Synchronized states in a ring of dissipatively coupled harmonic oscillators.

The question under which conditions oscillators with slightly different frequencies synchronize appears in various settings. We consider the case of a finite number of harmonic oscillators arranged on a ring, with bilinear, dissipative nearest-neighbor coupling. We show that by tuning the gain and loss appropriately, stable synchronized dynamics may be achieved. These findings are interpreted using the complex eigenvalues and eigenvectors of the non-Hermitian matrix describing the dynamics of the system. We provide a complete discussion for the case of two oscillators. Ring sizes with a small number of oscillators are discussed taking the case of N=5 oscillators as an example. For N≳10 we focus on the case where the frequency fluctuations of each oscillator are chosen from a Gaussian distribution with zero mean and standard deviation σ. We derive a scaling law for the largest standard deviation σ_{full} that still permits all oscillators to be fully synchronized: σ_{full}∼N^{-3/2}. Finally, we discuss how such random fluctuations influence the timescale on which the synchronized state is reached and on which timescale the synchronized state then decays.

Simulating optical linear absorption for mesoscale molecular aggregates: An adaptive hierarchy of pure states approach.

In this paper, we present dyadic adaptive HOPS (DadHOPS), a new method for calculating linear absorption spectra for large molecular aggregates. This method combines the adaptive HOPS (adHOPS) framework, which uses locality to improve computational scaling, with the dyadic HOPS method previously developed to calculate linear and nonlinear spectroscopic signals. To construct a local representation of dyadic HOPS, we introduce an initial state decomposition that reconstructs the linear absorption spectra from a sum over locally excited initial conditions. We demonstrate the sum over initial conditions can be efficiently Monte Carlo sampled and that the corresponding calculations achieve size-invariant [i.e., O(1)] scaling for sufficiently large aggregates while trivially incorporating static disorder in the Hamiltonian. We present calculations on the photosystem I core complex to explore the behavior of the initial state decomposition in complex molecular aggregates as well as proof-of-concept DadHOPS calculations on an artificial molecular aggregate inspired by perylene bis-imide to demonstrate the size-invariance of the method.

Calculating nonlinear response functions for multidimensional electronic spectroscopy using dyadic non-Markovian quantum state diffusion.

We present a methodology for simulating multidimensional electronic spectra of molecular aggregates with coupling of electronic excitation to a structured environment using the stochastic non-Markovian quantum state diffusion (NMQSD) method in combination with perturbation theory for the response functions. A crucial aspect of our approach is that we propagate the NMQSD equation in a doubled system Hilbert space but with the same noise. We demonstrate that our approach shows fast convergence with respect to the number of stochastic trajectories, providing a promising technique for numerical calculation of two-dimensional electronic spectra of large molecular aggregates.

Simulation of absorption spectra of molecular aggregates: A hierarchy of stochastic pure state approach.

Simulation of spectroscopic observables for molecular aggregates with strong and structured coupling of electronic excitation to vibrational degrees of freedom is an important but challenging task. The Hierarchy of Pure States (HOPS) provides a formally exact solution based on local, stochastic trajectories. Exploiting the localization of HOPS for the simulation of absorption spectra in large aggregates requires a formulation in terms of normalized trajectories. Here, we provide a normalized dyadic equation where the ket- and bra-states are propagated in different electronic Hilbert spaces. This work opens the door to applying adaptive HOPS methods for the simulation of absorption spectra.

Gaussian process regression for absorption spectra analysis of molecular dimers.

A common task is the determination of system parameters from spectroscopy, where one compares the experimental spectrum with calculated spectra, that depend on the desired parameters. Here we discuss an approach based on a machine learning technique, where the parameters for the numerical calculations are chosen from Gaussian Process Regression (GPR). This approach does not only quickly converge to an optimal parameter set, but in addition provides information about the complete parameter space, which allows for example to identify extended parameter regions where numerical spectra are consistent with the experimental one. We consider as example dimers of organic molecules and aim at extracting in particular the interaction between the monomers, and their mutual orientation. We find that indeed the GPR gives reliable results which are in agreement with direct calculations of these parameters using quantum chemical methods.

