Decoherence in an anharmonic oscillator coupled to a thermal environment: a semiclassical forward-backward approach

The decoherence of an anharmonic oscillator in a thermal harmonic bath is examined via a semiclassical approach. A computational strategy is presented and exploited to calculate the time dependence of the purity and the decay of individual matrix elements in the energy representation for a variety of initial states. The time dependence of the decoherence is found to depend on the temperature of the bath, the coupling strength, the initial state of the oscillator, and the choice of quantity measuring the decoherence. Recurrences in the purity and in the off-diagonal matrix elements are observed, as well as the collapse of these matrix elements to the diagonal, providing evidence for the retention of quantum coherence for time scales longer than that indicated by the purity. The results are used to analyze the utility of the Caldeira-Leggett and Redfield models of decoherence and to assess the dependence of dephasing rates on the degree of structure in phase space. In several cases we find that the dephasing dynamics can be described as an initial Zeno-effect regime, followed by a Caldeira-Leggett region, followed by recurrences.     

A new NMR method for determining the particle thickness in nanocomposites, using T2,H-selective X{1H} recoupling

A new nuclear magnetic resonance approach for characterizing the thickness of phosphate, silicate, carbonate, and other nanoparticles in organic-inorganic nanocomposites is presented. The particle thickness is probed using the strongly distant-dependent dipolar couplings between the abundant protons in the organic phase and X nuclei (31P, 29Si, 13C, 27Al, 23Na, etc.) in the inorganic phase. This approach requires pulse sequences with heteronuclear dephasing only by the polymer or surface protons that experience strong homonuclear interactions, but not by dispersed OH or water protons in the inorganic phase, which have long transverse relaxation times T2,H. This goal is achieved by heteronuclear recoupling with dephasing by strong homonuclear interactions of protons (HARDSHIP). The pulse sequence alternates heteronuclear recoupling for approximately 0.15 ms with periods of homonuclear dipolar dephasing that are flanked by canceling 90 degrees pulses. The heteronuclear evolution of the long-T2,H protons is refocused within two recoupling periods, so that 1H spin diffusion cannot significantly dephase these coherences. For the short-T2,H protons of a relatively immobile organic matrix, the heteronuclear dephasing rate depends simply on the heteronuclear second moment. Homonuclear interactions do not affect the dephasing, even though no homonuclear decoupling is applied, because long-range 1H-X dipolar couplings approximately commute with short-range 1H-1H couplings, and heteronuclear recoupling periods are relatively short. This is shown in a detailed analysis based on interaction representations. The algorithm for simulating the dephasing data is described. The new method is demonstrated on a clay-polymer nanocomposite, diamond nanocrystals with protonated surfaces, and the bioapatite-collagen nanocomposite in bone, as well as pure clay and hydroxyapatite. The diameters of the nanoparticles in these materials range between 1 and 5 nm. Simulations show that spherical particles of up to 10 nm diameter can be characterized quite easily.     

Intramolecular energy transfer in water

The evolution of the vibrational motion of a water molecule which has been excited locally is studied. An exact solution is obtained of a model Hamiltonian representing the non-harmonic behaviour of the molecule. Since this is obtained numerically it does not explain what is observed but it leads to a simplified model of the motion in which different aspects can be isolated and discussed. For many initial modes, especially those of higher energy, there is a large initial drop in the probability of finding the energy in the original local mode. This is due to dephasing. The factors involved in dephasing are discussed. A simple hypothesis is suggested which leads to a formula for this drop and this agrees substantially with the graphical evidence. The relation between the drop and the amplitude of the initial mode is also discussed.     

Pure optical dephasing dynamics in semiconducting single-walled carbon nanotubes

We report a detailed study of ultrafast exciton dephasing processes in semiconducting single-walled carbon nanotubes employing a sample highly enriched in a single tube species, the (6,5) tube. Systematic measurements of femtosecond pump-probe, two-pulse photon echo, and three-pulse photon echo peak shift over a broad range of excitation intensities and lattice temperature (from 4.4 to 292 K) enable us to quantify the timescales of pure optical dephasing (T(2)(*)), along with exciton-exciton and exciton-phonon scattering, environmental effects as well as spectral diffusion. While the exciton dephasing time (T(2)) increases from 205 fs at room temperature to 320 fs at 70 K, we found that further decrease of the lattice temperature leads to a shortening of the T(2) times. This complex temperature dependence was found to arise from an enhanced relaxation of exciton population at lattice temperatures below 80 K. By quantitatively accounting the contribution from the population relaxation, the corresponding pure optical dephasing times increase monotonically from 225 fs at room temperature to 508 fs at 4.4 K. We further found that below 180 K, the pure dephasing rate (1/T(2)(*)) scales linearly with temperature with a slope of 6.7 ± 0.6 μeV/K, which suggests dephasing arising from one-phonon scattering (i.e., acoustic phonons). In view of the large dynamic disorder of the surrounding environment, the origin of the long room temperature pure dephasing time is proposed to result from reduced strength of exciton-phonon coupling by motional narrowing over nuclear fluctuations. This consideration further suggests the occurrence of remarkable initial exciton delocalization and makes nanotubes ideal to study many-body effects in spatially confined systems.     

