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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. [ABSTRACT FROM AUTHOR]

Understanding the dynamics of photoinduced processes in complex systems is crucial for the development of advanced energy-conversion materials. In this study, we investigate the nonadiabatic dynamics using time-convolution (TC) and time-convolutionless (TCL) quantum master equations (QMEs) based on treating electronic couplings as perturbation within the framework of multistate harmonic (MSH) models. The MSH model Hamiltonians are mapped from all-atom simulations such that all pairwise reorganization energies are consistently incorporated, leading to a heterogeneous environment that couples to the multiple electronic states differently. Our exploration encompasses the photoinduced charge transfer dynamics in organic photovoltaic carotenoid–porphyrin–C60 triad dissolved in liquid solution and the excitation energy transfer (EET) dynamics in photosynthetic Fenna–Matthews–Olson complexes. By systematically comparing the perturbative TC and TCL QME approaches with exact quantum-mechanical and various semiclassical approximate kernels, we demonstrate their efficacy and accuracy in capturing the essential features of photoinduced dynamics. Our calculations show that TC QMEs generally yield more accurate results than TCL QMEs, especially in EET, although both methods offer versatile approaches adaptable across different systems. In addition, we investigate various semiclassical approximations featuring the Wigner-transformed and classical nuclear densities as well as the governing dynamics during the quantum coherence period, highlighting the trade-off between accuracy and computational cost. This work provides valuable insights into the applicability and performance of TC and TCL QME approaches via the MSH model, offering guidance for realistic applications to condensed-phase systems on the atomistic level. [ABSTRACT FROM AUTHOR]

The electron–phonon scattering plays a crucial role in determining the electronic, transport, optical, and thermal properties of materials. Here, we employ a non-Markovian stochastic Schrödinger equation (NMSSE) in momentum space, together with ab initio calculations for energy bands and electron–phonon interactions, to reveal the phonon-mediated ultrafast hole relaxation dynamics in the valence bands of monolayer black phosphorus. Our numerical simulations show that the hole can initially remain in the high-energy valence bands for more than 100 fs due to the weak interband scatterings, and its energy relaxation follows single-exponential decay toward the valence band maximum after scattering into low-energy valence bands. The total relaxation time of holes is much longer than that of electrons in the conduction band. This suggests that harnessing the excess energy of holes may be more effective than that of electrons. Compared to the semiclassical Boltzmann equation based on a hopping model, the NMSSE highlights the persistence of quantum coherence for a long time, which significantly impacts the relaxation dynamics. These findings complement the understanding of hot carrier relaxation dynamics in two-dimensional materials and may offer novel insights into harnessing hole energy in photocatalysis. [ABSTRACT FROM AUTHOR]

The light-harvesting excitonic properties of poly(phenylene ethynylene) (PPE) extended dendrimers (tree-like π-conjugated macromolecules) involve a directional cascade of local excitation energy transfer (EET) processes occurring from the "leaves" (shortest branches) to the "trunk" (longest branch), which can be viewed from a vibronic perspective as a sequence of internal conversions occurring among a connected graph of nonadiabatically coupled locally excited electronic states via conical intersections. The smallest PPE building block that is able to exhibit EET, the asymmetrically meta-substituted PPE oligomer with one acetylenic bond on one side and two parallel ones on the other side (hence, 2-ring and 3-ring para-substituted pseudo-fragments), is a prototype and the focus of the present work. From linear-response time-dependent density functional theory electronic-structure calculations of the molecule as regards its first two nonadiabatically coupled, optically active, singlet excited states, we built a (1 + 2)-state-8-dimensional vibronic-coupling Hamiltonian model for running subsequent multiconfiguration time-dependent Hartree wavepacket relaxations and propagations, yielding both steady-state absorption and emission spectra as well as real-time dynamics. The EET process from the shortest branch to the longest one occurs quite efficiently (about 80% quantum yield) within the first 25 fs after light excitation and is mediated vibrationally through acetylenic and quinoidal bond-stretching modes together with a particular role given to the central-ring anti-quinoidal rock-bending mode. Electronic and vibrational energy relaxations, together with redistributions of quantum populations and coherences, are interpreted herein through the lens of a nonadiabatic perspective, showing some interesting segregation among the foremost photoactive degrees of freedom as regards spectroscopy and reactivity. [ABSTRACT FROM AUTHOR]

The nonequilibrium Fermi's golden rule (NE-FGR) approach is developed to simulate the electronic transitions between multiple excited states in complex condensed-phase systems described by the recently proposed multi-state harmonic (MSH) model Hamiltonian. The MSH models were constructed to faithfully capture the photoinduced charge transfer dynamics in a prototypical organic photovoltaic carotenoid-porphyrin-C60 molecular triad dissolved in tetrahydrofuran. A general expression of the fully quantum-mechanical NE-FGR rate coefficients for transitions between all pairs of states in the MSH model is obtained. Besides, the linearized semiclassical NE-FGR formula and a series of semiclassical approximations featuring Wigner and classical nuclear sampling choices and different dynamics during the quantum coherence period for the MSH model are derived. The current approach enables all the possible population transfer pathways between the excited states of the triad, in contrast to the previous applications that only addressed the donor-to-acceptor transition. Our simulations for two triad conformations serve as a demonstration for benchmarking different NE-FGR approximations and show that the difference between all levels of approximation is small for the current system, especially at room temperature. By comparing with nonadiabatic semiclassical dynamics, we observe similar timescales for the electronic population transfer predicted by NE-FGR. It is believed that the general formulation of NE-FGR for the MSH Hamiltonian enables a variety of applications in realistic systems. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the time evolution of quantum coherence—the off-diagonal elements of the density matrix of a multistate quantum system—from the perspective of the Wigner–Moyal formalism. This approach provides an exact phase space representation of quantum mechanics. We consider the coherent evolution of nuclear wavepackets in a molecule with two electronic states. For harmonic potentials, the problem is analytically soluble for both a fully quantum mechanical description and a semiclassical description. We highlight the serious deficiencies of the semiclassical treatment of coherence for general systems and illustrate how even qualitative accuracy requires higher order terms in the Moyal expansion to be included. The model provides an experimentally relevant example of a molecular Schrödinger's cat state. The alive and dead cats of the exact two-state quantum evolution collapse into a "zombie" cat in the semiclassical limit—an averaged behavior, neither alive nor dead, leading to significant errors. The inclusion of the Moyal correction restores a faithful simultaneously alive and dead representation of the cat that is experimentally observable. [ABSTRACT FROM AUTHOR]

