Anharmonic Systems Research Articles

Internal conversion rates from the extended thawed Gaussian approximation: Theory and validation.

The theoretical prediction of the rates of nonradiative processes in molecules is fundamental in assessing their emissive properties. In this context, global harmonic models have been widely used to simulate vibronic spectra as well as internal conversion rates and to predict photoluminescence quantum yields. However, these simplified models suffer from the limitations that are inherent to the harmonic approximation and can have a severe effect on the calculated internal conversion rates. Therefore, the development of more accurate semiclassical methods is highly desirable. Here, we introduce a procedure for the calculation of nonradiative rates in the framework of the time-dependent semi-classical Extended Thawed Gaussian Approximation (ETGA). We systematically investigate the performance of the ETGA method by comparing it to the adiabatic and vertical harmonic methods, which belong to the class of widely used global harmonic models. Its performance is tested in potentials that cannot be treated adequately by global harmonic models, beginning with Morse potentials of varying anharmonicity followed by a double well potential. The calculated radiative and nonradiative internal conversion rates are compared to reference values based on exact quantum dynamics. We find that the ETGA has the capability to predict internal conversion rates in anharmonic systems with an appreciable energy gap, whereas the global harmonic models prove to be insufficient.

On the green factorization method and supersymmetry

The factorization method in operator language formalism and supersymmetric quantum mechanics are vastly studied in literature. The well-known factorization method goes to the early work by Infeld and Hull in 1951. However, a different formalism of factorization method introduced by Green in 1965 is less being considered by the researchers. We show that the Green factorization method, also known as the deductive method, has a connection with supersymmetric quantum mechanics. Some anharmonic quantum systems are discussed by obtaining their analytical expressions for the complete spectrum of bound states and superpotential through the Green factorization method.

Equilibrium and Non-Equilibrium Lattice Dynamics of Anharmonic Systems.

In this review, motivated by the recent interest in high-temperature materials, we review our recent progress in theories of lattice dynamics in and out of equilibrium. To investigate thermodynamic properties of anharmonic crystals, the self-consistent phonon theory was developed, mainly in the 1960s, for rare gas atoms and quantum crystals. We have extended this theory to investigate the properties of the equilibrium state of a crystal, including its unit cell shape and size, atomic positions and lattice dynamical properties. Using the equation-of-motion method combined with the fluctuation-dissipation theorem and the Donsker-Furutsu-Novikov (DFN) theorem, this approach was also extended to investigate the non-equilibrium case where there is heat flow across a junction or an interface. The formalism is a classical one and therefore valid at high temperatures.

Ab initio canonical sampling based on variational inference

Finite temperature calculations, based on ab initio molecular dynamics (AIMD) simulations, are a powerful tool able to predict material properties that cannot be deduced from ground state calculations. However, the high computational cost of AIMD limits its applicability for large or complex systems. To circumvent this limitation we introduce a new method named Machine Learning Assisted Canonical Sampling (MLACS), which accelerates the sampling of the Born--Oppenheimer potential surface in the canonical ensemble. Based on a self-consistent variational procedure, the method iteratively trains a Machine Learning Interatomic Potential to generate configurations that approximate the canonical distribution of positions associated with the ab initio potential energy. By proving the reliability of the method on anharmonic systems, we show that the method is able to reproduce the results of AIMD with an ab initio accuracy at a fraction of its computational cost.

Ultimate optimization of interface thermal resistance by utilizing interfacial nonlinear interaction

Decreasing interface thermal resistance (ITR or Kapitza resistance) is the key to solve the problem of heat dissipation in integrated circuits, which are the core elements for electronics. In this paper, interfacial nonlinear interaction is introduced to optimize ITR. Interestingly, it is found that the optimized ITR by introducing interfacial nonlinear interaction can be greatly decreased compared to the case optimized solely with interfacial linear interaction. A 51.2% reduction in ITR is achieved in a weak anharmonic system. The mechanism behind this is attributed to the expansion of inelastic channels and the decrease of mismatch for nonlinear coefficients which are verified by spectral analysis. The relationship of optimized interfacial nonlinear coefficient and interfacial linear coefficient k 12 can be approximately predicted by the self-consistent phonon theory. The studies here emphasize the importance of mutual controlling interfacial linear and nonlinear interactions for further decreasing ITR.

