Incoherent Limits Research Articles

Matrix-based integral transformations for Stokes imaging with partially polarized and partially coherent light

With the aid of the matrix-based integral transforms called matrix convolution and matrix direct correlation, we provide a simplified expression for the space- and frequency-domain calculations of polarization imaging with partially polarized and partially coherent light. As an example of practical interest, a formula for Stokes imaging, based on the generalized Stokes parameters, is presented, in which a hypermatrix-based transmission cross-coefficient matrix is introduced to represent the combined effects of diffraction and aberrations of a polarization-dependent imaging system and a partially polarized, partially coherent illumination system. The coherent and incoherent limits in Stokes imaging are discussed with the optical transfer matrix, along with its frequency response for a diffraction-limited incoherent polarization imaging system. A generalized concept of the apparent transfer matrix is introduced to deal with the nonlinearity inherent in the polarization imaging system under partially coherent illumination.

Perfect Absorption by an Atomically Thin Crystal

Optical absorption is one of fundamental light-matter interactions. In most materials, optical absorption is a weak perturbation to the light. In this regime, absorption and emission are irreversible, incoherent processes due to strong damping. Excitons in monolayer transition metal dichalcogenides, however, interact strongly with light, leading to optical absorption in the non-perturbative regime where coherent re-emission of the light has to be considered. Between the incoherent and coherent limits, we show that a robust critical coupling condition exists, leading to perfect optical absorption. Up to 99.6% absorption is measured in a sub-nanometer thick MoSe2 monolayer placed in front of a mirror. The perfect absorption is controlled by tuning the exciton-phonon, exciton-exciton, and exciton-photon interactions by temperature, pulsed laser excitation, and a movable mirror, respectively. Our work suggests unprecedented opportunities for engineering exciton-light interactions using two-dimensional atomically thin crystals, enabling novel photonic applications including ultrafast light modulators and sensitive optical sensing.

Silicon qubit fidelities approaching incoherent noise limits via pulse engineering

The performance requirements for fault-tolerant quantum computing are very stringent. Qubits must be manipulated, coupled, and measured with error rates well below 1%. For semiconductor implementations, silicon quantum dot spin qubits have demonstrated average single-qubit Clifford gate error rates that approach this threshold, notably with error rates of 0.14% in isotopically enriched $^{28}$Si/SiGe devices. This gate performance, together with high-fidelity two-qubit gates and measurements, is only known to meet the threshold for fault-tolerant quantum computing in some architectures when assuming that the noise is incoherent, and still lower error rates are needed to reduce overhead. Here we experimentally show that pulse engineering techniques, widely used in magnetic resonance, improve average Clifford gate error rates for silicon quantum dot spin qubits to 0.043%,a factor of 3 improvement on previous best results for silicon quantum dot devices. By including tomographically complete measurements in randomised benchmarking, we infer a higher-order feature of the noise called the unitarity, which measures the coherence of noise. This in turn allows us to theoretically predict that average gate error rates as low as 0.026% may be achievable with further pulse improvements. These fidelities are ultimately limited by Markovian noise, which we attribute to charge noise emanating from the silicon device structure itself, or the environment.

Interference between initial and final state radiation in a QCD medium

We investigate the color coherence pattern between initial and final state radiation in the presence of a QCD medium. We derive the medium-induced gluon spectrum of an “asymptotic” parton which suffers a hard scattering and subsequently crosses the medium. The angular distribution of the induced gluon spectrum is modified when one includes interference terms between the incoming and the outgoing parton at finite angle between them. The coherent, incoherent and soft limits of the medium-induced gluon spectrum are studied. In the soft limit, we provide a simple and intuitive probabilistic picture which could be of interest for Monte Carlo implementations. The configuration studied here may have phenomenological consequences in high-energy nuclear collisions.

Near infrared ex-vivo bovine and computer model thresholds for laser-induced retinal damage

AbstractThresholds for thermal damage of the retina were determined with excised bovine eyes and a computer model for 1090 nm laser radiation in the applicable pulse duration regime and for varying retinal laser spot diameters. The thresholds compare well with available rhesus monkey data, further validating the models for absolute threshold predictions and parameter studies including in the near infrared (NIR) range up to about 1340 nm. The variation of the spot size dependence for different pulse durations that was found in an earlier study for the wavelength of 532 nm was confirmed, which supports the proposed amendment of ICNIRP, ANSI and IEC laser and incoherent optical radiation exposure limits. The earlier conclusion that the damage mechanism at threshold determined 24 h and 1 h after exposure for the non-human primate (NHP) model is retinal pigment epithelium (RPE) cell damage and not thermal coagulation of the sensory retina was confirmed. The data in the NIR range indicate that scattering within the RPE and choroid does not significantly enlarge the effective spot size, and that the rhesus monkey minimal spot