In a multi-level quantum system Fano coherences stand for the formation of quantum coherences due to the interaction with the continuum of modes characterizing an incoherent process. In this paper we propose a V-type three-level quantum system on which we certify the presence of genuinely quantum traits underlying the generation of Fano coherences. We do this by determining work conditions that allows for the loss of positivity of the Kirkwood-Dirac quasiprobability distribution of the stochastic energy changes within the discrete system. We also show the existence of nonequilibrium regimes where the generation of Fano coherences leads to a non-negligible excess energy given by the amount of energy that is left over with respect to the energy of the system at the beginning of the transformation. Excess energy is attained provided the initial state of the discrete system is in a superposition of the energy eigenbasis. We conclude the paper by studying the thermodynamic efficiency of the whole process. [ABSTRACT FROM AUTHOR]

We investigate quantum non-equilibrium refrigerators with one- and two-qubit systems in a squeezed thermal bath. We characterise their performances in the presence of squeezed heat baths, in terms of their coefficients of performance, cooling rates and figures of merit. Our results show that the performance of the refrigerators is strongly influenced by the squeezing parameter and the number of qubits. The performance of the two-qubit refrigerator (TQR) is found to be better than that of the one-qubit refrigerator (OQR) under the same operating conditions. Our findings suggest that a squeezed thermal bath can be a promising resource for the design of efficient quantum refrigerators in the non-equilibrium regime. [ABSTRACT FROM AUTHOR]

Purpose: Sodium triple quantum (TQ) signal has been shown to be a valuable biomarker for cell viability. Despite its clinical potential, application of Sodium TQ signal is hindered by complex pulse sequences with long scan times. This study proposes a method to approximate the TQ signal using a single excitation pulse without phase cycling. Methods: The proposed method is based on a single excitation pulse and a comparison of the free induction decay (FID) with the integral of the FID combined with a shifting reconstruction window. The TQ signal is calculated from this FID only. As a proof of concept, the method was also combined with a multi‐echo UTE imaging sequence on a 9.4 T preclinical MRI scanner for the possibility of fast TQ MRI. Results: The extracted Sodium TQ signals of single‐pulse and spin echo FIDs were in close agreement with theory and TQ measurement by traditional three‐pulse sequence (TQ time proportional phase increment [TQTPPI)]. For 2%, 4%, and 6% agar samples, the absolute deviations of the maximum TQ signals between SE and theoretical (time proportional phase increment TQTPPI) TQ signals were less than 1.2% (2.4%), and relative deviations were less than 4.6% (6.8%). The impact of multi‐compartment systems and noise on the accuracy of the TQ signal was small for simulated data. The systematic error was <3.4% for a single quantum (SQ) SNR of 5 and at maximum <2.5% for a multi‐compartment system. The method also showed the potential of fast in vivo SQ and TQ imaging. Conclusion: Simultaneous SQ and TQ MRI using only a single‐pulse sequence and SQ time efficiency has been demonstrated. This may leverage the full potential of the Sodium TQ signal in clinical applications. [ABSTRACT FROM AUTHOR]

Quantum coherence is a crucial resource in numerous quantum processing tasks. The robustness of coherence provides an operational measure of quantum coherence, which can be calculated for various states using semidefinite programming. However, this method depends on convex optimization and can be time-intensive, especially as the dimensionality of the space increases. In this study, we employ machine learning techniques to quantify quantum coherence, focusing on the robustness of coherence. By leveraging artificial neural networks, we developed and trained models for systems with different dimensionalities. Testing on data samples shows that our approach substantially reduces computation time while maintaining strong generalizability. [ABSTRACT FROM AUTHOR]

The uncertainty relation reveals the intrinsic difference between the classical world and the quantum world. We investigate the quantum uncertainty relation of quantum channel in qubit systems. Under two general measurement bases, we first derive the quantum uncertainty relation for quantum channels with respect to the relative entropy of coherence. Then we obtain the quantum uncertainty relation for unitary channels with respect to the l 1 norm of coherence. Some examples are given in detail. [ABSTRACT FROM AUTHOR]

In this study, we explore the ground state phase diagram of the spin-1/2 XX chain model, which features X Z Y - Y Z X -type three-spin interactions (TSIs). This model, while seemingly simple, reveals a rich tapestry of quantum behaviors. Our analysis relies on several key metrics. The ' l 1 -norm of coherence' helps us identify coherent states within the phase diagram, which represent states capable of superposition and interference. We employ the 'spin squeezing parameter' to pinpoint unique coherent states characterized by isotropic noise in all directions, making them invaluable for quantum metrology. Additionally, we utilize the 'entanglement entropy' to determine which of these coherent states exhibit entanglement, indicating states that cannot be fully described by local variables. Our research unveils diverse regions within the phase diagram, each characterized by coherent, squeezed, or entangled states, offering insights into the quantum phenomena underling these systems. We also study the critical scaling versus the system size for the mentioned quantities. [ABSTRACT FROM AUTHOR]

This study investigates the dynamics of quantum coherence and entanglement in the spin‐1 Heisenberg XXZ model. Particularly, the effects of the Heitler‐London (HL) coupling and the Dzyaloshinskii‐Moriya (DM) interaction are examined. By utilizing tools from quantum information theory, the concept of quantum correlated coherence and negativity are explored. The results show intrinsic decoherence leads to a decay of both correlated coherence and negativity. Interestingly, it is found that a small value of the Dzyaloshinskii‐Moriya interaction can significantly enhance coherence and entanglement. Various factors influence the system dynamics, including the initial state, anisotropy parameter, and the coupling distance between spins. It is shown that, by fixing the anisotropy parameter, the isotropic Heisenberg models XX and XXX can be easily recovered. Ultimately, the findings highlight that the system maintains a coherent temporal evolution despite decoherence. [ABSTRACT FROM AUTHOR]

