Adiabatic Picture Research Articles

Observation of Attosecond Time Delays in Above-Threshold Ionization.

Attosecond-scale temporal characterization of photoionization is essential in understanding how light and matter interact on the most fundamental level. However, characterizing the temporal property of strong-field above-threshold ionization has remained unreached. Here, we propose a novel photoelectron interferometric method to disentangle the contribution of Coulomb effect from an attoclock, allowing us to clock energy-resolved time delays of strong-field above-threshold ionization. We disentangle two types of Coulomb effects for the attoclock, i.e., one arising from the Coulomb disturbance of a single electron trajectory and the second effect arising from the photoelectron phase space distortion due to the Coulomb field. We find that the second Coulomb effect manifests itself as an energy-resolved attosecond time delay in the electron emission, which is relevant to the effect of nonadiabatic initial longitudinal momentum at the tunnel exit. Our study further indicates a sensitivity of the time delay to the temporal profile of the released electron wave packet within one half laser cycle. The temporal width of the released electron wave packet is found to increase with energy, which contradicts the common assumption in the adiabatic picture.

Nonadiabatic wave packet dynamics and predissociation resonances in sodium hydride.

Vibrational wave packet dynamics provides an opportunity to explore the energy landscape and the population transfer between nonadiabatically coupled excited electronic states. Here the coupled nonadiabatic dynamics of the C1Σ+ and D1Σ+ states of sodium hydride (NaH) in the gas phase in the adiabatic picture is studied, using a sequence of ultra-fast laser pulses in the femtosecond region. Emergence of different population dynamics and dissociation probabilities is shown by carefully choosing the pulse wavelength, duration and time-shift between the pulses, exciting the molecule from the ground X1Σ+ state via the immediate A1Σ+ state. Quantum dynamics simulations were performed in the adiabatic picture, avoiding the adiabatic to diabatic transformation. Predissociation resonances, i.e. vibrational states with finite lifetimes, arise due to nonadiabatic couplings between bound and continuum states. Here accurate resonance energies and widths are computed providing further insight into the dissociation dynamics.

Breakdown of Adiabatic Superconductivity in Ca-Doped h-BN Monolayer

In the present paper, we report the breakdown of the adiabatic picture of superconductivity in a calcium-doped hexagonal boron nitride (Ca-h-BN) monolayer and discuss its implications for the selected properties of this phase. In particular, it is shown that the shallow conduction band of the Ca-h-BN superconductor potentially cause a violation of the adiabatic Migdal’s theorem. As a result, the pivotal parameters that describe the superconducting state in Ca-h-BN are found to be notably influenced by the non-adiabatic effects. This finding is described here within the vertex-corrected Eliashberg formalism that predicts a strong reduction of the order parameter, superconducting transition temperature and superconducting gap in comparison to the estimates obtained in the framework of the adiabatic theory. The observed trends are in agreement with the recent results on superconductivity in hexagonal monolayers and confirm that the non-adiabatic effects have to be taken into account during the design of such future low-dimensional superconductors.

Time- and angle-resolved photoelectron spectroscopy of strong-field light-dressed solids: Prevalence of the adiabatic band picture

In recent years, strong-field physics in condensed-matter was pioneered as a novel approach for controlling material properties through laser-dressing, as well as for ultrafast spectroscopy via nonlinear light-matter interactions (e.g. harmonic generation). A potential controversy arising from these advancements is that it is sometimes vague which band-picture should be used to interpret strong-field experiments: the field-free bands, the adiabatic (instantaneous) field-dressed bands, Floquet bands, or some other intermediate picture. We here try to resolve this issue by performing 'theoretical experiments' of time- and angle-resolved photoelectron spectroscopy (Tr-ARPES) for a strong-field laser-pumped solid, which should give access to the actual observable bands of the irradiated material. To our surprise, we find that the adiabatic band-picture survives quite well, up to high field intensities (~10^12 W/cm^2), and in a wide frequency range (driving wavelengths of 4000 to 800nm, with Keldysh parameters ranging up to ~7). We conclude that to first order, the adiabatic instantaneous bands should be the standard blueprint for interpreting ultrafast electron dynamics in solids when the field is highly off-resonant with characteristic energy scales of the material. We then discuss weaker effects of modifications of the bands beyond this picture that are non-adiabatic, showing that by using bi-chromatic fields the deviations from the standard picture can be probed with enhanced sensitivity. Our work outlines a clear band picture for the physics of strong-field interactions in solids, which should be useful for designing and analyzing strong-field experimental observables and also to formulate simpler semi-empirical models.

