Excited Wave Packet Research Articles

Direct Probe of Conical Intersection Photochemistry by Time-Resolved X-ray Magnetic Circular Dichroism.

The direct probing of photochemical dynamics by detecting the electronic coherence generated during passage through conical intersections is an intriguing challenge. The weak coherence signal and the difficulty in preparing purely excited wave packets that exclude coherence from other sources make it experimentally challenging. We propose to use time-resolved X-ray magnetic circular dichroism to probe the wave packet dynamics around the conical intersection. The magnetic field amplifies the relative strength of the electronic coherence signal compared to populations through the magnetic field response anisotropy. More importantly, since the excited state relaxation through conical intersections involves a change of parity, the magnetic coupling matches the symmetry of the response function with the electronic coherence, making the coherence signal only sensitive to the conical intersection induced coherence and excludes the pump pulse induced coherence between the ground state and excited state. In this theoretical study, we apply this technique to the photodissociation dynamics of a pyrrole molecule and demonstrate its capability of probing electronic coherence at a conical intersection as well as population transfer. We demonstrate that a magnetic field can be effectively used to extract novel information about electron and nuclear molecular dynamics.

On a Nonlinear Locally Resonant Metamaterial With Resistance-Inductance Shunt

Abstract Numerous recent works have established the potential of various types of metamaterials for simultaneous vibration control and energy harvesting. In this paper, we investigate a weakly nonlinear metamaterial with electromechanical (EM) local resonators coupled to a resistance-inductance shunt circuit, a system with no previous examination in the literature. An analytical solution is developed for the system, using the perturbation method of multiple scales, and validated through direct numerical integration. The resulting linear and nonlinear band structures are used for parametric analysis of the system, focusing on the effect of resonator and shunt circuit parameters on band gap formation and vibration attenuation. This band structure analysis informs further study of the system through wavepacket excitation as well as spectro-spatial analysis. The voltage response of the system is studied through spatial profiles and spectrograms to observe the effects of shunt inductance, nonlinearity, and their interactions. Results describe the impact of adding a shunted inductor, including significant changes to the band structure; multiple methods of tuning band gaps and pass bands of the system; and changes to wave propagation and voltage response. The results demonstrate the flexibility of the proposed metamaterial and its potential for both vibration control and energy harvesting, specifically compared to a previously studied system with resistance-only shunt.

Quantum tomography of molecules using ultrafast electron diffraction.

We propose a quantum tomography (QT) approach to retrieve the temporally evolving reduced density matrix in electronic state basis, where the populations and coherence between the ground state and excited state are reconstructed from the ultrafast electron diffraction signal. In order to showcase the capability of the proposed QT approach, we simulate the nuclear wavepacket dynamics and ultrafast electron diffraction of photoexcited pyrrole molecules using the abinitio quantum chemical CASSCF method. From the simulated time-resolved diffraction data, we retrieve the evolving density matrix in a crude diabatic representation basis and reveal the symmetry of the excited pyrrole wavepacket. Our QT approach opens the route to make a quantum version of "molecular movie" that covers the electronic degree of freedom and equips ultrafast electron diffraction with the power to reveal the coherence between electronic states, relaxation, and dynamics of population transfer.

Wave-packet spreading in the disordered and nonlinear Su-Schrieffer-Heeger chain

We numerically investigate the characteristics of the long-time dynamics of a single-site wave-packet excitation in a disordered and nonlinear Su-Schrieffer-Heeger model. In the linear regime, as the parameters controlling the topology of the system are varied, we show that the transition between two different topological phases is preceded by an anomalous diffusion, in contrast to Anderson localization within these topological phases. In the presence of onsite nonlinearity this feature is lost due to mode-mode interactions. Direct numerical simulations reveal that the characteristics of the asymptotic nonlinear wave-packet spreading are the same across the whole studied parameter space. Our findings underline the importance of mode-mode interactions in nonlinear topological systems, which must be studied in order to define reliable nonlinear topological markers.

Rehybridization dynamics into the pericyclic minimum of an electrocyclic reaction imaged in real-time

Electrocyclic reactions are characterized by the concerted formation and cleavage of both σ and π bonds through a cyclic structure. This structure is known as a pericyclic transition state for thermal reactions and a pericyclic minimum in the excited state for photochemical reactions. However, the structure of the pericyclic geometry has yet to be observed experimentally. We use a combination of ultrafast electron diffraction and excited state wavepacket simulations to image structural dynamics through the pericyclic minimum of a photochemical electrocyclic ring-opening reaction in the molecule α-terpinene. The structural motion into the pericyclic minimum is dominated by rehybridization of two carbon atoms, which is required for the transformation from two to three conjugated π bonds. The σ bond dissociation largely happens after internal conversion from the pericyclic minimum to the electronic ground state. These findings may be transferrable to electrocyclic reactions in general.

