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In previous work we have proposed a construction of quantum-like bits that could endow a large, complex classical system, for example of oscillators, with quantum-like function that is not compromised by decoherence. In the present paper we investigate further this platform of quantum-like states. Firstly, we discuss a general protocol on how to construct synchronizing networks that allow for emergent states. We then study how gates can be implemented on those states. This suggests the possibility of quantum-like computing on specially-constructed classical networks. Finally, we define a notion of measurement that allows for non-Kolmogorov interference, a feature that separates our model from a classical probabilistic system. This paper aims to explore the mathematical structure of quantum-like resources, and shows how arbitrary gates can be implemented by manipulating emergent states in those systems.

The power of quantum states arises in part from superpositions of product states. Can complex classical systems be designed to exhibit such superpositions of tensor products of basis states, thereby mimicking quantum states? We exhibit a one-to-one map between the product basis of quantum states comprising an arbitrary number of qubits and the eigenstates of a construction comprising classical oscillator networks. Specifically, we prove the existence of this map based on Cartesian products of graphs, where the graphs depict the layout of oscillator networks.

Recent work has exposed the idea that interesting quantum-like probability laws, including interference effects, can be manifest in classical systems. Here we propose a model for quantum-like (QL) states and QL bits. We suggest a way that huge, complex systems can host robust states that can process information in a QL fashion. Axioms that such states should satisfy are proposed. Specifically, it is shown that building blocks suited for QL states are networks, possibly very complex, that we defined based on $k$-regular random graphs. These networks can dynamically encode a lot of information that is distilled into the emergent states we can use for QL like processing. Although the emergent states are classical, they have properties analogous to quantum states. Concrete examples of how QL functions are possible are given. The possibility of a `QL advantage' for computing-type operations and the potential relevance for new kinds of function in the brain are discussed and left as open questions.

Quantum information, a field in which great advances have been made in the past decades, now presents opportunities for chemistry. One roadblock to progress, especially for experimental chemical science, is that new concepts and technical definitions need to be learned. In this paper, we review some basic, but sometimes misunderstood, concepts of quantum information based on the mathematical formulation of quantum mechanics that will be useful for chemists interested in discovering ways that chemistry can contribute to the quantum information field. We cover topics including qubits and their density matrix formalism, quantum measurement as a quantum operation, information theory, and entanglement. We focus on the difference between the concepts in the quantum context and the classic context. We also discuss the relation and distinction among entanglement, correlation, and coherence. We aim to clarify the rigorous definition of these concepts, and then indicate some examples in physical chemistry.

In organic bulk heterojunction materials, charge delocalization has been proposed to play a vital role in the generation of free carriers by reducing the Coulomb attraction via an interfacial charge transfer exciton (CTX). Pump-push-probe (PPP) experiments produced evidence that the excess energy given by a push pulse enhances delocalization, thereby increasing photocurrent. However, previous studies have employed near-IR push pulses in the range 0.4-0.6 eV which is larger than the binding energy of a typical CTX. This raises the doubt that the push pulse may directly promote dissociation without involving delocalized states. Here, we perform PPP experiments with mid-IR push pulses at energies that are well below the binding energy of a CTX state (0.12-0.25 eV). We identify three types of CTX: delocalized, localized, and trapped. The excitation resides over multiple polymer chains in delocalized CTXs, while is restricted to a single chain (albeit maintaining a degree of intrachain delocalization) in localized CTXs. Trapped CTXs are instead completely localized. The pump pulse generates a hot delocalized CTX, which relaxes to a localized CTX, and eventually to trapped states. We find that photo-exciting localized CTXs with push pulses resonant to the mid-IR charge transfer absorption can promote delocalization and contribute to the formation of long-lived charge separated states. On the other hand, we found that trapped CTX are non-responsive to the push pulses. We hypothesize that delocalized states identified in prior studies are only accessible in systems where there is significant interchain electronic coupling or regioregularity that supports either interchain or intrachain polaron delocalization. This emphasizes the importance of engineering the micromorphology and energetics of the donor-acceptor interface to exploit a full potential of a material for photovoltaic applications.

The efficiency of two-dimensional Dion-Jacobson-type materials relies on the complex interplay between electronic and lattice dynamics; however, questions remain about the functional role of exciton-phonon interactions. This study establishes the robust polaronic nature of the excitons in these materials at room temperature by combining ultrafast spectroscopy and electronic structural calculations. We show that polaronic distortion is associated with low-frequency (30-60 cm-1) lead iodide octahedral lattice motions. More importantly, we discover how targeted ligand modification of this two-dimensional perovskite structure controls exciton-phonon coupling, exciton-polaron population, and carrier cooling. At high excitation density, stronger exciton-phonon coupling increases the hot carrier lifetime, forming a hot-phonon bottleneck. Our study provides detailed insight into the exciton-phonon coupling and its role in carrier cooling in two-dimensional perovskites relevant for developing emerging hybrid semiconductor materials with tailored properties.

