Response Function Formalism Research Articles

Theoretical Study of the Two-Dimensional Vibrational Sum Frequency Generation Spectroscopy of the Air-Water Interface at Varying Temperature and Its Connections to the Interfacial Structure and Dynamics.

We performed a theoretical study of the temperature variation of two-dimensional vibrational sum frequency generation (2D-VSFG) spectra of the OH stretch modes at air-water interfaces in the mid-IR region. The calculations are performed at four different temperatures from 250 to 325 K by using a combination of techniques involving response function formalism of nonlinear spectroscopy, electronic structure calculations, and molecular dynamics simulations. Also, the calculations are performed for isotopically dilute solutions so that the intra- and intermolecular coupling between the vibrational modes of interest can be ignored. We have established the connections of temperature variation of various frequency- and time-dependent features of the calculated spectra to the changes in the underlying structure and dynamics of the interfaces. The results reveal that interfacial water is dynamically more heterogeneous than bulk water, with three dominant dynamical processes exhibiting their corresponding time-dependent features in the 2D-VSFG spectrum. These are the spectral diffusion of hydrogen-bonded OH groups at the interface, conversion of an initially hydrogen-bonded OH group to a dangling OH which is a stable state for surface water, unlike the bulk water, and the third one, which involves the conversion of an initially free or dangling OH group to its hydrogen-bonded state at the interface. The temporal appearance of the cross peaks corresponding to interconversion of the hydrogen-bonded state to the dangling state or vice versa of an interfacial OH group is found to take place at a slower rate than the dynamics of spectral diffusion of hydrogen-bonded molecules at the interface, which, in turn, is slower than the corresponding spectral diffusion of bulk water molecules. The temperature variation of these dynamic processes can be linked to the decay of appropriate hydrogen-bond and non-hydrogen-bond time correlation functions of interfacial water molecules for the different air-water systems studied in this work.

Non-Equilibrium Turbulent Transport in Convective Plumes Obtained from Closure Theory

The non-equilibrium property of turbulence modifies the characteristics of turbulent transport. With the aid of response function formalism, such non-equilibrium effects in turbulent transport can be represented by the temporal variation of the turbulent energy (K) and its dissipation rate (ε) along the mean stream through the advective derivatives of K and ε. Applications of this effect to the turbulent convection with plumes are considered for the first time in this work. The non-equilibrium transport effects associated with plumes are addressed in two aspects. Firstly, the effect associated with a single plume is evaluated using data measured in the recent plume/jet experiments. The second argument is developed for the collective turbulent transport associated with multiple plumes mimicking the stellar convection zone. In this second case, for the purpose of capturing the plume motions into the advective derivatives, use has to be made of the time–space double-averaging procedure, where the turbulent fluctuations are divided into the coherent or dispersion component (which represents plume motions) and the incoherent or random component. With the aid of the transport equations of the coherent velocity stress and the incoherent counterpart, the interaction between the dispersion and random fluctuations are also discussed in the context of convective turbulent flows with plumes. It is shown from these analyses that the non-equilibrium effect associated with plume motions is of a great deal of relevance in the convective turbulence modeling.

Non-Hermitian Hamiltonians for linear and nonlinear optical response: A model for plexcitons.

In polaritons, the properties of matter are modified by mixing the molecular transitions with light modes inside a cavity. Resultant hybrid light-matter states exhibit energy level shifts, are delocalized over many molecular units, and have a different excited-state potential energy landscape, which leads to modified exciton dynamics. Previously, non-Hermitian Hamiltonians have been derived to describe the excited states of molecules coupled to surface plasmons (i.e., plexcitons), and these operators have been successfully used in the description of linear and third order optical response. In this article, we rigorously derive non-Hermitian Hamiltonians in the response function formalism of nonlinear spectroscopy by means of Feshbach operators and apply them to explore spectroscopic signatures of plexcitons. In particular, we analyze the optical response below and above the exceptional point that arises for matching transition energies for plasmon and molecular components and study their decomposition using double-sided Feynman diagrams. We find a clear distinction between interference and Rabi splitting in linear spectroscopy and a qualitative change in the symmetry of the line shape of the nonlinear signal when crossing the exceptional point. This change corresponds to one in the symmetry of the eigenvalues of the Hamiltonian. Our work presents an approach for simulating the optical response of sublevels within an electronic system and opens new applications of nonlinear spectroscopy to examine the different regimes of the spectrum of non-Hermitian Hamiltonians.

