excitons, we derive a reduced model whereby optical excitons are coupled to an incoherent background via scattering as mediated by their screened Coulomb coupling. The Heisenberg equations of motion for the optical excitons are then driven by an auxiliary stochastic population variable, which we take to be the solution of an Ornstein–Uhlenbeck process. Here, we present an overview of the theoretical techniques we have developed as applied to predicting coherent nonlinear spectroscopic signals. We show how direct (Coulomb) and exchange coupling to the bath give rise to distinct spectral signatures and discuss mathematical limits on inverting spectral signatures to extract the background density of states. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 74 is April 2023. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates. 

Frenkel excitons are the primary photoexcitations in organic semiconductors and are ultimately responsible for the optical properties of such materials. They are also predicted to form bound exciton pairs, termed biexcitons, which are consequential intermediates in a wide range of photophysical processes. Generally, we think of bound states as arising from an attractive interaction. However, here, we report on our recent theoretical analysis, predicting the formation of stable biexciton states in a conjugated polymer material arising from both attractive and repulsive interactions. We show that in J-aggregate systems, 2J-biexcitons can arise from repulsive dipolar interactions with energies E 2 J > 2 E J , while in H-aggregates, 2H-biexciton states with energies E 2 H < 2 E H can arise corresponding to attractive dipole exciton/exciton interactions. These predictions are corroborated by using ultrafast double-quantum coherence spectroscopy on a [poly(2,5-bis(3-hexadecylthiophene-2-yl)thieno[3,2-b]thiophene)] material that exhibits both J- and H-like excitonic behavior. 

Spectral line shapes provide a window into the local environment coupled to a quantum transition in the condensed phase. In this paper, we build upon a stochastic model to account for non-stationary background processes produced by broad-band pulsed laser stimulation, as distinguished from those for stationary phonon bath. In particular, we consider the contribution of pair-fluctuations arising from the full bosonic many-body Hamiltonian within a mean-field approximation, treating the coupling to the system as a stochastic noise term. Using the Itô transformation, we consider two limiting cases for our model, which lead to a connection between the observed spectral fluctuations and the spectral density of the environment. In the first case, we consider a Brownian environment and show that this produces spectral dynamics that relax to form dressed excitonic states and recover an Anderson–Kubo-like form for the spectral correlations. In the second case, we assume that the spectrum is Anderson–Kubo like and invert to determine the corresponding background. Using the Jensen inequality, we obtain an upper limit for the spectral density for the background. The results presented here provide the technical tools for applying the stochastic model to a broad range of problems.