Anyonic Statistics Revealed by the Hong-Ou-Mandel Dip for Fractional Excitations.

The fractional quantum Hall effect (FQHE) is known to host anyons, quasiparticles whose statistics is intermediate between bosonic and fermionic. We show here that Hong-Ou-Mandel (HOM) interferences between excitations created by narrow voltage pulses on the edge states of a FQHE system at low temperature show a direct signature of anyonic statistics. The width of the HOM dip is universally fixed by the thermal time scale, independently of the intrinsic width of the excited fractional wave packets. This universal width can be related to the anyonic braiding of the incoming excitations with thermal fluctuations created at the quantum point contact. We show that this effect could be realistically observed with periodic trains of narrow voltage pulses using current experimental techniques.

Equatorial restriction of the photoinduced Jahn-Teller switch in Mn(iii)-cyclam complexes.

Ultrafast transient absorption spectra were recorded for solutions of [MnIII(cyclam)(H2O)(OTf)][OTf]2 (cyclam = 1,4,8,11-tetraazacyclotetradecane and OTf = trifluoromethanesulfonate) in water to explore the possibility to restrict the equatorial expansion following photoexcitation of the dxy ← dz2 electronic transition, often resulting in a switch from axial to equatorial Jahn-Teller distortion in MnIII complexes. Strong oscillations were observed in the excited state absorption signal and were attributed to an excited state wavepacket. The structural rigidity of the cyclam ligand causes a complex reaction coordinate with frequencies of 333, 368, 454 and 517 cm-1, and a significantly shorter compressed-state lifetime compared to other MnIII complexes with less restricted equatorial ligands. Complementary density functional theory quantum chemistry calculations indicate a switch from an axially elongated to a compressed structure in the first excited quintet state Q1, which is accompanied by a modulation of the axial tilt angle. Computed harmonic frequencies for the axial stretching mode (∼379 cm-1) and the equatorial expansions (∼410 and 503 cm-1) of the Q1 state agree well with the observed coherences and indicate that the axial bond length contraction is significantly larger than the equatorial expansion, which implies a successful restriction of the wavepacket motion. The weak oscillation observed around 517 cm-1 is assigned to a see-saw motion of the axial tilt (predicted ∼610 cm-1). The results provide insights into the structural perturbations to the molecular evolution along excited state potential energy surfaces of MnIII octahedral complexes and can be used to guide the synthesis of optically controlled MnIII-based single-molecule magnets.

Real-time electronic energy current and quantum energy flux in molecules.

Intra- and inter-molecular electronic energy current is formulated by defining the probability current of electronic energy, called the energy flux. Among vast possible applications to electronic energy transfer phenomena, including chemical reaction dynamics, here we present a first numerical example from highly excited nonadiabatic electron wavepacket dynamics of a boron cluster B12.

Effect of molecular orientation on predissociation of NaI molecules

Based on the time-depend quantum wave packet method, a scheme is proposed to investigate the effect of the molecular orientation on the predissociation of NaI molecules. The molecular orientation in the ground state is steered by THz half-cycle pulse. Then the oriented molecule is excited by femtosecond pump pulse. Molecular orientation has a significant effect on the angular distribution of wave packets. The excited wave packet is distributed in a more narrow region with the increase of molecular orientation degree. The angular distribution of dissociated products is essentially consistent with the angular distribution of excited wave packet. The dissociation probability is proportional to the excitation probability of pump pulse, which is related to the molecular orientations. Compared with the result of predissociation without molecular orientation, the maximal dissociation probability can increase by 6.5% in our work. The electric field intensity of the pump pulse also has a significant influence on dissociation probability.

Coherent Control of Molecular Dissociation by Selective Excitation of Nuclear Wave Packets.

