Quasi-Bell inequalities from symmetrized products of noncommuting qubit observables

Noncommuting observables cannot be simultaneously measured, however, under local hidden variable models, they must simultaneously hold premeasurement values, implying the existence of a joint probability distribution. We study the joint distributions of noncommuting observables on qubits, with possible criteria of positivity and the Fr\'echet bounds limiting the joint probabilities, concluding that the latter may be negative. We use symmetrization, justified heuristically and then more carefully via the Moyal characteristic function, to find the quantum operator corresponding to the product of noncommuting observables. This is then used to construct Quasi-Bell inequalities, Bell inequalities containing products of noncommuting observables, on two qubits. These inequalities place limits on local hidden variable models that define joint probabilities for noncommuting observables. We find Quasi-Bell inequalities have a quantum to classical violation as high as $\frac{3}{2}$, higher than conventional Bell inequalities. The result demonstrates the theoretical importance of noncommutativity in the nonlocality of quantum mechanics, and provides an insightful generalization of Bell inequalities.Comment: 17 page

Influences of quantum mechanically mixed electronic and vibrational pigment states in 2D electronic spectra of photosynthetic systems: Strong electronic coupling cases

In 2D electronic spectroscopy studies, long-lived quantum beats have recently been observed in photosynthetic systems, and it has been suggested that the beats are produced by quantum mechanically mixed electronic and vibrational states. Concerning the electronic-vibrational quantum mixtures, the impact of protein-induced fluctuations was examined by calculating the 2D electronic spectra of a weakly coupled dimer with vibrational modes in the resonant condition [J. Chem. Phys. 142, 212403 (2015)]. This analysis demonstrated that quantum mixtures of the vibronic resonance are rather robust under the influence of the fluctuations at cryogenic temperatures, whereas the mixtures are eradicated by the fluctuations at physiological temperatures. However, this conclusion cannot be generalized because the magnitude of the coupling inducing the quantum mixtures is proportional to the inter-pigment coupling. In this study, we explore the impact of the fluctuations on electronic-vibrational quantum mixtures in a strongly coupled dimer. with an off-resonant vibrational mode. Toward this end, we calculate electronic energy transfer (EET) dynamics and 2D electronic spectra of a dimer that corresponds to the most strongly coupled bacteriochlorophyll molecules in the Fenna-Matthews-Olson complex in a numerically accurate manner. The quantum mixtures are found to be robust under the exposure of protein-induced fluctuations at cryogenic temperatures, irrespective of the resonance. At 300 K, however, the quantum mixing is disturbed more strongly by the fluctuations, and therefore, the beats in the 2D spectra become obscure even in a strongly coupled dimer with a resonant vibrational mode. Further, the overall behaviors of the EET dynamics are demonstrated to be dominated by the environment and coupling between the 0-0 vibronic transitions as long as the Huang-Rhys factor of the vibrational mode is small.Comment: 20 pages, 4 figures. arXiv admin note: text overlap with arXiv:1505.0528

Energy-dependent quenching adjusts the excitation diffusion length to regulate photosynthetic light harvesting

An important determinant of crop yields is the regulation of photosystem II (PSII) light harvesting by energy-dependent quenching (qE). However, the molecular details of excitation quenching have not been quantitatively connected to the PSII yield, which only emerges on the 100 nm scale of the grana membrane and determines flux to downstream metabolism. Here, we incorporate excitation dissipation by qE into a pigment-scale model of excitation transfer and trapping for a 200 nm x 200 nm patch of the grana membrane. We demonstrate that single molecule measurements of qE are consistent with a weak-quenching regime. Consequently, excitation transport can be rigorously coarse-grained to a 2D random walk with an excitation diffusion length determined by the extent of quenching. A diffusion-corrected lake model substantially improves the PSII yield determined from variable chlorophyll fluorescence measurements and offers an improved model of PSII for photosynthetic metabolism.Comment: 19 pages, 4 figures, 3 supplementary figure

Models and measurements of energy-dependent quenching.