Quantum simulation of weak-field light-matter interactions

Simulation of the interaction of light with matter, including at the few-photon level, is important for understanding the optical and optoelectronic properties of materials, and for modeling next-generation non-linear spectroscopies that use entangled light. At the few-photon level the quantum properties of the electromagnetic field must be accounted for with a quantized treatment of the field, and then such simulations quickly become intractable, especially if the matter subsystem must be modeled with a large number of degrees of freedom, as can be required to accurately capture many-body effects and quantum noise sources. Motivated by this we develop a quantum simulation framework for simulating such light-matter interactions on platforms with controllable bosonic degrees of freedom, such as vibrational modes in the trapped ion platform. The key innovation in our work is a scheme for simulating interactions with a continuum field using only a few discrete bosonic modes, which is enabled by a Green's function (response function) formalism. We develop the simulation approach, sketch how the simulation can be performed using trapped ions, and then illustrate the method with numerical examples. Our work expands the reach of quantum simulation to important light-matter interaction models and illustrates the advantages of extracting dynamical quantities such as response functions from quantum simulations.

Frequency-resolved microscopic second-order hyperpolarizability of azochromophores: a study on nonlinear all-optical switching applications.

Azochromophores present interesting optical properties for application in all-optical switches (AOSs), such as ultrafast photoisomerization and considerable nonlinear optical response. However, determining the frequency-resolved microscopic second-order hyperpolarizability (real and imaginary parts) related to the pure electronic effects of molecules in solution is a challenging task. In this context, we have used femtosecond-laser induced nonlinear ellipse rotation (NER) measurements to obtain the electronic nonlinear refraction (n2(ω)) and two-photon absorption spectra (α2PA(ω)) of four azochromophores dissolved in methanol and acetone. The measurements ranging from ∼600 up to ∼1300 nm were performed in Disperse Red 1 (DR1), Disperse Red 13 (DR13), Disperse Red 19 (DR19), and Disperse Orange 3 (DO3). Because we carried the solution in a silica cuvette and used a short focal length, we were able to measure the solution's nonlinearities with high precision, as the silica from the cuvette walls worked as a suitable reference medium. Consequently, we precisely determined n2(ω), α2PA(ω), and the second-order hyperpolarizability (γ(ω)) for all molecules and explained the different magnitudes based on the push-pull character. Furthermore, the solvation effect due to the change from methanol to acetone solvent on the n2(ω), α2PA(ω), and γ(ω) is also reported. The results were elucidated using the sum-over-states (SOS) approach within the few-energy-level model and the results were obtained via quantum-chemical calculations using the cubic response function formalism within the density functional theory framework. Finally, we used these results to determine the frequency-resolved figure-of-merit for all-optical switching applications. Our results suggest that chromophores have the potential for applications in AOS based on Fabry-Perot filters.

Multiple Ensembles of the Hydrogen-bonded Network in Ethylammonium Nitrate versus Water from Vibrational Spectral Dynamics of SCN- Probe.

We performed classical molecular dynamics simulations to monitor the structural interactions and ultrafast dynamical and spectral response in the protic ionic liquid, ethylammonium nitrate (EAN) and water using the nitrile stretching mode of thiocyanate ion (SCN- ) as the vibrational probe. The normalized frequency distribution of the nitrile stretch in SCN- attains an asymmetric shape in EAN, indicating the existence of more than one hydrogen-bonding environment in EAN. Further, we computed the 2D IR spectrum from classical trajectories, applying the response function formalism. Spectral diffusion dynamics in EAN undergo an initial rattling of the SCN- inside the local ion-cage occurring at a timescale of 0.10 ps, followed by the breakup of the ion-cage activating molecular diffusion at 7.86 ps timescale. In contrast, the dynamics of structural reorganization occur at a timescale of 0.58 ps in H2 O. Hence, the time dependence of the frequency-frequency correlation function decay hints at the local molecular structure and ultrafast ion dynamics of the SCN- probe. The loss of frequency correlation read from the peak shape changes in the 2D correlation spectrum as a function of waiting time is faster in H2 O than in EAN due to the enhanced structural ordering and higher viscosity of the latter. We provide an atomic-level interpretation of the solvation environment around SCN- in EAN and water, which indicates multiple ensembles of the hydrogen bond network in EAN.

