The Optical Signatures of Stochastic Processes in Many-Body Exciton Scattering.

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.

Concerning the stability of biexcitons in hybrid HJ aggregates of π-conjugated polymers.

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 E2J > 2EJ, while in H-aggregates, 2H-biexciton states with energies E2H < 2EH 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.

Stochastic exciton-scattering theory of optical line shapes: Renormalized many-body contributions.

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.

Stochastic scattering theory for excitation-induced dephasing: Comparison to the Anderson-Kubo lineshape.

In this paper, we present a quantum stochastic model for spectroscopic lineshapes in the presence of a co-evolving and non-stationary 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. Itô's lemma then allows us to easily construct and evaluate correlation functions and response functions. Focusing on the linear response, we compare our model to the classic Anderson-Kubo model. While similar in motivation, there are differences in the predicted lineshapes, notably in terms of asymmetry, and variation with the increasing background population.

Stochastic scattering theory for excitation-induced dephasing: Time-dependent nonlinear coherent exciton lineshapes.

We develop a stochastic theory that treats time-dependent exciton-exciton s-wave scattering and that accounts for dynamic Coulomb screening, which we describe within a mean-field limit. With this theory, we model excitation-induced dephasing effects on time-resolved two-dimensional coherent optical lineshapes and we identify a number of features that can be attributed to the many-body dynamics occurring in the background of the exciton, including dynamic line narrowing, mixing of real and imaginary spectral components, and multi-quantum states. We test the model by means of multidimensional coherent spectroscopy on a two-dimensional metal-halide semiconductor that hosts tightly bound excitons and biexcitons that feature strong polaronic character. We find that the exciton nonlinear coherent lineshape reflects many-body correlations that give rise to excitation-induced dephasing. Furthermore, we observe that the exciton lineshape evolves with the population time over time windows in which the population itself is static in a manner that reveals the evolution of the multi-exciton many-body couplings. Specifically, the dephasing dynamics slow down with time, at a rate that is governed by the strength of exciton many-body interactions and on the dynamic Coulomb screening potential. The real part of the coherent optical lineshape displays strong dispersive character at zero time, which transforms to an absorptive lineshape on the dissipation timescale of excitation-induced dephasing effects, while the imaginary part displays converse behavior. Our microscopic theoretical approach is sufficiently flexible to allow for a wide exploration of how system-bath dynamics contribute to linear and non-linear time-resolved spectral behavior.

Probing exciton/exciton interactions with entangled photons: Theory.

Quantum entangled photons provide a sensitive probe of many-body interactions and offer a unique experimental portal for quantifying many-body correlations in a material system. In this paper, we present a theoretical demonstration of how photon-photon entanglement can be generated via interactions between coupled qubits. Here, we develop a model for the scattering of an entangled pair of photons from a molecular dimer. We develop a diagrammatic theory for the scattering matrix and show that one can correlate the von Neumann entropy of the outgoing bi-photon wave function with exciton exchange and repulsion interactions. We conclude by discussing possible experimental scenarios for realizing these ideas.

How charges separate: correlating disorder, free energy, and open-circuit voltage in organic photovoltaics.

In order for a photovoltaic cell to function, charge carriers produced by photoexcitation must fully dissociate and overcome their mutual Coulomb attraction to form free polarons. This becomes problematic in organic systems in which the low dielectric constant of the material portends a long separation distance between independent polaron pairs. In this paper, we discuss our recent efforts to correlate the role of density of states, entropy, and configurational and energetic disorder to the open-circuit voltage, VOC, of model type-II organic polymer photovoltaics. By comparing the results of a fully interacting lattice model to those predicted by a Wigner-Weisskopf type model we find that energetic disorder does play a significant role in determining the VOC; however, mobility perpendicular to the interface plays the deciding role in the eventual fate of a charge-separated pair.

Photon entanglement entropy as a probe of many-body correlations and fluctuations.

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.

Quantum Symmetry Breaking of Exciton/Polaritons in a Metal-Nanorod Plasmonic Array.

We study the collective, superradiant behavior in the system of emitter-dressed Ag nanorods. Starting from the Drude model for the plasmon oscillations, we arrive at a semiempirical Hamiltonian describing the coupling between quantized surface plasmon modes and the quantum emitters that can be controlled by manipulating their geometry, spacing, and orientation. Further, identifying the lowest polariton mode as SP-states dressed by excitons in the vicinity of k = 0, we examine conditions allowing for the polariton quantum-phase transition. Though the system is formally a 1D array, we show that the polariton states of interest can undergo a quantum-phase transition to form a Bose condensate at finite temperatures for physically accessible parameter ranges.

The role of structural fluctuations and environmental noise in the electron/hole separation kinetics at organic polymer bulk-heterojunction interfaces.