We report on pump-probe control schemes to manipulate fragmentation product yields in p-nitrotoluene (PNT) cation. Strong field ionization of PNT prepares the parent cation in the ground electronic state, with coherent vibrational excitation along two normal modes: the C–C–N–O torsional mode at 80 cm−1 and the in-plane ring-stretching mode at 650 cm−1. Both vibrational wave packets are observed as oscillations in parent and fragment ion yields in the mass spectrum upon optical excitation. Excitation with 650 nm selectively fragments the PNT cation into , whereas excitation with 400 nm selectively produces and . In both cases the ion yield oscillations result from torsional wave packet excitation, but 650 and 400 nm excitation produce oscillations with opposite phases. Ab initio calculations of the ground and excited electronic potential energy surfaces of PNT cation along the C–C–N–O dihedral angle reveal that 400 nm excitation accesses an allowed transition from D0 to D6 at 0° dihedral angle, whereas 650 nm excitation accesses a strongly allowed transition from D0 to D4 at a dihedral angle of 90°. This ability to access different electronic excited states at different locations along the potential energy surface accounts for the selective fragmentation observed with different probe wavelengths. The ring-stretching mode, only observed using 800 nm excitation, is attributed to a D0 to D2 transition at a geometry with 90° dihedral angle and elongated C–N bond length. Collectively, these results demonstrate that strong field ionization induces multimode coherent excitation and that the vibrational wave packets can be excited with specific photon energies at different points on their potential energy surfaces to induce selective fragmentation.

Population and coherence dynamics in large conjugated porphyrin nanorings

In photosynthesis, nature exploits the distinctive electronic properties of chromophores arranged in supramolecular rings for efficient light harvesting. Among synthetic supramolecular cyclic structures, porphyrin nanorings have attracted considerable attention as they have a resemblance to naturally occurring light-harvesting structures but offer the ability to control ring size and the level of disorder. Here, broadband femtosecond transient absorption spectroscopy, with pump pulses in resonance with either the high or the low energy sides of the inhomogeneously broadened absorption spectrum, is used to study the population dynamics and ground and excited state vibrational coherence in large porphyrin nanorings. A series of fully conjugated, alkyne bridged, nanorings constituted of between ten and forty porphyrin units is studied. Pump-wavelength dependent fast spectral evolution is found. A fast rise or decay of the stimulated emission is found when large porphyrin nanorings are excited on, respectively, the high or low energy side of the absorption spectrum. Such dynamics are consistent with the hypothesis of a variation in transition dipole moment across the inhomogeneously broadened ground state ensemble. The observed dynamics indicate the interplay of nanoring conformation and oscillator strength. Oscillatory dynamics on the sub-ps time domain are observed in both pumping conditions. A combined analysis of the excitation wavelength-dependent transient spectra along with the amplitude and phase evolution of the oscillations allows assignment to vibrational wavepackets evolving on either ground or excited states electronic potential energy surfaces. Even though porphyrin nanorings support highly delocalized electronic wavefunctions, with coherence length spanning tens of chromophores, the measured vibrational coherences remain localised on the monomers. The main contributions to the beatings are assigned to two vibrational modes localised on the porphyrin cores: a Zn–N stretching mode and a skeletal methinic/pyrrolic C–C stretching and in-plane bending mode.

Wave Packet Control and Simulation Protocol for Entangled Two-Photon Absorption of Molecules.

Quantum light spectroscopy, providing novel molecular information nonaccessible by classical light, necessitates new computational tools when applied to complex molecular systems. We introduce two computational protocols for the molecular nuclear wave packet dynamics interacting with an entangled photon pair to produce an entangled two-photon absorption signal. The first involves summing over transition pathways in a temporal grid defined by two light-matter interaction times accompanied by the field correlation functions of quantum light. The signal is obtained by averaging over the two time distribution characteristics of the entangled photon state. The other protocol involves a Schmidt decomposition of the entangled light and requires summing over the Schmidt modes. We demonstrate how photon entanglement can be used to control and manipulate the two-photon excited nuclear wave packets in a displaced harmonic oscillator model.

Effect of Pressure Gradient on Local Excitation of Boundary-layer Instability Due to Free-stream Turbulence and Micro Surface Roughness

The prediction and control of the laminar-turbulent transition is crucial to the designs of vehicles, turbines, etc. The initial condition of transition depends on the exciting process of boundary-layer instability, which is the key to implement its prediction and control. The current researches confirm that the exciting process of boundary-layer instability, namely receptivity, is affected not only by different types of free-stream disturbances and shape parameters of surface roughness elements, but also by the pressure gradient of mean flow. Hence, we study the effect of pressure-gradient on local excitation of boundary-layer instability under the interaction of the low-level, isotropic free-stream turbulence and micro surface roughness in this work. The numerical results reveal the pressure-gradient effect on the receptive process and the group speed of excited wave packets in the Falkner-Skan boundary layer. The favorable/adverse pressure gradients (FPG/APG) are found to be able to promote/suppress the excitation and subsequent evolution of Tollmien–Schlichting (T-S) waves. Then the relations of the pressure gradient with the amplitude, growth rate, wave number, phase speed and shape function of excited T-S waves are studied.