Calculating nonadiabatic couplings and Berry's phase by variational quantum eigensolvers

The variational quantum eigensolver (VQE) is an algorithm to find eigenenergies and eigenstates of systems in quantum chemistry and quantum many-body physics. The VQE is one of the most promising applications of near-term quantum devices to investigate such systems. Here we propose an extension of the VQE to calculate the nonadiabatic couplings of molecules in quantum chemical systems and Berry's phase in quantum many-body systems. Both quantities play an important role to understand the properties of a system beyond the naive adiabatic picture, e.g., nonadiabatic dynamics and topological phase of matter. We provide quantum circuits and classical post-processings to calculate the nonadiabatic couplings and Berry's phase. Specifically, we show that the evaluation of the nonadiabatic couplings reduces to that of expectation values of observables while that of Berry's phase also requires one additional Hadamard test. Furthermore, we simulate the photodissociation dynamics of a lithium fluoride molecule using the nonadiabatic couplings evaluated on a real quantum device. Our proposal widens the applicability of the VQE and the possibility of near-term quantum devices to study molecules and quantum many-body systems.

Molecule Based Materials for Quantum Cellular Automata: A Short Overview and Challenging Problems

AbstractIn this review we shortly summarize in an accessible way the physical and nanoscale material science aspects of the promising field of molecular quantum cellular automata (QCA). QCA is a revolutionary paradigm in quantum electronics with promising application in the conceptually new computing scheme which can be referred to as “computing with molecules”. This scheme of devices have vitally important advantages compared with conventional schemes of quantum computing in which the binary information is stored in the eigenvectors of a two‐level quantum system and therefore their practical application is strongly limited by the requirement of coherence. Molecular QCA promise nanometer‐scale units with ultra‐high device densities, as well as room temperature operation with extremely small heat release. Molecular materials provide at the same time options to control the key properties of the active molecules by chemical means. Hereunder we summarize the background of the electronic and vibronic problems in QCA cells represented by the tetrameric mixed‐valence (MV) complexes and organic molecules proposed for implementation as four‐site molecular QCA. We discuss the basic model of the molecular cell that include the following ingredients: 1) intracell Coulomb repulsion energy of the electrons in different electronic distributions among the redox sites; 2) electron transfer between redox sites which changes electronic distributions; 3) interaction of the itinerant electrons with molecular vibrations which is referred to as the vibronic interactions; 4) intercell Coulomb interaction by mean of which the binary information is transmitted from cell to cell. On the basis of this model we will study the cell polarization, adiabatic picture of the switching cycle describing interaction between the “input” and “output” molecular cells, non‐linear cell‐cell response function whose shape describes the action of molecular logic gates. Along with developed and current problems, we discuss new challenging trends of research in this fascinating area.

A parametric two-mode vibronic model of a dimeric mixed-valence cell for molecular quantum cellular automata and computational ab initio verification.

In this article we propose a two-mode vibronic model of a molecular cell for quantum cellular automata. The molecular cell is represented by a mixed-valence dimeric cluster in which the mobile electron is coupled to two kinds of molecular vibrations. The first type of vibration is represented by the so-called "breathing" modes localized on the redox sites, which are traditionally considered within the Piepho, Krausz and Schatz vibronic model as a source of the trapping effect. The second type includes the "intercenter" vibration, which changes the distance between the redox centers enhancing thus the degree of delocalization in the bonding orbital of the cell. The cell-cell response function as a key characteristic of the cell is evaluated in the framework of the dynamic (quantum-mechanical) solution of the two-mode vibronic problem. To elucidate the physical sense of precise quantum-mechanical results, a more imaginative semiclassical (adiabatic) picture is used. Competitive effects of the two kinds of active vibrations on the cell-cell response function are analyzed and the conditions are established under which a mixed-valence dimer can work as a functioning molecular cell in a quantum cellular automation device. One of the aims of this article was to combine the parametric approach that gives a very common description (that allows the qualitative comparison of properties in a series of compounds) with the ab initio evaluations providing numerical estimations of the parameters involved in the semiempirical approach for a real molecule. Along with the parametric approach the quantum-chemical modelling is used for investigating the cation-radical of the tetramethyleneethane molecule which was shown to belong to the class of strongly delocalized systems. It was demonstrated that an efficient control over the electronic and vibronic parameters can be achieved through the design of its derivatives through a spacer interposed between the two allyl fragments. The strongly conjugated C[double bond, length as m-dash]C spacer was shown to partially block the channel mediating electronic communication so that the molecule becomes strongly localized. The interconnection between the parametric and ab initio approaches is established.

