Numerical evidence for robustness of environment-assisted quantum transport.

Recent theoretical studies show that decoherence process can enhance transport efficiency in quantum systems. This effect is known as environment-assisted quantum transport (ENAQT). The role of ENAQT in optimal quantum transport is well investigated; however, it is less known how robust ENAQT is with respect to variations in the system or its environment characteristic. Toward answering this question, we simulated excitonic energy transfer in Fenna-Matthews-Olson photosynthetic complex. We found that ENAQT is robust with respect to many relevant parameters of environmental interactions and Frenkel-exciton Hamiltonians, including reorganization energy, bath-frequency cutoff, temperature, initial excitations, dissipation rate, trapping rate, disorders, and dipole moments orientations. Our study suggests that the ENAQT phenomenon can be exploited in robust design of highly efficient quantum transport systems.

Energy-scales convergence for optimal and robust quantum transport in photosynthetic complexes.

Underlying physical principles for the high efficiency of excitation energy transfer in light-harvesting complexes are not fully understood. Notably, the degree of robustness of these systems for transporting energy is not known considering their realistic interactions with vibrational and radiative environments within the surrounding solvent and scaffold proteins. In this work, we employ an efficient technique to estimate energy transfer efficiency of such complex excitonic systems. We observe that the dynamics of the Fenna-Matthews-Olson (FMO) complex leads to optimal and robust energy transport due to a convergence of energy scales among all important internal and external parameters. In particular, we show that the FMO energy transfer efficiency is optimum and stable with respect to important parameters of environmental interactions including reorganization energy λ, bath frequency cutoff γ, temperature T, and bath spatial correlations. We identify the ratio of kBλT/ℏγ⁢g as a single key parameter governing quantum transport efficiency, where g is the average excitonic energy gap.

Geometrical effects on energy transfer in disordered open quantum systems.

We explore various design principles for efficient excitation energy transport in complex quantum systems. We investigate energy transfer efficiency in randomly disordered geometries consisting of up to 20 chromophores to explore spatial and spectral properties of small natural/artificial Light-Harvesting Complexes (LHC). We find significant statistical correlations among highly efficient random structures with respect to ground state properties, excitonic energy gaps, multichromophoric spatial connectivity, and path strengths. These correlations can even exist beyond the optimal regime of environment-assisted quantum transport. For random configurations embedded in spatial dimensions of 30 Å or 50 Å, we observe that the transport efficiency saturates to its maximum value if the systems contain around 7 or 14 chromophores, respectively. Remarkably, these optimum values coincide with the number of chlorophylls in the Fenna-Matthews-Olson protein complex and LHC II monomers, respectively, suggesting a potential natural optimization with respect to chromophoric density.

Efficient estimation of energy transfer efficiency in light-harvesting complexes.

The fundamental physical mechanisms of energy transfer in photosynthetic complexes is not yet fully understood. In particular, the degree of efficiency or sensitivity of these systems for energy transfer is not known given their realistic with surrounding photonic and phononic environments. One major problem in studying light-harvesting complexes has been the lack of an efficient method for simulation of their dynamics in biological environments. To this end, here we revisit the second order time-convolution (TC2) master equation and examine its reliability beyond extreme Markovian and perturbative limits. In particular, we present a derivation of TC2 without making the usual weak system-bath coupling assumption. Using this equation, we explore the long-time behavior of exciton dynamics of Fenna-Matthews-Olson (FMO) portein complex. Moreover, we introduce a constructive error analysis to estimate the accuracy of TC2 equation in calculating energy transfer efficiency, exhibiting reliable performance for system-bath interactions with weak and intermediate memory and strength. Furthermore, we numerically show that energy transfer efficiency is optimal and robust for the FMO protein complex of green sulfur bacteria with respect to variations in reorganization energy and bath correlation time scales.

Efficient measurement of quantum dynamics via compressive sensing.

