Sensing ultrashort electronic coherent beating at conical intersections by single-electron pulses

Coherent raman scattering for optical detection of NMR in Pr³⁺:YAIO₃

Coherent excitation of materials via ultrafast laser pulses can have interesting, observable dynamics in time-resolved photoemission measurements. The broad spectral width of ultrafast pump pulses can coherently excite multiple exciton energy levels. When such coherently excited states are probed by means of photoemission spectroscopy, interference between the polarization of different exciton levels can lead to observable coherent exciton beats. Here, we present the theoretical formalism for evaluating the Time- and Angle- Resolved Photoemission Spectra (tr-ARPES) arising from the coherently excited exciton states. We subsequently apply our formalism to a simple model example of hydrogenic exciton energy levels to identify the dependencies that control the quantum beats. Our findings indicate that the most pronounced effect of coherent quantum excitonic beats is seen midway between the excited exciton energy levels and the central energy of the pump pulse provides tunability of this effect.

Conical intersections are formed when 2 or more electronic states become degenerate and give rise to ultrafast nonadiabatic processes such as radiation-less decay channels and geometric phase effects. The branching of nuclear wave packets near a conical intersection creates a coherent superposition of electronic states, which carries information about the energy difference of the involved states. X-ray Raman techniques have been proposed to observe the coherent superposition of the electronic states and to monitor the evolving electronic state separation. However, these techniques rely on the coherence generated as the wave packet passes through the conical intersection, and the electronic energy gap before the wave packet passes through the conical intersection is not tracked. In this paper, we theoretically demonstrate how a nonlinear Raman detection scheme can be used to gain further insight into the nonadiabatic dynamics in the vicinity of the conical intersection. We employ a combination of a resonant visible/infrared pulse and an off-resonant x-ray Raman probe to map the electronic state separation around the conical intersection. We demonstrate that this technique can achieve high contrast and is able to selectively probe the narrow electronic state separation around the conical intersection.

Acoustic phonon pulse generation and detection are investigated in a sample with three embedded GaAs/AlGaAs quantum wells by an ultrafast optical pump and probe technique at the temperatures 20 K and 300 K. Scanning the pump photon energies around the hh1-e1 resonances we find a strong variation of the transient reflectance and phase changes. These changes are compared with a numerical simulation based on probe light scattering due to the inhomogeneous photoelastic effect. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Spatiotemporal mapping of surface acoustic waves in isotropic and anisotropic materials

The transient reflectance is imaged in real time at surface plasmon polariton resonances in multilayer waveguide structures with an ultrafast optical pump and probe technique. We reveal a plasmon-mode dependence of the ultrafast temporal response.

We use an ultrafast optical pump and probe technique to investigate the propagation of subgigahertz surface acoustic waves on a 1 mm diameter glass sphere with an aluminum coating. A fiber-based pump setup generates the surface waves and a common-path interferometer images them in the time domain over the sphere surface as they pass through the pole opposite the source of excitation. Fourier analysis allows the acoustic spectrum of the acoustic source to be extracted and waves traveling in opposite directions to be isolated.

We report experimental and theoretical investigations of the behavior of coherent acoustic phonon pulses after propagation through millimeter-scale distances in crystalline Si. An ultrafast optical pump and probe technique is used to generate and detect the phonon pulses. The geometry of our experiment is such that we can make this measurement in either the far field or the near field of the acoustic source, allowing studies of diffraction effects in addition to dispersion and nonlinearity in the Si. We also present a rigorous derivation of the Korteweg--de Vries equation, which describes the behavior of these acoustic pulses in the nonlinear regime in one dimension. This one-dimensional (1D) model is combined with a 3D analysis of diffraction effects in anisotropic media in order to analyze far-field data.