Site-specific generation of excited state wavepackets with high-intensity attosecond x rays.

High-intensity attosecond x rays can produce coherent superpositions of valence-excited states through two-photon Raman transitions. The broad-bandwidth, high-field nature of the pulses results in a multitude of accessible excited states. Multiconfigurational quantum chemistry with the time-dependent Schrödinger equation is used to examine population transfer dynamics in stimulated x-ray Raman scattering of the nitric oxide oxygen and nitrogen K-edges. Two pulse schemes initiate wavepackets of different characters and demonstrate how chemical differences between core-excitation pathways affect the dynamics. The population transfer to valence-excited states is found to be sensitive to the electronic structure and pulse conditions, highlighting complexities attributed to the Rabi frequency. The orthogonally polarized two-color-pulse setup has increased selectivity while facilitating longer, less intense pulses than the one-pulse setup. Population transfer in the 1s → Rydberg region is more effective but less selective at the nitrogen K-edge; the selectivity is reduced by double core-excited states. Result interpretation is aided by resonant inelastic x-ray scattering maps.

Validating fewest-switches surface hopping in the presence of laser fields.

The capability of fewest-switches surface hopping (FSSH) to describe non-adiabatic dynamics under explicit excitation with external fields is evaluated. Different FSSH parameters are benchmarked against multi-configurational time dependent Hartree (MCTDH) reference calculations using SO2 and 2-thiocytosine as model, yet realistic, molecular systems. Qualitatively, FSSH is able to reproduce the trends in the MCTDH dynamics with (also without) an explicit external field; however, no set of FSSH parameters is ideal. The adequate treatment of the overcoherence in FSSH is revealed as the driving factor to improve the description of the excitation process with respect to the MCTDH reference. Here, two corrections were tested: the augmented-FSSH (AFSSH) correction and the energy-based decoherence correction. A dependence on the employed basis is detected in AFSSH, performing better when spin-orbit and external laser field couplings are treated as off-diagonal elements instead of projecting them onto the diagonal of the Hamilton operator. In the presence of an electric field, the excited state dynamics was found to depend strongly on the vector used to rescale the kinetic energy along after a transition between surfaces. For SO2, recurrence of the excited wave packet throughout the duration of the applied laser pulse is observed for laser pulses (>100 fs), resulting in additional interferences missed by FSSH and only visible in variational multi-configurational Gaussian when utilizing a large number of Gaussian basis functions. This feature vanishes when going toward larger molecules, such as 2-thiocytosine, where this effect is barely visible in a laser pulse 200 fs long.

Vibronic resonance is inadequately described by one-particle basis sets

Vibrational-electronic (vibronic) resonance and its possible role in energy and charge transfer have been experimentally and theoretically investigated in several photosynthetic proteins. Using a dimer modeled on a typical photosynthetic protein, we contrast the description of such excitons provided by an exact basis set description, as opposed to a basis set with reduced vibrational dimensionality. Using a reduced analytical description of the full Hamiltonian, we show that in the presence of vibrational excitation both on electronically excited as well as unexcited sites, constructive interference between such basis states causes vibronic coupling between excitons to become progressively stronger with increasing quanta of vibrational excitation. This effect leads to three distinguishing features of excitons coupled through a vibronic resonance, which are not captured in basis sets that restrict ground state vibrations: (1) the vibronic resonance criterion itself, (2) vibronically assisted perfect delocalization between sites even though purely electronic mixing between the sites is imperfect due to energetic disorder, and (3) the nuclear distortion accompanying vibronic excitons becoming increasingly larger for resonant vibronic coupling involving higher vibrational quanta. In terms of spectroscopically observable limitations of reduced basis set descriptions of vibronic resonance, several differences are seen in absorption and emission spectra but may be obscured on account of overwhelming line broadening. However, we show that several features such as vibronic exciton delocalization and vibrational distortions associated with electronic excitations, which ultimately dictate the excited state wavepacket motions and relaxation processes, are fundamentally not described by basis sets that restrict ground state vibrations.

