Pathway selectivity in time-resolved spectroscopy using two-photon coincidence counting with quantum entangled photons.

Ultrafast optical spectroscopy is a powerful technique for studying the dynamic processes of molecular systems in condensed phases. However, in molecular systems containing many dye molecules, the spectra can become crowded and difficult to interpret owing to the presence of multiple nonlinear optical contributions. In this work, we theoretically propose time-resolved spectroscopy based on the coincidence counting of two entangled photons generated via parametric down-conversion with a monochromatic laser. We demonstrate that the use of two-photon counting detection of entangled photon pairs enables the selective elimination of the excited-state absorption signal. This selective elimination cannot be realized with classical coherent light. We anticipate that the proposed spectroscopy will help simplify the spectral interpretation of complex molecular and material systems comprising multiple molecules.

Probing exciton dynamics with spectral selectivity through the use of quantum entangled photons.

Quantum light is increasingly recognized as a promising resource for developing optical measurement techniques. Particular attention has been paid to enhancing the precision of the measurements beyond classical techniques by using nonclassical correlations between quantum entangled photons. Recent advances in the quantum optics technology have made it possible to manipulate spectral and temporal properties of entangled photons, and photon correlations can facilitate the extraction of matter information with relatively simple optical systems compared to conventional schemes. In these respects, the applications of entangled photons to time-resolved spectroscopy can open new avenues for unambiguously extracting information on dynamical processes in complex molecular and materials systems. Here, we propose time-resolved spectroscopy in which specific signal contributions are selectively enhanced by harnessing nonclassical correlations of entangled photons. The entanglement time characterizes the mutual delay between an entangled twin and determines the spectral distribution of photon correlations. The entanglement time plays a dual role as the knob for controlling the accessible time region of dynamical processes and the degrees of spectral selectivity. In this sense, the role of the entanglement time is substantially equivalent to the temporal width of the classical laser pulse. The results demonstrate that the application of quantum entangled photons to time-resolved spectroscopy leads to monitoring dynamical processes in complex molecular and materials systems by selectively extracting desired signal contributions from congested spectra. We anticipate that more elaborately engineered photon states would broaden the availability of quantum light spectroscopy.

Achieving two-dimensional optical spectroscopy with temporal and spectral resolution using quantum entangled three photons.

Recent advances in techniques for generating quantum light have stimulated research on novel spectroscopic measurements using quantum entangled photons. One such spectroscopy technique utilizes non-classical correlations among entangled photons to enable measurements with enhanced sensitivity and selectivity. Here, we investigate the spectroscopic measurement utilizing entangled three photons. In this measurement, time-resolved entangled photon spectroscopy with monochromatic pumping [A. Ishizaki, J. Chem. Phys. 153, 051102 (2020)] is integrated with the frequency-dispersed two-photon counting technique, which suppresses undesired accidental photon counts in the detector and thus allows one to separate the weak desired signal. This time-resolved frequency-dispersed two-photon counting signal, which is a function of two frequencies, is shown to provide the same information as that of coherent two-dimensional optical spectra. The spectral distribution of the phase-matching function works as a frequency filter to selectively resolve a specific region of the two-dimensional spectra, whereas the excited-state dynamics under investigation are temporally resolved in the time region longer than the entanglement time. The signal is not subject to Fourier limitations on the joint temporal and spectral resolution, and therefore, it is expected to be useful for investigating complex molecular systems in which multiple electronic states are present within a narrow energy range.

Intramolecular Vibrations Complement the Robustness of Primary Charge Separation in a Dimer Model of the Photosystem II Reaction Center.

The energy conversion of oxygenic photosynthesis is triggered by primary charge separation in proteins at the photosystem II reaction center. Here, we investigate the impacts of the protein environment and intramolecular vibrations on primary charge separation at the photosystem II reaction center. This is accomplished by combining the quantum dynamic theories of condensed phase electron transfer with quantum chemical calculations to evaluate the vibrational Huang-Rhys factors of chlorophyll and pheophytin molecules. We report that individual vibrational modes play a minor role in promoting charge separation, contrary to the discussion in recent publications. Nevertheless, these small contributions accumulate to considerably influence the charge separation rate, resulting in subpicosecond charge separation almost independent of the driving force and temperature. We suggest that the intramolecular vibrations complement the robustness of the charge separation in the photosystem II reaction center against the inherently large static disorder of the involved electronic energies.

Direct evaluation of boson dynamics via finite-temperature time-dependent variation with multiple Davydov states.

Recent advances in quantum optics allow for exploration of boson dynamics in dissipative many-body systems. However, the traditional descriptions of quantum dissipation using reduced density matrices are unable to capture explicit information of bath dynamics. In this work, efficient evaluation of boson dynamics is demonstrated by combining the multiple Davydov Ansatz with finite-temperature time-dependent variation, going beyond what state-of-the-art density matrix approaches are capable to offer for coupled electron-boson systems. To this end, applications are made to excitation energy transfer in photosynthetic systems, singlet fission in organic thin films, and circuit quantum electrodynamics in superconducting devices. Thanks to the multiple Davydov Ansatz, our analysis of boson dynamics leads to clear revelation of boson modes strongly coupled to electronic states, as well as in-depth description of polaron creation and destruction in the presence of thermal fluctuations.