Semiclassical initial value series solution of the spin boson problem

A numerical solution for the quantum dynamics of the spin boson problem is obtained using the semiclassical initial value series representation approach to the quantum dynamics. The zeroth order term of the series is computed using the new forward-backward representation for correlation functions presented in the preceding adjacent paper. This leads to a rapid convergence of the Monte Carlo sampling, as compared to previous attempts. The zeroth order results are already quite accurate. The first order term of the series is small, demonstrating the rapid convergence of the semiclassical initial value representation series. This is the first time that the first order term in the semiclassical initial value representation series has been converged for systems with the order of 50 degrees of freedom.     

Vibrational dephasing and energy relaxation of admolecules by phonons

An investigation is made of the vibrational dephasing of a diatomic molecule adsorbed on a surface. Explicit analytic forms for the rate of dephasing by phonons are derived. For comparison, an expression for energy relaxation is given which is appropriate for OH on SiO₂. It is found that the dephasing rate is considerably faster for this system than the energy relaxation rate. These conclusions are compared with the results of a recent experiment.     

Single-Shot Gas-Phase Thermometry by Time-to-Frequency Mapping of Coherence Dephasing

We demonstrate a single-beam coherent anti-Stokes Raman scattering (CARS) technique for gas-phase thermometry that assesses the species-specific local gas temperature by single-shot time-to-frequency mapping of Raman-coherence dephasing. The proof-of-principle experiments are performed with air in a temperature-controlled gas cell. Impulsive excitation of molecular vibrations by an ultrashort pump/Stokes pulse is followed by multipulse probing of the 2330 cm(-1) Raman transition of N(2). This sequence of colored probe pulses, delayed in time with respect to each other and corresponding to three isolated spectral bands, imprints the coherence dephasing onto the measured CARS spectrum. For calibration purposes, the dephasing rates are recorded at various gas temperatures, and the relationship is fitted to a linear regression. The calibration data are then used to determine the gas temperature and are shown to provide better than 15 K accuracy. The described approach is insensitive to pulse energy fluctuations and can, in principle, gauge the temperature of multiple chemical species in a single laser shot, which is deemed particularly valuable for temperature profiling of reacting flows in gas-turbine combustors.     

Using the local elevation method to construct optimized umbrella sampling potentials: Calculation of the relative free energies and interconversion barriers of glucopyranose ring conformers in water

A method is proposed to combine the local elevation (LE) conformational searching and the umbrella sampling (US) conformational sampling approaches into a single local elevation umbrella sampling (LEUS) scheme for (explicit‐solvent) molecular dynamics (MD) simulations. In this approach, an initial (relatively short) LE build‐up (searching) phase is used to construct an optimized biasing potential within a subspace of conformationally relevant degrees of freedom, that is then used in a (comparatively longer) US sampling phase. This scheme dramatically enhances (in comparison with plain MD) the sampling power of MD simulations, taking advantage of the fact that the preoptimized biasing potential represents a reasonable approximation to the negative of the free energy surface in the considered conformational subspace. The method is applied to the calculation of the relative free energies of β‐D ‐glucopyranose ring conformers in water (within the GROMOS 45A4 force field). Different schemes to assign sampled conformational regions to distinct states are also compared. This approach, which bears some analogies with adaptive umbrella sampling and metadynamics (but within a very distinct implementation), is shown to be: (i) efficient (nearly all the computational effort is invested in the actual sampling phase rather than in searching and equilibration); (ii) robust (the method is only weakly sensitive to the details of the build‐up protocol, even for relatively short build‐up times); (iii) versatile (a LEUS biasing potential database could easily be preoptimized for small molecules and assembled on a fragment basis for larger ones). © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Measurement of 13C-1H dipolar couplings in solids by using ultra-fast magic-angle spinning NMR spectroscopy with symmetry-based sequences

We show that (13)C-(1)H dipolar couplings in fully protonated organic solids can be measured by applying a Symmetry-based Resonance-Echo DOuble-Resonance (S-REDOR) experiment at ultra-fast Magic-Angle Spinning (MAS). The (13)C-(1)H dipolar couplings are recovered by using the R12 recoupling scheme, while the interference of (1)H-(1)H dipolar couplings are suppressed by the symmetry properties of this sequence and the use of high MAS frequency (65 kHz). The R12 method is especially advantageous for large (13)C-(1)H dipolar interactions, since the dipolar recoupling time can be incremented by steps as short as one rotor period. This allows a fine sampling for the rising part of the dipolar dephasing curve. We demonstrate experimentally that one-bond (13)C-(1)H dipolar coupling in the order of 22 kHz can be accurately determined. Furthermore, the proposed method allows a rapid evaluation of the dipolar coupling by fitting the S-REDOR dipolar dephasing curve with an analytical expression.     

