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.
In photosynthesis, absorbed light energy transfers through a network of antenna proteins with near-unity quantum efficiency to reach the reaction center, which initiates the downstream biochemical reactions. While the energy transfer dynamics within individual antenna proteins have been extensively studied over the past decades, the dynamics between the proteins are poorly understood due to the heterogeneous organization of the network. Previously reported timescales averaged over such heterogeneity, obscuring individual interprotein energy transfer steps. Here, we isolated and interrogated interprotein energy transfer by embedding two variants of the primary antenna protein from purple bacteria, light-harvesting complex 2 (LH2), together into a near-native membrane disc, known as a nanodisc. We integrated ultrafast transient absorption spectroscopy, quantum dynamics simulations, and cryogenic electron microscopy to determine interprotein energy transfer timescales. By varying the diameter of the nanodiscs, we replicated a range of distances between the proteins. The closest distance possible between neighboring LH2, which is the most common in native membranes, is 25 Å and resulted in a timescale of 5.7 ps. Larger distances of 28 to 31 Å resulted in timescales of 10 to 14 ps. Corresponding simulations showed that the fast energy transfer steps between closely spaced LH2 increase transport distances by â¼15%. Overall, our results introduce a framework for well-controlled studies of interprotein energy transfer dynamics and suggest that protein pairs serve as the primary pathway for the efficient transport of solar energy.
Light-Harvesting Protein Complexes , Proteobacteria , Proteobacteria/metabolism , Light-Harvesting Protein Complexes/metabolism , Photosynthesis , Spectrum Analysis , Energy Transfer
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.
Photons , Vibration , Diffusion , Thermodynamics
A general rate theory for resonance energy transfer (gRET) is formulated to incorporate any degrees of freedom (e.g., rotation, vibration, exciton, and polariton) as well as coherently coupled composite donor or acceptor states. The compact rate expression allows us to establish useful relationships: (i) detailed balance condition when the donor and acceptor are at the same temperature; (ii) proportionality to the product of dipole correlation tensors, which is not necessarily equivalent to spectral overlap; (iii) scaling with the effective coherent size, i.e., the number of coherently coupled molecules or modes; (iv) decomposition of collective rate in homogeneous systems into the monomer and coherence contributions such that the ratio of the two defines the quantum enhancement factor F; (v) spatial and orientational dependences as derived from the interaction potential. For the special case of exciton transfer, the general rate formalism reduces to FRET or its multichromophoric extension. When applied to cavity-assisted vibrational energy transfer between molecules or within a molecule, the general rate expression provides an intuitive explanation of intriguing phenomena such as cooperativity, resonance, and nonlinearity in the collective vibrational strong coupling (VSC) regime, as demonstrated in recent simulations. The relevance of gRET to cavity-catalyzed reactions and intramolecular vibrational redistribution is discussed and will lead to further theoretical developments.
Achieving superradiance in solids is challenging due to fast dephasing processes from inherent disorder and thermal fluctuations. Perovskite quantum dots (QDs) are an exciting class of exciton emitters with large oscillator strength and high quantum efficiency, making them promising for solid-state superradiance. However, a thorough understanding of the competition between coherence and dephasing from phonon scattering and energetic disorder is currently unavailable. Here, we present an investigation of exciton coherence in perovskite QD solids using temperature-dependent photoluminescence line width and lifetime measurements. Our results demonstrate that excitons are coherently delocalized over 3 QDs at 11 K in superlattices leading to superradiant emission. Scattering from optical phonons leads to the loss of coherence and exciton localization to a single QD at temperatures above 100 K. At low temperatures, static disorder and defects limit exciton coherence. These results highlight the promise and challenge in achieving coherence in perovskite QD solids.