Excitation dynamics in polyacene molecules on rare-gas clusters.

Laser-induced fluorescence spectra and excitation lifetimes of anthracene, tetracene, and pentacene molecules attached to the surface of solid argon clusters have been measured with respect to cluster size, density of molecules, and excitation density. Results are compared to previous studies on the same sample molecules attached to neon clusters. A contrasting lifetime behavior of anthracene on neon and argon clusters is discussed, and mechanisms are suggested to interpret the results. Although both neon and argon clusters are considered to be weakly interacting environments, we find that the excitation decay dynamics of the studied acenes depends significantly on the cluster material. Moreover, we find even qualitative differences regarding the dependence on the dopant density. Based on these observations, previous assignments of collective radiative and non-radiative decay mechanisms are discussed in the context of the new experimental findings.

Near-field scanning optical microscopy of molecular aggregates: The role of light polarization.

We consider theoretically near-field absorption spectra of molecular aggregates stemming from a scattering scanning near-field optical microscopy type setup. Our focus is on the dependence on the direction and polarization of the incoming electromagnetic radiation, which induces a Hertz dipole with a specific orientation at the tip-apex. Within a simple description, which is based on the eigenstates of the aggregate, absorption spectra are calculated for the near field created by this dipole. We find that the spatial patterns of the spectra have a strong dependence on the orientation of this tip-dipole, which can be understood by considering three basic functions that only depend on the arrangement of the aggregate and the molecule tip distance, but not on the orientation of the tip-dipole. This allows direct access to spatial dependence of the aggregate eigenstates. For the important cases of one- and two-dimensional systems with parallel molecules, we discuss these spectra in detail. The simple numerically efficient approach is validated by a more detailed description where the incoming radiation and the interaction between the tip and molecules are explicitly taken into account.

Extended Coherently Delocalized States in a Frozen Rydberg Gas.

The long-range dipole-dipole interaction can create delocalized states due to the exchange of excitation between Rydberg atoms. We show that even in a random gas many of the single-exciton eigenstates are surprisingly delocalized, composed of roughly one quarter of the participating atoms. We identify two different types of eigenstates: one which stems from strongly-interacting clusters, resulting in localized states, and one which extends over large delocalized networks of atoms. These two types of states can be excited and distinguished by appropriately tuned microwave pulses, and their relative contributions can be modified by the Rydberg blockade and the choice of microwave parameters.

Excitonic Wave Function Reconstruction from Near-Field Spectra Using Machine Learning Techniques.

A general problem in quantum mechanics is the reconstruction of eigenstate wave functions from measured data. In the case of molecular aggregates, information about excitonic eigenstates is vitally important to understand their optical and transport properties. Here we show that from spatially resolved near field spectra it is possible to reconstruct the underlying delocalized aggregate eigenfunctions. Although this high-dimensional nonlinear problem defies standard numerical or analytical approaches, we have found that it can be solved using a convolutional neural network. For both one-dimensional and two-dimensional aggregates we find that the reconstruction is robust to various types of disorder and noise.

Charge and energy transfer in large molecular assemblies: Quantum state diffusion with an adaptive basis.

We show that the stochastic, wave-function based quantum state diffusion approach in combination with an adaptive basis is well suited to numerically treat the motion of an excitation in large molecular aggregates in the complicated regime where the transfer-time between molecules is comparable to the decoherence caused by environmental degrees of freedom.

Delocalized excitons and interaction effects in extremely dilute thermal ensembles.