Vibronic coherence has been studied for years, but direct comparisons between the rich experimental features and theory remain rare. In this work, we investigate the vibronic coherent quantum beat of a four-layer platinum carbonyl cluster [Pt3(CO)6]42- in a solution utilizing femtosecond vis-pump/vis-probe transient absorption spectroscopy. By varying the excitational wavelength, quantum beats coupled to either the electronic ground state or the excited state are selectively prepared. A 41cm-1 beat at the ground state with a phase flip at 615nm and a 28cm-1 beat at the excited state with a phase node at 735nm are observed. The beat amplitudes are asymmetric, stronger on the red side for ground state beats but weaker for excited state beats. Quantum chemistry calculations suggest that these beats result from coupling between the [Pt3(CO)6] layer motions and the electronic excitation. Theoretical model calculations for quantum beats at both electronic states are performed following the doorway-window approach. The calculations explain the oscillation frequency difference, the node positions, and the asymmetry. The beats with different frequencies result from vibronic coupling with different electronic states with the Herzberg-Teller (ground) or Franck-Condon term (excited) involved. The theoretical nodes occur at absorption and fluorescence centers, respectively, although experimental results show a slight blueshift. Quantum window operator calculations link the beat amplitude asymmetry to the Franck-Condon factor matrix imbalances, with the number of nodes dependent on the electronic dephasing rate. The theoretical insights for quantum beats are expected to be general, potentially helpful for the interpretation of observations in other systems.

The effect of a dissipative environment on the ultrafast nonadiabatic dynamics at conical intersections is analyzed for a two-state two-mode model chosen to represent the S2(ππ*)-S1(nπ*) conical intersection in pyrazine (the system) which is bilinearly coupled to infinitely many harmonic oscillators in thermal equilibrium (the bath). The system-bath coupling is modeled by the Drude spectral function. The equation of motion for the reduced density matrix of the system is solved numerically exactly with the hierarchy equation of motion method using graphics-processor-unit (GPU) technology. The simulations are valid for arbitrary strength of the system-bath coupling and arbitrary bath memory relaxation time. The present computational studies overcome the limitations of weak system-bath coupling and short memory relaxation time inherent in previous simulations based on multi-level Redfield theory [A. Kühl and W. Domcke, J. Chem. Phys. 2002, 116, 263]. Time evolutions of electronic state populations and time-dependent reduced probability densities of the coupling and tuning modes of the conical intersection have been obtained. It is found that even weak coupling to the bath effectively suppresses the irregular fluctuations of the electronic populations of the isolated two-mode conical intersection. While the population of the upper adiabatic electronic state (S2) is very efficiently quenched by the system-bath coupling, the population of the diabatic ππ* electronic state exhibits long-lived oscillations driven by coherent motion of the tuning mode. Counterintuitively, the coupling to the bath can lead to an enhanced lifetime of the coherence of the tuning mode as a result of effective damping of the highly excited coupling mode, which reduces the strong mode-mode coupling inherent to the conical intersection. The present results extend previous studies of the dissipative dynamics at conical intersections to the nonperturbative regime of system-bath coupling. They pave the way for future first-principles simulations of femtosecond time-resolved four-wave-mixing spectra of chromophores in condensed phases which are nonperturbative in the system dynamics, the system-bath coupling as well as the field-matter coupling.

The rates and outcomes of virtually all photophysical and photochemical processes are determined by conical intersections. These are regions of degeneracy between electronic states on the nuclear landscape of molecules where electrons and nuclei evolve on comparable timescales and thus become strongly coupled, enabling radiationless relaxation channels upon optical excitation. Due to their ultrafast nature and vast complexity, monitoring conical intersections experimentally is an open challenge. We present a simulation study on the ultrafast photorelaxation of uracil, based on a quantum description of the nuclei. We demonstrate an additional window into conical intersections obtained by recording the transient wavepacket coherence during this passage with an X-ray free-electron laser pulse. Two major findings are reported. First, we find that the vibronic coherence at the conical intersection lives for several hundred femtoseconds and can be measured during this entire time. Second, the time-dependent energy-splitting landscape of the participating vibrational and electronic states is directly extracted from Wigner spectrograms of the signal. These offer a physical picture of the quantum conical intersection pathways through visualizing their transient vibronic coherence distributions. The path of a nuclear wavepacket in the vicinity of the conical intersection is directly mapped by the proposed experiment.