Molecular polaritons are hybrid states of photonic and molecular character that form when molecules strongly interact with light. Strong coupling tunes energy levels and importantly, can modify molecular properties (e.g. photoreaction rates) opening an avenue for novel polariton chemistry. In this perspective, we focus on the collective aspects of strongly coupled molecular systems and how this pertains to the dynamical response of such systems, which though of key importance for attaining modified function under polariton formation, is still not well understood. We discuss how the ultrafast time and spectral resolution make pump-probe spectroscopy an ideal tool to reveal the energy transfer pathways from polariton states to other molecular states of functional interest. Finally, we illustrate how analyzing the free (rather than electronic) energy structure in molecular polariton systems may provide new clues into how energy flows and thus how strong coupling may be exploited.

Time-resolved dynamics in charge-density-wave materials have revealed interesting out-of-equilibrium electronic responses. However these are typically only performed in a single material possessing a CDW. As such, it is challenging to separate subtle effects originating from the CDW. Here, we report on the ultrafast dynamics of the GdSb$_{x}$Te$_{2-x-\delta}$ series of materials where E$_{F}$ can be tuned, resulting in a change from an undistorted tetraganal phase to a CDW with a wavevector that depends on $x$. Using mid-infrared, near-infrared, and visible excitation, we find the dynamics are sensitive to both E$_{F}$ and the presence of the CDW. Specifically, as the Sb content of the compounds increases, transient spectral features shift to higher probe energies. In addition, we observe an enhanced lifetime and change in the sign of the transient signal upon removing the CDW with high Sb concentrations. Finally, we reveal fluence- and temperature-dependent photo-induced responses of the differential reflectivity, which provide evidence of transient charge density wave suppression in related telluride materials. Taken together our results provide a blueprint for future ultrafast studies of CDW systems.

Color centers in diamond are promising platforms for quantum technologies. Most color centers in diamond discovered thus far emit in the visible or near-infrared wavelength range, which are incompatible with long-distance fiber communication and unfavorable for imaging in biological tissues. Here, we report the experimental observation of a new color center that emits in the telecom O-band, which we observe in silicon-doped bulk single crystal diamonds and microdiamonds. Combining absorption and photoluminescence measurements, we identify a zero-phonon line at 1221 nm and phonon replicas separated by 42 meV. Using transient absorption spectroscopy, we measure an excited state lifetime of around 270 ps and observe a long-lived baseline that may arise from intersystem crossing to another spin manifold.

Cavity quantum electrodynamics has been studied as a potential approach to modify free charge carrier generation in donor-acceptor heterojunctions because of the delocalization and controllable energy level properties of hybridized light-matter states known as polaritons. However, in many experimental systems, cavity coupling decreases charge separation. Here, we theoretically study the quantum dynamics of a coherent and dissipative donor-acceptor cavity system, to investigate the dynamical mechanism and further discover the conditions under which polaritons may enhance free charge carrier generation. We use open quantum system methods based on single-pulse pumping to find that polaritons have the potential to connect excitonic states and charge separated states, further enhancing free charge generation on an ultrafast timescale of several hundred femtoseconds. The mechanism involves that polaritons with proper energy levels allow the exciton to overcome the high Coulomb barrier induced by electron-hole attraction. Moreover, we propose that a second-hybridization between a polariton state and dark states with similar energy enables the formation of the hybrid charge separated states that are optically active. These two mechanisms lead to a maximum of 50% enhancement of free charge carrier generation on a short timescale. However, our simulation reveals that on the longer timescale of picoseconds, internal conversion and cavity loss dominate and suppress free charge carrier generation, reproducing the experimental results. Thus, our work shows that polaritons can affect the charge separation mechanism and promote free charge carrier generation efficiency, but predominantly on a short timescale after photoexcitation.

The repeating arrangement of tubulin dimers confers great mechanical strength to microtubules, which are used as scaffolds for intracellular macromolecular transport in cells and exploited in biohybrid devices. The crystalline order in a microtubule, with lattice constants short enough to allow energy transfer between amino acid chromophores, is similar to synthetic structures designed for light harvesting. After photoexcitation, can these amino acid chromophores transfer excitation energy along the microtubule like a natural or artificial light-harvesting system? Here, we use tryptophan autofluorescence lifetimes to probe inter-tryptophan energy hopping in tubulin and microtubules. By studying how quencher concentration alters tryptophan autofluorescence lifetimes, we demonstrate that electronic energy can diffuse over 6.6 nm in microtubules. We discover that while diffusion lengths are influenced by tubulin polymerization state (free tubulin versus tubulin in the microtubule lattice), they are not significantly altered by the average number of protofilaments (13 versus 14). We also demonstrate that the presence of the anesthetics etomidate and isoflurane reduce exciton diffusion. Energy transport as explained by conventional F\"orster theory (accommodating for interactions between tryptophan and tyrosine residues) does not sufficiently explain our observations. Our studies indicate that microtubules are, unexpectedly, effective light harvesters.