Fractional electron transfer kinetics and a quantum breaking of ergodicity.

The dissipative curve-crossing problem provides a paradigm for electron-transfer (ET) processes in condensed media. It establishes the simplest conceptual test bed to study the influence of the medium's dynamics on ET kinetics both on the ensemble level, and on the level of single particles. Single electron description is particularly important for nanoscaled systems like proteins, or molecular wires. Especially insightful is this framework in the semiclassical limit, where the environment can be treated classically, and an exact analytical treatment becomes feasible. Slow medium's dynamics is capable of enslaving ET and bringing it on the ensemble level from a quantum regime of nonadiabatic tunneling to the classical adiabatic regime, where electrons follow the nuclei rearrangements. This classical adiabatic textbook picture contradicts, however, in a very spectacular fashion to the statistics of single electron transitions, even in the Debye, memoryless media, also named Ohmic in the parlance of the famed spin-boson model. On the single particle level, ET always remains quantum, and this was named a quantum breaking of ergodicity in the adiabatic ET regime. What happens in the case of subdiffusive, fractional, or sub-Ohmic medium's dynamics, which is featured by power-law decaying dynamical memory effects typical, e.g., for protein macromolecules, and other viscoelastic media? Such a memory is vividly manifested by anomalous Cole-Cole dielectric response in such media. We address this question based both on accurate numerics and analytical theory. The ensemble theory remarkably agrees with the numerical dynamics of electronic populations, revealing a power-law relaxation tail even in a profoundly nonadiabatic electron transfer regime. In other words, ET in such media should typically display fractional kinetics. However, a profound difference with the numerically accurate results occurs for the distribution of residence times in the electronic states, both on the ensemble level and the level of single trajectories. Ergodicity is broken dynamically even in a more spectacular way than in the memoryless case. Our results question the applicability of all the existing and widely accepted ensemble theories of electron transfer in fractional, sub-Ohmic environments, on the level of single molecules, and provide a real challenge to face, both for theorists and experimentalists.

Ultrafast asymmetric Rosen-Zener-like coherent phonon responses observed in silicon

We investigate the spectral profiles of time signals attributed to coherent phonon generation in an undoped Si crystal. Here, the retarded longitudinal-optical (LO) phonon Green function relevant to the temporal variance of induced charge density of ionic cores is calculated by employing the polaronic quasiparticle model developed by the authors [Y. Watanabe et al., Phys. Rev. B 95, 014301 (2017); ibid., 96, 125204 (2017)]. The spectral asymmetry is revealed in the frequency domain of the signals under the condition that an LO phonon mode stays almost energetically resonant with a plasmon mode in the early time region; this lasts for approximately 100 fs immediately after the irradiation of an ultrashort pump-laser pulse. It is understood that based on the adiabatic picture in time, this asymmetry is caused by the Rosen-Zener coupling between both modes. The associated experimental results are obtained by measuring time-dependent electro-optic reflectivity signals, and it is proved that these are in harmony with the calculated ones. The spectra become more symmetric, as the photoexcited carrier density further changes from that meeting the above condition to higher and lower sides of carrier densities. Moreover, the effect of optical nutation of carrier density on the CP signals is addressed, and the present results are compared with the asymmetry caused by transient Fano resonance, and the spectral profiles observed in a GaAs crystal in the text.

Mechanism of Spin-Exchange Internal Conversion: Practical Proxies for Diabatic and Nonadiabatic Couplings.