Effect of Off-Diagonal Exciton-Phonon Coupling on Intramolecular Singlet Fission.

Intramolecular singlet fission (iSF) materials provide remarkable advantages in terms of tunable electronic structures, and quantum chemistry studies have indicated strong electronic coupling modulation by high frequency phonon modes. In this work, we formulate a microscopic model of iSF with simultaneous diagonal and off-diagonal coupling to high-frequency modes. A nonperturbative treatment, the Dirac-Frenkel time-dependent variational approach is adopted using the multiple Davydov trial states. It is shown that both diagonal and off-diagonal coupling can aid efficient singlet fission if excitonic coupling is weak, and fission is only facilitated by diagonal coupling if excitonic coupling is strong. In the presence of off-diagonal coupling, it is found that high frequency modes create additional fission channels for rapid iSF. Results presented here may help provide guiding principles for design of efficient singlet fission materials by directly tuning singlet-triplet interstate coupling.

Finite-temperature time-dependent variation with multiple Davydov states.

The Dirac-Frenkel time-dependent variational approach with Davydov Ansätze is a sophisticated, yet efficient technique to obtain an accurate solution to many-body Schrödinger equations for energy and charge transfer dynamics in molecular aggregates and light-harvesting complexes. We extend this variational approach to finite temperature dynamics of the spin-boson model by adopting a Monte Carlo importance sampling method. In order to demonstrate the applicability of this approach, we compare calculated real-time quantum dynamics of the spin-boson model with that from numerically exact iterative quasiadiabatic propagator path integral (QUAPI) technique. The comparison shows that our variational approach with the single Davydov Ansätze is in excellent agreement with the QUAPI method at high temperatures, while the two differ at low temperatures. Accuracy in dynamics calculations employing a multitude of Davydov trial states is found to improve substantially over the single Davydov Ansatz, especially at low temperatures. At a moderate computational cost, our variational approach with the multiple Davydov Ansatz is shown to provide accurate spin-boson dynamics over a wide range of temperatures and bath spectral densities.

Effect of high-frequency modes on singlet fission dynamics.

Singlet fission is a spin-allowed energy conversion process whereby a singlet excitation splits into two spin-correlated triplet excitations residing on adjacent molecules and has a potential to dramatically increase the efficiency of organic photovoltaics. Recent time-resolved nonlinear spectra of pentacene derivatives have shown the importance of high frequency vibrational modes in efficient fission. In this work, we explore impacts of vibration-induced fluctuations on fission dynamics through quantum dynamics calculations with parameters from fitting measured linear and nonlinear spectra. We demonstrate that fission dynamics strongly depends on the frequency of the intramolecular vibrational mode. Furthermore, we examine the effect of two vibrational modes on fission dynamics. Inclusion of a second vibrational mode creates an additional fission channel even when its Huang-Rhys factor is relatively small. Addition of more vibrational modes may not enhance the fission per se, but can dramatically affect the interplay between fission dynamics and the dominant vibrational mode.

A variational master equation approach to quantum dynamics with off-diagonal coupling in a sub-Ohmic environment.

A master equation approach based on an optimized polaron transformation is adopted for dynamics simulation with simultaneous diagonal and off-diagonal spin-boson coupling. Two types of bath spectral density functions are considered, the Ohmic and the sub-Ohmic. The off-diagonal coupling leads asymptotically to a thermal equilibrium with a nonzero population difference Pz(t → ∞) ≠ 0, which implies localization of the system, and it also plays a role in restraining coherent dynamics for the sub-Ohmic case. Since the new method can extend to the stronger coupling regime, we can investigate the coherent-incoherent transition in the sub-Ohmic environment. Relevant phase diagrams are obtained for different temperatures. It is found that the sub-Ohmic environment allows coherent dynamics at a higher temperature than the Ohmic environment.

Fluctuations in Electronic Energy Affecting Singlet Fission Dynamics and Mixing with Charge-Transfer State: Quantum Dynamics Study.

Singlet fission is a spin-allowed process by which a singlet excited state is converted to two triplet states. To understand mechanisms of the ultrafast fission via a charge transfer (CT) state, one has investigated the dynamics through quantum-dynamical calculations with the uncorrelated fluctuation model; however, the electronic states are expected to experience the same fluctuations induced by the surrounding molecules because the electronic structure of the triplet pair state is similar to that of the singlet state except for the spin configuration. Therefore, the fluctuations in the electronic energies could be correlated, and the 1D reaction coordinate model may adequately describe the fission dynamics. In this work we develop a model for describing the fission dynamics to explain the experimentally observed behaviors. We also explore impacts of fluctuations in the energy of the CT state on the fission dynamics and the mixing with the CT state. The overall behavior of the dynamics is insensitive to values of the reorganization energy associated with the transition from the singlet state to the CT state, although the coherent oscillation is affected by the fluctuations. This result indicates that the mixing with the CT state is rather robust under the fluctuations in the energy of the CT state as well as the high-lying CT state.