Ninety years ago, Wigner derived the leading order expansion term in â2 for the tunneling rate through a symmetric barrier. His derivation included two contributions: one came from the parabolic barrier, but a second term involved the fourth-order derivative of the potential at the barrier top. He left us with a challenge, which is answered in this paper, to derive the same but for an asymmetric barrier. A crucial element of the derivation is obtaining the â2 expansion term for the projection operator, which appears in the flux-side expression for the rate. It is also reassuring that an analytical calculation of semiclassical transition state theory (TST) reproduces the anharmonic corrections to the leading order of â2. The efficacy of the resulting expression is demonstrated for an Eckart barrier, leading to the conclusion that especially when considering heavy atom tunneling, one should use the expansion derived in this paper, rather than the parabolic barrier approximation. The rate expression derived here reveals how the classical TST limit is approached as a function of â and, thus, provides critical insights to understand the validity of popular approximate theories, such as the classical Wigner, centroid molecular dynamics, and ring polymer molecular dynamics methods.
Molecular Dynamics Simulation , Probability
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 âω and the bias δϵ occurs not only at integer but also fractional ratios δϵ/(âω) = 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.
The electromagnetic field in an optical cavity can dramatically modify and even control chemical reactivity via vibrational strong coupling (VSC). Since the typical vibration and cavity frequencies are considerably larger than thermal energy, it is essential to adopt a quantum description of cavity-catalyzed adiabatic chemical reactions. Using quantum transition state theory (TST), we examine the coherent nature of adiabatic reactions in cavities and derive the cavity-induced changes in eigenfrequencies, zero-point energy, and quantum tunneling. The resulting quantum TST calculation allows us to explain and predict the resonance effect (i.e., maximal kinetic modification via tuning the cavity frequency), collective effect (i.e., linear scaling with the molecular density), and selectivity (i.e., cavity-induced control of the branching ratio). The TST calculation is further supported by perturbative analysis of polariton normal modes, which not only provides physical insights to cavity-catalyzed chemical reactions but also presents a general approach to treat other VSC phenomena.
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^{â¼0.5} scaling of the system density of states and predicts unique spectroscopic signatures including: (1) disorder-induced absorption linewidth, W(σ)â¼σ^{2.8}, with σ the disorder strength, (2) temperature dependent absorption linewidth, W(T)â¼T^{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)âsin^{2}θ. These predictions are confirmed quantitatively with numerical simulations of molecular thin films and tubules.
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.
The cooperativity of a monomeric enzyme arises from dynamic correlation instead of spatial correlation and is a consequence of nonequilibrium conformation fluctuations. We investigate the conformation-modulated kinetics of human glucokinase, a monomeric enzyme with important physiological functions, using a five-state kinetic model. We derive the non-Michealis-Menten (MM) correction term of the activity (i.e., turnover rate), predict its relationship to cooperativity, and reveal the violation of conformational detailed balance. Most importantly, we reproduce and explain the observed resonance effect in human glucokinase (i.e., maximal cooperativity when the conformational fluctuation rate is comparable to the catalytic rate). With the realistic parameters, our theoretical results are in quantitative agreement with the reported measurement by Miller and co-workers. The analysis can be extended to a general chemical network beyond the five-state model, suggesting the generality of kinetic cooperativity and resonance.
Glucokinase/metabolism , Biocatalysis , Glucokinase/chemistry , Glucose/metabolism , Humans , Kinetics , Protein Conformation
The exciton Hamiltonian of multichromophoric aggregates can be probed by spectroscopic techniques such as linear absorption and circular dichroism. To compare calculated Hamiltonians to experiments, a lineshape theory is needed, which takes into account the coupling of the excitons with inter- and intramolecular vibrations. This coupling is normally introduced in a perturbative way through the cumulant expansion formalism and further approximated by assuming a Markovian exciton dynamics, for example with the modified Redfield theory. Here, we present the implementation of the full cumulant expansion (FCE) formalism ( J. Chem. Phys. 142, 2015, 094106) to efficiently compute absorption and circular dichroism spectra of molecular aggregates beyond the Markov approximation, without restrictions on the form of exciton-phonon coupling. By employing the LH2 system of purple bacteria as a challenging test case, we compare the FCE lineshapes with the Markovian lineshapes obtained with the modified Redfield theory, showing that the latter presents a less satisfying agreement with experiments. The FCE approach instead accurately describes the lineshapes, especially in the vibronic sideband of the B800 peak. We envision that the FCE approach will become a valuable tool for accurately comparing model exciton Hamiltonians with optical spectroscopy experiments.