Extracellular diffusion coupled with degradation is considered a dominant mechanism behind the establishment of morphogen gradients. However, the fundamental nature of these biophysical processes, visa viz, the Bicoid (Bcd) morphogen gradient, remains unclear. Fluorescence correlation spectroscopy has recently revealed multiple modes of Bcd transport at different spatial and temporal locations across the embryo. Here, we show that these observations are best fitted by a model fundamentally based on quantum mechanics. It is thus hypothesized that the transient quantum coherences in collaboration with unitary noise are responsible for the observed dynamics and relaxation to a non-equilibrium steady-state of the Bcd morphogen gradient. Furthermore, simulating the associated probability distribution for the model shows that the observed non-zero concentration of the Bcd molecules in the posterior-most parts of the embryo is a result of non-Gaussian distribution characteristic to quantum evolution. We conclude that with the Bcd gradient being essentially a one-dimensional problem, a simple one-dimensional model suffices for its analysis. [ABSTRACT FROM AUTHOR]

The potential of spin-based quantum devices in quantum information processing (QIP) is continuously expanding. Recent models with off-diagonal couplings offer new opportunities to explore quantum phenomena in condensed matter. Non-classical correlations (NCCs), quantum coherence (QC) based on Jensen–Shannon divergence (JSD), the entropic uncertainty relation (EUR), and mixedness are crucial concepts in QIP. Understanding their dynamics in condensed matter systems has practical implications for QIP. In this regard, we explore the influence of temperature, off-diagonal exchange couplings, and the magnetic field on the NCCs, QC, EUR, and mixedness of a two-qubit X Y - Γ spin chain in thermal equilibrium. We find that NCCs exhibit sudden transitions with a smooth change in the system parameters, whereas QC does not. The off-diagonal exchange couplings significantly enhance both NCCs and QC in the system, while the temperature and the transverse field tend to counteract this enhancement. As the temperature increases, the EUR expands, and mixedness increases. The EUR reaches its peak when mixedness is at its highest. The off-diagonal interaction reduces entropic uncertainty, and increasing its amplitude Γ offsets the adverse effects of temperature and the magnetic field. Besides, we propose a comprehensive and effective strategy using the filtering operation to manipulate measurement uncertainty. Although the local non-unitary operation is selectively applied to qubit A, it immediately affects the memory qubit B, limiting the transfer of information from qubit A to qubit B in quantum communication protocols. However, by properly controlling the two-qubit X Y - Γ system parameters and fine-tuning the strength of the filtering operation parameter, it is possible to reduce measurement uncertainty and facilitate the transfer of information from qubit A to qubit B. [ABSTRACT FROM AUTHOR]

With rational designability, versatile tunability, and quantum coherence, molecular electron spin qubits could offer new opportunities for quantum information science, enabling simplified implementation of quantum algorithms and chemical‐specific quantum sensing. The development of these transformative technologies relies on coherent addressing of single molecular electron spin qubits with high initialization, manipulation, and readout fidelities. This is unfeasible to conventional electron spin resonance spectroscopy, which is widely used for coherent addressing of ensemble electron spins, due to its low initialization efficiency and readout sensitivity. Taking advantage of single spin detectability of single‐molecule spectroscopy, scanning tunneling microscopy, atomic force microscopy, and quantum metrology, several strategies have been developed to empower electron spin resonance spectroscopy with single qubit addressability. In this Emerging Topic, we introduce principles and technical implementation of strategies for coherent addressing of single molecular electron spin qubits, discuss their potential applicability in quantum technologies, and point out their challenges in terms of scalability, molecular design, and/or decoherence suppression. We discuss future directions to overcome these challenges and to improve single qubit addressing technologies, which will facilitate the advancement of molecular quantum information science. [ABSTRACT FROM AUTHOR]

Previous research suggests that sharing emotionally intense experiences with others, for example by undergoing dysphoric collective rituals together, can lead to "identity fusion," a visceral feeling of oneness that predicts group cohesion and self-sacrifice for the group. In this pre-registered research, we provide the first quantitative investigation of identity fusion following participation in a national funeral, surveying 1632 members of the British public. As predicted, individuals reporting intense sadness during Queen Elizabeth II's funeral exhibited higher levels of identity fusion and pro-group commitment, as evidenced by generosity pledges to a British Monarchist charity. Also consistent with our hypotheses, feelings of unity in grief and emotional sharedness during the event mediated the relationship between sadness intensity and pro-group commitment. These findings shed light on importance of collective rituals in fostering group cohesion, cooperation, and the dynamics of shared emotional experiences within communities. [ABSTRACT FROM AUTHOR]

Simple Summary: The human brain is still an enigma, and the relation between its physiology and function is still poorly understood. Advancements in quantum computations led to the hypothesis that neurons can also exercise quantum coherence, and a model for neuronal activity with quantum correlations appearing from the nuclei entanglement was proposed. However, whether such correlations can survive in a high-temperature biological environment to propagate through a neural network is still an open question. In this work, we examine one of the first steps in this process, the diffusion of neurotransmitters through the synaptic cleft, and show that, at least at this step, the correlations are persistent. Our results do not confirm the "quantum brain" hypothesis, but at least, they do not disprove it either, with studies on further steps needed. The "quantum brain" proposal can revolutionize our understanding of cognition if proven valid. The core of the most common "quantum brain" mechanism is the appearance of correlated neuron triggering induced by quantum correlations between ions. In this work, we examine the preservation of the correlations created in the pre-synaptic neurons through the transfer of neurotransmitters across the synaptic cleft, a critical ingredient for the validity of the "quantum brain" hypothesis. We simulated the transport of two neurotransmitters at two different clefts, with the only assumption that they start simultaneously, and determined the difference in their first passage times. We show that in physiological conditions, the correlations are persistent even if the parameters of the two neurons are different. [ABSTRACT FROM AUTHOR]

Generation of lignin-carbohydrate complex (LCC) between dehydrogenation polymer (DHP) and pulp fibers may have an important impact on the properties of pulp. In this work, the benzyl ester-type LCC was formed between oxidized cellulose and DHP. The effect of pH on the addition reaction of oxidized cellulose to quinone methide in the synthesis of DHP-cellulose complex (DHPCC) was investigated. The structure of the product was characterized by Fourier Transform Infrared (FTIR), Carbon 13-Nuclear Magnetic Resonance (13C-NMR), and 2-Dimensional Heteronuclear Single Quantum Coherence Nuclear Magnetic Resonance (2D HSQC NMR) analyses. The results indicated that cellulose was indeed oxidized and carboxyl groups were introduced into cellulose by the oxidation process. The formed DHPCC was connected by benzyl ester linkage. In addition, the pH of the reaction system had an important role in the formation of the benzyl ester bonds. The acidic condition (pH = 4.0) was conducive to the addition reaction of quinone methide with carboxyl groups of cellulose. Overall, this study provides helpful guidance for the generation of LCC between DHP and paper pulp fibers. [ABSTRACT FROM AUTHOR]