Spin-exchange internal conversion (SEIC) is a general class of reactions having singlet fission and triplet fusion as particular cases. Based on a charge transfer (CT) mediated mechanism and analytical derivation with a model Hamiltonian, we propose proxies for estimating the coupling strength in both diabatic and adiabatic pictures for general SEIC reactions. In the diabatic picture, we demonstrated the existence of a bilinear relationship between the coupling strength and molecular orbital overlap, which provides a practical way to predict diabatic couplings. In the adiabatic picture, we showed that nonadiabatic couplings can be approximated by simple functions of the wave function CT coefficients. These approaches were verified through the investigation of singlet oxygen photosensitization, where both 1Δg and 1Σg oxygen states can be competitively generated by a triplet fusion reaction. The interplay between the CT-mediated mechanism, the spatial factors of the bimolecular complex, and the electronic structure of the oxygen molecule during the reaction explains the curiously small coupling to the 1Σg state along specific incidence directions. The results from both the diabatic and adiabatic pictures provide a comprehensive understanding of the reaction mechanism, which applies to general SEIC problems.

Energy decomposition analysis in an adiabatic picture.

Energy decomposition analysis (EDA) of electronic structure calculations has facilitated quantitative understanding of diverse intermolecular interactions. Nevertheless, such analyses are usually performed at a single geometry and thus decompose a "single-point" interaction energy. As a result, the influence of the physically meaningful EDA components on the molecular structure and other properties are not directly obtained. To address this gap, the absolutely localized molecular orbital (ALMO)-EDA is reformulated in an adiabatic picture, where the frozen, polarization, and charge transfer energy contributions are defined as energy differences between the stationary points on different potential energy surfaces (PESs), which are accessed by geometry optimizations at the frozen, polarized and fully relaxed levels of density functional theory (DFT). Other molecular properties such as vibrational frequencies can thus be obtained at the stationary points on each PES. We apply the adiabatic ALMO-EDA to different configurations of the water dimer, the water-Cl- and water-Mg2+/Ca2+ complexes, metallocenes (Fe2+, Ni2+, Cu2+, Zn2+), and the ammonia-borane complex. This method appears to be very useful for unraveling how physical effects such as polarization and charge transfer modulate changes in molecular properties induced by intermolecular interactions. As an example of the insight obtained, we find that a linear hydrogen bond geometry for the water dimer is preferred even without the presence of polarization and charge transfer, while the red shift in the OH stretch frequency is primarily a charge transfer effect; by contrast, a near-linear geometry for the water-chloride hydrogen bond is achieved only when charge transfer is allowed.

Reply to the 'Comment on "Proton transport in barium stannate: classical, semi-classical and quantum regime"'.

We respond to the erroneous criticisms about our modeling of proton transport in barium stannate [G. Geneste et al., Phys. Chem. Chem. Phys., 2015, 17, 19104]. In this previous work, we described, on the basis of density-functional calculations, proton transport in the classical and semi-classical regimes, and provided arguments in favor of an adiabatic picture for proton transfer at low temperature. We re-explain here our article (with more detail and precision), the content of which has been distorted in the Comment, and reiterate our arguments in this reply. We refute all criticisms. They are completely wrong in the context of our article. Even though a few of them are based on considerations probably true in some metals, they make no sense here since they do not correspond to the content of our work. It has not been understood in the Comment that two competitive configurations, associated with radically different transfer mechanisms, have been studied in our work. It has also not been understood in the Comment that the adiabatic regime described for transfer occurs in the protonic ground state, in a very-low barrier configuration with the protonic ground state energy larger than the barrier. Serious confusion has been made in the Comment with the case of H in metals like Nb or Ta, leading to the introduction of the notion of (protonic) "excited-state proton transfer", relevant for H in some metals, but (i) that does not correspond to the (ground state) adiabatic transfers here described, and (ii) that does not correspond to what is commonly described as the "adiabatic limit for proton transfer" in the scientific literature. We emphasize, accordingly, the large differences between proton transfer in the present oxide and hydrogen jumps in metals like Nb or Ta, and the similarities between proton transfer in the present oxide and in acid-base solutions. We finally describe a scenario for proton transfer in the present oxide regardless of the temperature regime.

Revisiting Vertical Models To Simulate the Line Shape of Electronic Spectra Adopting Cartesian and Internal Coordinates.

