Quantum Diffusion on Molecular Tubes: Universal Scaling of the 1D to 2D Transition

Using the Haken-Strobl-Reineker Model to Determine the Temperature Dependence of the Diffusion Coefficient

Stochastic quantum Liouville equations (SQLE) are widely used to model energy and charge dynamics in molecular systems. The Haken-Strobl-Reineker (HSR) SQLE is a particular paradigm in which the dynamical noise that destroys quantum coherences arises from a white noise (i.e., constant-frequency) spectrum. A system subject to the HSR SQLE thus evolves to its "high-temperature" limit, whereby all the eigenstates are equally populated. This result would seem to imply that the predictions of the HSR model, e.g., the temperature dependence of the diffusion coefficient, have no validity for temperatures lower than the particle bandwidth. The purpose of this paper is to show that this assumption is incorrect for translationally invariant systems. In particular, provided that the diffusion coefficient is determined via the mean-squared-displacement, considerations about detailed-balance are irrelevant. Consequently, the high-temperature prediction for the temperature dependence of the diffusion coefficient may be extrapolated to lower temperatures, provided that the bath remains classical. Thus, for diagonal dynamical disorder the long-time diffusion coefficient, D∞(T) = c1/T, while for both diagonal and off-diagonal disorder, D∞(T) = c1/T + c2T, where c2 ≪ c1. An appendix discusses an alternative interpretation from the HSR model of the "quantum to classical" dynamics transition, whereby the dynamics is described as stochastically punctuated coherent motion.

Coherent Spatial Control of Wave Packet Dynamics on Quantum Lattices

Quantum lattices are pivotal in the burgeoning fields of quantum materials and information science. Novel experimental techniques allow the preparation and monitoring of wave packet dynamics on quantum lattices with high spatiotemporal resolution. We present an analytical study of wave packet diffusivity and diffusion length on tight-binding quantum lattices subject to stochastic noise. Our analysis reveals the crucial role of spatial coherence and predicts a set of novel phenomena: (1) noise can enhance the transient diffusivity and diffusion length of spatially extended initial states; (2) standing or traveling initial states, with large momentum, spread faster than a localized initial state and exhibit a noise-induced peak in the transient diffusivity; (3) the differences in the diffusivity or diffusion length of extended and localized initial states have a universal dependence on initial width. These predictions suggest the possibility of controlling the wave packet dynamics by spatial manipulations, which will have implications for materials science and quantum technologies.

Impact of Spatial Inhomogeneity on Excitation Energy Transport in the Fenna-Matthews-Olson Complex

The dynamics of the excitation energy transfer (EET) in photosynthetic complexes is an interesting question both from the perspective of fundamental understanding and the research in artificial photosynthesis. Over the past decade, very accurate spectral densities have been developed to capture spatial inhomogeneities in the Fenna-Matthews-Olson (FMO) complex. However, challenges persist in numerically simulating these systems, both in terms of parameterizing them and following their dynamics over long periods of time because of long non-Markovian memories. We investigate the dynamics of FMO with the exact treatment of various theoretical spectral densities using the new tensor network path integral-based methods, which are uniquely capable of addressing the difficulty of long memory length and incoherent Förster theory. It is also important to be able to analyze the pathway of EET flow, which can be difficult to identify given the non-trivial structure of connections between bacteriochlorophyll molecules in FMO. We use the recently introduced ideas of relating coherence to population derivatives to analyze the transport process and reveal some new routes of transport. The combination of exact and approximate methods sheds light on the role of coherences in affecting the fine details of the transport and promises to be a powerful toolbox for future exploration of other open systems with quantum transport.