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≠jFijκj = 2c∑i≠jJijIm[ρij]κj, 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, Fij = 2JijIm[ρij]. 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.
Understanding nonequilibrium transport is crucial for controlling energy flow in nanoscale systems. We study thermal energy transfer in a generalized nonequilibrium spin-boson model (NESB) with noncommutative system-bath coupling operators and discover its unusual transport properties. Compared to the conventional NESB, the energy current is greatly enhanced by rotating the system-bath coupling operators. Constructive contribution to thermal rectification can be optimized when two sources of asymmetry, system-bath coupling strength and coupling operators, coexist. At the weak coupling and the adiabatic limit, the scaling dependence of energy current on the coupling strength and the system energy gap changes drastically when the coupling operators become noncommutative. These scaling relations can further be explained analytically by the nonequilibrium polaron-transformed Redfield equation (NE-PTRE). These novel transport properties, arising from the pure quantum effect of noncommutative coupling operators, suggest an unvisited dimension of controlling transport in nanoscale systems and should generally appear in other nonequilibrium set-ups and driven systems.
Photosynthesis is a highly optimized process from which valuable lessons can be learned about the operating principles in nature. Its primary steps involve energy transport operating near theoretical quantum limits in efficiency. Recently, extensive research was motivated by the hypothesis that nature used quantum coherences to direct energy transfer. This body of work, a cornerstone for the field of quantum biology, rests on the interpretation of small-amplitude oscillations in two-dimensional electronic spectra of photosynthetic complexes. This Review discusses recent work reexamining these claims and demonstrates that interexciton coherences are too short lived to have any functional significance in photosynthetic energy transfer. Instead, the observed long-lived coherences originate from impulsively excited vibrations, generally observed in femtosecond spectroscopy. These efforts, collectively, lead to a more detailed understanding of the quantum aspects of dissipation. Nature, rather than trying to avoid dissipation, exploits it via engineering of exciton-bath interaction to create efficient energy flow.
Energy Transfer , Photosynthesis , Quantum Theory , Algorithms , Light-Harvesting Protein Complexes/metabolism , Models, Theoretical , Spectrum Analysis
Plasmodium falciparum malaria-infected red blood cells (IRBCs), or erythrocytes, avoid splenic clearance by adhering to host endothelium. Upregulation of endothelial receptors intercellular adhesion molecule-1 (ICAM-1) and cluster of differentiation 36 (CD36) are associated with severe disease pathology. Most in vitro studies of IRBCs interacting with these molecules were conducted at room temperature. However, as IRBCs are exposed to temperature variations between 37°C (body temperature) and 41°C (febrile temperature) in the host, it is important to understand IRBC-receptor interactions at these physiologically relevant temperatures. Here, we probe IRBC interactions against ICAM-1 and CD36 at 37 and 41°C. Single bond force-clamp spectroscopy is used to determine the bond dissociation rates and hence, unravel the nature of the IRBC-receptor interaction. The association rates are also extracted from a multiple bond flow assay using a cellular stochastic model. Surprisingly, IRBC-ICAM-1 bond transits from a catch-slip bond at 37°C toward a slip bond at 41°C. Moreover, binding affinities of both IRBC-ICAM-1 and IRBC-CD36 decrease as the temperature rises from 37 to 41°C. This study highlights the significance of examining receptor-ligand interactions at physiologically relevant temperatures and reveals biophysical insight into the temperature dependence of P. falciparum malaria cytoadherent bonds.