Theory of two-dimensional spectroscopy with intense laser fields.

Two-dimensional vibrational and electronic spectroscopic observables of isotropically oriented molecular samples in solution are sensitive to laser field intensities and polarization. The third-order response function formalism predicts a signal that grows linearly with the field strength of each laser pulse, thus lacking a way of accounting for non-trivial intensity-dependent effects, such as saturation and finite bleaching. An analytical expression to describe the orientational part of the molecular response, which, in the weak-field limit, becomes equivalent to a four-point correlation function, is presented. Such an expression is evaluated for Liouville-space pathways accounting for diagonal and cross peaks for all-parallel and cross-polarized pulse sequences, in both the weak- and strong-field conditions, via truncation of a Taylor series expansion at different orders. The results obtained in the strong-field conditions suggest how a careful analysis of two-dimensional spectroscopic experimental data should include laser pulse intensity considerations when determining molecular internal coordinates.

Anisotropy in fifth-order exciton-exciton-interaction two-dimensional spectroscopy.

Exciton-exciton-interaction two-dimensional (EEI2D) spectroscopy is a fifth-order variant of 2D electronic spectroscopy. It can be used to probe biexciton dynamics in molecular systems and to observe exciton diffusion in extended systems such as polymers or light-harvesting complexes. The exciton transport strongly depends on the geometrical and energetic landscape and its perturbations. These can be of both local character, such as molecular orientation and energetic disorder, and long-range character, such as polymer kinks and structural domains. In the present theoretical work, we investigate the anisotropy in EEI2D spectroscopy. We introduce a general approach for how to calculate the anisotropy by using the response-function formalism in an efficient way. In numerical simulations, using a Frenkel exciton model with Redfield-theory dynamics, we demonstrate how the measurement of anisotropy in EEI2D spectroscopy can be used to identify various geometrical effects on exciton transport in dimers and polymers. Investigating a molecular heterodimer as an example, we demonstrate the utility of anisotropy in EEI2D spectroscopy for disentangling dynamic localization and annihilation. We further calculate the annihilation in extended systems such as conjugated polymers. In a polymer, a change in the anisotropy provides a unique signature for exciton transport between differently oriented sections. We analyze three types of geometry variations in polymers: a kink, varying geometric and energetic disorder, and different geometric domains. Our findings underline that employing anisotropy in EEI2D spectroscopy provides a way to distinguish between different geometries and can be used to obtain a better understanding of long-range exciton transport.

Understanding radiative transitions and relaxation pathways in plexcitons

Summary Molecular aggregates on plasmonic nanoparticles have emerged as attractive systems for the studies of polaritonic light-matter states, called plexcitons. Such systems are tunable, scalable, easy to synthesize, and offer sub-wavelength confinement, all while giving access to the ultrastrong light-matter coupling regime, promising a plethora of applications. However, the complexity of these materials prevented the understanding of their excitation and relaxation phenomena. Here, we follow the relaxation pathways in plexcitons and conclude that while the metal destroys the optical coherence, the molecular aggregate coupled to surface processes significantly contributes to the energy dissipation. We use two-dimensional electronic spectroscopy with theoretical modeling to assign the different relaxation processes to either molecules or metal nanoparticle. We show that the dynamics beyond a few femtoseconds has to be considered in the language of hot electron distributions instead of the accepted lower and upper polariton branches and establish the framework for further understanding.

Efficient simulation of time- and frequency-resolved four-wave-mixing signals with a multiconfigurational Ehrenfest approach.