The resources required to characterize the dynamics of engineered quantum systems--such as quantum computers and quantum sensors--grow exponentially with system size. Here we adapt techniques from compressive sensing to exponentially reduce the experimental configurations required for quantum process tomography. Our method is applicable to processes that are nearly sparse in a certain basis and can be implemented using only single-body preparations and measurements. We perform efficient, high-fidelity estimation of process matrices of a photonic two-qubit logic gate. The database is obtained under various decoherence strengths. Our technique is both accurate and noise robust, thus removing a key roadblock to the development and scaling of quantum technologies.

Quantum control by means of hamiltonian structure manipulation.

A traditional quantum optimal control experiment begins with a specific physical system and seeks an optimal time-dependent field to steer the evolution towards a target observable value. In a more general framework, the Hamiltonian structure may also be manipulated when the material or molecular 'stockroom' is accessible as a part of the controls. The current work takes a step in this direction by considering the converse of the normal perspective to now start with a specific fixed field and employ the system's time-independent Hamiltonian structure as the control to identify an optimal form. The Hamiltonian structure control variables are taken as the system energies and transition dipole matrix elements. An analysis is presented of the Hamiltonian structure control landscape, defined by the observable as a function of the Hamiltonian structure. A proof of system controllability is provided, showing the existence of a Hamiltonian structure that yields an arbitrary unitary transformation when working with virtually any field. The landscape analysis shows that there are no suboptimal traps (i.e., local extrema) for controllable quantum systems when unconstrained structural controls are utilized to optimize a state-to-state transition probability. This analysis is corroborated by numerical simulations on model multilevel systems. The search effort to reach the top of the Hamiltonian structure landscape is found to be nearly invariant to system dimension. A control mechanism analysis is performed, showing a wide variety of behavior for different systems at the top of the Hamiltonian structure landscape. It is also shown that reducing the number of available Hamiltonian structure controls, thus constraining the system, does not always prevent reaching the landscape top. The results from this work lay a foundation for considering the laboratory implementation of optimal Hamiltonian structure manipulation for seeking the best control performance, especially with limited electromagnetic resources.

Simulating bioremediation of uranium-contaminated aquifers; uncertainty assessment of model parameters.

Bioremediation of trace metals and radionuclides in groundwater may require the manipulation of redox conditions via the injection of a carbon source. For example, after nitrate has been reduced, soluble U(VI) can be reduced simultaneously with other electron acceptors such as Fe(III) or sulfate to U(IV), which may precipitate as a solid (uraninite). To simulate the numerous biogeochemical processes that will occur during the bioremediation of trace-metal-contaminated aquifers, a time-dependent one-dimensional reactive transport model has been developed. The model consists of a set of coupled mass balance equations, accounting for advection, hydrodynamic dispersion, and a kinetic formulation of the biological or chemical transformations affecting an organic substrate, electron acceptors, corresponding reduced species, and trace metal contaminants of interest, uranium in this study. This set of equations is solved numerically, using a finite difference approximation. The redox conditions of the domain are characterized by estimating the pE, based on the concentration of the dominant terminal electron acceptor and its corresponding reduced species. This pE and the concentrations of relevant species are then used by a modified version of MINTEQA2, which calculates the speciation/sorption and precipitation/dissolution of the species of interest under equilibrium conditions. Kinetics of precipitation/dissolution processes are described as being proportional to the difference between the actual and calculated equilibrium concentration. A global uncertainty assessment, determined by Random Sampling High Dimensional Model Representation (RS-HDMR), was performed to attain a phenomenological understanding of the origins of output variability and to suggest input parameter refinements as well as to provide guidance for field experiments to improve the quality of the model predictions. By decomposing the model output variance into its different input contributions, RS-HDMR can identify the model inputs with the most influence on various model outputs, as well as their behavior pattern on the model output. Simulations are performed to illustrate the effect of biostimulation on the fate of uranium in a saturated aquifer, and to identify the key processes that need to be characterized with the highest accuracy prior to designing a uranium bioremediation scheme.

Molecular alignment by trains of short laser pulses.

