Abstract:
A general theory of electronic excitations in aggregates of molecules coupled to intramolecular vibrations and the harmonic environment is developed for simulation of the third-order nonlinear spectroscopy signals. The model is applied in studies of the time-resolved two-dimensional coherent spectra of four characteristic model systems: weakly / strongly vibronically coupled molecular dimers coupled to high / low frequency intramolecular vibrations. The results allow us to classify the typical spectroscopic features as well as to define the limiting cases, when the long-lived quantum coherences are present due to vibrational lifetime borrowing, when the complete exciton-vibronic mixing occurs and when separation of excitonic and vibrational coherences is proper.

Abstract:
A semiempirical parametric method is proposed for modeling three-dimensional (time-resolved) vibronic spectra of polyatomic molecules. The method is based on the use of the fragment approach in the formation of molecular models for excited electronic states and parametrization of these molecular fragments by modeling conventional (one-dimensional) absorption and fluorescence spectra of polyatomic molecules. All matrix elements that are required for calculation of the spectra can be found by the methods developed. The time dependencies of the populations of a great number (>10^3) of vibronic levels can be most conveniently found by using the iterative numerical method of integration of kinetic equations. Convenient numerical algorithms and specialized software for PC are developed. Computer experiments showed the possibility of the real-time modeling of three-dimensional spectra of polyatomic molecules containing several tens of atoms.

Abstract:
A vibronic-exciton model is applied to investigate the mechanism of enhancement of coherent oscillations due to mixing of electronic and nuclear degrees of freedom recently proposed as the origin of the long-lived oscillations in 2D spectra of the FMO complex [Christensson et al. J. Phys. Chem. B 116 (2012) 7449]. We reduce the problem to a model BChl dimer to elucidate the role of resonance coupling, site energies, nuclear mode and energy disorder in the enhancement of vibronic-exciton and ground-state vibrational coherences, and to identify regimes where this enhancement is significant. For a heterodimer representing the two coupled BChls 3 and 4 of the FMO complex, the initial amplitude of the vibronic-exciton and vibrational coherences are enhanced by up to 15 and 5 times, respectively, compared to the vibrational coherences in the isolated monomer. This maximum initial amplitude enhancement occurs when there is a resonance between the electronic energy gap and the frequency of the vibrational mode. The bandwidth of this enhancement is about 100 cm-1 for both mechanisms. The excitonic mixing of electronic and vibrational DOF leads to additional dephasing relative to the vibrational coherences. We evaluate the dephasing dynamics by solving the quantum master equation in Markovian approximation and observe a strong dependence of the life-time enhancement on the mode frequency. Long-lived vibronic-exciton coherences are found to be generated only when the frequency of the mode is in the vicinity of the electronic resonance. Although the vibronic-exciton coherences exhibit a larger initial amplitude compared to the ground-state vibrational coherences, we conclude that both type have a similar magnitude at long time for the present model. The ability to distinguish between vibronic-exciton and ground-state vibrational coherences in the general case of molecular aggregate is discussed.

Abstract:
In this work we proof that boson sampling with $N$ particles in $M$ modes is equivalent to short-time evolution with $N$ excitations in an XY model of $2N$ spins. This mapping is efficient whenever the boson bunching probability is small, and errors can be efficiently postselected. This mapping opens the door to boson sampling with quantum simulators or general purpose quantum computers, and highlights the complexity of time-evolution with critical spin models, even for very short times.

Abstract:
The prevalence of long-lasting oscillatory signals in the 2d echo-spectroscopy of light-harvesting complexes has led to a search for possible mechanisms. We investigate how two causes of oscillatory signals are intertwined: (i) electronic coherences supporting delocalized wave-like motion, and (ii) narrow bands in the vibronic spectral density. To disentangle the vibronic and electronic contributions we introduce a time-windowed Fourier transform of the signal amplitude. We find that 2d spectra can be dominated by excitations of pathways which are absent in excitonic energy transport. This leads to an underestimation of the life-time of electronic coherences by 2d spectra.

Abstract:
We discuss semiempirical approaches and parametric methods developed for modeling molecular vibronic spectra. These methods, together with databases of molecular fragments, have proved efficient and flexible for solving various problems ranging from detailed interpretation of conventional vibronic spectra and calculation of radiative transition probabilities to direct simulations of dynamical (time-resolved) spectra and spectrochemical analysis of individual substances and mixtures. A number of specific examples and applications presented here show the potential of the semiempirical approach for predictive calculations of spectra and solution of inverse spectral problems. It is noteworthy that these advances provide computational insights into developing theories of photoinduced isomer transformations and nonradiative transitions in polyatomic molecules and molecular ensembles, theory of new methods for standardless quantitative spectral analysis.

Abstract:
The oxygen dopant concentration dependence of the "quasiparticle" feature at 600-750 cm-1 of the infrared spectrum of Bi2Sr2CaCu2O8+delta (BSCCO), lying near and above the top of the host phonon spectrum at 600 cm-1, is strongly correlated with superconductivity. Using parameter-free topological methods, theory assigns this feature to split apical oxygen interstitials. It explains both the qualitative similarities and the quantitative differences between "quasiparticle" features identified in infrared and phtoemission data, as well as identifying new features in the infrared spectra.

Abstract:
Long-lived oscillations in 2D spectra of chlorophylls are at the heart of an ongoing debate. Their physical origin is either a multi-pigment effect, such as excitonic coherence, or primarily stems from localized vibrations. In the present work, we analyze distinguishing characteristics of relative phase difference measured between diagonal- and cross-peak oscillations. While direct discrimination between the two scenarios is obscured when peaks overlap, their sensitivity to temperature provides a stronger argument. We show that vibrational (vibronic) oscillations change relative phase with temperature, while electronic oscillations are only weakly dependent. This highlights that studies of relative phase difference as a function of temperature provide a clear and easily accessible method to distinguish between vibrational and electronic coherences.

Abstract:
Natural and artificial light harvesting processes have recently gained new interest. Signatures of long lasting coherence in spectroscopic signals of biological systems have been repeatedly observed, albeit their origin is a matter of ongoing debate, as it is unclear how the loss of coherence due to interaction with the noisy environments in such systems is averted. Here we report experimental and theoretical verification of coherent exciton-vibrational (vibronic) coupling as the origin of long-lasting coherence in an artificial light harvester, a molecular J-aggregate. In this macroscopically aligned tubular system, polarization controlled 2D spectroscopy delivers an uncongested and specific optical response as an ideal foundation for an in-depth theoretical description. We derive analytical expressions that show under which general conditions vibronic coupling leads to prolonged excited-state coherence.

Abstract:
We study the electron transport through a magnetic molecular transistor in the Kondo limit using the slave boson technique. We include the electron-phonon coupling and analyze the cases where the spin of the molecule is either S=1/2 or S=1. We use the Schrieffer-Wolff transformation to write down a low energy Hamiltonian for the system. In the presence of electron-phonon coupling, and for $S\smeq1$, the resulting Kondo Hamiltonian has two active channels. At low temperature, these two channels interfere destructively, leading to a zero conductance.