Homogeneity and Markovity of electronic dephasing in liquid solutions

The electronic dephasing dynamics of a solvated chromophore is formulated in terms of a non-Markovian master equation. Within this formulation, one describes the effect of the nuclear degrees of freedom on the electronic degrees of freedom in terms of a memory kernel function, which is explicitly dependent on the initial solvent configuration. In the case of homogeneous dynamics, this memory kernel becomes independent of the initial configuration. The Markovity of the dephasing process is also the most conveniently explored by comparing the results obtained via the non-Markovian master equation to these obtained via its Markovian counterpart. The homogeneous memory kernel is calculated for a two-state chromophore in liquid solution, and used to explore the sensitivity of photon echo signals to the heterogeneity and non-Markovity of the underlying solvation dynamics.     

Communication: Time-domain measurement of high-pressure N2 and O2 self-broadened linewidths using hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering

The direct measurement of self-broadened linewidths using the time decay of pure-rotational hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering (fs/ps RCARS) signals is demonstrated in gas-phase N(2) and O(2) from 1-20 atm. Using fs pump and Stokes pulses and a spectrally narrowed ps probe pulse, collisional dephasing rates with time constants as short as 2.5 ps are captured with high accuracy for individual rotational transitions. S-branch linewidths of N(2) and O(2) from ~0.06 to 2.2 cm(-1) and the line separation of O(2) triplet states are obtained from the measured dephasing rates and compared with high-resolution, frequency-domain measurements and S-branch approximations using the modified exponential gap model. The accuracy of the current measurements suggests that the fs/ps RCARS approach is well suited for tracking the collisional dynamics of gas-phase mixtures over a wide range of pressures.     

On the orientational dependence of resolution in 1H solid-state NMR, and its role in MAS, CRAMPS and delayed-acquisition experiments

Numerical simulations and experiments are used to show that the spin dynamics of the dipolar-coupled networks in solids is often strongly dependent on crystallite orientation. In particular, different rates of dephasing of the magnetisation mean that NMR signals obtained at longer dephasing times are dominated by orientations in which the local dipolar coupling strength is relatively weak. This often leads to a distinct improvement in spectral resolution as the dephasing time is increased. The effects are particularly noticeable under magic-angle spinning (MAS), but are also observed when homonuclear decoupling is used to reduce the rate of dipolar dephasing. Numerical simulation is seen to be a powerful and easily used tool for understanding the behaviour of solid-state NMR experiments involving dipolar-coupled networks. The implications for solid-state NMR spectra of abundant spins acquired under MAS and homonuclear decoupling are discussed, as well as insights provided into the performance of 'delayed-acquisition' and 'constant-time' experiments.     

Ultrafast dynamics of myoglobin without the distal histidine: stimulated vibrational echo experiments and molecular dynamics simulations

Ultrafast protein dynamics of the CO adduct of a myoglobin mutant with the polar distal histidine replaced by a nonpolar valine (H64V) have been investigated by spectrally resolved infrared stimulated vibrational echo experiments and molecular dynamics (MD) simulations. In aqueous solution at room temperature, the vibrational dephasing rate of CO in the mutant is reduced by approximately 50% relative to the native protein. This finding confirms that the dephasing of the CO vibration in the native protein is sensitive to the interaction between the ligand and the distal histidine. The stimulated vibrational echo observable is calculated from MD simulations of H64V within a model in which vibrational dephasing is driven by electrostatic forces. In agreement with experiment, calculated vibrational echoes show slower dephasing for the mutant than for the native protein. However, vibrational echoes calculated for H64V do not show the quantitative agreement with measurements demonstrated previously for the native protein.     

