Quantum Coherence and Its Signatures in Extended Quantum Systems

Memory effects in the efficiency control of energy transfer under incoherent light excitation in noisy environments

Fluctuations in energy gap and coupling constants between chromophores can play an important role in absorption and energy transfer across a collection of two-level systems. In photosynthesis, light-induced quantum coherence can affect the efficiency of energy transfer to the designated "trap" state. Theoretically, the interplay between fluctuations and coherence has been studied often, employing either a Markovian or a perturbative approximation. In this study, we depart from these approaches to incorporate memory effects by using Kubo's quantum stochastic Liouville equation. We introduce the effects of decay of the created excitation (to the ground state) on the desired propagation and trapping that provides a direction of flow of the excitation. In the presence of light-induced pumping, we establish a relation between the efficiency, the mean survival time, and the correlation decay time of the bath-induced fluctuations. A decrease in the steady-state coherence during the transition from the non-Markovian regime to the Markovian limit results in a decrease in efficiency. As in the well-known Haken-Strobl model, the ratio of the square of fluctuation strength to the rate plays a critical role in determining the mechanism of energy transfer and in shaping the characteristics of the efficiency profile. We recover a connection between the transfer flux and the imaginary part of coherences in both equilibrium and excited bath states, in both correlated and uncorrelated bath models. We uncover a non-monotonic dependence of efficiency on site energy heterogeneity for both correlated and uncorrelated bath models.

Existence of Quantum Pharmacology in Sartans: Evidence in Isolated Rabbit Iliac Arteries

Quantum pharmacology introduces theoretical models to describe the possibility of ultra-high dilutions to produce biological effects, which may help to explain the placebo effect observed in hypertensive clinical trials. To determine this within physiology and to evaluate novel ARBs, we tested the ability of known angiotensin II receptor blockers (ARBs) (candesartan and telmisartan) used to treat hypertension and other cardiovascular diseases, as well as novel ARBs (benzimidazole-N-biphenyl tetrazole (ACC519T), benzimidazole-bis-N,N'-biphenyl tetrazole (ACC519T(2)) and 4-butyl-N,N0-bis[[20-2Htetrazol-5-yl)biphenyl-4-yl]methyl)imidazolium bromide (BV6(K+)2), and nirmatrelvir (the active ingredient in Paxlovid) to modulate vascular contraction in iliac rings from healthy male New Zealand White rabbits in responses to various vasopressors (angiotensin A, angiotensin II and phenylephrine). Additionally, the hemodynamic effect of ACC519T and telmisartan on mean arterial pressure in conscious rabbits was determined, while the ex vivo ability of BV6(K+)2 to activate angiotensin-converting enzyme-2 (ACE2) was also investigated. We show that commercially available and novel ARBs can modulate contraction responses at ultra-high dilutions to different vasopressors. ACC519T produced a dose-dependent reduction in rabbit mean arterial pressure while BV6(K+)2 significantly increased ACE2 metabolism. The ability of ARBs to inhibit contraction responses even at ultra-low concentrations provides evidence of the existence of quantum pharmacology. Furthermore, the ability of ACC519T and BV6(K+)2 to modulate blood pressure and ACE2 activity, respectively, indicates their therapeutic potential against hypertension.

Role of Spatially Correlated Fluctuations in Photosynthetic Excitation Energy Transfer with an Equilibrium and a Nonequilibrium Initial Bath

The transfer of excitation energy in photosynthetic light-harvesting complexes has inspired growing interest for its scientific and engineering significance. Recent experimental findings have suggested that spatially correlated environmental fluctuations may account for the existence of long-lived quantum coherent energy transfer observed even at physiological temperature. In this paper, we investigate the effects of spatial correlations on the excitation energy transfer dynamics by including a nonequilibrium initial bath in a simulated donor-acceptor model. The initial bath state, which is assumed to be either equilibrium or nonequilibrium, is expanded in powers of coupling strength within the polaron formalism of a quantum master equation. The spatial correlations of bath fluctuations strongly influence the decay of coherence in the dynamics. The role of a nonequilibrium initial bath is also influenced by spatial correlations and becomes the most conspicuous for certain degrees of spatial correlations from which we propose a picture that the spatial correlations of bath fluctuations open up new energy transfer pathways, playing a role of protecting coherence. Besides, we apply the polaron master equation approach to study the dynamics in a two-site subsystem of the FMO complex and provide a practical example that shows the versatility of this approach.

Cooperation between Excitation Energy Transfer and Antisynchronously Coupled Vibrations

The effects of the environment in energy transfer systems have been continuously studied for decades. Here, we investigate how the energy transfer and the emergence of vibrational correlations cooperate with each other based on simulations with a few numerically approximate mixed quantum classical (MQC) methods. By adopting a two-state system with locally coupled underdamped vibrations that are resonant with the electronic energy gap, we observe prominent energy dissipations from the electronic system to the vibrations, rehighlighting the role of underdamped vibrations as a temporal electronic energy buffer. More importantly, this energy dissipation generates specific phase relations between the two vibrations. Namely, the vibrations become anticorrelated right after the initiation of the energy transfer but then synchronized as the transfer completes. These phase relations are interpreted as a selective activation of an anticorrelated motion of the vibrations and a subsequent deactivation by thermal energy redistribution. Furthermore, we show that a single vibration simultaneously coupled to the two electronic states with opposite phases induces a completely equivalent energy transfer dynamics as the two localized vibrations. Finally, we discuss how the vibrational energy dissipation dynamics is affected by the adopted MQC approaches and warn about the increased subtlety toward properly treating dissipation effects over having reliable population dynamics.