We have extended the multiconfigurational Ehrenfest approach to the simulation of four-wave-mixing signals of systems involving multiple electronic and vibrational degrees of freedom. As an illustration, we calculate signals of three widely used spectroscopic techniques, time- and frequency-resolved fluorescence spectroscopy, transient absorption spectroscopy, and two-dimensional (2D) electronic spectroscopy, for a two-electronic-state, twenty-four vibrational-mode conical intersection model. It has been shown that all these three spectroscopic signals characterize fast population transfer from the higher excited electronic state to the lower excited electronic state. While the time- and frequency-resolved spectrum maps the wave packet propagation exclusively on the electronically excited states, the transient absorption and 2D electronic spectra reflect the wave packet dynamics on both electronically excited states and the electronic ground state. Combining trajectory-guided Gaussian basis functions and the nonlinear response function formalism, the present approach provides a promising general technique for the applications of various Gaussian basis methods to the calculations of four-wave-mixing spectra of polyatomic molecules.

Baryonic effects on the matter bispectrum

ABSTRACT The large-scale clustering of matter is impacted by baryonic physics, particularly active galactic nuclei (AGN) feedback. Modelling or mitigating this impact will be essential for making full use of upcoming measurements of cosmic shear and other large-scale structure probes. We study baryonic effects on the matter bispectrum, using measurements from a selection of state-of-the-art hydrodynamical simulations: IllustrisTNG, Illustris, EAGLE, and BAHAMAS. We identify a low-redshift enhancement of the bispectrum, peaking at $k\sim 3\,h\, {\rm Mpc}^{-1}$, which is present in several simulations, and discuss how it can be associated to the evolving nature of AGN feedback at late times. This enhancement does not appear in the matter power spectrum, and therefore represents a new source of degeneracy breaking between two- and three-point statistics. In addition, we provide physical interpretations for other aspects of these measurements, and make initial comparisons to predictions from perturbation theory, empirical fitting formulas, and the response function formalism. We publicly release our measurements (including estimates of their uncertainty due to sample variance) and bispectrum measurement code as resources for the community.

Nonequilibrium nature of nonlinear optical response: Application to the bulk photovoltaic effect

The bulk photovoltaic effect is an example of a nonlinear optical response that leads to a DC current that is relevant for photovoltaic applications. In this paper, we theoretically study this effect in the presence of electron-phonon interactions. Using the response function formalism, we find that the nonlinear optical response, in general, contains three operator correlation functions, one of which is not ordered in time. This latter correlator cannot be computed from equilibrium field theory. Using a semiclassical approach instead, we show that the bulk photovoltaic effect can be attributed to the dipole moment of the generated excitons. We then confirm the validity of the semiclassical result (which agrees with the noninteracting result) for nonlinear DC response from a quantum master equation approach. From this formalism we find that, in contrast to usual linear response, the scattering rate has a strong implicit effect on the nonlinear DC response. Most interestingly, the semiclassical treatment shows that the nonlinear DC response for spatially inhomogeneous excitation profiles is strongly nonlocal and must involve the aforementioned out-of-time-ordered correlators that cannot be computed by equilibrium field theory.

A simplified response function formalism for medium-heavy Λ hypernuclei

There is a variety of spectra for Λ hypernuclei (from light to heavy) which contain many peaks ranging from the deepest orbits to the surface ones. An approach is presented for the calculation of the bound state specrum of Λ hypernuclei, where the cross section is expressed through the response function. This was achieved in the framework of the Green function method with a square well optical potential using the plane waves. An analytic treatment was made for the prominent peaks with the contribution of only the valence neutron-hole series and a Gaussian folding was obtained for the rest spectrum. The method was applied mainly to the (π+,Κ+) medium to heavy Λ hypernuclei and also to the (Ä"~in-flight, π~) Λ hypernuclear spectra (with respect to their differences). The results are satisfactory compared to the experimental values. The main advantage of the proposed model is its simplicity. Possible extensions and improvements of this method are also suggested.

Dose-response linearization in radiochromic film dosimetry based on multichannel normalized pixel value with an integrated spectral correction for scanner response variations.