We show that a dramatic field-free molecular alignment can be achieved after exciting molecules with proper trains of strong ultrashort laser pulses. Optimal two- and three-pulse excitation schemes are defined, providing an efficient and robust molecular alignment. This opens new prospects for various applications requiring macroscopic ensembles of highly aligned molecules.

Phase mixing, induced relaxation, and chaos in one-dimensional dynamical systems.

This paper investigates the mechanism of induced phase mixing, which leads to effective dissipation in classical nonlinear dynamical systems with a fast modulation of the potential. The suggested model can be applied to a classical dynamical description of cold atomic clouds in optical traps. We show that the parametric nonadiabatic modulation of the laser intensity can provide a tool for dynamical control of the effective relaxation in such systems.

Selective bond dissociation and rearrangement with optimally tailored, strong-field laser pulses.

We used strong-field laser pulses that were tailored with closed-loop optimal control to govern specified chemical dissociation and reactivity channels in a series of organic molecules. Selective cleavage and rearrangement of chemical bonds having dissociation energies up to approximately 100 kilocalories per mole (about 4 electron volts) are reported for polyatomic molecules, including (CH3)2CO (acetone), CH3COCF3 (trifluoroacetone), and C6H5COCH3 (acetophenone). Control over the formation of CH(3)CO from (CH3)2CO, CF3 (or CH3) from CH3COCF3, and C6H5CH3 (toluene) from C6H5COCH3 was observed with high selectivity. Strong-field control appears to have generic applicability for manipulating molecular reactivity because the tailored intense laser fields (about 10(13) watts per square centimeter) can dynamically Stark shift many excited states into resonance, and consequently, the method is not confined by resonant spectral restrictions found in the perturbative (weak-field) regime.

Solution of the quantum fluid dynamical equations with radial basis function interpolation

The paper proposes a numerical technique within the Lagrangian description for propagating the quantum fluid dynamical (QFD) equations in terms of the Madelung field variables R and S, which are connected to the wave function via the transformation psi = exp(R + iS)/[symbol: see text]. The technique rests on the QFD equations depending only on the form, not the magnitude, of the probability density rho = magnitude of psi 2 and on the structure of R = [symbol: see text]/2 ln rho generally being simpler and smoother than rho. The spatially smooth functions R and S are especially suitable for multivariate radial basis function interpolation to enable the implementation of a robust numerical scheme. Examples of two-dimensional model systems show that the method rivals, in both efficiency and accuracy, the split-operator and Chebychev expansion methods. The results on a three-dimensional model system indicates that the present method is superior to the existing ones, especially, for its low storage requirement and its uniform accuracy. The advantage of the new algorithm is expected to increase for higher dimensional systems to provide a practical computational tool.

Solving the bound-state Schrodinger equation by reproducing kernel interpolation

Based on reproducing kernel Hilbert space theory and radial basis approximation theory, a grid method is developed for numerically solving the N-dimensional bound-state Schrodinger equation. Central to the method is the construction of an appropriate bounded reproducing kernel (RK) Lambda(alpha)( ||r ||) from the linear operator -nabla(2)(r)+lambda(2) where nabla(2)(r) is the N-dimensional Laplacian, lambda>0 is a parameter related to the binding energy of the system under study, and the real number alpha>N. The proposed (Sobolev) RK Lambda(alpha)(r,r(')) is shown to be a positive-definite radial basis function, and it matches the asymptotic solutions of the bound-state Schrodinger equation. Numerical tests for the one-dimensional (1D) Morse potential and 2D Henon-Heiles potential reveal that the method can accurately and efficiently yield all the energy levels up to the dissociation limit. Comparisons are also made with the results based on the distributed Gaussian basis method in the 1D case as well as the distributed approximating functional method in both 1D and 2D cases.

Optimal control of molecular motion: design, implementation, and inversion.