Anharmonicity-induced phonon hardening and phonon transport enhancement in crystalline perovskite BaZrO3

We investigated the effects of cubic and quartic anharmonicity on lattice dynamics and thermal transport in highly anharmonic ${\mathrm{BaZrO}}_{3}$ crystal over a wide temperature range (300--2000 K) by combining the first-principles-based self-consistent phonon theory and a unified theory of thermal transport including population and coherence contributions. By considering the effects from bubble and loop diagrams, the contributions of both three-phonon (3ph) and four-phonon (4ph) interaction processes to phonon scattering rates and energy shifts were clarified. Anharmonic phonon renormalization is found to play a crucial role in determining the finite-temperature phonon energies and lattice thermal conductivity ${\ensuremath{\kappa}}_{\mathrm{L}}$ in ${\mathrm{BaZrO}}_{3}$. Specifically, the lattice anharmonicity induces significant low-frequency optical phonon hardening at elevated temperatures, which is correlated with the U-shaped potential energy surfaces for these modes. The low-frequency optical phonon hardening significantly suppresses phonon scattering rates by altering the phonon weighted phase space of both 3ph and 4ph interaction processes, thereby leading to significant enhancement in the ${\ensuremath{\kappa}}_{\mathrm{L}}$ and weaker temperature dependence of ${\ensuremath{\kappa}}_{L}\ensuremath{\sim}{T}^{\ensuremath{-}0.75}$ than traditional harmonic treatments. Moreover, although the coherent thermal transport channel is suppressed by anharmonic phonon renormalization, it is enhanced by the 4ph scattering processes. The coherence contribution becomes nonnegligible at elevated temperatures and may contribute up to 17.38% of the total ${\ensuremath{\kappa}}_{\mathrm{L}}$ at 1500 K. In this paper, we highlight the strong influence of the lattice anharmonicity on thermal conductivity in severely anharmonic systems and the importance of coherent thermal transport channel at elevated temperatures.

Generalization of the Tavis-Cummings model for multi-level anharmonic systems: Insights on the second excitation manifold.

Confined electromagnetic modes strongly couple to collective excitations in ensembles of quantum emitters, producing light-matter hybrid states known as polaritons. Under such conditions, the discrete multilevel spectrum of molecular systems offers an appealing playground for exploring multiphoton processes. This work contrasts predictions from the Tavis-Cummings model in which the material is a collection of two-level systems, with the implications of considering additional energy levels with harmonic and anharmonic structures. We discuss the exact eigenspectrum, up to the second excitation manifold, of an arbitrary number N of oscillators collectively coupled to a single cavity mode in the rotating-wave approximation. Elaborating on our group-theoretic approach [New J. Phys. 23, 063081 (2021)], we simplify the brute-force diagonalization of N2 × N2 Hamiltonians to the eigendecomposition of, at most, 4 × 4 matrices for arbitrary N. We thoroughly discuss the eigenstates and the consequences of weak and strong anharmonicities. Furthermore, we find resonant conditions between bipolaritons and anharmonic transitions where two-photon absorption can be enhanced. Finally, we conclude that energy shifts in the polaritonic states induced by anharmonicities become negligible for large N. Thus, calculations with a single or few quantum emitters qualitatively fail to represent the nonlinear optical response of the collective strong coupling regime. Our work highlights the rich physics of multilevel anharmonic systems coupled to cavities absent in standard models of quantum optics. We also provide concise tabulated expressions for eigenfrequencies and transition amplitudes, which should serve as a reference for future spectroscopic studies of molecular polaritons.