Vertical models for the simulation of spectroscopic line shapes expand the potential energy surface (PES) of the final state around the equilibrium geometry of the initial state. These models provide, in principle, a better approximation of the region of the band maximum. At variance, adiabatic models expand each PES around its own minimum. In the harmonic approximation, when the minimum energy structures of the two electronic states are connected by large structural displacements, adiabatic models can breakdown and are outperformed by vertical models. However, the practical application of vertical models faces the issues related to the necessity to perform a frequency analysis at a nonstationary point. In this contribution we revisit vertical models in harmonic approximation adopting both Cartesian (x) and valence internal curvilinear coordinates (s). We show that when x coordinates are used, the vibrational analysis at nonstationary points leads to a deficient description of low-frequency modes, for which spurious imaginary frequencies may even appear. This issue is solved when s coordinates are adopted. It is however necessary to account for the second derivative of s with respect to x, which here we compute analytically. We compare the performance of the vertical model in the s-frame with respect to adiabatic models and previously proposed vertical models in x- or Q1-frame, where Q1 are the normal coordinates of the initial state computed as combination of Cartesian coordinates. We show that for rigid molecules the vertical approach in the s-frame provides a description of the final state very close to the adiabatic picture. For sizable displacements it is a solid alternative to adiabatic models, and it is not affected by the issues of vertical models in x- and Q1-frames, which mainly arise when temperature effects are included. In principle the G matrix depends on s, and this creates nonorthogonality problems of the Duschinsky matrix connecting the normal modes of initial and final states in adiabatic approaches. We highlight that such a dependence of G on s is also an issue in vertical models, due to the necessity to approximate the kinetic term in the Hamiltonian when setting up the so-called GF problem. When large structural differences exist between the initial and the final-state minima, the changes in the G matrix can become too large to be disregarded.

Heterotic-type IIA duality and degenerations of K3 surfaces

We study the duality between four-dimensional N=2 compactifications of heterotic and type IIA string theories. Via adiabatic fibration of the duality in six dimensions, type IIA string theory compactified on a K3-fibred Calabi-Yau threefold has a potential heterotic dual compactification. This adiabatic picture fails whenever the K3 fibre degenerates into multiple components over points in the base of the fibration. Guided by monodromy, we identify such degenerate K3 fibres as solitons generalizing the NS5-brane in heterotic string theory. The theory of degenerations of K3 surfaces can then be used to find which solitons can be present on the heterotic side. Similar to small instanton transitions, these solitons escort singular transitions between different Calabi-Yau threefolds. Starting from well-known examples of heterotic--type IIA duality, such transitions can take us to type IIA compactifications with unknown heterotic duals.

Quantum annealing and nonequilibrium dynamics of Floquet Chern insulators

Inducing topological transitions by a time-periodic perturbation offers a route to controlling the properties of materials. Here we show that the adiabatic preparation of a non-trivial state involves a selective population of edge-states, due to exponentially-small gaps preventing adiabaticity. We illustrate this by studying graphene-like ribbons with hopping's phases of slowly increasing amplitude, as for, e.g., a circularly polarized laser slowly turned-on. The induced currents have large periodic oscillations, but flow solely at the edges upon time-averaging, and can be controlled by focusing the laser on either edge. The bulk undergoes a non-equilibrium topological transition, as signaled by the local Chern marker introduced by Bianco & Resta in equilibrium. The failure of the adiabatic picture in presence of intraband resonances is discussed.

Dzyaloshinskii-Moriya Interaction and Hall Effects in the Skyrmion Phase of Mn(1-x) Fe(x)Ge.

We carry out density functional theory calculations which demonstrate that the electron dynamics in the Skyrmion phase of Fe-rich Mn_{1-x}Fe_{x}Ge alloys is governed by Berry phase physics. We observe that the magnitude of the Dzyaloshinskii-Moriya interaction directly related to the mixed space-momentum Berry phases, changes sign and magnitude with concentration x in direct correlation with the data of Shibata etal. [Nat. Nanotechnol. 8, 723 (2013)]. The computed anomalous and topological Hall effects in FeGe are also in good agreement with available experiments. We further develop a simple tight-binding model able to explain these findings. Finally, we show that the adiabatic Berry phase picture is violated in the Mn-rich limit of the alloys.