Shared-mode assisted resonant energy transfer in the weak coupling regime

Recent work has suggested that correlations in the environments of chromophores can lead to a change in the dynamics of excitation transfer in both the coherent and incoherent limits. An example of this effect that is relevant to many single molecule experiments occurs in the standard Forster model for resonant energy transfer (RET). The standard formula for the FRET rate breaks down when the electronic excitations on weakly interacting donor and acceptor couple to the same vibrational modes. The transfer rate can then no longer be factored into donor emission and acceptor absorption lineshapes, but must be recast in terms of a renormalized phonon reorganization energy accounting for the magnitude and sign of the excitation-vibration couplings. In this paper, we derive theoretically how the FRET rate depends on the shared mode structure and coupling, examine the simplified case of Gaussian lineshapes and then provide a quantitative calculation for a system of current interest.

DENSITY MATRIX ANALYSIS AND SIMULATION OF ELECTRON DYNAMICS IN MULTIPLE-BRIDGED DONOR/ACCEPTOR MOLECULES UNDER DISSIPATIVE ENVIRONMENTS

Feynman and Vernon path integral approach is adopted to investigate electron transfer dynamics in donor–bridge–acceptor molecules under dissipative environments. Especially, we focus on the solvent effect on the superexchange process of electron transfer. The results reveal that at high enough bridge energies or low enough temperature, electron can transfer with a superexchange mechanism no matter whether solvent is incorporated or not. However, the superexchange changes from coherent to incoherent limits when the dissipative strength increases, and electron transfer rates are much dependent on the dissipative strength.

Ex vivo and computer model study on retinal thermal laser-induced damage in the visible wavelength range

Excised bovine eyes are used as models for threshold determination of 532-nm laser-induced thermal damage of the retina in the pulse duration regime of 100 micros to 2 s for varying laser spot size diameters. The thresholds as determined by fluorescence viability staining compare well with the prediction of an extended Thompson-Gerstman computer model. Both models compare well with published Rhesus monkey threshold data. A previously unknown variation of the spot size dependence is seen for different pulse durations, which allows for a more complete understanding of the retinal thermal damage. Current International Commission on Nonionized Radiation Protection (ICNIRP), American National Standards Institute (ANS), and International Electromechanical Commission (IEC) laser and incoherent optical radiation exposure limits can be increased for extended sources for pulsed exposures. We conclude that the damage mechanism at threshold detected at 24 and 1 h for the nonhuman primate model is retinal pigment epithelium (RPE) cell damage and not thermal coagulation of the sensory retina. This work validates the bovine ex vivo and computer models for prediction of thresholds of thermally induced damage in the time domain of 10 micros to 2 s, which provides the basis for safety analysis of more complicated retinal exposure scenarios such as repetitive pulses, nonconstant retinal irradiance profiles, and scanned exposure.

Asymmetric doublets in MAS NMR: coherent and incoherent mechanisms

It has been long noted that J-resolved doublets observed in solid-state MAS experiments are asymmetric. The asymmetry has been attributed to a coherent interference effect involving dipolar and CSA interactions. Recently, Bernd Reif and co-workers suggested that under fast MAS conditions the coherent portion of the effect is suppressed and it becomes possible to observe an incoherent mechanism reminiscent of TROSY. The researchers were able to observe the characteristic TROSY-type patterns in (15)N-(1)H(N) spectra of heavily deuterated protein samples (Chevlekov, Diehl, and Reif, previous article in this issue). In the present computer simulation study, we seek to obtain a unified picture of this phenomenon, including both coherent and incoherent aspects. The chosen model focuses on the (15)N-(1)H(N) pair from a polycrystalline sample subject to magic angle spinning. To mimic local dynamics, we assume that the corresponding peptide plane jumps between two orientations. The simulations demonstrate that this simple model reproduces both coherent and incoherent behavior, depending on the MAS speed and the time scale of local dynamics. Furthermore, semianalytical expressions can be derived for both coherent and incoherent (Redfield) limits. Of particular interest is the possibility to use solution-style Redfield results to probe internal protein motions, especially slower motions on the nanosecond time scale. Our simulations show that the differential relaxation measurement permits accurate determination of (15)N dipolar-CSA cross correlations already at moderately high MAS speed (ca 15 kHz).