Polariton Localization and Dispersion Properties of Disordered Quantum Emitters in Multimode Microcavities

Experiments have demonstrated that the strong light-matter coupling in polaritonic microcavities significantly enhances transport. Motivated by these experiments, we have solved the disordered multimode Tavis-Cummings model in the thermodynamic limit and used this solution to analyze its dispersion and localization properties. The solution implies that wave-vector-resolved spectroscopic quantities can be described by single-mode models, but spatially resolved quantities require the multimode solution. Nondiagonal elements of the Green's function decay exponentially with distance, which defines the coherence length. The coherent length is strongly correlated with the photon weight and exhibits inverse scaling with respect to the Rabi frequency and an unusual dependence on disorder. For energies away from the average molecular energy E_{M} and above the confinement energy E_{C}, the coherence length rapidly diverges such that it exceeds the photon resonance wavelength λ_{0}. The rapid divergence allows us to differentiate the localized and delocalized regimes and identify the transition from diffusive to ballistic transport.

Exploring the design of superradiant J-aggregates from amphiphilic monomer units

Excitonic chromophore aggregates have wide-ranging applicability in fields such as imaging and energy harvesting; however their rational design requires adapting principles of self-assembly to the requirements of excited state coupling. Using the well-studied amphiphilic cyanine dye C8S3 as a template-known to assemble into tubular excitonic aggregates-we synthesize several redshifted variants and study their self-assembly and photophysics. The new pentamethine dyes retain their tubular self-assembly and demonstrate nearly identical bathochromic shifts and lineshapes well into near-infrared wavelengths. However, detailed photophysical analysis finds that the new aggregates show a significant decline in superradiance. Additionally, cryo-TEM reveals that these aggregates readily form short bundles of nanotubes that have nearly half the radii of their trimethine comparators. We employ computational screening to gain intuition on how the structural components of these new aggregates affect their excitonic states, finding that the narrower tubes are able to assemble into a larger number of arrangements, resulting in more disordered aggregates (i.e. less superradiant) with highly similar degrees of redshift.

Long-Range Nonequilibrium Coherent Tunneling Induced by Fractional Vibronic Resonances

We study the influence of a linear energy bias on a nonequilibrium excitation on a chain of molecules coupled to local vibrations (a tilted Holstein model) using both a random-walk rate kernel theory and a nonperturbative, massively parallelized adaptive-basis algorithm. We uncover structured and discrete vibronic resonance behavior fundamentally different from both linear response theory and homogeneous polaron dynamics. Remarkably, resonance between the phonon energy ℏω and the bias δ_ϵ occurs not only at integer but also fractional ratios δ_ϵ/(ℏω) = m/n, which effect long-range n-bond m-phonon tunneling. These observations are reproduced in a model calculation of a recently demonstrated Cy3 system, and the effect of dipole-dipole-type non-nearest-neighbor coupling and vibrationally relaxed initial states is also considered. Potential applications range from molecular electronics to optical lattices and artificial light harvesting via vibronic engineering of coherent quantum transport.

Scaling relations of exciton diffusion in linear aggregates with static and dynamic disorder

Exciton diffusion plays an important role in many opto-electronic processes and phenomena. Understanding the interplay of intermolecular coupling, static energetic disorder, and dephasing caused by environmental fluctuations (dynamic disorder) is crucial to optimize exciton diffusion under various physical conditions. We report on a systematic analysis of the exciton diffusion constant in linear aggregates using the Haken-Strobl-Reineker model to describe this interplay. We numerically investigate the static-disorder scaling of (i) the diffusion constant in the limit of small dephasing rate, (ii) the dephasing rate at which the diffusion is optimized, and (iii) the value of the diffusion constant at the optimal dephasing rate. Three scaling regimes are found, associated with, respectively, fully delocalized exciton states (finite-size effects), weakly localized states, and strongly localized states. The scaling powers agree well with analytically estimated ones. In particular, in the weakly localized regime, the numerical results corroborate the so-called quantum Goldilocks principle to find the optimal dephasing rate and maximum diffusion constant as a function of static disorder, while in the strong-localization regime, these quantities can be derived fully analytically.

