Systematic Coarse Graining of Environments for the Nonperturbative Simulation of Open Quantum Systems.

Conducting precise electronic-vibrational dynamics simulations of molecular systems poses significant challenges when dealing with realistic environments composed of numerous vibrational modes. Here, we introduce a technique for the construction of effective phonon spectral densities that capture accurately open-system dynamics over a finite time interval of interest. When combined with existing nonperturbative simulation tools, our approach can reduce significantly the computational costs associated with many-body open-system dynamics.

Spin-Dependent Momentum Conservation of Electron-Phonon Scattering in Chirality-Induced Spin Selectivity.

The elucidation of the mechanisms underpinning chirality-induced spin selectivity remains an outstanding scientific challenge. Here we consider the role of delocalized phonon modes in electron transport in chiral structures and demonstrate that spin selectivity can originate from spin-dependent energy and momentum conservation in electron-phonon scattering events. While this mechanism is robust to the specific nature of the vibrational modes, the degree of spin polarization depends on environmental factors, such as the specific temperature and phonon relaxation rates, as well as the presence of external driving fields. This parametric dependence is used to present experimentally testable predictions of our model.

Fingerprint and Universal Markovian Closure of Structured Bosonic Environments.

We exploit the properties of chain mapping transformations of bosonic environments to identify a finite collection of modes able to capture the characteristic features, or fingerprint, of the environment. Moreover we show that the countable infinity of residual bath modes can be replaced by a universal Markovian closure, namely, a small collection of damped modes undergoing a Lindblad-type dynamics whose parametrization is independent of the spectral density under consideration. We show that the Markovian closure provides a quadratic speedup with respect to standard chain mapping techniques and makes the memory requirement independent of the simulation time, while preserving all the information on the fingerprint modes. We illustrate the application of the Markovian closure to the computation of linear spectra but also to nonlinear spectral response, a relevant experimentally accessible many body coherence witness for which efficient numerically exact calculations in realistic environments are currently lacking.

Interface-Induced Conservation of Momentum Leads to Chiral-Induced Spin Selectivity.

We study the nonequilibrium dynamics of electron transmission from a straight waveguide to a helix with spin-orbit coupling. Transmission is found to be spin-selective and can lead to large spin polarizations of the itinerant electrons. The degree of spin selectivity depends on the width of the interface region, and no polarization is found for single-point couplings. We show that this is due to momentum conservation conditions arising from extended interfaces. We therefore identify interface structure and conservation of momentum as crucial ingredients for chiral-induced spin selectivity, and we confirm that this mechanism is robust against static disorder.

Universal Anti-Kibble-Zurek Scaling in Fully Connected Systems.

We investigate the quench dynamics of an open quantum system involving a quantum phase transition. In the isolated case, the quench dynamics involving the phase transition exhibits a number of scaling relations with the quench rate as predicted by the celebrated Kibble-Zurek mechanism. In contact with an environment however, these scaling laws break down and one may observe an anti-Kibble-Zurek behavior: slower ramps lead to less adiabatic dynamics, increasing thus nonadiabatic effects with the quench time. In contrast to previous works, we show here that such anti-Kibble-Zurek scaling can acquire a universal form in the sense that it is determined by the equilibrium critical exponents of the phase transition, provided the excited states of the system exhibit singular behavior, as observed in fully connected models. This demonstrates novel universal scaling laws granted by a system-environment interaction in a critical system. We illustrate these findings in two fully connected models, namely, the quantum Rabi and the Lipkin-Meshkov-Glick models. In addition, we discuss the impact of nonlinear ramps and finite-size systems.

A Complex Comprising a Cyanine Dye Rotaxane and a Porphyrin Nanoring as a Model Light-Harvesting System.

A nanoring-rotaxane supramolecular assembly with a Cy7 cyanine dye (hexamethylindotricarbocyanine) threaded along the axis of the nanoring was synthesized as a model for the energy transfer between the light-harvesting complex LH1 and the reaction center in purple bacteria photosynthesis. The complex displays efficient energy transfer from the central cyanine dye to the surrounding zinc porphyrin nanoring. We present a theoretical model that reproduces the absorption spectrum of the nanoring and quantifies the excitonic coupling between the nanoring and the central dye, thereby explaining the efficient energy transfer and demonstrating similarity with structurally related natural light-harvesting systems.