Speed limits for two-qubit gates with weakly anharmonic qubits

We consider the implementation of two-qubit gates when the physical systems used to realize the qubits possess additional quantum states in the accessible energy range. We use optimal control theory to determine the maximum achievable gate speed for two-qubit gates in the qubit subspace of the many-level Hilbert space, and we analyze the effect of the additional quantum states on the gate speed. We identify two competing mechanisms. On one hand, higher energy levels are generally more strongly coupled to each other. Under suitable conditions, this stronger coupling can be utilized to make two-qubit gates significantly faster than the reference value based on simple qubits. On the other hand, a weak anharmonicity constrains the speed at which the system can be adequately controlled: according to the intuitive picture, faster operations require stronger control fields, which are more likely to excite higher levels in a weakly anharmonic system, which in turn leads to faster decoherence and uncontrolled leakage outside the qubit space. In order to account for this constraint, we modify the pulse optimization algorithm to avoid pulses that lead to appreciable population of the higher levels. In this case we find that the presence of the higher levels can lead to a significant reduction in the maximum achievable gate speed. We also compare the optimal-control gate speeds with those obtained using the cross-resonance/selective-darkening gate protocol. We find that the latter, with some parameter optimization, can be used to achieve a relatively fast implementation of the CNOT gate. These results can help the search for optimized gate implementations in realistic quantum computing architectures, such as those based on superconducting circuits. They also provide guidelines for desirable conditions on anharmonicity that allow optimal utilization of the higher levels to achieve fast quantum gates.

Applicability of the Thawed Gaussian Wavepacket Dynamics to the Calculation of Vibronic Spectra of Molecules with Double-Well Potential Energy Surfaces.

Simulating vibrationally resolved electronic spectra of anharmonic systems, especially those involving double-well potential energy surfaces, often requires expensive quantum dynamics methods. Here, we explore the applicability and limitations of the recently proposed single-Hessian thawed Gaussian approximation for the simulation of spectra of systems with double-well potentials, including 1,2,4,5-tetrafluorobenzene, ammonia, phosphine, and arsine. This semiclassical wavepacket approach is shown to be more robust and to provide more accurate spectra than the conventional harmonic approximation. Specifically, we identify two cases in which the Gaussian wavepacket method is especially useful due to the breakdown of the harmonic approximation: (i) when the nuclear wavepacket is initially at the top of the potential barrier but delocalized over both wells, e.g., along a low-frequency mode, and (ii) when the wavepacket has enough energy to classically go over the low potential energy barrier connecting the two wells. The method is efficient and requires only a single classical ab initio molecular dynamics trajectory, in addition to the data required to compute the harmonic spectra. We also present an improved algorithm for computing the wavepacket autocorrelation function, which guarantees that the evaluated correlation function is continuous for arbitrary size of the time step.

The Phonon Quasiparticle Approach for Anharmonic Properties of Solids

Knowledge of lattice anharmonicity is essential to elucidate distinctive thermal properties in crystalline solids. Yet, accurate ab initio investigations of lattice anharmonicity encounter difficulties owing to the cumbersome computations. Here we introduce the phonon quasiparticle approach and review its application to various materials. This method efficiently and reliably addresses lattice anharmonicity by combining ab initio molecular dynamics and lattice dynamics calculations. Thus, in principle, it accounts for full anharmonic effects and overcomes finite-size effects typical of ab initio molecular dynamics. The validity and effectiveness of the current approach are demonstrated in the computation of thermodynamic and heat transport properties of weakly and strongly anharmonic systems.

On negative effective mass and negative group velocity in anharmonic seismic metamaterials

In this work, an anharmonic mass-in-mass system that can be employed as a nonlinear seismic metamaterial is represented as an equivalent anharmonic mass-spring system via an effective medium approach. The dispersion relation and the behavior of the effective mass as a function of the angular frequency obtained in the regime of weak anharmonicity deviate from those of the corresponding linear system because of the effect of the fourth-order potential anharmonicity. In the presence of anharmonic soft springs it is found a range of wave vectors close to the Brillouin border zone at which the group velocity of the acoustic and optical modes is negative, namely it is opposite to the phase velocity, and a wider band gap at the border of the first Brillouin zone with respect to that of the linear case. Both effects can be tuned by varying the anharmonicity strength. The huge band gap amplitude together with the strong reduction of the frequency of the acoustic mode could be exploited for the design of nonlinear seismic metamaterials at the basis of composite foundations operating in the stop band frequencies.

Compacting the density matrix in quantum dynamics: Singular value decomposition of the surprisal and the dominant constraints for anharmonic systems.