A theoretical scheme is proposed for improving the performance of cooling and entanglement, where the physical model is based on a double cavity optomechanical system assisted by the field‐mediated coherent feedback. The cooling performance is evaluated by calculating the final mean phonon number. The steady‐state bipartite entanglement between the optical mode and mechanical mode is measured by the logarithmic negativity. The result manifests that with assistance of the quantum coherent feedback, the mechanical resonator (MR) can be cooled close to its quantum ground state and the steady‐state optomechanical entanglement is simultaneously created, all of which are obtained under the condition beyond the resolved sideband. The presented feedback strategy is measurement‐independent, which can effectively preserve the quantum coherence of system. The scheme is conducive to relaxing the current experimental condition and it may provide a new path for the optomechanical manipulation involving the low‐frequency MR. [ABSTRACT FROM AUTHOR]

In this review, we discuss some of the usages of dissipative dipolar systems in the context of quantum technology. Due to the presence of a thermal environment, long-time storage and processing of quantum information is challenging. We provide two examples, where the quantum coherence and entanglement can be preserved for a long time scale using the dissipative dipolar systems. In the third example, we discuss the effect of the rapid rotation in reducing the line broadening of NMR spectrum of such systems. Our main focus is on the second-order effect of dipolar coupling in all the cases mentioned above. There are several ways to calculate such second-order effects. Hence, we present a brief overview of the dynamics of a dissipative dipolar coupled system and also show that the recently proposed fluctuation-regulated quantum master equation (FRQME) is an efficient tool for the theoretical analysis of such systems. [ABSTRACT FROM AUTHOR]

The metrological limits of thermometry operated in nonequilibrium dynamical regimes are analyzed. We consider a finite-dimensional quantum system, employed as a quantum thermometer, in contact with a thermal bath inducing Markovian thermalization dynamics. The quantum thermometer is initialized in a generic quantum state, possibly including quantum coherence with respect to the Hamiltonian basis. We prove that the precision of the thermometer, quantified by the Quantum Fisher Information, is enhanced by the quantum coherence in its initial state. We analytically show this in the specific case of qubit thermometers for which the maximization of the Quantum Fisher Information occurs at a finite time during the transient thermalization dynamics. Such a finite-time precision enhancement can be better than the precision that is achieved asymptotically. [ABSTRACT FROM AUTHOR]

Electronic or nuclear spins represent promising candidates of qubits for applications in quantum information technologies and spintronic devices. However, it remains a challenge to achieve scalable and spatially defined organization of a large number of spins as qubits, which is essential in the feasible fabrication of quantum circuits. We report a strategy of block copolymer self‐assembly to organize molecular spins as qubits across molecular to micro‐/nano‐scales in polymeric films of organic luminescent radicals centered in star‐like block copolymers. We have achieved not only scalable and spatially defined organization of the molecular spins in polymeric films with long‐range periodic ordering but also controllable spin‐lattice relaxation dynamics and spin coherence lifetimes that can be finely tuned by the domain sizes and rigidities of the polymeric matrices. [ABSTRACT FROM AUTHOR]

Introduction: Rydberg atoms are ideal for measuring electric fields due to their unique physical properties. However, low-frequency electric fields below MHz can be challenging due to the accumulation of ionized free electrons on the atomic vapor cell's surface, acting as a shield. Method: This paper proposes a Cavity-enhanced three-photon system (CETPS) measurement scheme, which uses a long-wavelength laser to excite the Rydberg state, reducing atomic ionization and enhancing detection spectrum resolution. A theoretical model is proposed to explain the quantum coherence effect of the light field, measured electric field, and the atomic system. Result: The results show that the proposed scheme significantly increases the electromagnetically induced transparency (EIT) spectral peak and narrows the spectral width, resulting in the maximum slope increasing by more than an order of magnitude. Discussion: The paper also discusses the impact of the Rabi frequency of the two laser fields and the coupling coefficient of the optical cavity on the transmission spectrum amplitude and linewidth, along with the optimal configuration of these parameters in the CEPTS scheme. [ABSTRACT FROM AUTHOR]

We study the electron-induced ion-pair dissociation to gas-phase oxygen molecules using a state-of-the-art velocity-map ion-imaging technique. The analysis is entirely based on the conical time-gated wedge-shaped velocity slice images of O−/O2 nascent anionic fragments, and the resulting observations are in favor of Van Brunt et al.'s report [R. J. Van Brunt and L. J. Kieffer, J. Chem. Phys. 60, 3057 (1974)]. A new image reconstruction method, Jacobian over parallel slicing, is introduced to overcome the drawback of ion exaggeration in determining the kinetic energy distribution from the time-gated parallel slicing technique, which offers an alternative approach to the wedge slicing method. Most importantly, the role of the quintet-heavy Rydberg state has been drawn out to the complex ion-pair formalism. The extracted kinetic energy and angular distributions from the wedge slice images reveal a high momentum transfer during the ion-pair dissociation process, which could be the finest rationale to observe the breakdown of dipole Born approximation driven by multipole moment associated with the incident electron beam. Three distinct dissociative momentum bands have been precisely identified for O− dissociation. However, radiationless Rydberg's predissociation continuum (≥15%) has become an inherent character of electron-induced ion-pair dissociation, which could be dealt with using the beyond Born–Oppenheimer treatment. The incoherent sum of Σ and Π symmetric-associated ion-pair final states has been precisely identified by modeling the angular distribution of O−/O2 for each of the kinetic energy bands. A negligibly small amount of forward–backward asymmetry is observed in the angular distribution of O−/O2, which might be explained by the dissociative state-specific quantum coherence mechanism as reported [Krishnakumar et al., Nat. Phys. 14, 149 (2018); Kumar et al., arXiv:2206.15024 (2022)] by Prabhudesai et al. [ABSTRACT FROM AUTHOR]