Out-of-equilibrium effects provide an elegant pathway to probing and understanding the underlying physics of topological materials. Creating exotic states of matter using ultrafast optical pulses in particular has shown promise towards controlling electronic band structure properties. Of recent interest is band renormalization in Dirac and Weyl semimetals as it leads to direct physical observables through the enhancement of the effective mass, or, in the shift of resonant energies. Here we provide experimental and theoretical signatures of photo-induced renormalization of the electronic band structure in a topological nodal line semimetal ZrSiS. Specifically, we show how the change of the transient reflectivity spectra under femtosecond optical excitations is induced by out-of-equilibrium effects that renormalize the kinetic energy of electrons. We associate the observed spectral shift to an enhancement of the effective mass and to a red-shift of the resonant frequency as a function of pump field strength. Finally, we show that the transient relaxation dynamics of the reflectivity is primarily an electronic effect with negligible phononic contribution. Our study presents the modifications of electronic properties in ZrSiS using ultrashort pulses, and demonstrates the potential of this approach in creating photo-induced phases in topological quantum mater through an all-optical route., Comment: 9 pages, 4 figures

Thermally-activated delayed fluorescence (TADF) enables organic semiconductors with charge transfer (CT)-type excitons to convert dark triplet states into bright singlets via a reverse intersystem crossing (rISC) process. Here, we consider the role of the dielectric environment in a range of TADF materials with varying changes in dipole moment upon optical excitation. In a dipolar reference emitter, TXO-TPA, environmental reorganisation after excitation in both solution and doped films triggers the formation of the full CT product state. This lowers the singlet excitation energy by 0.3 eV and minimises the singlet-triplet energy gap ({\Delta}EST). Using impulsive Raman measurements, we observe the emergence of two (reactant-inactive) modes at 412 and 813 cm-1 as a vibrational fingerprint of the CT product. In contrast, the dielectric environment plays a smaller role in the electronic excitations of a less dipolar material, 4CzIPN. Quantum-chemical calculations corroborate the appearance of these new product modes in TXO-TPA and show that the dynamic environment fluctuations are large compared to {\Delta}EST. The analysis of the energy-time trajectories and the corresponding free energy functions reveals that the dielectric environment significantly reduces the activation energy for rISC, thus increasing the rISC rate by up to three orders of magnitude when compared to a vacuum environment., Comment: 67 pages, 7 main-text figures

Entanglement is a defining feature of quantum mechanics that can be a resource in engineered and natural systems, but measuring entanglement in experiment remains elusive especially for large chemical systems. Most practical approaches require determining and measuring a suitable entanglement witness which provides some level of information about the entanglement structure of the probed state. A fundamental quantity of quantum metrology is the quantum Fisher information (QFI) which is a rigorous witness of multipartite entanglement that can be evaluated from linear response functions for certain states. In this work, we explore measuring the QFI of molecular exciton states of the first-excitation subspace from spectroscopy. In particular, we utilize the fact that the linear response of a pure state subject to a weak electric field over all possible driving frequencies encodes the variance of the collective dipole moment in the probed state, which is a valid measure for QFI. The systems that are investigated include the molecular dimer, $N$-site linear aggregate with nearest-neighbor coupling, and $N$-site circular aggregate, all modeled as a collection of interacting qubits. Our theoretical analysis shows that the variance of the collective dipole moment in the brightest dipole-allowed eigenstate is the maximum QFI. The optical response of a thermally equilibrated state in the first-excitation subspace is also a valid QFI. Theoretical predictions of the measured QFI for realistic linear dye aggregates as a function of temperature and energetic disorder due to static variations of the host matrix show that 2- to 3-partite entanglement is realizable. This work lays some groundwork and inspires measurement of multipartite entanglement of molecular excitons with ultrafast pump-probe experiments.

Here we report an ultrafast optical spectroscopic study of the nodal-line semimetal ZrSiTe. Our measurements reveal that, converse to other compounds of the family, the sudden injection of electronic excitations results in a strongly coherent response of an $A_{1g}$ phonon mode which dynamically modifies the distance between Zr and Te atoms and Si layers. "Frozen phonon" DFT calculations, in which band structures are calculated as a function of nuclear position along the phonon mode coordinate, show that large displacements along this mode alter the material's electronic structure significantly, forcing bands to approach and even cross the Fermi energy. The incoherent part of the time domain response reveals that a delayed electronic response at low fluence discontinuously evolves into an instantaneous one for excitation densities larger than $3.43 \times 10^{17}$ cm$^{-3}$. This sudden change of the dissipative channels for electronic excitations is indicative of an ultrafast Lifshitz transition which we tentatively associate to a change in topology of the Fermi surface driven by a symmetry preserving $A_{1g}$ phonon mode.