We introduce a practical method for compacting the time evolution of the quantum state of a closed physical system. The density matrix is specified as a function of a few time-independent observables where their coefficients are time-dependent. The key mathematical step is the vectorization of the surprisal, the logarithm of the density matrix, at each time pointof interest. The time span used depends on the required spectral resolution. The entire course of the system evolution is represented as a matrix where each column is the vectorized surprisal at the given time point. Using the singular value decomposition (SVD) of this matrix, we generate realistic approximations for the time-independent observables and their respective time-dependent coefficients. This allows for a simplification of the algebraic procedure for determining the dominant constraints (the time-independent observables) in the sense of the maximal entropy approach. A non-stationary coherent initial state of a Morse oscillator is used to introduce the approach. We derive the analytical exact expression for the surprisal as a function of time, and this offers a benchmark for comparison with the accurate but approximate SVD results. We discuss two examples of a Morse potential of different anharmonicities, H2 and I2 molecules. We further demonstrate the approach for a two-coupled electronic state problem, the well-studied non-radiative decay of pyrazine from its bright state. Five constraints are found to be enough to capture the ultrafast electronic population exchange and to recover the dynamics of the wave packet in both electronic states.

Heat transport in long-ranged Fermi-Pasta-Ulam-Tsingou-type models.

We perform a detailed study of heat transport in one-dimensional long-ranged anharmonic oscillator systems, such as the long-ranged Fermi-Pasta-Ulam-Tsingou model. For these systems, the long-ranged anharmonic potential decays with distance as a power law, controlled by an exponent δ≥0. For such a nonintegrable model, one of the recent results that has captured quite some attention is the puzzling ballisticlike transport observed for δ=2, reminiscent of integrable systems. Here, we first employ the reverse nonequilibrium molecular dynamics simulations to look closely at the δ=2 transport in three long-ranged models and point out a few problematic issues with this simulation method. Next, we examine the process of energy relaxation, and find that relaxation can be appreciably slow for δ=2 in some situations. We invoke the concept of nonlinear localized modes of excitation, also known as discrete breathers, and demonstrate that the slow relaxation and the ballisticlike transport properties can be consistently explained in terms of a novel depinning of the discrete breathers that makes them highly mobile at δ=2. Finally, in the presence of quartic pinning potentials we find that the long-ranged model exhibits Fourier (diffusive) transport at δ=2, as one would expect from short-ranged interacting systems with broken momentum conservation. Such a diffusive regime is not observed for harmonic pinning.

Diagrammatic approach to classical coherent two-dimensional infrared spectroscopy

The authors develop a diagrammatic theory for the classical description of nonlinear response functions of anharmonic oscillators. Based on the theory, the authors demonstrate that the third-order response of a weakly anharmonic system can be qualitatively described using classical dynamics, clarifying the boundary of classical and purely quantum phenomena in relation to observations of molecular coherence.

Parametric Analysis for Underwater Flapping Foil Propulsor

This paper researched into the harmonic and anharmonic underwater flapping foil propulsion systems to improve the efficiency of these bioinspired propulsors. The angle of attack, the pitching angle, the heaving amplitude, and the phase difference are parametrically investigated in this paper. A rigid two-dimensional NACA (National Advisory Committee for Aeronautics) 0012 airfoil is modeled with the aid of a commercial computational fluid dynamics software, FINE™/Marine. Unsteady Reynolds Average Navier-Stokes (URANS) equation is solved together with dynamic mesh to simulate the foil motion. The investigation first verifies the reliability of the developed modeling method against the benchmark data. Then, the systematic investigation is conducted and identifies that the heaving amplitude is most influential factor for the propulsion efficiency. Secondly, phase difference also has a significant influence on efficiency, but this effect is related to the reference working condition, which needs further study. Then, the pitching amplitude has little effect on the maximum efficiency value of flapping foil, while it will affect its optimal speed range. When the heaving amplitude ratio reaches 3 and the corresponding maximum angle of attack is about 9°, the maximum efficiency can reach 87%. The effect of anharmonic motion on the efficiency is very small and varies with the St number, but in summary, it can maintain the peak efficiency over a wider range of operations. In addition, the force and flow field characteristics of different efficiency points are compared and analyzed to distinguish their corresponding relationship with the propulsion efficiency.

Excited state distribution function for probing Herzberg–Teller vibronic coupling using linear optical response theory: Application to glassy pheophytin a

The goal of the present work is to develop an excited-state distribution function that can be used to calculate electronic transition dipole moment time correlation functions at a considerably low computational cost. An additional merit of the distribution function is its capability to probe the Hertzberg-Teller vibronic coupling effect in terms of the previously reported Condon correlation functions in the literature without having to start from the equilibrium density operator to probe spectral non-Condon effects, thereby exploring Hertzberg-Teller vibronic coupling by building on the Condon regime. It is easily extendable to anharmonic systems. Model calculations are reported to show the high degree of accuracy and computational efficiency of the presented approach. Application to a photosynthetic system such as pheophytin a in triethylamine is provided.