Erythrocytes/parasitology , Plasmodium falciparum/physiology , Temperature , CD36 Antigens/metabolism , Cell Differentiation , Erythrocytes/cytology , Erythrocytes/metabolism , Humans , Intercellular Adhesion Molecule-1/metabolism
If an open quantum system is periodically driven with high frequency and the driving commutes with the system-bath coupling operator, it is known that the system approaches a Floquet-Gibbs state, a generalization of Gibbs states to periodically driven systems. Here, we investigate the stationary state of an ac-driven system when the driving and dissipation are noncommutative. Then, the resulting stationary state does not obey the Floquet-Gibbs distribution, and the system dynamics is determined by inelastic scattering processes of the driving field. Based on the Floquet-Redfield formalism, we show that the probability distribution can exhibit population inversion and discontinuities, i.e., jumps, for parameters at which coherent destruction of tunneling takes place. These discontinuities can be observed as intensity jumps in the emission into the bath.
To investigate frequency-dependent current noise (FDCN) in open quantum systems at steady states, we present a theory which combines Markovian quantum master equations with a finite time full counting statistics. Our formulation of the FDCN generalizes previous zero-frequency expressions and can be viewed as an application of MacDonald's formula for electron transport to heat transfer. As a demonstration, we consider the paradigmatic example of quantum heat transfer in the context of a non-equilibrium spin-boson model. We adopt a recently developed polaron-transformed Redfield equation which allows us to accurately investigate heat transfer with arbitrary system-reservoir coupling strength, arbitrary values of spin bias, and temperature differences. We observe a turn-over of FDCN in the intermediate coupling regimes, similar to the zero-frequency case. We find that the FDCN with varying coupling strengths or bias displays a universal Lorentzian-shape scaling form in the weak coupling regime, and a white noise spectrum emerges with zero bias in the strong coupling regime due to distinctive spin dynamics. We also find that the bias can suppress the FDCN in the strong coupling regime, in contrast to its zero-frequency counterpart which is insensitive to bias changes. Furthermore, we utilize the Saito-Utsumi relation as a benchmark to validate our theory and study the impact of temperature differences at finite frequencies. Together, our results provide detailed dissections of the finite time fluctuation of heat current in open quantum systems.
Photosynthetic purple bacteria convert solar energy to chemical energy with near unity quantum efficiency. The light-harvesting process begins with absorption of solar energy by an antenna protein called Light-Harvesting Complex 2 (LH2). Energy is subsequently transferred within LH2 and then through a network of additional light-harvesting proteins to a central location, termed the reaction center, where charge separation occurs. The energy transfer dynamics of LH2 are highly sensitive to intermolecular distances and relative organizations. As a result, minor structural perturbations can cause significant changes in these dynamics. Previous experiments have primarily been performed in two ways. One uses non-native samples where LH2 is solubilized in detergent, which can alter protein structure. The other uses complex membranes that contain multiple proteins within a large lipid area, which make it difficult to identify and distinguish perturbations caused by protein-protein interactions and lipid-protein interactions. Here, we introduce the use of the biochemical platform of model membrane discs to study the energy transfer dynamics of photosynthetic light-harvesting complexes in a near-native environment. We incorporate a single LH2 from Rhodobacter sphaeroides into membrane discs that provide a spectroscopically amenable sample in an environment more physiological than detergent but less complex than traditional membranes. This provides a simplified system to understand an individual protein and how the lipid-protein interaction affects energy transfer dynamics. We compare the energy transfer rates of detergent-solubilized LH2 with those of LH2 in membrane discs using transient absorption spectroscopy and transient absorption anisotropy. For one key energy transfer step in LH2, we observe a 30% enhancement of the rate for LH2 in membrane discs compared to that in detergent. Based on experimental results and theoretical modeling, we attribute this difference to tilting of the peripheral bacteriochlorophyll in the B800 band. These results highlight the importance of well-defined systems with near-native membrane conditions for physiologically-relevant measurements.
Quantum coherence has been demonstrated in various systems including organic solar cells and solid state devices. In this article, we report the lower and upper bounds for the performance of quantum heat engines determined by the efficiency at maximum power. Our prediction based on the canonical three-level Scovil and Schulz-Dubois maser model strongly depends on the ratio of system-bath couplings for the hot and cold baths and recovers the theoretical bounds established previously for the Carnot engine. Further, introducing a fourth level to the maser model can enhance the maximal power and its efficiency, thus demonstrating the importance of quantum coherence in the thermodynamics and operation of the heat engines beyond the classical limit.