The ultrafast optical response of two nodal-line semimetals, ZrSiS and ZrSiSe, was studied in the near-infrared using transient reflectivity. The two materials exhibit similar responses, characterized by two features, well resolved in time and energy. The first transient feature decays after a few hundred femtoseconds, while the second lasts for nanoseconds. Using Drude-Lorentz fits of the materials' equilibrium reflectance, we show that the fast response is well-represented by a decrease of the Drude plasma frequency, and the second feature by an increase of the Drude scattering rate. This directly connects the transient data to a physical picture in which carriers, after being excited away from the Fermi energy, return to that vicinity within a few hundred femtoseconds by sharing their excess energy with the phonon bath, resulting in a hot lattice that relaxes only through slow diffusion processes (ns). The emerging picture reveals that the sudden change of the density of carriers at the Fermi level instantaneously modifies the transport properties of the materials on a timescale not compatible with electron phonon thermalization and is largely driven by the reduced density of states at the nodal line.

The hierarchical equations of motion (HEOM) theory is one of the standard methods to rigorously describe open quantum dynamics coupled to harmonic environments. Such a model is used to capture non-Markovian and non-perturbative effects of environments appearing in ultra-fast phenomena. In the regular framework of the HEOM theory, the environment correlation functions are restricted into linear combinations of exponential functions. In this article, we present a new formulation of the HEOM theory including treatments of non-exponential correlation functions, which enables us to describe general environmental effects more efficiently and stably than the original theory and other generalizations. The library and its Python binding we developed to perform simulations based on our approach, named LibHEOM and PyHEOM respectively, are provided as supplementary material., Comment: 18 pages, 6 figures

Mechanisms controlling excitation energy transport (EET) in light-harvesting complexes remain controversial. Following the observation of long-lived beats in two-dimensional electronic spectroscopy of PC645, vibronic coherence, the delocalization of excited states between pigments supported by a resonant vibration, has been proposed to enable direct down-conversion from the highest-energy states to the lowest-energy pigments. Here, we instead show that for phycobiliprotein PC645 an incoherent vibronic transport mechanism is at play. We quantify the solvation dynamics of individual pigments using ab initio QM/MM nuclear dynamics. Our atomistic spectral densities reproduce experimental observations ranging from absorption and fluorescence spectra to the timescales and selectivity of down-conversion observed in transient absorption measurements. We demonstrate that bilin solvation controls EET pathways and that direct down-conversion proceeds incoherently, enhanced by large reorganization energies and a broad collection of high-frequency vibrations. We thus suggest that engineering local solvation dynamics represents a potential design principle for nanoscale control of EET.

Conjugated polymers are complex multi-chromophore systems, with emission properties strongly dependent on the electronic energy transfer through active sub-units. Although the packing of the conjugated chains in the solid state is known to be a key factor to tailor the electronic energy transfer and the resulting optical properties, most of the current solution-based processing methods do not allow for effectively controlling the molecular order, thus making the full unveiling of energy transfer mechanisms very complex. Here we report on conjugated polymer fibers with tailored internal molecular order, leading to a significant enhancement of the emission quantum yield. Steady state and femtosecond time-resolved polarized spectroscopies evidence that excitation is directed toward those chromophores oriented along the fiber axis, on a typical timescale of picoseconds. These aligned and more extended chromophores, resulting from the high stretching rate and electric field applied during the fiber spinning process, lead to improved emission properties. Conjugated polymer fibers are relevant to develop optoelectronic plastic devices with enhanced and anisotropic properties., Comment: 43 pages, 15 figures, 1 table in Journal of the American Chemical Society, (2016)

We ask whether or not thermal light can be represented as a mixture of single broadband coherent pulses. We find that it cannot. Such a mixture is simply not rich enough to mimic thermal light; indeed, it cannot even reproduce the first-order correlation function. We show that it is possible to construct a modified mixture of single coherent pulses that does yield the correct first-order correlation function at equal space points. However, as we then demonstrate, such a mixture cannot reproduce the second-order correlation function., Comment: 5 pages, 2 figures. Published version

We present a method of developing analytical measures of $k$-partite delocalization in arbitrary $n$-body W-like states, otherwise known as mixed states in the single excitation subspace. These measures calculate the distance of a state to its closest reference state with $k-1$ entanglement. We find that the reference state is determined by the purity of the state undergoing measurement. Measures with up to 6-body delocalization for a 6-body system are derived in full, while an algorithm for general $k$-partite measures is given., Comment: 8 pages, 3 figures