Probing size variations of molecular aggregates inside chlorosomes using single-object spectroscopy

We theoretically investigate the possibility to use single-object spectroscopy to probe size variations of the bacteriochlorophyll aggregates inside chlorosomes. Chlorosomes are the light-harvesting organelles of green sulfur and non-sulfur bacteria. They are known to be the most efficient light-harvesting systems in nature. Key to this efficiency is the organization of bacteriochlorophyll molecules in large self-assembled aggregates that define the secondary structure inside the chlorosomes. Many studies have been reported to elucidate the morphology of these aggregates and the molecular packing inside them. It is widely believed that tubular aggregates play an important role. Because the size (radius and length) of these aggregates affects the optical and excitation energy transport properties, it is of interest to be able to probe these quantities inside chlorosomes. We show that a combination of single-chlorosome linear polarization resolved spectroscopy and single-chlorosome circular dichroism spectroscopy may be used to access the typical size of the tubular aggregates within a chlorosome and, thus, probe possible variations between individual chlorosomes that may result, for instance, from different stages in growth or different growth conditions.

Universal Scalings in Two-Dimensional Anisotropic Dipolar Excitonic Systems

Low-dimensional excitonic materials have inspired much interest owing to their novel physical and technological prospects. In particular, those with strong in-plane anisotropy are among the most intriguing but short of general analyses. We establish the universal functional form of the anisotropic dispersion in the small k limit for 2D dipolar excitonic systems. While the energy is linearly dispersed in the direction parallel to the dipole in plane, the perpendicular direction is dispersionless up to linear order, which can be explained by the quantum interference effect of the interaction among the constituents of 1D subsystems. The anisotropic dispersion results in a E^{∼0.5} scaling of the system density of states and predicts unique spectroscopic signatures including: (1) disorder-induced absorption linewidth, W(σ)∼σ^{2.8}, with σ the disorder strength, (2) temperature dependent absorption linewidth, W(T)∼T^{s+1.5}, with s the exponent of the environment spectral density, and (3) the out-of-plane angular θ dependence of the peak splittings in absorption spectra, ΔE(θ)∝sin^{2}θ. These predictions are confirmed quantitatively with numerical simulations of molecular thin films and tubules.

Dynamical Symmetries and Symmetry-Protected Selection Rules in Periodically Driven Quantum Systems

In recent experiments, the light-matter interaction has reached the ultrastrong coupling limit, which can give rise to dynamical generalizations of spatial symmetries in periodically driven systems. Here, we present a unified framework of dynamical-symmetry-protected selection rules based on Floquet response theory. Within this framework, we study rotational, parity, particle-hole, chiral, and time-reversal symmetries and the resulting selection rules in spectroscopy, including symmetry-protected dark states (spDS), symmetry-protected dark bands, and symmetry-induced transparency. Specifically, dynamical rotational and parity symmetries establish spDS and symmetry-protected dark band conditions. A particle-hole symmetry introduces spDSs for symmetry-related Floquet states and also a symmetry-induced transparency at quasienergy crossings. Chiral symmetry and time-reversal symmetry alone do not imply spDS conditions but can be combined to define a particle-hole symmetry. These symmetry conditions arise from destructive interference due to the synchronization of symmetric quantum systems with the periodic driving. Our predictions reveal new physical phenomena when a quantum system reaches the strong light-matter coupling regime, which is important for superconducting qubits, atoms and molecules in optical or plasmonic field cavities, and optomechanical systems.

Stochastically Realized Observables for Excitonic Molecular Aggregates

We show that a stochastic approach enables calculations of the optical properties of large 2-dimensional and nanotubular excitonic molecular aggregates. Previous studies of such systems relied on numerically diagonalizing the dense and disordered Frenkel Hamiltonian, which scales approximately as O(N3) for N dye molecules. Our approach scales much more efficiently as O(Nlog(N)), enabling quick study of systems with a million of coupled molecules on the micrometer size scale. We calculate several important experimental observables, including the optical absorption spectrum and density of states, and develop a stochastic formalism for the participation ratio. Quantitative agreement with traditional matrix diagonalization methods is demonstrated for both small- and intermediate-size systems. The stochastic methodology enables the study of the effects of spatial-correlation in site energies on the optical signatures of large 2D aggregates. Our results demonstrate that stochastic methods present a path forward for screening structural parameters and validating experiments and theoretical predictions in large excitonic aggregates.