We investigate the electronic dynamics of a model organic photovoltaic (OPV) system consisting of polyphenylene vinylene (PPV) oligomers and a [6,6]-phenyl C61-butyric acid methylester (PCBM) blend using a mixed molecular mechanics/quantum mechanics (MM/QM) approach. Using a heuristic model that connects energy gap fluctuations to the average electronic couplings and decoherence times, we provide an estimate of the state-to-state internal conversion rates within the manifold of the lowest few electronic excitations. We find that the lowest few excited states of a model interface are rapidly mixed by C[double bond, length as m-dash]C bond fluctuations such that the system can sample both intermolecular charge-transfer and charge-separated electronic configurations on a time scale of 20 fs. Our simulations support an emerging picture of carrier generation in OPV systems in which interfacial electronic states can rapidly decay into charge-separated and current producing states via coupling to vibronic degrees of freedom.

Computing intramolecular charge and energy transfer rates using optimal modes.

In our recent work [X. Yang and E. R. Bittner, J. Phys. Chem. A 118, 5196 (2014)], we showed how to construct a reduced set of nuclear motions that capture the coupling between electronic and nuclear degrees of freedom over the course of an electronic transition. We construct these modes, referred to as "Lanczos modes," by applying a search algorithm to find linear combinations of vibrational normal modes that optimize the electronic/nuclear coupling operator. Here, we analyze the irreducible representations of the dominant contributions of these modes and find that for the cases considered here, these belong to totally symmetric irreducible representations of the donor and acceptor moieties. Upon investigating the molecular geometry changes following the transition, we propose that the electronic transition process can be broken into two steps, in the agreement of Born-Oppenheimer approximation: a fast excitation transfer occurs, facilitated by the "primary Lanczos mode," followed by slow nuclear relaxation on the final electronic diabatic surface.

How disorder controls the kinetics of triplet charge recombination in semiconducting organic polymer photovoltaics.

Recent experiments by Rao et al. (Nature, 2013, 500, 435-439) indicate that recombination of triplet charge-separated states is suppressed in organic polymer-fullerene based bulk-heterojunction (BHJ) photovoltaic cells exhibiting a high degree of crystallinity in the fullerene phase relative to systems with more disorder. In this paper, we use a series of Frenkel-exciton lattice models to rationalize these results in terms of wave-function localization, interface geometry, and density of states. In one-dimensional co-linear and co-facial models of the interface, increasing local energetic disorder in one phase localizes the interfacial triplet charge-transfer ((3)CT) states and increases the rate at which these states relax to form lower-energy triplet excitons. In two dimensional BHJ models, energetic disorder within the fullerene phase plays little role in further localizing states pinned to the interface. However, inhomogeneous broadening introduces strong coupling between the interfacial (3)CT and nearby fullerene triplet excitons and can enhance the decay of these states in systems with higher degrees of energetic disorder.

Intramolecular charge- and energy-transfer rates with reduced modes: comparison to Marcus theory for donor-bridge-acceptor systems.

We present a new, fully ab initio approach for computing intramolecular charge- and energy-transfer rates. Using a time-convolutionless master equation approach and parametrizing using couplings obtained using an accurate quantum chemical approach, we benchmark the approach against experimental results and Marcus theory rates for triplet energy transfer for a series of donor-bridge-acceptor systems. An important component of our analysis is the use of a projection operator scheme that parses out specific internal nuclear motions that accompany the electronic transition. Using an iterative Lanczos approach, we concentrate the coupling between the electronic and nuclear degrees of freedom into a small number of reduced harmonic modes. We find that by using only a single reduced mode termed the "primary mode", one obtains an accurate evaluation of the golden rule rate constant and insight into the nuclear motions responsible for coupling the initial and final electronic states. In particular, the primary mode reflects the irreducible representation of the donor and acceptor excited states.

Noise-Induced Quantum Synchronization and Entanglement in a Quantum Analogue of Huygens' Clock.

We propose a quantum analogue of the Huygens clock, where the phases of two spins synchronize through their interaction with a shared environment. This environment acts like the escapement mechanism in a mechanical clock, regulating the gear train and allowing discrete timing advances. In our model, the relative phases of the two spins synchronize via a mutually correlated environment. We demonstrate that several arguments can significantly reduce the cardinality of the allowed measurements for a system of qubits, thus simplifying the problem. We present a numerically efficient method to calculate the degree of quantumness in the correlations of the final density matrix, providing a tight upper bound for rank 3 and rank 4 density matrices. We suggest a potential realization of noise-induced synchronization between two nuclear spins coupled to a common ancilla undergoing dynamical decoupling.

Many-Exciton Quantum Dynamics in a Ruddlesden-Popper Tin Iodide.