To introduce a model that reproducibly linearizes the response from radiochromic film (RCF) dosimetry systems at extended dose range. To introduce a correction method, generated from the same scanned images, which corrects for scanner temporal response variation and scanner bed inhomogeneity. Six calibration curves were established for different lot numbers of EBT3 GAFCHROMIC™ film model based on four EPSON scanners [10000XL (2 units), 11000XL, 12000XL] at three different centers. These films were calibrated in terms of absorbed dose to water based on TG51 protocol or TRS398 with dose ranges up to 40Gy. The film response was defined in terms of a proposed normalized pixel value ( ) as a summation of first-order equations based on information from red, green, and blue channels. The fitting parameters of these equations are chosen in a way that makes the film response equal to dose at the time of calibration. An integrated set of correction factors (one per color channel) was also introduced. These factors account for the spatial and temporal changes in scanning states during calibration and measurements. The combination of and this "fingerprint" correction formed the basis of this new protocol and it was tested against net optical density ( ) single-channel dosimetry in terms of accuracy, precision, scanner response variability, scanner bed inhomogeneity, noise, and long-term stability. Incorporating multichannel features (RGB) into the normalized pixel value produced linear response to absorbed dose (slope of 1) in all six RCF dosimetry systems considered in this study. The "fingerprint" correction factors of each of these six systems displayed unique patterns at the time of calibration. The application of to all of these six systems could achieve a level of accuracy of±2.0% in the dose range of interest within modeled uncertainty level of 2.0%-3.0% depending on the dose level. Consistent positioning of control and measurement film pieces and integrating the multichannel correction into the response function formalism mitigated possible scanner response variations of as much as±10% at lower doses and scanner bed inhomogeneity of±8% to the established level of uncertainty at the time of calibration. The system was also able to maintain the same level of accuracy after 3 and 6months post calibration. Combining response linearity with the integrated correction for scanner response variation lead to a sustainable and practical RCF dosimetry system that mitigated systematic response shifts and it has the potential to reduce errors in reporting relative information from the film response.

Numerical method for nonlinear optical spectroscopies: Ultrafast ultrafast spectroscopy.

We outline a novel numerical method, called Ultrafast Ultrafast (UF2) spectroscopy, for calculating the nth-order wavepackets required for calculating n-wave mixing signals. The method is simple to implement, and we demonstrate that it is computationally more efficient than other methods in a wide range of use cases. The resulting spectra are identical to those calculated using the standard response function formalism but with increased efficiency. The computational speed-ups of UF2 come from (a) nonperturbative and costless propagation of the system time-evolution, (b) numerical propagation only at times when perturbative optical pulses are nonzero, and (c) use of the fast Fourier transform convolution algorithm for efficient numerical propagation. The simplicity of this formalism allows us to write a simple software package that is as easy to use and understand as the Feynman diagrams that organize the understanding of n-wave mixing processes.

Theory of single-charge exchange heavy-ion reactions

The theory of heavy ion single charge exchange reactions is reformulated. In momentum space the reaction amplitude factorizes into a product of projectile and target transition form factors, folded with the nucleon-nucleon isovector interaction and a distortion coefficient which accounts for initial and final state ion-ion elastic interactions. The multipole structure of the transition form factors is studied in detail for Fermi-type non-spin flip and Gamow-Teller-type spin flip transitions, also serving to establish the connection to nuclear beta decay. The reaction kernel is evaluated for central and rank-2 tensor interactions. Initial and final state elastic ion-ion interaction are shown to be dominated by the imaginary part of the optical potential allowing to evaluate the reaction coefficients in the strong absorption limit, realized by the black disk approximation. In that limit the distortion coefficient is evaluated in closed form, revealing the relation to the total reaction cross section and the geometry of the transition form factors. It is shown that at small momentum transfer distortion effects reduce to a simple scaling factor, allowing to define reduced forward-angle cross section which is given by nuclear matrix elements of beta decay-type. The response function formalism is used to describe nuclear charge changing transitions. Spectral distributions obtained by a self-consistent HFB and QRPA approach are discussed for $\tau_\pm$ excitations of $^{18}O$ and $^{40}Ca$, respectively, and compared to spectroscopic data. The interplay of nuclear structure and reaction dynamics is illustrated for the single charge exchange reaction $^{18}O+^{40}Ca \to ^{18}F+^{40}K$ at $T_{lab}=270$ MeV.