Unraveling intra-aggregate structural disorder using single-molecule spectroscopy

Structural disorder within self-assembled molecular aggregates may have strong effects on their optical functionality. Such disorder, however, is hard to explore using standard ensemble measurements. In this paper, we report on the characterization of intra-aggregate structural disorder through a linewidth analysis of fluorescence excitation experiments on individual zinc-chlorin (ZnChl) nanotubular molecular aggregates. Recent experiments suggest an anomaly in the linewidths of the two absorption bands that dominate the spectra: the higher-energy bands on average show a smaller linewidth than the lower-energy bands. This anomaly is explored in this paper by analyzing and modeling the correlation of the two linewidths for each aggregate. We exploit a Frenkel exciton model to show that the experimentally observed correlation of linewidths and other statistical properties of the single-aggregate spectra can be explained from small variations of the molecular orientations within individual aggregates.

Supertransport of excitons in atomically thin organic semiconductors at the 2D quantum limit

Long-range and fast transport of coherent excitons is important for the development of high-speed excitonic circuits and quantum computing applications. However, most of these coherent excitons have only been observed in some low-dimensional semiconductors when coupled with cavities, as there are large inhomogeneous broadening and dephasing effects on the transport of excitons in their native states in materials. Here, by confining coherent excitons at the 2D quantum limit, we first observed molecular aggregation-enabled 'supertransport' of excitons in atomically thin two-dimensional (2D) organic semiconductors between coherent states, with a measured high effective exciton diffusion coefficient of ~346.9 cm2/s at room temperature. This value is one to several orders of magnitude higher than the values reported for other organic molecular aggregates and low-dimensional inorganic materials. Without coupling to any optical cavities, the monolayer pentacene sample, a very clean 2D quantum system (~1.2 nm thick) with high crystallinity (J-type aggregation) and minimal interfacial states, showed superradiant emission from Frenkel excitons, which was experimentally confirmed by the temperature-dependent photoluminescence (PL) emission, highly enhanced radiative decay rate, significantly narrowed PL peak width and strongly directional in-plane emission. The coherence in monolayer pentacene samples was observed to be delocalised over ~135 molecules, which is significantly larger than the values (a few molecules) observed for other organic thin films. In addition, the supertransport of excitons in monolayer pentacene samples showed highly anisotropic behaviour. Our results pave the way for the development of future high-speed excitonic circuits, fast OLEDs, and other optoelectronic devices.

Exciton localization in tubular molecular aggregates: Size effects and optical response

We study the exciton localization and resulting optical response for disordered tubular aggregates of optically active molecules. It has previously been shown that such tubular structures allow for excitons delocalized over more than a thousand molecules, owing to the combined effects of long-range dipole-dipole interactions and the higher-dimensional (not truly one-dimensional) nature of the aggregate. Such large delocalization sizes prompt the question to what extent in experimental systems the delocalization may still be determined by the aggregate size (diameter and length) and how this affects the aggregate's optical response and dynamics. We perform a systematic study of the size effects on the localization properties using numerical simulations of the exciton states in a cylindrical model structure inspired by the previously derived geometry of a cylindrical aggregate of cyanine dye molecules (C8S3). To characterize the exciton localization, we calculate the participation ratio and the autocorrelation function of the exciton wave function. We also calculate the density of states and absorption spectrum. We find strong effects of the tube's radius on the localization and optical properties in the range of parameters relevant to the experiment. In addition, surprisingly, we find that even for tubes as long as 750 nm, the localization size is limited by the tube's length for disorder values that are relevant to experimental circumstances, while observable effects of the tube's length in the absorption spectrum still occur for tube lengths up to about 150 nm. The latter may explain the changes in the optical spectra observed during the aging process of bromine-substituted C8S3 aggregates. For weak disorder, the exciton wave functions exhibit a scattered, fractal-like nature, similar to the quasi-particles in two-dimensional disordered systems.