Energy-dependent quenching (qE) in photosystem II (PSII) is a pH-dependent response that enables plants to regulate light harvesting in response to rapid fluctuations in light intensity. In this review, we aim to provide a physical picture for understanding the interplay between the triggering of qE by a pH gradient across the thylakoid membrane and subsequent changes in PSII. We discuss how these changes alter the energy transfer network of chlorophyll in the grana membrane and allow it to switch between an unquenched and quenched state. Within this conceptual framework, we describe the biochemical and spectroscopic measurements and models that have been used to understand the mechanism of qE in plants with a focus on measurements of samples that perform qE in response to light. In addition, we address the outstanding questions and challenges in the field. One of the current challenges in gaining a full understanding of qE is the difficulty in simultaneously measuring both the photophysical mechanism of quenching and the physiological state of the thylakoid membrane. We suggest that new experimental and modeling efforts that can monitor the many processes that occur on multiple timescales and length scales will be important for elucidating the quantitative details of the mechanism of qE

Coherent exciton dynamics in the presence of underdamped vibrations

Recent ultrafast optical experiments show that excitons in large biological light-harvesting complexes are coupled to molecular vibration modes. These high-frequency vibrations will not only affect the optical response, but also drive the exciton transport. Here, using a model dimer system, the frequency of the underdamped vibration is shown to have a strong effect on the exciton dynamics such that quantum coherent oscillations in the system can be present even in the case of strong noise. Two mechanisms are identified to be responsible for the enhanced transport efficiency: critical damping due to the tunable effective strength of the coupling to the bath, and resonance coupling where the vibrational frequency coincides with the energy gap in the system. The interplay of these two mechanisms determines parameters responsible for the most efficient transport, and these optimal control parameters are comparable to those in realistic light-harvesting complexes. Interestingly, oscillations in the excitonic coherence at resonance are suppressed in comparison to the case of an off-resonant vibration

Insights into photosynthetic energy transfer gained from free-energy structure: Coherent transport, incoherent hopping, and vibrational assistance revisited

Giant strides in ultrashort laser pulse technology have enabled real-time observation of dynamical processes in complex molecular systems. Specifically, the discovery of oscillatory transients in the two-dimensional electronic spectra of photosynthetic systems stimulated a number of theoretical investigations exploring possible physical mechanisms of the remarkable quantum efficiency of light harvesting processes. However, the theories employed have reached a high degree of sophistication and have become complex, making it difficult to gain insights into microscopic processes and biologically significant questions. In this work, we revisit the elementary aspects of environment-induced fluctuations in the involved electronic energies and present a simple way to understand energy flow with the intuitive picture of relaxation in a funnel-type free-energy landscape. The presented free-energy description of energy transfer reveals that typical photosynthetic systems operate in an almost barrierless regime. The approach also provides insights into the distinction between coherent and incoherent energy transfer and criteria by which the necessity of the vibrational assistance is considered

Competition between Energy and Phase Relaxation in Electronic Curve Cross- ing Processes

We present results from simulations of vibrational energy and phase relaxation and electronic curve crossing using a multilevel formulation of Redfield theory, which demonstrate the shortcomings of the optical Bloch approximation and the importance of coherence transfer processes in the relaxation dynamics of multilevel systems. Specifically, we show that for a harmonic well, energy relaxation can occur with retention of vibrational phase, and that for sufficiently strong electronic coupling, the product of an electronic curve crossing process can be formed vibrationally coherent even when no coherence is present in the initially excited state

Solvation Dynamics in Protein Environments Studied by Photon Echo Spectroscopy

Photon echo spectroscopy is used to study the mechanisms of solvation dynamics in protein environments at room temperature. Ultrafast and additional multi-exponential long time scales are observed in the three-pulse photon echo peak shift data of the fluorescein dye eosin bound to lysozyme in aqueous solution. The dynamics of the solvated lysozyme are characterized with dielectric continuum models that integrate dielectric data for water with that for lysozyme. By comparing our data with previous results for eosin in water [Lang, M. J.; Jordanides, X. J.; Song, X.; Fleming, G. R. J. Chem. Phys. 1999, 110, 5584], we find that the total coupling of the electronic transition frequency of eosin to the nuclear motions of the aqueous lysozyme solution is smaller than in the aqueous solution. On an ultrafast time scale, solvation appears to be dominated by the surrounding water and not by the ultrafast internal motions of lysozyme. However, over long time scales, lysozyme does contribute significantly, either directly through motions of polar side chains or indirectly through reorientation of the water “bound” to the surface of the protein