This paper reviews recent theoretical and experimental developments aimed at controlling molecular motion using tailored laser fields. Emphasis is given to seeking optimal designs for the laser controls and optimal implementation of the controls in the laboratory. Optimization on both counts provides a rigorous, flexible, and physically attractive means for obtaining the best possible control over molecular motion under any specified conditions. The theoretical design and laboratory implementation of control are best effected by a closed-loop process that draws on observations of the evolving molecular sample to steer it toward the desired target. Going beyond control, similar closed-loop laboratory learning concepts may lead to automated molecular monitors for inversion to systematically identify details of molecular Hamiltonians.

Whither the future of controlling quantum phenomena?

This review puts into perspective the present state and prospects for controlling quantum phenomena in atoms and molecules. The topics considered include the nature of physical and chemical control objectives, the development of possible quantum control rules of thumb, the theoretical design of controls and their laboratory realization, quantum learning and feedback control in the laboratory, bulk media influences, and the ability to utilize coherent quantum manipulation as a means for extracting microscopic information. The preview of the field presented here suggests that important advances in the control of molecules and the capability of learning about molecular interactions may be reached through the application of emerging theoretical concepts and laboratory technologies.

Constructing multidimensional molecular potential energy surfaces from ab initio data.

This paper describes the reproducing kernel Hilbert space (RKHS) method for constructing accurate, smooth, and efficient global potential energy surface (PES) representations for polyatomic systems using high-level ab initio data. The RKHS method provides a rigorous and effective framework for smooth multivariate interpolation of arbitrarily scattered data points and also for incorporating various physical requirements onto the PESs. Smoothness, permutation symmetry, and the asymptotic properties of polyatomic systems can be incorporated into the construction of reproducing kernels to render globally accurate PESs. Tensor products of one-dimensional generalized-spline-reproducing kernels are amenable to a fast algorithm, which makes a single evaluation of RKHS PESs essentially independent of the number of interpolated ab initio data points. This efficient implementation enables the study of the detailed dynamics of polyatomic systems based on high-quality RKHS PESs.

Simulating energy flow in biomolecules: application to tuna cytochrome c.

By constructing a continuity equation of energy flow, one can utilize results from a molecular dynamics simulation to calculate the energy flux or flow in different parts of a biomolecule. Such calculations can yield useful insights into the pathways of energy flow in biomolecules. The method was first tested on a small system of a cluster of 13 argon atoms and then applied to the study of the pathways of energy flow after a tuna ferrocytochrome c molecule was oxidized. Initially, energy propagated faster along the direction perpendicular to the heme plane. This was due to an efficient through-bond mechanism, because the heme iron in cytochrome c was covalently bonded to a cysteine and a histidine. For the oxidation of cytochrome c, electrostatic interactions also facilitated a long-range through-space mechanism of energy flow. As a result, polar or charged groups that were further away from the oxidation site could receive energy earlier than nonpolar groups closer to the site. Another bridging mechanism facilitating efficient long-range responses to cytochrome c oxidation involved the coupling of far-off atoms with atoms that were nearer to, and interacted directly with, the oxidation site. The different characteristics of these energy transfer mechanisms defied a simple correlation between the time that the excess energy of the oxidation site first dissipated to an atom and the distance of the atom from the oxidation site. For tuna cytochrome c, all of the atoms of the protein had sensed the effects of the oxidation within approximately 40 fs. For the length scale of energy transfer considered in this study, the speed of the energy propagation in the protein was on the order of 10(5) m/s.

Configurational disorder and the local field effects in nonlinear optical systems.

We argue that in nonlinear optical systems with atoms randomly distributed in crystals or amorphous hosts one should go beyond the Clausius-Mossoti limit in order to take into account the effect of local eld uctuations induced by congurational disorder in atom position. This eect is analyzed by means of a random local mean field approach with neglect of correlations between dipole moments of different atoms. The formalism is applied to 3-level type systems with quantum coherence possessing an absorptionless index of refraction and lasing without inversion. We show that the eect of congurational fluctuations results in the suppression of the atom susceptibility compared with the predictions based on the Clausious-Mossoti equation.