Photochemical dynamics under incoherent illumination: Light harvesting in self-assembled molecular J-aggregates

Transport phenomena in organic, self-assembled molecular J-aggregates have long attracted a great deal of attention due to their potential role in designing novel organic photovoltaic devices. A large number of theoretical and experimental studies have been carried out describing excitonic energy transfer in J-aggregates under the assumption that excitons are induced by a coherent laser-light source or initialized by a localized excitation on a particular chromophore. However, these assumptions may not provide an accurate description to assess the efficiency of J-aggregates, particularly as building blocks of organic solar cells. Under natural conditions, J-aggregates would be subjected to an incoherent source of light (as is sunlight), which would illuminate the whole photosynthetic complex rather than a single molecule. In this work, we present the first study of the efficiency of photosynthetic energy transport in self-assembled molecular aggregates under incoherent sunlight illumination. By making use of a minimalistic model of a cyanine dye J-aggregate, we demonstrate that long-range transport efficiency is enhanced when exciting the aggregate with incoherent light. Our results thus support the conclusion that J-aggregates are, indeed, excellent candidates for devices where efficient long-range incoherently induced exciton transport is desired, such as in highly efficient organic solar cells.

Interplay between structural hierarchy and exciton diffusion in artificial light harvesting

Unraveling the nature of energy transport in multi-chromophoric photosynthetic complexes is essential to extract valuable design blueprints for light-harvesting applications. Long-range exciton transport in such systems is facilitated by a combination of delocalized excitation wavefunctions (excitons) and exciton diffusion. The unambiguous identification of the exciton transport is intrinsically challenging due to the system's sheer complexity. Here we address this challenge by employing a spectroscopic lab-on-a-chip approach: ultrafast coherent two-dimensional spectroscopy and microfluidics working in tandem with theoretical modeling. We show that at low excitation fluences, the outer layer acts as an exciton antenna supplying excitons to the inner tube, while under high excitation fluences the former converts its functionality into an exciton annihilator which depletes the exciton population prior to any exciton transfer. Our findings shed light on the excitonic trajectories across different sub-units of a multi-layered artificial light-harvesting complex and underpin their great potential for directional excitation energy transport.

Enhancement of exciton transport in porphyrin aggregate nanostructures by controlling the hierarchical self-assembly

Exciton transport in meso-tetra(4-sulfonatophenyl) porphyrin (TPPS) J-aggregates was directly imaged using the emission profile analysis method with confocal fluorescence microscopy. By controlling the structural hierarchy of TPPS aggregates, we could comparatively study the exciton transport properties in single nanotubes and bundled structures. Using the one-dimensional diffusion model, the exciton diffusion coefficients of TPPS nanotubes and bundles were estimated as 95 and 393 nm2 ps-1, respectively, showing a dramatic enhancement of exciton transport in bundled structures. To reveal the underlying mechanism of enhanced exciton transport in bundle compared to that in single strands, the spatially resolved measurements of exciton transport images were correlated with the spectral information at each local sites. We have confirmed that nanotube and its bundled form possess different energetic landscapes and exciton migration dynamics. Agglomeration into bundles led to an increase in system-environment coupling and denser distribution of energy states, facilitating longer migration length and accelerated transport. Detailed analysis in this study provides important insights into the structure-dependent exciton transport properties of self-assembled J-aggregate nanostructures.

Photochemical Control of Exciton Superradiance in Light-Harvesting Nanotubes

Photosynthetic antennae and organic electronic materials use topological, structural, and molecular control of delocalized excitons to enhance and direct energy transfer. Interactions between the transition dipoles of individual chromophore units allow for coherent delocalization across multiple molecular sites. This delocalization, for specific geometries, greatly enhances the transition dipole moment of the lowest energy excitonic state relative to the chromophore and increases its radiative rate, a phenomenon known as superradiance. In this study, we show that ordered, self-assembled light-harvesting nanotubes (LHNs) display excitation-induced photobrightening and photodarkening. These changes in quantum yield arise due to changes in energetic disorder, which in turn increases/decreases excitonic superradiance. Through a combination of experiment and modeling, we show that intense illumination induces different types of chemical change in LHNs that reproducibly alter absorption and fluorescence properties, indicating control over excitonic delocalization. We also show that changes in spectral width and shift can be sensitive measures of system dimensionality, illustrating the mixed 1-2D nature of LHN excitons. Our results demonstrate a path forward for mastery of energetic disorder in an excitonic antenna, with implications for fundamental studies of coherent energy transport.

