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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. 

We have previously demonstrated that in the context of two-dimensional (2D) coherent electronic spectroscopy measured by phase modulation and phase-sensitive detection, an incoherent nonlinear response due to pairs of photoexcitations produced via linear excitation pathways contributes to the measured signal as an unexpected background [Grégoire et al., J. Chem. Phys. 147, 114201 (2017)]. Here, we simulate the effect of such incoherent population mixing in the photocurrent signal collected from a GaAs solar cell by acting externally on the transimpedance amplifier circuit used for phase-sensitive detection, and we identify an effective strategy to recognize the presence of incoherent population mixing in 2D data. While we find that incoherent mixing is reflected by the crosstalk between the linear amplitudes at the two time-delay variables in the four-pulse excitation sequence, we do not observe any strict phase correlations between the coherent and incoherent contributions, as expected from modeling of a simple system. 

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. 

Hybrid organic–inorganic semiconductors feature complex lattice dynamics due to the ionic character of the crystal and the softness arising from non-covalent bonds between molecular moieties and the inorganic network. Here we establish that such dynamic structural complexity in a prototypical two dimensional lead iodide perovskite gives rise to the coexistence of diverse excitonic resonances, each with a distinct degree of polaronic character. By means of high-resolution resonant impul- sive stimulated Raman spectroscopy, we identify vibrational wavepacket dynamics that evolve along different configurational coordinates for distinct excitons and photocarriers. Employing density functional theory calculations, we assign the observed coherent vibrational modes to various low-frequency (≲50 cm−1) optical phonons involving motion in the lead iodide layers. We thus conclude that different excitons induce specific lattice reorganizations, which are signatures of polaronic binding. This insight into the energetic/configurational landscape involving globally neutral primary photoexcitations may be relevant to a broader class of emerging hybrid semiconductor materials.