Stochastic Dipolar Recoupling in Nuclear Magnetic Resonance of Solids

I describe a nuclear magnetic resonance (NMR) technique, called stochastic dipolar recoupling (SDR), that permits continuous experimental control of the character of spin dynamics between coherent and incoherent limits in a system of magnetic dipole-coupled nuclei. In the fully incoherent limit of SDR, spin polarization transfers occur at distance-dependent rates without the quantum mechanical interferences among pairwise dipole-dipole couplings that often limit the feasibility or precision of structural studies of solids by NMR. In addition to facilitating structural studies, SDR represents a possible route to experimental studies of effects of decoherence on the dynamics of quantum many-body systems.

UNIFIED analytical formulation of thin-film radiative properties including partial coherence

Radiative properties of thin films are derived based on the concept of optical coherence theory. Instead of the previous approach of deriving the property formulas based on the degree of coherence, a direct integration approach to obtain the averaged properties over a finite spectral resolution is developed. The analytical results are in excellent agreement with the measured spectra. The formulas are compact in form and easy to use to invert optical properties or film thicknesses with measured reflectance or transmittance. Rigorous criteria for incoherent and coherent limits can be easily reduced from the general formulas and the resulting equations corresponding to those of geometric and wave optics, respectively. These criteria are very useful in determining under what situations simpler wave optics and geometric optics formulas can be applied.

THEORY OF BICRYSTAL c-AXIS TWIST JOSEPHSON JUNCTIONS

We calculate the critical current density [Formula: see text] for Josephson tunneling between identical high temperature superconductors twisted an angle (ϕ0) about the c-axis. Regardless of the shape of the two-dimensional Fermi surface and for very general tunneling matrix elements, an order parameter (OP) with general d-wave symmetry leads to [Formula: see text]. This general result is inconsistent with the data of Li et al. on Bi2Sr2CaCu2O8+δ (Bi2212), which showed [Formula: see text] to be independent of ϕ0. If the momentum parallel to the barrier is conserved in the tunneling process, [Formula: see text] should vary substantially with the twist angle (ϕ0) when the tight-binding Fermi surface appropriate for Bi2212 is taken into account, even if the OP is completely isotropic. We quantify the degree of momentum non-conservation necessary to render [Formula: see text] constant within experimental error for a variety of pair states by interpolating between the coherent and incoherent limits using five specific models to describe the momentum dependence of the tunneling matrix element squared. From the data of Li et al., we conclude that the c-axis tunneling in Bi2212 must be very nearly incoherent, and that the OP must have a non-vanishing Fermi surface average for T≤Tc.

Gluon radiation off hard quarks in a nuclear environment: opacity expansion

We study the relation between the Baier-Dokshitzer-Mueller-Peigne-Schiff (BDMPS) and Zakharov formalisms for medium-induced gluon radiation off hard quarks, and the radiation off very few scattering centers. Based on the non-abelian Furry approximation for the motion of hard partons in a spatially extended colour field, we derive a compact diagrammatic and explicitly colour trivial expression for the N-th order term of the kt-differential gluon radiation cross section in an expansion in the opacity of the medium. Resumming this quantity to all orders in opacity, we obtain Zakharov's path-integral expression (supplemented with a regularization prescription). This provides a new proof of the equivalence of the BDMPS and Zakharov formalisms which extends previous arguments to the kt-differential cross section. We give explicit analytical results up to third order in opacity for both the gluon radiation cross section of free incoming and of in-medium produced quarks. The N-th order term in the opacity expansion of the radiation cross section is found to be a convolution of the radiation associated to N-fold rescattering and a readjustment of the probabilities that rescattering occurs with less than N scattering centers. Both informations can be disentangled by factorizing out of the radiation cross section a term which depends only on the mean free path of the projectile. This allows to infer analytical expressions for the totally coherent and totally incoherent limits of the radiation cross section to arbitrary orders in opacity.

The Ni-Ni3Al phase diagram: thermodynamic modelling and therequirements of coherent equilibrium

The Ni-rich portion of the Ni-Al phase diagram is examined in light of dataon coherent equilibrium between the γ (Ni-Al solid solution) andγ' (Ni3Al) phases, as well as on the thermodynamicrequirements of coherent equilibrium. The model of Ardell and Maheshwari wasused to calculate the difference between the incoherent and coherentsolubility limits over the temperature range of 400-800 °C. New dataon the elastic constants of Ni3Al as a function of temperatureand composition, as well as the Gibbs free energy functions of the most recentthermodynamic model of the Ni-Al alloy system, were used in the calculations.With these input parameters the predicted differences between the incoherentand coherent solubility limits are very small, and inconsistent with recentexperimental data on the variation of the coherent solubility with theγ' volume fraction. The inconsistency is a consequence of the largecurvature of the Gibbs free energy function for the γ phase obtainedfrom the thermodynamic model. These findings are discussed in the context ofthe accuracy of thermodynamic modelling of phase diagrams.