Tubular J-aggregates of a new thiacarbocyanine Cy5 dye for the far-red spectral region – a spectroscopic and cryo-transmission electron microscopy study

A new phenol-substituted Cy5 dye forms tubular J-aggregates that are active in the far-red spectral region.

Direct Imaging of Frenkel Exciton Transport by Ultrafast Microscopy

Long-range transport of Frenkel excitons is crucial for achieving efficient molecular-based solar energy harvesting. Understanding of exciton transport mechanisms is important for designing materials for solar energy applications. One major bottleneck in unraveling of exciton transport mechanisms is the lack of direct measurements to provide information in both spatial and temporal domains, imposed by the combination of fast energy transfer (typically ≤1 ps) and short exciton diffusion lengths (typically ≤100 nm). This challenge requires developing experimental tools to directly characterize excitation energy transport, and thus facilitate the elucidation of mechanisms. To address this challenge, we have employed ultrafast transient absorption microscopy (TAM) as a means to directly image exciton transport with ∼200 fs time resolution and ∼50 nm spatial precision. By mapping population in spatial and temporal domains, such approach has unraveled otherwise obscured information and provided important parameters for testing exciton transport models. In this Account, we discuss the recent progress in imaging Frenkel exciton migration in molecular crystals and aggregates by ultrafast microscopy. First, we establish the validity of the TAM methods by imaging singlet and triplet exciton transport in a series of polyacene single crystals that undergo singlet fission. A new singlet-mediated triplet transport pathway has been revealed by TAM, resulting from the equilibrium between triplet and singlet exciton populations. Such enhancement of triplet exciton transport enables triplet excitons to migrate as singlet excitons and leads to orders of magnitude faster apparent triplet exciton diffusion rate in the picosecond and nanosecond time scales, favorable for solar cell applications. Next we discuss how information obtained by ultrafast microscopy can evaluate coherent effects in exciton transport. We use tubular molecular aggregates that could support large exciton delocalization sizes as a model system. The initial experiments measure exciton diffusion constants of 3-6 cm² s^-1, 3-5 times higher than the incoherent limit predicted by theory, suggesting that coherent effects play a role. In summary, combining ultrafast spectroscopic methods with microscopic techniques provides a direct approach for obtaining important parameters to unravel the underlying exciton transport mechanisms in molecular solids. We discuss future directions to bridge the gap in understanding of fundamental energy transfer theories to include coherent and incoherent effects. We are still in the infancy of ultrafast microscopy, and the vast potential is not limited to the systems discussed in this Account.

Steering Self-Assembly of Amphiphilic Molecular Nanostructures via Halogen Exchange

In the field of self-assembly, the quest for gaining control over the supramolecular architecture without affecting the functionality of the individual molecular building blocks is intrinsically challenging. By using a combination of synthetic chemistry, cryogenic transmission electron microscopy, optical absorption measurements, and exciton theory, we demonstrate that halogen exchange in carbocyanine dye molecules allows for fine-tuning the diameter of the self-assembled nanotubes formed by these molecules, while hardly affecting the molecular packing determined by hydrophobic/hydrophilic interactions. Our findings open a unique way to study size effects on the optical properties and exciton dynamics of self-assembled systems under well-controlled conditions.

An extension of stochastic hierarchy equations of motion for the equilibrium correlation functions

A traditional stochastic hierarchy equations of motion method is extended into the correlated real-time and imaginary-time propagations, in this paper, for its applications in calculating the equilibrium correlation functions. The central idea is based on a combined employment of stochastic unravelling and hierarchical techniques for the temperature-dependent and temperature-free parts of the influence functional, respectively, in the path integral formalism of the open quantum systems coupled to a harmonic bath. The feasibility and validity of the proposed method are justified in the emission spectra of homodimer compared to those obtained through the deterministic hierarchy equations of motion. Besides, it is interesting to find that the complex noises generated from a small portion of real-time and imaginary-time cross terms can be safely dropped to produce the stable and accurate position and flux correlation functions in a broad parameter regime.