The double quantum coherence (DQC) signal in nonlinear spectroscopy gives information about the many-body correlation effects not easily available by other methods. The signal is short-lived, consequently, a significant part of it is generated during the pulse overlap. Since the signal is at two times the laser frequency, one may intuitively expect that the pulse overlap-related artifacts are filtered out by the Fourier transform. Here, we show that this is not the case. We perform explicit calculations of phase-modulated two-pulse experiments of a two-level system where the DQC is impossible. Still, we obtain a significant signal at the modulation frequency, which corresponds to the DQC, while the Fourier transform over the pulse delay shows a double frequency. We repeat the calculations with a three-level system where the true DQC signal occurs. We conclude that with realistic dephasing times, the pulse-overlap artifact can be significantly stronger than the DQC signal. Our results call for great care when analyzing such experiments. As a rule of thumb, we recommend that only delays larger than 1.5 times the pulse length should be used. [ABSTRACT FROM AUTHOR]

Mixed quantum classical (MQC)-initial value representation (IVR) is a recently introduced semiclassical framework that allows for selective quantization of the modes of a complex system. In the quantum limit, MQC reproduces the semiclassical Double Herman–Kluk IVR results, accurately capturing nuclear quantum coherences and conserving zero-point energy. However, in the classical limit, although MQC mimics the Husimi-IVR for real-time correlation functions with linear operators, it is significantly less accurate for non-linear correlation functions with errors even at time zero. Here, we identify the origin of this discrepancy in the MQC formulation and propose a modification. We analytically show that the modified MQC approach is exact for all correlation functions at time zero, and in a study of zero-point energy (ZPE) flow, we numerically demonstrate that it correctly obtains the quantum and classical limits as a function of time. Interestingly, although classical-limit MQC simulations show the expected, unphysical ZPE leakage, we find that it is possible to predict and even modify the direction of ZPE flow through selective quantization of the system, with the quantum-limit modes accepting energy but preserving the minimum quantum mechanically required energy. [ABSTRACT FROM AUTHOR]

The interplay of nuclear and electronic dynamics characterizes the multidimensional electronic spectra of various molecular and solid-state systems. Theoretically, the observable effect of such interplay can be accounted for by response functions. Here, we report analytical expressions for the response functions corresponding to a class of model systems. These are characterized by coupling between the diabatic electronic states and the vibrational degrees of freedom, resulting in linear displacements of the corresponding harmonic oscillators, and by nonadiabatic couplings between pairs of diabatic states. In order to derive the linear response functions, we first perform the Dyson expansion of the relevant propagators with respect to the nonadiabatic component of the Hamiltonian, then derive and expand with respect to the displacements the propagators at given interaction times, and finally provide analytical expressions for the time integrals that lead to the different contributions to the linear response function. The approach is then applied to the derivation of third-order response functions describing different physical processes: ground state bleaching, stimulated emission, excited state absorption, and double quantum coherence. Comparisons between the results obtained up to sixth order in the Dyson expansion and independent numerical calculation of the response functions provide evidence of the series convergence in a few representative cases. [ABSTRACT FROM AUTHOR]

Fluorescence-detected multidimensional electronic spectroscopy (fMES) promises high sensitivity compared to conventional approaches and is an emerging spectroscopic approach toward combining the advantages of MES with the spatial resolution of a microscope. Here, we present a visible white light continuum-based fMES spectrometer and systematically explore the sensitivity enhancement expected from fluorescence detection. As a demonstration of sensitivity, we report room temperature two-dimensional coherence maps of vibrational quantum coherences in a laser dye at optical densities of ∼2–3 orders of magnitude lower than conventional approaches. This high sensitivity is enabled by a combination of biased sampling along the optical coherence time axes and a rapid scan of the pump–probe waiting time T at each sample. A combination of this approach with acousto-optic phase modulation and phase-sensitive lock-in detection enables measurements of room temperature vibrational wavepackets even at the lowest ODs. Alternative faster data collection schemes, which are enabled by the flexibility of choosing a non-uniform undersampled grid in the continuous T scanning approach, are also demonstrated. [ABSTRACT FROM AUTHOR]

Quantum coherence serves as a crucial physical resource, with its quantification emerging as a focal point in contemporary research. Superadditivity constitutes one of the most fundamental attributes in characterizing the coherence distribution in multipartite quantum systems. In this paper, we provide a way to derive tighter superadditivity inequalities of l1-norm coherence measure for arbitrary multiqubit states. We present a category of superadditivity relations related to the αth (α ≥ 2) power of l1-norm coherence Cl1 under certain conditions. Our results are better than the existing ones and are illustrated in detail with examples. [ABSTRACT FROM AUTHOR]

Just a few years after the inception of quantum mechanics, there has been a research program using the nonclassical values of some quasiprobability distributions to delineate the nonclassical aspects of quantum phenomena. In particular, in Kirkwood–Dirac (KD) quasiprobability distribution, the distinctive quantum mechanical feature of noncommutativity which underlies many nonclassical phenomena, manifests in the nonreal values and/or the negative values of the real part. Here, we develop a faithful quantifier of quantum coherence based on the KD nonclassicality which captures simultaneously the nonreality and the negativity of the KD quasiprobability. The KD-nonclassicality coherence thus defined, is upper bounded by the uncertainty of the outcomes of measurement described by a rank-1 orthogonal projection-valued measure (PVM) corresponding to the incoherent orthonormal basis which is quantified by the Tsallis 1 2 -entropy. Moreover, they are identical for pure states so that the KD-nonclassicality coherence for pure state admits a simple closed expression in terms of measurement probabilities. We then use the Maassen–Uffink uncertainty relation for min-entropy and max-entropy to obtain a lower bound for the KD-nonclassicality coherence of a pure state in terms of optimal guessing probability in measurement described by a PVM noncommuting with the incoherent orthonormal basis. We also derive a trade-off relation for the KD-nonclassicality coherences of a pure state relative to a pair of noncommuting orthonormal bases with a state-independent lower bound. Finally, we sketch a variational scheme for a direct estimation of the KD-nonclassicality coherence based on weak value measurement and thereby discuss its relation with quantum contextuality. [ABSTRACT FROM AUTHOR]