We present a study on the many-body exciton interactions in a Ruddlesden-Popper tin halide, namely, (PEA)2SnI4 (PEA = phenylethylammonium), using coherent two-dimensional electronic spectroscopy. The optical dephasing times of the third-order polarization observed in these systems are determined by exciton many-body interactions and lattice fluctuations. We investigate the excitation-induced dephasing (EID) and observe a significant reduction of the dephasing time with increasing excitation density as compared to its lead counterpart (PEA)2PbI4, which we have previously reported in a separate publication [J. Chem. Phys.2020, 153, 164706]. Surprisingly, we find that the EID interaction parameter is four orders of magnitude higher in (PEA)2SnI4 than that in (PEA)2PbI4. This increase in the EID rate may be due to exciton localization arising from a more statically disordered lattice in the tin derivative. This is supported by the observation of multiple closely spaced exciton states and the broadening of the linewidth with increasing population time (spectral diffusion), which suggests a static disordered structure relative to the highly dynamic lead-halide. Additionally, we find that the exciton nonlinear coherent lineshape shows evidence of a biexcitonic state with low binding energy (<10 meV) not observed in the lead system. We model the lineshapes based on a stochastic scattering theory that accounts for the interaction with a nonstationary population of dark background excitations. Our study provides evidence of differences in the exciton quantum dynamics between tin- and lead-based Ruddlesden-Popper metal halides (RPMHs) and links them to the exciton-exciton interaction strength and the static disorder aspect of the crystalline structure.

Thermodynamics of exciton/polaritons in one and two dimensional organic single-crystal microcavities.

We consider here the thermodynamics and phase-diagram of exciton/polaritons formed in low-dimensional organic single-crystal microcavities. Using the Dicke model for a lattice of Frenkel excitons coupled to a common cavity mode, we explore the transition between normal and condensate regimes as depending upon the exciton band-width and temperature of the polariton gas. We show that for one-dimensional conjugated polymers, the coexistence curve at low temperatures shifts towards lower critical coupling strengths as the exciton band-width is increased. We also consider the effect of orientational disorder in a two-dimensional polyacene slab on the formation of the polariton BEC. Our results indicate that while a small degree of orientational disorder will not have a profound effect on the critical exciton/photon coupling strength needed to produce the transition from normal to BEC regimes, BEC will likely be suppressed in glassy or strongly disordered molecular films.

Exciton dynamics in disordered poly(p-phenylenevinylene). 2. Exciton diffusion.

We present a first principles theory of exciton diffusion in conformationally disordered conjugated polymers. Central to our theory is that exciton transfer occurs from vibrationally relaxed states (VRSs) to local exciton ground states (LEGSs). LEGSs are determined by the diagonal and off-diagonal disorder induced by static density and torsional fluctuations, and VRSs are further localized by exciton-phonon coupling. The theory is implemented using the Frenkel-Holstein model to calculate the wave functions and energies of the LEGSs and VRSs. The coupling of VRSs and LEGSs via long-range dipole-dipole interactions leads to the familiar line-dipole approximation for the exciton transfer integral. The exciton transfer rates are derived from the Fermi Golden rule. The theory is applied to an ensemble of conformationally disordered poly(p-phenylenevinylene) chains using a kinetic Monte Carlo algorithm. The following are shown: (i) Torsional disorder and trans-cis defects reduce the exciton diffusion length. (ii) Radiative recombination occurs from VRSs in the tail of their density of states. (iii) Torsional disorder increases the band gap, the line width of the density of states, and the Stokes shift. As a consequence, it causes a blue shift in the vertical absorption, but a red shift in the emission. (iv) The energy of the radiated photon decreases as -log t, with a gradient that increases with torsional disorder. The predicted exciton diffusion lengths of ~8-11 nm are in good agreement with experimental values.

Estimating the conditions for polariton condensation in organic thin-film microcavities.

We examine the possibility of observing Bose condensation of a confined two-dimensional polariton gas in an organic quantum well. We deduce a suitable parameterization of a model polynomial Hamiltonian based upon the cavity geometry, the biexciton binding energy, and similar spectroscopic and structural data. By converting the sum-over-states to a semiclassical integration over D-dimensional phase space, we arrive at a principle of correspondence between ideal and non-ideal Bose gases that share a common critical exponent. Using our results, we can calculate the properties for a model cavity containing an anthracene thin film.

Quantum origins of molecular recognition and olfaction in Drosophila.

The standard model for molecular recognition of an odorant is that receptor sites discriminate by molecular geometry as evidenced that two chiral molecules may smell very differently. However, recent studies of isotopically labeled olfactants indicate that there may be a molecular vibration-sensing component to olfactory reception, specifically in the spectral region around 2300 cm(-1). Here, we present a donor-bridge-acceptor model for olfaction which attempts to explain this effect. Our model, based upon accurate quantum chemical calculations of the olfactant (bridge) in its neutral and ionized states, posits that internal modes of the olfactant are excited impulsively during hole transfer from a donor to acceptor site on the receptor, specifically those modes that are resonant with the tunneling gap. By projecting the impulsive force onto the internal modes, we can determine which modes are excited at a given value of the donor-acceptor tunneling gap. Only those modes resonant with the tunneling gap and are impulsively excited will give a significant contribution to the inelastic transfer rate. Using acetophenone as a test case, our model and experiments on D. melanogaster suggest that isotopomers of a given olfactant give rise to different odorant qualities. These results support the notion that inelastic scattering effects may play a role in discriminating between isotopomers but that this is not a general spectroscopic effect.