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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. 

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. 

Recent theories and experiments have explored the use of entangled photons as a spectroscopic probe of physical systems. We describe here a theoretical description for entropy production in the scattering of an entangled biphoton Fock state within an optical cavity. We develop this using perturbation theory by expanding the biphoton scattering matrix in terms of single-photon terms in which we introduce the photon-photon interaction via a complex coupling constant, ξ. We show that the von Neumann entropy provides a concise measure of this interaction. We then develop a microscopic model and show that in the limit of fast fluctuations, the entanglement entropy vanishes, whereas in the limit of slow fluctuations, the entanglement entropy depends on the magnitude of the fluctuations and reaches a maximum. Our result suggests that experiments measuring biphoton entanglement give microscopic information pertaining to exciton-exciton correlations.