Dissipation-Assisted Matrix Product Factorization.

Charge and energy transfer in biological and synthetic organic materials are strongly influenced by the coupling of electronic states to a highly structured dissipative environment. Nonperturbative simulations of these systems require a substantial computational effort, and current methods can only be applied to large systems if environmental structures are severely coarse grained. Time evolution methods based on tensor networks are fundamentally limited by the times that can be reached due to the buildup of entanglement in time, which quickly increases the size of the tensor representation, i.e., the bond dimension. In this Letter, we introduce a dissipation-assisted matrix product factorization (DAMPF) method that combines a tensor network representation of the vibronic state within a pseudomode description of the environment where a continuous bosonic environment is mapped into a few harmonic oscillators under Lindblad damping. This framework is particularly suitable for a tensor network representation, since damping suppresses the entanglement growth among oscillators and significantly reduces the bond dimension required to achieve a desired accuracy. We show that dissipation removes the "time-wall" limitation of existing methods, enabling the long-time simulation of large vibronic systems consisting of 10-50 sites coupled to 100-1000 underdamped modes in total and for a wide range of parameter regimes. For these reasons, we believe that our formalism will facilitate the investigation of spatially extended systems with applications to quantum biology, organic photovoltaics, and quantum thermodynamics.

Theory of Excitonic Delocalization for Robust Vibronic Dynamics in LH2.

Nonlinear spectroscopy has revealed long-lasting oscillations in the optical response of a variety of photosynthetic complexes. Different theoretical models that involve the coherent coupling of electronic (excitonic) or electronic-vibrational (vibronic) degrees of freedom have been put forward to explain these observations. The ensuing debate concerning the relevance of either mechanism may have obscured their complementarity. To illustrate this balance, we quantify how the excitonic delocalization in the LH2 unit of Rhodopseudomonas acidophila purple bacterium leads to correlations of excitonic energy fluctuations, relevant coherent vibronic coupling, and importantly, a decrease in the excitonic dephasing rates. Combining these effects, we identify a feasible origin for the long-lasting oscillations observed in fluorescent traces from time-delayed two-pulse single-molecule experiments performed on this photosynthetic complex and use this approach to discuss the role of this complementarity in other photosynthetic systems.

Quantum Redirection of Antenna Absorption to Photosynthetic Reaction Centers.

The early steps of photosynthesis involve the photoexcitation of reaction centers (RCs) and light-harvesting (LH) units. Here, we show that the historically overlooked excitonic delocalization across RC and LH pigments results in a redistribution of absorption amplitudes that benefits the absorption cross section of the optical bands associated with the RC of several species. While we prove that this redistribution is robust to the microscopic details of the dephasing between these units in the purple bacterium Rhodospirillum rubrum, we are able to show that the redistribution witnesses a more fragile, but persistent, coherent population dynamics which directs excitations from the LH toward the RC units under incoherent illumination and physiological conditions. Even though the redirection does not seem to affect importantly the overall efficiency in photosynthesis, stochastic optimization allows us to delineate clear guidelines and develop simple analytic expressions in order to amplify the coherent redirection in artificial nanostructures.

Signatures of spatially correlated noise and non-secular effects in two-dimensional electronic spectroscopy.

We investigate how correlated fluctuations affect oscillatory features in rephasing and non-rephasing two-dimensional (2D) electronic spectra of a model dimer system. Based on a beating map analysis, we show that non-secular environmental couplings induced by uncorrelated fluctuations lead to oscillations centered at both cross- and diagonal-peaks in rephasing spectra as well as in non-rephasing spectra. Using an analytical approach, we provide a quantitative description of the non-secular effects in terms of the Feynman diagrams and show that the environment-induced mixing of different inter-excitonic coherences leads to oscillations in the rephasing diagonal-peaks and non-rephasing cross-peaks. We demonstrate that as correlations in the noise increase, the lifetime of oscillatory 2D signals is enhanced at rephasing cross-peaks and non-rephasing diagonal-peaks, while the other non-secular oscillatory signals are suppressed. We discuss that the asymmetry of 2D lineshapes in the beating map provides information on the degree of correlations in environmental fluctuations. Finally we investigate how the oscillatory features in 2D spectra are affected by inhomogeneous broadening.