A six-dimensional analytic potential-energy surface of the three valence states (N, V, Z) of ethene has been constructed on the basis of complete-active-space ab initio calculations and ab initio calculations with perturbation theory of second order based on a complete active reference space. The nuclear coordinate space is spanned by the torsion, the C–C stretch coordinate, the left and right pyramidalization and the symmetric and antisymmetric scissor coordinates. The C–H stretch coordinates and the CH2 rocking angles are kept frozen at their ground-state equilibrium value. A diabatic representation of the valence states of ethene has been constructed within the framework of a Hückel-type model. The diabatic potential-energy elements are represented as analytic functions of the relevant coordinates. The parameters of the analytic functions have been determined by a least-squares fit of the eigenvalues of the diabatic potential-energy matrix to the ab initio data for one-dimensional and two-dimensional cuts of the six-dimensional surface. As a function of the torsion, the analytic potential-energy surface describes the intersections of the V and Z states for torsional angles near 90°, which are converted into conical intersections by the antisymmetric scissor mode. As a function of pyramidalization of perpendicular ethene, it describes the intersections of the diabatic N and Z states, which are converted into conical intersections by displacements in the torsional mode. The analytic potential-energy surfaces can provide the basis for a quantum wave packet description of the internal conversion of photoexcited ethene to the electronic ground state via conical intersections.

The electronic structure of energetically low-lying excited singlet states of fluorobenzene molecules is investigated here. Increasing fluorine substitution alters the nature of the excited electronic states and the so-called perfluoro effect is observed for penta- and hexafluorobenzene. Detailed quantum chemistry calculations are carried out at the equation-of-motion coupled-cluster singles and doubles level of theory to establish the potential energy surfaces of the low-lying electronic states of mono-, di- (ortho- and meta-), and pentafluorobenzene molecules. A sequence of low-energy conical intersections among the electronic potential energy surfaces is established. It is found that increasing fluorine substitution lowers the energy of the pisigma* electronic state and leads to conical intersections between the S(1) and S(2) electronic states of pentafluorobenzene. Existence of numerous conical intersections among the excited electronic states of these molecules forms the mechanistic details underlying their nonradiative internal conversion. In particular, the slow and biexponential fluorescence emission in pentafluorobenzene is attributed to the existence of low-lying S(1)-S(2) conical intersections. The electronic structure data are analyzed in detail and the coupling mechanism among various electronic excited states of mono-, di-, and pentafluorobenzene molecules is established.

Elucidating the role of quantum coherences in energy migration within biological and artificial multichromophoric antenna systems is the subject of an intense debate. It is also a practical matter because of the decisive implications for understanding the biological processes and engineering artificial materials for solar energy harvesting. A supramolecular rhodamine heterodimer on a DNA scaffold was suitably engineered to mimic the basic donor-acceptor unit of light-harvesting antennas. Ultrafast 2D electronic spectroscopic measurements allowed identifying clear features attributable to a coherent superposition of dimer electronic and vibrational states contributing to the coherent electronic charge beating between the donor and the acceptor. The frequency of electronic charge beating is found to be 970 cm-1 (34 fs) and can be observed for 150 fs. Through the support of high level ab initio TD-DFT computations of the entire dimer, we established that the vibrational modes preferentially optically accessed do not drive subsequent coupling between the electronic states on the 600 fs of the experiment. It was thereby possible to characterize the time scales of the early time femtosecond dynamics of the electronic coherence built by the optical excitation in a large rigid supramolecular system at a room temperature in solution.

In the Born-Oppenheimer approximation for molecular dynamics as generalized by Born and Huang, nuclei move on multiple potential-energy surfaces corresponding to different electronic states. These surfaces may intersect at a point in the nuclear coordinates with the topology of a double cone. These conical intersections have important consequences for the dynamics. When an adiabatic electronic wave function is transported around a closed loop in nuclear coordinate space that encloses a conical intersection point, it acquires an additional geometric, or Berry, phase. The Schr\"odinger equation for nuclear motion must be modified accordingly. A conical intersection also permits efficient nonadiabatic transitions between potential-energy surfaces. Most examples of the geometric phase in molecular dynamics have been in situations in which a molecular point-group symmetry required the electronic degeneracy and the consequent conical intersection. Similarly, it has been commonly assumed that the conical intersections facilitating nonadiabatic transitions were largely symmetry driven. However, conical intersections also occur in the absence of any symmetry considerations. This review discusses computational tools for finding and characterizing the conical intersections in such systems. Because these purely accidental intersections are difficult to anticipate, they may occur more frequently than previously thought and in unexpected situations, making the geometric phase effect and the occurrence of efficient nonadiabatic transitions more commonplace phenomena. [S0034-6861(96)00404-7]