Excitation Energy Transfer Efficiency in Fluctuating Environments: Role of Quantum Coherence in the Presence of Memory Effects

Several recent studies have interrogated the role of quantum coherence in affecting the transfer efficiency of an optical excitation to the designated "trap" state where the energy can be used for subsequent reactions, as in photosynthesis. However, these studies invoke a Markovian approximation for the time correlation function describing the environment-induced stochastic fluctuations. Here, we employ Kubo's quantum stochastic Liouville equation (QSLE) to include memory effects. We extend the existing QSLE scheme to introduce decay of a newly created excitation due to radiative and nonradiative channels and also by desired trapping toward the targeted chromophore. We show that the theoretical formalism based on the QSLE correctly reproduces the rate equation description in the Markovian limit, with the rate constants determined by an appropriate quantum limiting procedure. We find that under certain conditions, the efficiency of excitation transfer to the trap gains from the combined presence of quantum coherence and temporally correlated stochastic fluctuations. We work out different limiting situations in order to discover and quantify the optimum conditions for the energy transfer to the trapped state. We find that maximum energy transfer efficiency is achieved in the intermediate limit between coherent and incoherent transport.

An exact solution in the theory of fluorescence resonance energy transfer with vibrational relaxation

The elegant expression of Förster that predicts the well-known 1/R⁶ distance (R) dependence of the rate of energy transfer, although widely used, was derived using several approximations. Notable among them is the neglect of the vibrational relaxation in the reactant (donor) and product (acceptor) manifolds. Vibrational relaxation can play an important role when the energy transfer rate is faster than the vibrational relaxation rate. Under such conditions, donor to acceptor energy transfer can occur from the excited vibrational states. This phenomenon is not captured by the usual formulation based on the overlap of donor emission and acceptor absorption spectra. Here, we develop a Green's function-based generalized formalism and obtain an exact solution for the excited state population relaxation and the rate of energy transfer in the presence of vibrational relaxation. We find that the application of the well-known Förster's expression might lead to overestimation of R.

Exploring the State Space Structure of Multiple Spins via Modular Tensor Diagram Approach: Going beyond the Exciton Pair State

Fully understanding of multistate quantum systems could become formidable if not impossible as the system dimensionality increases. One ideal strategy to comprehend complex systems is to transform the system representation into a more structural one so that major characteristics, connections, and even underlying mechanisms can stand out from the huge unstructured information, e.g., the construction of spin eigenfunctions for a system of multiple spins through the diagonalization of the system Hamiltonian matrix. Here, instead of direct matrix diagonalization, the recently developed modular tensor diagram approach is applied to reorganize the state space structure of multispin systems, extending previous investigations on exciton pair states to exciton trimer states. This implementation demonstrates that the proposed approach not only provides a systematical way to transform the high dimensional multistate system into a well organized structure based on basic (exciton) modules but also paves the way to further analysis on potential applications. For example, the analysis on the state space of the exciton trimer system suggests a possible scheme to improve the laser performance via single fission involving multiexcitations and/or multiple fission steps.

Steady-State Analysis of Light-Harvesting Energy Transfer Driven by Incoherent Light: From Dimers to Networks

The question of how quantum coherence facilitates energy transfer has been intensively debated in the scientific community. Since natural and artificial light-harvesting units operate under the stationary condition, we address this question via a nonequilibrium steady-state analysis of a molecular dimer irradiated by incoherent sunlight and then generalize the key predictions to arbitrarily complex exciton networks. The central result of the steady-state analysis is the coherence-flux-efficiency relation: η = c∑_i≠jF_ijκ_j = 2c∑_i≠jJ_ijIm[ρ_ij]κ_j, where c is the normalization constant. In this relation, the first equality indicates that the energy transfer efficiency, η, is uniquely determined by the trapping flux, which is the product of the flux, F, and branching ratio, κ, for trapping at the reaction centers, and the second equality indicates that the energy transfer flux, F, is equivalent to the quantum coherence measured by the imaginary part of the off-diagonal density matrix, that is, F_ij = 2J_ijIm[ρ_ij]. Consequently, maximal steady-state coherence gives rise to optimal efficiency. The coherence-flux-efficiency relation holds rigorously and generally for any exciton network of arbitrary connectivity under the stationary condition and is not limited to incoherent radiation or incoherent pumping. For light-harvesting systems under incoherent light, the nonequilibrium energy transfer flux (i.e., steady-state coherence) is driven by the breakdown of detailed balance and by the quantum interference of light excitations and leads to the optimization of energy transfer efficiency. It should be noted that the steady-state coherence or, equivalently, efficiency is the combined result of light-induced transient coherence, inhomogeneous depletion, and the system-bath correlation and is thus not necessarily correlated with quantum beatings. These findings are generally applicable to quantum networks and have implications for quantum optics and devices.