Long-range interparticle interactions are revealed in extremely dilute thermal atomic ensembles using highly sensitive nonlinear femtosecond spectroscopy. Delocalized excitons are detected in the atomic systems at particle densities where the mean interatomic distance (>10 µm) is much greater than the laser wavelength and multi-particle coherences should destructively interfere over the ensemble average. With a combined experimental and theoretical analysis, we identify an effective interaction mechanism, presumably of dipolar nature, as the origin of the excitonic signals. Our study implies that even in highly-dilute thermal atom ensembles, significant transition dipole-dipole interaction networks may form that require advanced modeling beyond the nearest neighbor approximation to quantitatively capture the details of their many-body properties.

Near-Field Spectroscopy of Nanoscale Molecular Aggregates.

When molecules are assembled into an aggregate, their mutual dipole-dipole interaction leads to electronic eigenstates that are coherently delocalized over many molecules. Knowledge about these states is important to understand the optical and transfer properties of the aggregates. Optical spectroscopy, in principle, allows one to infer information on these eigenstates and about the interactions between the molecules. However, traditional optical techniques using an electromagnetic field which is uniform over the relevant size of the aggregate cannot access most of the excited states because of selection rules. We demonstrate that by using localized fields one can obtain information about these otherwise inaccessible states. As an example, we discuss in detail the case of local excitation via radiation from the apex of a metallic tip, which allows also scanning across the aggregate. The resulting spatially resolved spectra provide extensive information on the eigenenergies and wave functions. Finally we show that the technique will elucidate the anomalous temperature dependence of superradiance found recently for two-dimensional aggregates of the semiconductor PTCDA formed on a KCl surface.

Superradiance from Two Dimensional Brick-Wall Aggregates of Dye Molecules: The Role of Size and Shape for the Temperature Dependence.

Aggregates of interacting molecules can exhibit electronically excited states that are coherently delocalized over many molecules. This can lead to a strong enhancement of the fluorescence decay rate which is referred to as superradiance (SR). To date, the temperature dependence of SR is described by a 1/T law. Using an epitaxial dye layer and a Frenkel-exciton based model we provide both experimental and theoretical evidence that significant deviations from the 1/T behavior can occur for brick-wall-type aggregates of finite size leading even to a maximum of the SR at finite temperature. This is due to the presence of low energy excitations of weak or zero transition strength. These findings are relevant for designing light-emitting molecular materials.

Closures of the functional expansion hierarchy in the non-Markovian quantum state diffusion approach.

To find a practical scheme to numerically solve the non-Markovian Quantum State Diffusion equation (NMQSD), one often uses a functional expansion of the functional derivative that appears in the general NMQSD equation. This expansion leads to a hierarchy of coupled operators. It turned out that if one takes only the zeroth order term into account, one has a very efficient method that agrees remarkably well with the exact results for many cases of interest. We denote this approach as zeroth order functional expansion (ZOFE). In the present work, we investigate two extensions of ZOFE. Firstly, we investigate how the hierarchy converges when taking higher orders into account (which, however, leads to a fast increase in numerical size). Secondly, we demonstrate that by using a terminator that approximates the higher order contributions, one can obtain significant improvement, at hardly any additional computational cost. We carry out our investigations for the case of absorption spectra of molecular aggregates.

Tuning Nonradiative Lifetimes via Molecular Aggregation.

We show that molecular aggregation can strongly influence the nonradiative decay (NRD) lifetime of an electronic excitation. As a demonstrative example, we consider a transition-dipole-dipole-interacting dimer whose monomers have harmonic potential energy surfaces (PESs). Depending on the position of the NRD channel (qnr), we find that the NRD lifetime (τnrdim) can exhibit a completely different dependence on the intermolecular-interaction strength. We observe that (i) for qnr near the Franck-Condon region, τnrdim increases with the interaction strength; (ii) for qnr near the minimum of the monomer excited PES, the intermolecular interaction has little influence on τnrdim; and (iii) for qnr near the classical turning point of the monomer nuclear dynamics, on the other side of the minimum, τnrdim decreases with the interaction strength. Our findings suggest design principles for molecular systems where a specific fluorescence quantum yield is desired.