Time–Energy Uncertainty and Electronic Correlation in H+–Graphite Collisions

The formation of negative ions in the scattering of protons by a highly oriented pyrolytic graphite (HOPG) surface is theoretically and experimentally analyzed for a large scattering angle and compared with previous results obtained in the same system but for a forward scattering geometry. These experiments were motivated by the fact that the interaction of a hydrogen atom with a surface is the prototype system for studying the intra-atomic Coulomb repulsion in an s-like valence orbital localized in the atom. We tried to answer the open questions related to the electronic correlation effects and the influence of the detailed surface band structure by using appropriate theoretical models. The comparison with the experiment of theoretical results obtained by using different limit approximations of the electronic repulsion in the atomic state shows the expected validity ranges according to the ion velocity. However, the most remarkable conclusion obtained from this comparison is the nonvalidity of an adiabatic picture of the energy levels shifted by the interactions with the surface atoms, when the energy uncertainty introduced by the ion velocity becomes of the order of the electronic repulsion in the hydrogen ground state.

Influence of light-induced conical intersection on the photodissociation dynamics of D2(+) starting from individual vibrational levels.

Previous works have shown that dressing of diatomic molecules by standing or by running laser waves gives rise to the appearance of so-called light-induced conical intersections (LICIs). Because of the strong nonadiabatic couplings, the existence of such LICIs may significantly change the dynamical properties of a molecular system. In our former paper (J. Phys. Chem. A 2013, 117, 8528), the photodissociation dynamics of the D(2)(+) molecule were studied in the LICI framework starting the initial vibrational nuclear wave packet from the superposition of all the vibrational states initially produced by ionizing D(2). The present work complements our previous investigation by letting the initial nuclear wave packets start from different individual vibrational levels of D(2)(+), in particular, above the energy of the LICI. The kinetic energy release spectra, the total dissociation probabilities, and the angular distributions of the photofragments are calculated and discussed. An interesting phenomenon has been found in the spectra of the photofragments. Applying the light-induced adiabatic picture supported by LICI, explanations are given for the unexpected structure of the spectra.

Investigation of geometric phase effects in photodissociation dynamics at a conical intersection

We investigate the effect of the geometric phase (GP) on photodissociation dynamics at a two-dimensional symmetry-allowed conical intersection (CI). To disentangle the pure effect of the GP from other effects due to non-adiabatic couplings between the two coupled potential energy surfaces, we perform two different calculations, one adopting the diabatic representation which implicitly includes the GP, and another one using the adiabatic picture where GP effects are excluded. To interpret the impact of the GP on nuclear dynamics, we use a recent topological approach (Althorpe et al., 2008 [45]) to completely unwind the nuclear wavefunction from around the CI. This unwinding allows us to extract from the nuclear wavepacket two contributions of reaction paths that wind in different senses around the CI. The solely effect of the GP is to change the sign of the relative phase between their corresponding wavefunctions, and hence to convert any constructive (destructive) interference of the two components, in the asymptotic dissociative limit, into a destructive (constructive) one. This results in a change of the product-state vibrational distribution from only-even (-odd) quanta progression to only-odd (-even) quanta progression. Although our calculations are based on a reduced-dimensionality model Hamiltonian, our observations and conclusions should apply to realistic polyatomic molecules, and could be useful to interpret product-state vibrational distributions of photodissociation experiments.

Vibrational conical intersections in the water dimer

A recent paper by Hamm and Stock [Phys. Rev. Lett. 109, 173201 (2012)] has introduced the concept of vibrational conical intersections as a potential source of ultrafast vibrational relaxation, using the coupling between high-frequency OH modes and low-frequency intramolecular hydrogen bonding modes of malonaldehyde as an example. Here, the question is addressed whether such conical intersections may also appear for intermolecular hydrogen bonds. To that end, the water dimer [(H2O)2] is studied as a minimal model for the hydrogen bonding in liquid water. Although a significant separation of time scales between intramolecular and intermolecular degrees of freedom exists in (H2O)2, a standard normal-mode description is found to lead to a complete breakdown of the adiabatic ansatz. This is due to strong nonlinear couplings between high- and low-frequency normal modes, which in turn give rise to large overall non-adiabatic couplings. A valid adiabatic picture is obtained, on the other hand, when internal coordinates are employed. The resulting adiabatic potential energy surfaces indeed exhibit low-lying conical intersections, whose possible relevance for ultrafast relaxation and energy transfer in water is discussed.