Smooth periodic gauge satisfying crystal symmetry and periodicity to study high-harmonic generation in solids

Transition dipole moments (TDM) between energy bands of solids deserve special attention nowadays as intense lasers can easily drive non-adiabatic transitions of excited electron wave packets across the Brillouin zones. The TDM is required to be continuous, satisfying crystal symmetry, and periodic at zone boundaries. While present day ab-initio algorithms are powerful in calculating band structures of solids, they all introduced random phases into the eigenfunctions at each crystal momentum k. In this paper, we show how to choose a ``smooth-periodic'' gauge where TDMs can be smooth versus k, preserving crystal symmetry, as well as maintaining periodic at zone boundaries. Based on band structure and TDMs in the ``smooth-periodic'' gauge calculated from ab-initio algorithms, we revisit high-order harmonic generation from MgO which exhibits inversion symmetry and ZnO which has broken symmetry. The symmetry properties of TDMs with respect to k ensure the absence of even-order harmonics in system with inversion symmetry, while the TDM in the `smooth-periodic'' gauge for ZnO is shown to enhance even harmonics that were underestimated in previous simulations. These results reveal the importance of correctly treating the complex TDMs in nonlinear laser-solid interactions which has been elusive so far.

Stochastic core spin-up in massive stars – implications of 3D simulations of oxygen shell burning

ABSTRACT It has been suggested based on analytic theory that even in non-rotating supernova progenitors stochastic spin-up by internal gravity waves (IGWs) during the late burning stages can impart enough angular momentum to the core to result in neutron star birth spin periods below $100\, \mathrm{ms}$, and a relatively firm upper limit of $500\, \mathrm{ms}$ for the spin period. We here investigate this process using a 3D simulation of oxygen shell burning in a 3 M⊙ He star. Our model indicates that stochastic spin-up by IGWs is less efficient than previously thought. We find that the stochastic angular momentum flux carried by waves excited at the shell boundary is significantly smaller for a given convective luminosity and turnover time than would be expected from simple dimensional analysis. This can be explained by noting that the waves launched by overshooting convective plumes contain modes of opposite angular wavenumber with similar amplitudes, so that the net angular momentum of excited wave packets almost cancels. We find that the wave-mediated angular momentum flux from the oxygen shell follows a random walk, but again dimensional analysis overestimates the random walk amplitudes since the correlation time is only a fraction of the convective turnover time. Extrapolating our findings over the entire lifetime of the last burning stages prior to collapse, we predict that the core angular momentum from stochastic spin-up would translate into long birth spin periods of several seconds for low-mass progenitors and no less than $100\, \mathrm{ms}$ even for high-mass progenitors.

ON GENERATION OF A WAVE PACKAGE IN A WAVEGUIDE, FILLED ACTIVE MEDIUM

Excitation of electromagnetic waves in a waveguide with a medium, which is a two-level system, is considered. To describe the processes, both classical electrodynamics methods and quantum mechanics methods are used. The nature of the processes under study turns out to depend on the relationship between the Rabi frequency and the line width of the excited wave packet. It is shown that if the field energy density is high, then spatially inhomogeneous Rabi frequencies arise, which leads to oscillatory behavior of the wave field amplitudes. If the levels of the excited field are small, then the dynamics of the two-level quantum system becomes monotonic and the population inversion tends to zero.

Substituent effects on nonadiabatic excited state dynamics: Inertial, steric, and electronic effects in methylated butadienes.

The photochemical dynamics of double-bond-containing hydrocarbons is exemplified by the smallest alkenes, ethylene and butadiene. Chemical substituents can alter both decay timescales and photoproducts through a combination of inertial effects due to substituent mass, steric effects due to substituent size, and electronic (or potential) effects due to perturbative changes to the electronic potential energy surface. Here, we demonstrate the interplay of different substituent effects on 1,3-butadiene and its methylated derivatives using a combination of ab initio simulation of nonadiabatic dynamics and time-resolved photoelectron spectroscopy. The purely inertial effects of methyl substitution are simulated through the use of mass 15 "heavy-hydrogen" atoms. As expected from both inertial and electronic influences, the excited-state dynamics is dominated by pyramidalization at the unsubstituted carbon sites. Although the electronic effects of methyl group substitution are weak, they alter both decay timescales and branching ratios by influencing the initial path taken by the excited wavepacket following photoexcitation.