Simple model for decay of superdeformed nuclei

Recent theoretical investigations of the decay mechanism out of a superdeformed nuclear band have yielded qualitatively different results, depending on the relative values of the relevant decay widths. We present a simple two-level model for the dynamics of the tunneling between the superdeformed and normal-deformed bands, which treats decay and tunneling processes on an equal footing. The previous theoretical results are shown to correspond to coherent and incoherent limits of the full tunneling dynamics. Our model accounts for experimental data in both the A~150 mass region, where the tunneling dynamics is coherent, and in the A~190 mass region, where the tunneling dynamics is incoherent.

The incoherent γ/γ′ solvus in Ni-Al alloys

Analysis of the kinetics of solute (Al) depletion during the coarsening of γ′ (Ni 3 Al)precipitates has been used in earlier investigations to provide values of the coherent solubility of the γ phase in binary Ni-Al alloys. As demonstrated in recent experimental investigations, the coherent solubility is a function of the total concentration of Al in the two-phase alloy. Using the model of Ardell and Maheshwari to analyze the data on coherent equilibrium, the authors estimated the incoherent equilibrium solubility of the γ′ phase over the temperature range 400 to 800 ° C. The calculated incoherent solubility limits are 3 to 5 % smaller than previously published measurements, the differences decreasing as the temperature increases. The authors argue that the calculations in this article provide the first estimates of the incoherent solvus of the γ′ phase in Ni-Al alloys.

Effects of partial coherence on the scattering of x rays by matter

We discuss the scattering of x rays by matter using the Huygens-Fresnel method, i.e., in the kinematic regime. We derive expressions for how the mutual coherence function (MCF) of the scattered radiation defined across an exit aperture, arises from the MCF of the incident radiation across the entrance aperture and the electron density distribution of the scatterer, and in particular calculate the intensity measured in a detector placed behind the exit aperture as a function of the nominal wave vector transfer q. We discuss the exact relationship between this intensity function and the usual density-density correlation function of the scatterer, and discuss the relationship between coherence and instrumental resolution effects in various regimes. The Fraunhofer and Fresnel regimes are distinguished and the incoherent and coherent limits are discussed. We illustrate the results with explicit calculations for (a) Bragg reflections from crystals and (b) scattering from surfaces.

Collective coordinates for nuclear spectral densities in energy transfer and femtosecond spectroscopy of molecular aggregates

A theory for Frenkel exciton dynamics in molecular aggregates which incorporates coupling to vibrational motions (intramolecular, intermolecular and solvent) with multiple spectral densities of arbitrary nature and interpolates between the coherent and the incoherent limits is developed. A rigorous procedure for identifying the relevant collective nuclear coordinates necessary to represent a given set of spectral densities is obtained. Additional coordinates are required as the temperature is lowered. Exciton dynamics is calculated by following the evolution of wavepackets representing the electronic density matrix in the collective coordinates phase space. The signatures of excitonic and nuclear motions in ultrafast fluorescence spectroscopy are explored using a hierarchy of reduction schemes with varying numbers of collective coordinates.

Semiclassical limits in quantum-transport theory.

Semiclassical limits for the dynamics of the Wigner function, and for the dynamics of the low-order moments of physical interest, are discussed in fluid-dynamical terms. The harmonic-oscillator solution yields local Maxwellian (ideal) fluid-dynamical behavior, and this is extended to locally quadratic problems in a straightforward manner. Coherent states are shown to have a particularly simple fluid-dynamical interpretation, and coherence may be easily demonstrated for mixed states having an arbitrary degree of uncertainty in the field variables. The semiclassical behavior of pure and mixed states is conveniently discussed in terms of coherent and incoherent limits, and the origin of quantum-mechanical behavior in the simple low-order approximations proposed is simply explained. The relation to the pure-state theory of Madelung is made explicit. A recently proposed method for the solution of a certain hierarchy of quantum-fluid-dynamical equations is analyzed in detail, and is demonstrated to be inconsistent with these semiclassical limits.

IVR: Its Coherent and Incoherent Dynamics

AbstractIn this paper, we discuss the dynamics of intramolecular vibrational‐energy redistribution (IVR) in two limits: the coherent and incoherent limits. These descriptions are introduced to account for experiments done in time and frequency domains. We present a more general model for IVR, namely the model of overlapping resonances, which describes coherence (quantum beats), congestion and nonexponentional decays.