Nanomechanical oscillators offer numerous advantages for quantum technologies. Their integration with superconducting qubits shows promise for hardware-efficient quantum error-correction protocols involving superpositions of mechanical coherent states. Limitations of this approach include mechanical decoherence processes, particularly two-level system (TLS) defects, which have been widely studied using classical fields and detectors. In this manuscript, we use a superconducting qubit as a quantum sensor to perform phonon number-resolved measurements on a piezoelectrically coupled phononic crystal cavity. This enables a high-resolution study of mechanical dissipation and dephasing in coherent states of variable size ( n ¯ ≃ 1 − 10 phonons). We observe nonexponential relaxation and state size-dependent reduction of the dephasing rate, which we attribute to TLS. Using a numerical model, we reproduce the dissipation signatures (and to a lesser extent, the dephasing signatures) via emission into a small ensemble (N = 5) of rapidly dephasing TLS. Our findings comprise a detailed examination of TLS-induced phonon decoherence in the quantum regime. Understanding decoherence in mechanical resonators in the quantum regime is crucial for realizing their potential in hybrid quantum devices. Cleland et al. study dissipation and dephasing induced by tunnelling defects in a nanomechanical resonator coupled to a transmon qubit, which serves as a quantum sensor. [ABSTRACT FROM AUTHOR]

The moiré potential serves as a periodic quantum confinement for optically generated excitons, creating spatially ordered zero-dimensional quantum systems. However, a broad emission spectrum resulting from inhomogeneity among moiré potentials hinders the investigation of their intrinsic properties. In this study, we demonstrated a method for the optical observation of quantum coherence and interference of a single moiré exciton in a twisted semiconducting heterobilayer beyond the diffraction limit of light. We observed a single and sharp photoluminescence peak from a single moiré exciton following nanofabrication. Our findings revealed the extended duration of quantum coherence in a single moiré exciton, persisting beyond 10 ps, and an accelerated decoherence process with increasing temperature and excitation power density. Moreover, quantum interference experiments revealed the coupling between moiré excitons in different moiré potential minima. The observed quantum coherence and interference of moiré exciton will facilitate potential applications of moiré quantum systems in quantum technologies. Here, the authors develop a microfabrication method to realize the optical observation of quantum coherence and interference of a single moiré exciton in twisted semiconducting heterobilayers of transition metal dichalcogenides, persisting beyond 10 ps. [ABSTRACT FROM AUTHOR]

Quantum coherence constitutes a foundational characteristic of quantum mechanics and is integral to emerging quantum resource theories. However, quantum coherence is severely restricted by environmental noise in general quantum processing, indicated by the loss of information of a quantum system. Such processing can be described by the trade-offs between the coherence and the mixedness. Based on the l 2 norm coherence, conditional von Neumann entropy and Wigner–Yanase skew information, we derive basis-independent constraints on the attainable quantum coherence imposed by the mixedness of a quantum state, which generalize the prior basis-dependent relations, provide fundamental insights into the latent coherence resources present within arbitrary quantum systems that undergo decoherence and quantify the inherent limits on extractable coherence imposed by environmental noise. [ABSTRACT FROM AUTHOR]

We explore the dynamics of l 1 -norm of steered quantum coherence (SQC), steered quantum relative entropy (SQRE), and magic resource quantifier (MRQ) in the one-dimensional XY spin chain in the presence of time-dependent transverse magnetic field. We find that the system's response is highly sensitive to the initial state and magnetic field strength. We show the dynamics of SQC, SQRE, and MRQ revealing the critical point associated with equilibrium quantum phase transition (QPT) of the system. All quantities show maximum at QPT when the initial state is prepared in the ferromagnetic phase. Conversely, they undergo abrupt changes at quantum critical point if the initial state of the system is paramagnetic. Moreover, our results confirm that when quench is done to the quantum critical point, the first suppression (revival) time scales linearly with the system size, and remarkably, its scaling ratio remains consistent for all quenches, irrespective of the initial phase of the system. These results highlight the interplay between the quantum information resources and dynamics of quantum systems away from the equilibrium. Such insights could be vital for quantum information processing and understanding non-equilibrium phenomena in quantum many-body systems. [ABSTRACT FROM AUTHOR]

Understanding the quantum coherence effects is crucial for their promising applications, such as engineering artificial photosynthesis, manipulating chemical reactions, and designing coherence‐based functional devices. Considering that a molecule is the smallest unit that can exist independently and maintain its physical and chemical properties, investigating the quantum coherence effects of molecules is of great significance in understanding their features. In this case, exploring quantum coherence effects in the interaction of light and molecules has been one of the leading topics. This review presents an overview of state‐of‐the‐art spectroscopic techniques and deep insights into molecular quantum coherence effects. It also offers prospects for future advancement. First, the history of development and origins of quantum coherence effects are briefly introduced in molecules. Then, the principle and exciting experimental progress of sophisticated techniques for investigating molecular quantum coherence effects are discussed. Late, molecular quantum coherence effects and their promising applications in various areas have been evaluated. Finally, the challenges and potential solutions are look ahead for studying the effects of quantum coherence on molecules. This review may offer some guidance to boost the understanding and employing the molecular quantum coherence effects. [ABSTRACT FROM AUTHOR]

The unitary dynamics of a quantum system initialized in a selected basis state yield, generically, a state that is a superposition of all the basis states. This process, associated with the quantum information scrambling and intimately tied to the resource theory of coherence, may be viewed as a gradual delocalization of the system's state in the Hilbert space. This work analyzes the Hilbert space delocalization under the dynamics of random quantum circuits, which serve as a minimal model of the chaotic dynamics of quantum many-body systems. We employ analytical methods based on the replica trick and Weingarten calculus to investigate the time evolution of the participation entropies which quantify the Hilbert space delocalization. We demonstrate that the participation entropies approach, up to a fixed accuracy, their long-time saturation value in times that scale logarithmically with the system size. Exact numerical simulations and tensor network techniques corroborate our findings. [ABSTRACT FROM AUTHOR]