Regulating the Energy Flow in a Cyanobacterial Light-Harvesting Antenna Complex.

Photosynthetic organisms harvest light energy, utilizing the absorption and energy-transfer properties of protein-bound chromophores. Controlling the harvesting efficiency is critical for the optimal function of the photosynthetic apparatus. Here, we show that the cyanobacterial light-harvesting antenna complex may be able to regulate the flow of energy to switch reversibly from efficient energy conversion to photoprotective quenching via a structural change. We isolated cyanobacterial light-harvesting proteins, phycocyanin and allophycocyanin, and measured their optical properties in solution and in an aggregated-desiccated state. The results indicate that energy band structures are changed, generating a switch between the two modes of operation, exciton transfer and quenching, achieved without dedicated carotenoid quenchers. This flexibility can contribute greatly to the large dynamic range of cyanobacterial light-harvesting systems.

Tracking the coherent generation of polaron pairs in conjugated polymers.

The optical excitation of organic semiconductors not only generates charge-neutral electron-hole pairs (excitons), but also charge-separated polaron pairs with high yield. The microscopic mechanisms underlying this charge separation have been debated for many years. Here we use ultrafast two-dimensional electronic spectroscopy to study the dynamics of polaron pair formation in a prototypical polymer thin film on a sub-20-fs time scale. We observe multi-period peak oscillations persisting for up to about 1 ps as distinct signatures of vibronic quantum coherence at room temperature. The measured two-dimensional spectra show pronounced peak splittings revealing that the elementary optical excitations of this polymer are hybridized exciton-polaron-pairs, strongly coupled to a dominant underdamped vibrational mode. Coherent vibronic coupling induces ultrafast polaron pair formation, accelerates the charge separation dynamics and makes it insensitive to disorder. These findings open up new perspectives for tailoring light-to-current conversion in organic materials.

Ultimate Precision Limits for Noisy Frequency Estimation.

Quantum metrology protocols allow us to surpass precision limits typical to classical statistics. However, in recent years, no-go theorems have been formulated, which state that typical forms of uncorrelated noise can constrain the quantum enhancement to a constant factor and, thus, bound the error to the standard asymptotic scaling. In particular, that is the case of time-homogeneous (Lindbladian) dephasing and, more generally, all semigroup dynamics that include phase covariant terms, which commute with the system Hamiltonian. We show that the standard scaling can be surpassed when the dynamics is no longer ruled by a semigroup and becomes time inhomogeneous. In this case, the ultimate precision is determined by the system short-time behavior, which when exhibiting the natural Zeno regime leads to a nonstandard asymptotic resolution. In particular, we demonstrate that the relevant noise feature dictating the precision is the violation of the semigroup property at short time scales, while non-Markovianity does not play any specific role.

Experimental detection of quantum coherent evolution through the violation of Leggett-Garg-type inequalities.

We discuss the use of inequalities of the Leggett-Garg type (LGtI) to witness quantum coherence and present the first experimental violation of this type of inequalities using a light-matter interfaced system. By separately benchmarking the Markovian character of the evolution and the translational invariance of the conditional probabilities, the observed violation of a LGtI is attributed to the quantum coherent character of the process. These results provide a general method to benchmark "quantumness" when the absence of memory effects can be independently certified and confirm the persistence of quantum coherent features within systems of increasing complexity.

Optical Signatures of Quantum Delocalization over Extended Domains in Photosynthetic Membranes.

The prospect of coherent dynamics and excitonic delocalization across several light-harvesting structures in photosynthetic membranes is of considerable interest, but challenging to explore experimentally. Here we demonstrate theoretically that the excitonic delocalization across extended domains involving several light-harvesting complexes can lead to unambiguous signatures in the optical response, specifically, linear absorption spectra. We characterize, under experimentally established conditions of molecular assembly and protein-induced inhomogeneities, the optical absorption in these arrays from polarized and unpolarized excitation, and demonstrate that it can be used as a diagnostic tool to determine the resonance coupling between iso-energetic light-harvesting structures. The knowledge of these couplings would then provide further insight into the dynamical properties of transfer, such as facilitating the accurate determination of Förster rates.