Laser-Driven Anharmonic Oscillator: Ground-State Dissociation of the Helium Hydride Molecular Ion by Midinfrared Pulses.

The vibrational motion of molecules represents a fundamental example of an anharmonic oscillator. Using a prototype molecular system, HeH^{+}, we demonstrate that appropriate laser pulses make it possible to drive the nuclear motion in the anharmonic potential of the electronic ground state, increasing its energy above the potential barrier and facilitating dissociation by purely vibrational excitation. We find excellent agreement between the frequency-dependent response of the helium hydride molecular cation to both classical and quantum mechanical simulations, thus removing any ambiguities through electronic excitation. Our results provide access to the rich dynamics of anharmonic quantum oscillator systems and pave the way to state-selective control schemes in ground-state chemistry by the adequate choice of the laser parameters.

Oscillating states of periodically driven anharmonic Langevin systems.

We investigate the asymptotic distributions of periodically driven anharmonic Langevin systems. Utilizing the underlying SL_{2} symmetry of the Langevin dynamics, we develop a perturbative scheme in which the effect of periodic driving can be treated nonperturbatively to any order of perturbation in anharmonicity. We spell out the conditions under which the asymptotic distributions exist and are periodic and show that the distributions can be determined exactly in terms of the solutions of the associated Hill equations. We further find that the oscillating states of these driven systems are stable against anharmonic perturbations.

Enhanced optical nonlinearities under collective strong light-matter coupling

Optical microcavities and metallic nanostructures have been shown to significantly modulate the dynamics and spectroscopic response of molecular systems. We present a study of the nonlinear optics of a model consisting of $N$ anharmonic multilevel systems (e.g., Morse oscillators) undergoing collective strong coupling with a resonant infrared microcavity. We find that, under experimentally accessible conditions, molecular systems in microcavities may have nonlinear phenomena significantly intensified due to the high quality of polariton resonances and the enhanced microcavity electromagnetic energy density relative to free space. Particularly large enhancement of multiphoton absorption happens when multipolariton states are resonant with bare molecule multiphoton transitions. In particular, our model predicts two-photon absorption cross section enhancements by several orders of magnitude relative to free space when the Rabi splitting $\Omega_R$ is approximately equal to the molecular anharmonic shift $2\Delta$. Our results provide rough upper bounds to resonant nonlinear response enhancement factors as relaxation to dark states is treated phenomenologically. Notably, ensembles of two-level systems undergoing strong coupling with a cavity (described by the Tavis-Cummings model) show no such optical nonlinearity enhancements, highlighting the rich phenomenology afforded by multilevel anharmonic systems. Similar conclusions are expected to hold for excitonic systems that share features with our model (e.g., molecular dyes with accessible S_0 -> S_1 -> S_2 transitions) and strongly interact with a UV-visible cavity.

Origin of micrometer-scale propagation lengths of heat-carrying acoustic excitations in amorphous silicon

The heat-carrying acoustic excitations of amorphous silicon are of interest because their mean free paths may approach micron scales at room temperature. Despite extensive investigation, the origin of the weak acoustic damping in the heat-carrying frequencies remains a topic of debate. Here, we report measurements of the thermal conductivity mean free path accumulation function in amorphous silicon thin films from 60 - 315 K using transient grating spectroscopy. With additional picosecond acoustics measurements and considering the known frequency-dependencies of damping mechanisms in glasses, we reconstruct the mean free paths from $\sim 0.1-3$ THz. The mean free paths are independent of temperature and exhibit a Rayleigh scattering trend over most of this frequency range. The observed trend is inconsistent with the predictions of numerical studies based on normal mode analysis but agrees with diverse measurements on other glasses. The micron-scale MFPs in amorphous Si arise from the absence of anharmonic or two-level system damping in the sub-THz frequencies, leading to heat-carrying acoustic excitations with room-temperature damping comparable to that of other glasses at cryogenic temperatures.