In this report, we discuss the synthesis of a compound obtained from the derivatization of the natural compound celastrol. This derivative is connected to PEG azide moiety through an amide linkage. The linkage was achieved through the activation of the carboxylic acid using HOBt/EDC. The compound was fully characterized by proton (1H), carbon-13 (13C), heteronuclear single quantum coherence (HSQC), correlation spectroscopy (1H-1H-COSY), and distortionless enhancement by polarization transfer (DEPT) NMR. Ultraviolet (UV), Fourier-transform infrared (FTIR), and high-resolution mass spectrometry (HRMS) were also adopted. Computational investigations were conducted to forecast the binding mode between the synthesized compound and sarco-endoplasmic reticulum (SR) Ca2+ transport ATPase (SERCA), a known target for the development of novel therapeutics for rheumatoid arthritis. Additionally, the drug-likeness of the synthesized compound was assessed by predicting its pharmacokinetic properties. [ABSTRACT FROM AUTHOR]

A reaction center is a unique biological system that performs the initial charge separation within a Photosystem II (PSII) multiunit enzyme, which eventually drives the catalytic water-splitting in plants and algae. The possible role of quantum coherences coinciding with the energy and charge transfer processes in PSII reaction center is one of the active areas of research. Here, we study these quantum coherences by using a numerically exact method on an excitonic dimer model, including linear vibronic coupling and employing optimal parameters from experimental two-dimensional coherent spectroscopic measurements. This enables us to precisely capture the excitonic interaction between pigments and the dissipation of the energy from electronic and charge-transfer (CT) states to the protein environment. We employ the time nonlocal (TNL) quantum master equation to calculate the population dynamics, which yields numerically reliable results. The calculated results show that, due to the strong dissipation, the lifetime of electronic coherence is too short to have direct participation in the charge transfer processes. However, there are long-lived vibrational coherences present in the system at frequencies close to the excitionic energy gap. These are strongly coupled with the electronic coherences, which makes the detection of the electronic coherences with conventional techniques very challenging. Additionally, we unravel the strong excitonic interaction of radical pair ( P D 1 and P D 2 ) in the reaction center, which results in a long-lived electronic coherence of >100 fs, even at room temperature. Our work provide important physical insight to the charge separation process in PSII reaction center, which may be helpful for better understanding of photophysical processes in other natural and artificial light-harvesting systems. [ABSTRACT FROM AUTHOR]

This paper delves into the exploration of quantum resources within a two-qubit system composed of two 2-level atoms connected to distinct thermal baths. Various quantifiers are employed to evaluate different aspects of the system's quantum characteristics. Specifically, the ℓ 1 -norm and relative entropy of coherence ( ℓ 1 and r ) are utilized to gauge quantum coherence, while local quantum Fisher information (LQFI) is used to quantify non-classical correlations within the system. The findings suggest that the amount of quantum correlations and coherence decline as the spontaneous emission rate γ t and the mean thermal photon number n increase. However, it is observed that manipulating parameters defining the initial state of the two-level atoms system can enhance non-classical correlations and quantum coherence between the two atoms. Additionally, it is noted that these three key metrics entirely vanish in the asymptotic limit of time. Our research underscores the importance of precisely adjusting the parameters of the initial system state, which is prepared in an extended Werner-like state (EWL), to protect quantum resources shared between the two atoms from environmental influences. [ABSTRACT FROM AUTHOR]

While strategies to enhance the quantum coherence of plasmonic resonances have attracted a lot of attention in the past, the advent of non-Hermitian optics carries promising possibilities in this direction, mostly of which are still unexplored. In this work, we show that the quantum coherence of plasmonic resonances can be enhanced by integrating a plasmonic antenna in a photonic cavity operated at a chiral exceptional point (CEP), where the phase of light offers an additional degree of freedom for flexibly manipulating the quantum dynamics. The few-mode quantization theory is employed to demonstrate the advantages and related quantum-optics applications of the proposed hybrid cavity in both off- and on-resonance plasmon-photon coupling. For the former case, the local density of states evolves into sub-Lorentzian lineshape, resulting in reduced dissipation of polaritonic states. On resonance, we identify two mechanisms improving the quantum yield by two orders of magnitude at room temperature: the reduction of plasmonic absorption through Fano interference and the enhancement of cavity radiation through superscattering. Our results establish CEP-engineered plasmonic resonances as a promising platform for controlling quantum states and building high-performance quantum devices. The advent of non-Hermitian optics carries new possibilities in manipulating optical response, offering alternative ways to enhance the quantum coherence of plasmonic resonances. Based on a theoretical model, the authors calculate a quantum yield enhanced by two orders of magnitude at room temperature, achieved by integration of a plasmonic antenna in a photonic cavity operated at a chiral exceptional point. [ABSTRACT FROM AUTHOR]

We theoretically investigate continuous variable entanglement and macroscopic quantum coherence in the hybrid L–G rotational cavity optomechanical system containing two YIG spheres. In this system, a single L–G cavity mode and both magnon modes (which are due to the collective excitation of spins in two YIG spheres) are coupled through the magnetic dipole interaction whereas the L–G cavity mode can also exchange orbital angular momentum (OAM) with the rotating mirror (RM). We study in detail the effects of various physical parameters like cavity and both magnon detunings, environment temperature, optorotational and magnon coupling strengths on the bipartite entanglement and the macroscopic quantum coherence as well. We also explore parameter regimes to achieve maximum values for both of these quantum correlations. We also observed that the parameters regime for achieving maximum bipartite entanglement is completely different from macroscopic quantum coherence. So, our present study shall provide a method to control various nonclassical quantum correlations of macroscopic objects in the hybrid L–G rotational cavity optomechanical system and have potential applications in quantum sensing, quantum meteorology, and quantum information science. [ABSTRACT FROM AUTHOR]

The coherence dynamics of the central systems are investigated in the spin-chain environment with topological characterization. For the single- and two-spin coherence, their critical behaviors can detect the topological quantum phase transitions (TQPTs) in weaker coupling regions. Their noncritical behaviors show periodic oscillations or keep constant. For the quantum coherence of a symmetric W state, the bipartite coherence is dominant due to its polygamy. The critical behaviors of global coherence ( QC a : bc and QC b : c ) and multipartite monogamy can also detect the TQPTs. In the strong coupling regions ( g a (b , c) ≫ 1 ), the coherence dynamics of single-spin, two-spin, and bipartite block of three-spin system can be characterized by Gaussian envelope, but the envelope line of three-spin coherence can be only described by negative logarithmic function. Finally, the resistance to the topological spin-chain environment becomes stronger from the single- to three-spin coherence. [ABSTRACT FROM AUTHOR]