Vibronic origin of long-lived coherence in an artificial molecular light harvester.

Natural and artificial light-harvesting processes have recently gained new interest. Signatures of long-lasting coherence in spectroscopic signals of biological systems have been repeatedly observed, albeit their origin is a matter of ongoing debate, as it is unclear how the loss of coherence due to interaction with the noisy environments in such systems is averted. Here we report experimental and theoretical verification of coherent exciton-vibrational (vibronic) coupling as the origin of long-lasting coherence in an artificial light harvester, a molecular J-aggregate. In this macroscopically aligned tubular system, polarization-controlled 2D spectroscopy delivers an uncongested and specific optical response as an ideal foundation for an in-depth theoretical description. We derive analytical expressions that show under which general conditions vibronic coupling leads to prolonged excited-state coherence.

Bloch-Redfield equations for modeling light-harvesting complexes.

We challenge the misconception that Bloch-Redfield equations are a less powerful tool than phenomenological Lindblad equations for modeling exciton transport in photosynthetic complexes. This view predominantly originates from an indiscriminate use of the secular approximation. We provide a detailed description of how to model both coherent oscillations and several types of noise, giving explicit examples. All issues with non-positivity are overcome by a consistent straightforward physical noise model. Herein also lies the strength of the Bloch-Redfield approach because it facilitates the analysis of noise-effects by linking them back to physical parameters of the noise environment. This includes temporal and spatial correlations and the strength and type of interaction between the noise and the system of interest. Finally, we analyze a prototypical dimer system as well as a 7-site Fenna-Matthews-Olson complex in regards to spatial correlation length of the noise, noise strength, temperature, and their connection to the transfer time and transfer probability.

Quantum non-Markovianity: characterization, quantification and detection.

We present a comprehensive and up-to-date review of the concept of quantum non-Markovianity, a central theme in the theory of open quantum systems. We introduce the concept of a quantum Markovian process as a generalization of the classical definition of Markovianity via the so-called divisibility property and relate this notion to the intuitive idea that links non-Markovianity with the persistence of memory effects. A detailed comparison with other definitions presented in the literature is provided. We then discuss several existing proposals to quantify the degree of non-Markovianity of quantum dynamics and to witness non-Markovian behavior, the latter providing sufficient conditions to detect deviations from strict Markovianity. Finally, we conclude by enumerating some timely open problems in the field and provide an outlook on possible research directions.

Wavelet analysis of molecular dynamics: efficient extraction of time-frequency information in ultrafast optical processes.

New experimental techniques based on nonlinear ultrafast spectroscopies have been developed over the last few years, and have been demonstrated to provide powerful probes of quantum dynamics in different types of molecular aggregates, including both natural and artificial light harvesting complexes. Fourier transform-based spectroscopies have been particularly successful, yet "complete" spectral information normally necessitates the loss of all information on the temporal sequence of events in a signal. This information though is particularly important in transient or multi-stage processes, in which the spectral decomposition of the data evolves in time. By going through several examples of ultrafast quantum dynamics, we demonstrate that the use of wavelets provide an efficient and accurate way to simultaneously acquire both temporal and frequency information about a signal, and argue that this greatly aids the elucidation and interpretation of physical process responsible for non-stationary spectroscopic features, such as those encountered in coherent excitonic energy transport.

Exploiting Structured Environments for Efficient Energy Transfer: The Phonon Antenna Mechanism.

A nontrivial interplay between quantum coherence and dissipative environment-driven dynamics is becoming increasingly recognized as the key for efficient energy transport in photosynthetic pigment-protein complexes, and converting these biologically inspired insights into a set of design principles that can be implemented in artificial light-harvesting systems has become an active research field. Here we identify a specific design principle, the phonon antenna, by which interpigment coherence is able to modify and optimize the way that excitations spectrally sample their local environmental fluctuations. We provide numerical simulations that suggest that the Fenna-Matthews-Olson complex of green sulfur bacteria has an excitonic structure that is close to such an optimal operating point, and place the phonon antenna concept into a broader context that leads us to conjecture that this general design principle might well be exploited in other biomolecular systems.