Calculations of coherent two-dimensional electronic spectra using forward and backward stochastic wavefunctions.

Within the well-established optical response function formalism, a new strategy with the central idea of employing the forward-backward stochastic Schrödinger equations in a segmented way to accurately obtain the two-dimensional (2D) electronic spectrum is presented in this paper. Based on the simple excitonically coupled dimer model system, the validity and efficiency of the proposed schemes are demonstrated in detail, along with the comparison against the deterministic hierarchy equations of motion and perturbative second-order time-convolutionless quantum master equations. In addition, an important insight is provided in this paper that the characteristic frequency of the overdamped environment is an extremely crucial factor to regulate the lifetimes of the oscillating signals in 2D electronic spectra and of quantum coherence features of system dynamics. It is worth noting that the proposed scheme benefiting from its stochastic nature and wavefunction framework and many other advantages of substantially reducing the numerical cost has a great potential to systematically investigate various quantum effects observed in realistic large-scale natural and artificial photosynthetic systems.

Oxazole Dyes with Potential for Photoluminescence Bioprobes: A Two-Photon Absorption Study

In this work, six π-conjugated oxazole compounds dissolved in dichloromethane were characterized with linear and nonlinear optical measurements. Z-scan with femtosecond laser pulses was employed to determine the two-photon absorption (TPA) spectra. Other photophysical parameters, such as absorbance, solvatochromism, lifetime fluorescence, and fluorescence anisotropy, were evaluated with linear optical techniques. The experimental TPA cross section spectra were adjusted by the sum-over-states (SOS) model, by which important parameters such as transition dipole moments and broadening parameters were determined. To better understand the TPA spectra of the oxazole compounds, quantum-chemical calculations using the response function formalism and the density functional theory level of theory were performed. Using the results provided by the quantum-chemical calculations and the broadening parameters estimated through the application of the SOS model, the TPA spectra were simulated by the superposition (summati...

Bispectrum supersample covariance

Modes with wavelengths larger than the survey window can have significant impact on the covariance within the survey window. The supersample covariance has been recognized as an important source of covariance for the power spectrum on small scales, and it can potentially be important for the bispectrum covariance as well. In this paper, using the response function formalism, we model the supersample covariance contributions to the bispectrum covariance and the cross covariance between the power spectrum and the bispectrum. The supersample covariances due to the long wavelength density and tidal perturbations are investigated, and the tidal contribution is a few orders of magnitude smaller than the density one because in configuration space the bispectrum estimator involves angular averaging and the tidal response function is anisotropic. The impact of the super-survey modes is quantified using numerical measurements with periodic box and subbox setups. For the matter bispectrum, the ratio between the supersample covariance correction and the small scale covariance, which can be computed using a periodic box, is roughly an order of magnitude smaller than that for the matter power spectrum. This is because for the bispectrum, the small scale non-Gaussian covariance is significantly larger than that for the power spectrum. For the cross covariance, the supersample covariance is as important as for the power spectrum covariance. The supersample covariance prediction with the halo model response function is in good agreement with numerical results.

Synthesis and two-photon absorption spectrum of fluorenone-based molecules

The two-photon absorption (2PA) of five symmetrical fluorenone-based molecules is studied by femtosecond wavelength-tunable Z-scan, as well as quantum-chemical calculations. The molecules are transparent for wavelengths greater than 500nm and two main one-photon absorption bands are observed in the blue region; one weak, centered at 450nm, and a stronger one at approximately 360nm. We observed a strong 2PA band located around 720nm with maxima 2PA cross-sections between 100 and 230GM. Quantum chemical calculations employing the response function formalism were performed at the Density Function Theory level to support the interpretation of the experimental nonlinear spectra.