Based on the quantum coherence theory, we employ the l 1 -norm measure to explore the steady-state coherence (SSC) in the spin-boson model. In this model, the environment is a non-Markovian bosonic bath with Ohmic-like spectral density. More generally, the interaction coupling between the qubit and the environment is a linear superposition of pure dephasing and pure damping coupling. Governed by the non-Markovian dynamics, some compact expressions of the SSC have been obtained at both zero temperature and high temperature. It shows that the hybrid coupling significantly affects the SSC. Moreover, a comprehensive analysis has been conducted to investigate the effects of various crucial factors, including the temperature of the bosonic bath, the qubit's tunneling and the Ohmicity parameter. This analysis provides an effective approach for maintaining a relatively high SSC by manipulating system parameters. [ABSTRACT FROM AUTHOR]

We propose a theoretical scheme to enhance quantum coherence and obtain steady-state coherence by combining quantum feedback control and noise-assisted preparation. We investigate the effects of quantum-jump-based feedback control and noise field on the quantum coherence and excited-state population between two atoms inside an optical cavity where a noise field drives one, and the other is under quantum feedback control. It is found that steady quantum coherence can be achieved by adding an external noise field, and the quantum feedback can prolong the coherence time with partial suppression of the spontaneous emission of atoms. In addition, we study the influence of the joint action of quantum feedback and noise-assisted preparation on quantum coherence and show that the combined action of feedback control and noise-assisted preparation is more effective in enhancing steady coherence. The findings of our research offer some general guidelines for improving the steady-state coherence of coupled qubit systems and have the potential to be applied in the realm of quantum information technology. [ABSTRACT FROM AUTHOR]

Over the last two decades, time- and angle-resolved photoemission spectroscopy (trARPES) has become a mature and established experimental technique for the study of ultrafast electronic and structural dynamics in materials. To date, most trARPES investigations have focused on the investigation of processes occurring on time scales of ≳30 fs, in particular, relaxation and thermalization, and have therefore been blind to the initial sub-10 fs dynamics related to electronic coherence and correlation effects. In this article, we illustrate how current trARPES setups reach their limits when it comes to addressing such extraordinarily short time scales and present an experimental configuration that provides the time, energy, and momentum resolutions required to monitor few-femtosecond dynamics on the relevant energy and momentum scales. We discuss the potential capabilities of such an experiment to study the electronic response of materials in the strong-field interaction regime at PHz frequencies and finally review a theoretical concept that may in the future even overcome the competing resolution limitations of trARPES experiments, as imposed by the time–bandwidth product of the probing laser pulse. Our roadmap for ultrafast trARPES indicates a path to break new experimental ground in quantum nonequilibrium electronic dynamics, from which new possibilities for ultrafast control of optical and electronic signals in quantum materials can be explored. [ABSTRACT FROM AUTHOR]

Gaining insight into nanostructure devices represents a crucial step in unlocking their full quantum potential. Solid-state quantum dots provide a practical and scalable foundation for accommodating qubits, which are essential for quantum information processing. In this context, we introduce a model involving a pair of qubits within a double quantum dot configuration. We extensively investigate its quantum coherence and the quantum-memory-assisted entropic uncertainty relation ( QMA - EUR ), considering the influence of the thermal environment and Rashba spin–orbit coupling. Our findings reveal a monotonic increase in QMA - EUR with rising temperatures (T), while the Jensen–Shannon coherence consistently decreases as T increases. Furthermore, fine-tuning the Rashba coupling can enhance the system's coherence and reduce measurement uncertainty. We show that obtaining higher measurement precisions is achievable when the two-qubit system, made up of the double quantum dots with Rashba interaction, demonstrates higher levels of coherence. Additionally, we demonstrate that adjusting other Hamiltonian parameters offers advantages in preserving quantum resources. These reported results indicate promising prospects for developing quantum technologies that leverage such a quantum dot system. [ABSTRACT FROM AUTHOR]

Conventional formulation of QED since the 50s works very well for stationary states and for scattering problems, but with newly arisen challenges from the 80s on, where real time evolution of particles in a nonequilibrium setting are required, and quantum features such as coherence, dissipation, correlation and entanglement in a system interacting with its quantum field environment are sought after, new ways to formulate QED suitable for these purposes beckon. In this paper we present a linearized effective theory using a Gaussian wavepacket description of a charged relativistic particle coupled to quantum electromagnetic fields to study the interplay between single electrons and quantum fields in free space, at a scale well below the Schwinger limit. The proper values of the regulators in our effective theory are determined from the data of individual experiments, and will be time-dependent in the laboratory frame if the single electrons are accelerated. Using this new theoretical tool, we address the issues of decoherence of flying electrons in free space and the impact of Unruh effect on the electrons. Our result suggests that vacuum fluctuations may be a major source of blurring the interference pattern in electron microscopes. For a single electron accelerated in a uniform electric field, we identify the Unruh effect in the two-point correlators of the deviations from the electron's classical trajectory. From our calculations we also bring out some subtleties, involving the bosonic versus fermionic spectral functions. [ABSTRACT FROM AUTHOR]

Quantum time correlation functions (TCFs) involving two states are important for describing nonadiabatic dynamical processes such as charge transfer (CT). Based on a previous single-state method, we propose an imaginary-time open-chain path-integral (OCPI) approach for evaluating the two-state symmetrized TCFs. Expressing the forward and backward propagation on different electronic potential energy surfaces as a complex-time path integral, we then transform the path variables to average and difference variables such that the integration over the difference variables up to the second order can be performed analytically. The resulting expression for the symmetrized TCF is equivalent to sampling the open-chain configurations in an effective potential that corresponds to the average surface. Using importance sampling over the extended OCPI space via open path-integral molecular dynamics, we tested the resulting path-integral approximation by calculating the Fermi's golden rule CT rate constant within a widely used spin-boson model. Comparing with the real-time linearized semiclassical method and analytical result, we show that the imaginary-time OCPI provides an accurate two-state symmetrized TCF and rate constant in the typical turnover region. It is shown that the first bead of the open chain corresponds to physical zero-time and that the endpoint bead corresponds to final time t; oscillations of the end-to-end distance perfectly match the nuclear mode frequency. The two-state OCPI scheme is seen to capture the tested model's electronic quantum coherence and nuclear quantum effects accurately. [ABSTRACT FROM AUTHOR]