Impact of environmentally induced fluctuations on quantum mechanically mixed electronic and vibrational pigment states in photosynthetic energy transfer and 2D electronic spectra.

Recently, nuclear vibrational contribution signatures in two-dimensional (2D) electronic spectroscopy have attracted considerable interest, in particular as regards interpretation of the oscillatory transients observed in light-harvesting complexes. These transients have dephasing times that persist for much longer than theoretically predicted electronic coherence lifetime. As a plausible explanation for this long-lived spectral beating in 2D electronic spectra, quantum-mechanically mixed electronic and vibrational states (vibronic excitons) were proposed by Christensson et al. [J. Phys. Chem. B 116, 7449 (2012)] and have since been explored. In this work, we address a dimer which produces little beating of electronic origin in the absence of vibronic contributions, and examine the impact of protein-induced fluctuations upon electronic-vibrational quantum mixtures by calculating the electronic energy transfer dynamics and 2D electronic spectra in a numerically accurate manner. It is found that, at cryogenic temperatures, the electronic-vibrational quantum mixtures are rather robust, even under the influence of the fluctuations and despite the small Huang-Rhys factors of the Franck-Condon active vibrational modes. This results in long-lasting beating behavior of vibrational origin in the 2D electronic spectra. At physiological temperatures, however, the fluctuations eradicate the mixing, and hence, the beating in the 2D spectra disappears. Further, it is demonstrated that such electronic-vibrational quantum mixtures do not necessarily play a significant role in electronic energy transfer dynamics, despite contributing to the enhancement of long-lived quantum beating in 2D electronic spectra, contrary to speculations in recent publications.

Assignment of Exciton Domain in Light Harvesting Systems Based on the Variational Polaron Approach.

In large light harvesting systems, not all pigments are coupled strongly. This is evidenced by the formation of delocalized states in certain domains of strongly coupled pigments. The threshold value for assigning pigments to domains is usually defined, and the pigment pairs in which the electronic coupling is greater than this value are included in the same domain to describe the dynamic localization effect implicitly. However, domain assignment by a single threshold value may make it difficult to include the possible localization of exciton states by temperature and the difference in the electronic excitation energy between pigments. In this study, we use the variational polaron approach for domain assignment to include such possible localization. To demonstrate the validity of domain assignment by the variational approach, we applied it to pigments in photosystem II (PSII) and compared the domain model constructed by the single threshold value. We showed that domain assignment by the variational approach could be used to determine the valid domain model in PSII without using the empirical threshold value at least at 77 K.

Quantitative correction of the rate constant in the improved variational master equation for excitation energy transfer.

Understanding the excitation energy transfer (EET) mechanism is a ubiquitous field of study in photosynthetic antennas. Recently, we qualitatively improved the theory of the variational master equation by introducing the second Bogoliubov inequality to determine the proper perturbative term. However, there were quantitative differences in the EET rate compared with the results from exact numerical calculations. In this study, we attempt to correct the differences in the intermediate coupling region. As a result, we found two methods to reproduce more exact results than those previously reported.

A model for population dynamics of the mimetic butterfly Papilio polytes in the Sakishima Islands, Japan.

We present a mathematical model for population dynamics of the mimetic swallowtail butterfly Papilio polytes in the Sakishima Islands, Japan. The model includes four major variables, that is, population densities of three kinds of butterflies (two female forms f. cyrus, f. polytes and the unpalatable butterfly Pachliopta aristolochiae) and their predator. It is well-known that the non-mimic f. cyrus resembles and attracts the male most, and the mimic f. polytes mimics the model butterfly P. aristolochiae. Based on experimental evidence, we assume that two forms f. cyrus and f. polytes interact under intraspecific competition for resources including the male, and the growth rate of f. cyrus is higher than that of f. polytes. We further assume that both the benefit of mimicry for the mimic f. polytes and the cost for the model are dependent on their relative frequencies, i.e. the motality of the mimic by predation decreases with increase in frequency of the model, while the motality of the model increases as the frequency of the mimic increases. Taking the density-dependent effect through carrying capacity into account, we set up a model system consisting of three ordinary differential equations (ODEs), analyze it mathematically and provide computer simulations that confirm the analytical results. Our results reproduce field records on population dynamics of P. polytes in the Miyako-jima Island. They also explain the positive dependence of the relative abundance (RA) of the mimic on the advantage index (AI) of the mimicry in the Sakishima Islands defined in Section 2.