Singlet Fission in Weakly Interacting Acene Molecules.

The energy conversion in solar cells has conventionally been limited by the Shockley-Queisser limit. Singlet fission (SF), a decay mechanism where a single excited singlet state is converted into two triplet states, can drastically improve this efficiency. For the most part, observation of SF has been limited to crystalline structures in solids and films, where strong ordering was present. Here we report on singlet fission in a disordered system where organic chromophores are distributed on the surface of a rare gas cluster. In this case, the intermolecular distances and degree of excitation can be varied to obtain their effects on the rate of singlet fission. We introduce a kinematic model that takes into account the details of the geometrical arrangement of the system as well as the time-dependent populations of the relevant states of each molecule and evaluate the trends obtained by SF on the experimental observables.

Non-Perturbative Calculation of Two-Dimensional Spectra Using the Stochastic Hierarchy of Pure States.

Two-dimensional electronic spectroscopy has become an important experimental technique to obtain information on, for example, electronic coherences in large molecular complexes or vibronic couplings. For the correct interpretation of two-dimensional spectra, however, detailed theoretical calculations are required. Reliable theoretical calculations are impeded by large system sizes and large numbers of vibrational degrees of freedom that need to be explicitly taken into account. Here, we demonstrate that a numerical approach based on a stochastic hierarchy of pure states (HOPS) does allow the calculation of two-dimensional spectra, notwithstanding the stochasticity of the method. The number of coupled equations as well as the hierarchy depth shows a superior scaling with system size as compared to the previously developed hierarchical equations of motion (HEOM). Large systems thus become accessible for numerical calculation of two-dimensional spectra.

Open quantum system parameters for light harvesting complexes from molecular dynamics.

We extract the site energies and spectral densities of the Fenna-Matthews-Olson (FMO) pigment protein complex of green sulphur bacteria from simulations of molecular dynamics combined with energy gap calculations. Comparing four different combinations of methods, we investigate the origin of quantitative differences regarding site energies and spectral densities obtained previously in the literature. We find that different forcefields for molecular dynamics and varying local energy minima found by the structure relaxation yield significantly different results. Nevertheless, a picture averaged over these variations is in good agreement with experiments and some other theory results. Throughout, we discuss how vibrations-external or internal to the pigment molecules-enter the extracted quantities differently and can be distinguished. Our results offer some guidance to set up computationally more intensive calculations for a precise determination of spectral densities in the future. These are required to determine absorption spectra as well as transport properties of light harvesting complexes.

Extended quantum jump description of vibronic two-dimensional spectroscopy.

We calculate two-dimensional (2D) vibronic spectra for a model system involving two electronic molecular states. The influence of a bath is simulated using a quantum-jump approach. We use a method introduced by Makarov and Metiu [J. Chem. Phys. 111, 10126 (1999)] which includes an explicit treatment of dephasing. In this way it is possible to characterize the influence of dissipation and dephasing on the 2D-spectra, using a wave function based method. The latter scales with the number of stochastic runs and the number of system eigenstates included in the expansion of the wave-packets to be propagated with the stochastic method and provides an efficient method for the calculation of the 2D-spectra.

Non-Markovian Quantum State Diffusion for temperature-dependent linear spectra of light harvesting aggregates.

Non-Markovian Quantum State Diffusion (NMQSD) has turned out to be an efficient method to calculate excitonic properties of aggregates composed of organic chromophores, taking into account the coupling of electronic transitions to vibrational modes of the chromophores. NMQSD is an open quantum system approach that incorporates environmental degrees of freedom (the vibrations in our case) in a stochastic way. We show in this paper that for linear optical spectra (absorption, circular dichroism), no stochastics is needed, even for finite temperatures. Thus, the spectra can be obtained by propagating a single trajectory. To this end, we map a finite temperature environment to the zero temperature case using the so-called thermofield method. The resulting equations can then be solved efficiently by standard integrators.