Two-dimensional spectroscopy can distinguish between decoherence and dephasing of zero-quantum coherences

Recent experiments on a variety of photosynthetic antenna systems have revealed that coherences among electronic states persist longer than previously anticipated. In an ensemble measurement, the observed dephasing of a coherent state can occur because of either disorder across the ensemble or decoherence from interactions with the bath. Distinguishing how much such disorder affects the experimentally observed dephasing rate is paramount for understanding the role that quantum coherence may play in energy transfer through these complexes. Here, we show that two-dimensional electronic spectra can distinguish between the limiting cases of homogeneous dephasing (decoherence) and inhomogeneous dephasing by examining how the quantum beat frequency changes within a cross peak. For the antenna complex LH2 isolated from Rhodobacter sphaeroides , we find that dephasing of the coherence between the B850 and B800 rings arises predominantly from inhomogeneity. In contrast, within the Fenna-Matthews-Olson (FMO) complex from Chlorobium tepidum , dephasing of the coherence between the first two excitons appears quite homogeneous. Thus, the observed dephasing rate sets an upper bound on decoherence for the LH2 complex while establishing both an upper and lower bound for the FMO complex.     

A canonical averaging in the second-order quantized Hamilton dynamics

Quantized Hamilton dynamics (QHD) is a simple and elegant extension of classical Hamilton dynamics that accurately includes zero-point energy, tunneling, dephasing, and other quantum effects. Formulated as a hierarchy of approximations to exact quantum dynamics in the Heisenberg formulation, QHD has been used to study evolution of observables subject to a single initial condition. In present, we develop a practical solution for generating canonical ensembles in the second-order QHD for position and momentum operators, which can be mapped onto classical phase space in doubled dimensionality and which in certain limits is equivalent to thawed Gaussian. We define a thermal distribution in the space of the QHD-2 variables and show that the standard beta=1/kT relationship becomes beta'=2/kT in the high temperature limit due to an overcounting of states in the extended phase space, and a more complicated function at low temperatures. The QHD thermal distribution is used to compute total energy, kinetic energy, heat capacity, and other canonical averages for a series of quartic potentials, showing good agreement with the quantum results.     

Time-resolved coherent anti-Stokes Raman-scattering measurements of I2 in solid Kr: vibrational dephasing on the ground electronic state at 2.6-32 K

Time-resolved coherent anti-Stokes Raman-scattering (CARS) measurements are carried out for iodine (I2) in solid krypton matrices. The dependence of vibrational dephasing time on temperature and vibrational quantum number v is studied. The v dependence is approximately quadratic, while the temperature dependence of both vibrational dephasing and spectral shift, although weak, fits the exponential form characteristic of dephasing by pseudolocal phonons. The analysis of the data indicates that the frequency of the pseudolocal phonons is approximately 30 cm(-1). The longest dephasing times are observed for v = 2 being approximately 300 ps and limited by inhomogeneous broadening. An increase in the dephasing rate of v = 2 as the temperature is lowered to T = 2.6 K is taken as a clear indication of lattice-strain-induced inhomogeneity of the ensemble coherence.     

The Hund paradox and stabilization of molecular chiral states

The “paradox of optical isomers” revealed by Hund in 1927 is re-examined taking into account the interaction of a chiral molecule with phonons of optically inactive solids below the Debye temperature θ_D. It has been shown, that in the strong coupling limit, where the dephasing rate is much higher than the energy splitting frequency, the interaction can lead to a complete loss of coherence between mirror-antipodal states of the molecule due to the phonon-induced dephasing. This, in turn, suppresses tunnelling oscillations between them, so that transitions, which are reversible in time for an isolated chiral molecule become irreversible for the same molecule placed in a low-temperature matrix. In order to propose a particular mechanism of such stabilization, contributions of a single- and multi-phonon processes in the dephasing rate have been evaluated. It has been established that only the two-phonon scattering provides the sufficiently strong dephasing in low-temperature solids. Such a two-phonon mechanism is responsible for the stabilization of molecular chiral states as long as the temperature of the medium is lower θ_D, but exceeds a few Kelvin degrees. These findings are discussed in the context of the evolutionary concept known as “the cold prehistory of life”.     

Geometric constraints in semiclassical initial value representation calculations in Cartesian coordinates: accurate reduction in zero-point energy

An approach for the inclusion of geometric constraints in semiclassical initial value representation calculations is introduced. An important aspect of the approach is that Cartesian coordinates are used throughout. We devised an algorithm for the constrained sampling of initial conditions through the use of multivariate Gaussian distribution based on a projected Hessian. We also propose an approach for the constrained evaluation of the so-called Herman-Kluk prefactor in its exact log-derivative form. Sample calculations are performed for free and constrained rare-gas trimers. The results show that the proposed approach provides an accurate evaluation of the reduction in zero-point energy. Exact basis set calculations are used to assess the accuracy of the semiclassical results. Since Cartesian coordinates are used, the approach is general and applicable to a variety of molecular and atomic systems.