Scattering theory of one and two-photon molecular processes

Using a perturbation expansion of the transition operator T, a scattering theory of one and two-photon processes is developed. Distinction is made between Franck-Condon and Herzberg-Teller effects. The influence of each effect is analysed for vibrational and electronic absorption and finally for Raman scattering.     

Application of the finite element method to time-dependent quantum mechanics: II. H 2 + in a laser field

A finite element method in Cartesian coordinates in three dimensions is described to solve the time-dependent Schrödinger equation for H ₂ ⁺ in the presence of time-dependent electromagnetic fields. The ionization rates, nonlinear optical polarizabilities and harmonic generation spectrum of H ₂ ⁺ have been calculated for field directions parallel or perpendicular to the hydrogen molecule ion axis. Comparisons of the present numerical results with previously published calculations show that the finite element method reproduces perturbative results and can treat nonperturbativity arbitrary intense short pulses as it includes automatically both bound and continuum electronic states.     

Excitation profiles of resonance raman spectra in condensed media

A simple model, obtained by reducing a multimode system to a simple coordinate, is proposed to explain the broadening of RRS in liquid or solid media. It is shown that the coherent excitation of the near continuous background of low-frequency modes can cause homogeneous broadening of RRS profiles. The model is applied to the excitation profile of β-carotene.     

Coherent control of harmonic generation in superlattices: single-mode response

We study the harmonic generation spectrum in a semiconductor superlattice (a quantum-dot array) at slow relaxation. The effect of a single-mode response in an alternating rectangular (meander) electric field is demonstrated: For certain values of field parameters, the extremely wide discrete output spectrum with slowly decaying tails (multiharmonic generation) shrinks to one single harmonic (single-harmonic generation). Similarly, the effect is manifested in the transient continuous spectrum by diminishing the divergencies (peaks) at all odd harmonics but one. Substantial control over the spectrum is demonstrated.     

Quantum control of electron‐proton symmetry breaking in dissociative ionization of H2 by intense laser pulses

Forward and backward electron/proton ionization/dissociation spectra from one‐dimensional non‐Born‐Oppenheimer H₂ molecule exposed to ultrashort intense laser pulses ( W/cm², λ = 800 nm) have been computed by numerically solving the time‐dependent Schrödinger equation. The resulting above‐threshold ionization and above‐threshold dissociation spectra exhibit the characteristic forward‐backward asymmetry and sensitivity to the carrier‐envelope phase (CEP), particularly for high energies. A general framework for understanding CEP effects in the asymmetry of dissociative ionization of H₂ has been established. It is found that the symmetry breaking of electron‐proton distribution with π periodic modulation occurs for all CEPs except for ( integer) and the largest asymmetry coming from the CEP of . At least one of the electron and proton distributions is asymmetric when measured simultaneously. Inspection of the nuclear and electron wave packet dynamics provides further information about the relative contribution of the gerade and ungerade states of to the dissociation channel and the time delay of electrons in asymmetric ionization. © 2014 Wiley Periodicals, Inc.     

Imaging attosecond coherent electron motion in molecules

Molecular high harmonic generation (MHOHG) is obtained from numerical solution of the time dependent Schrödinger equation (TDSE) for the 3-D one electron linear system exposed to ultrashort (two-cycle) intense (I = 10¹⁴ W/cm²) IR laser pulse in order to illustrate and image coherent electron motion on attosecond (1 asec = 10⁻¹⁸ sec) time scale. Such electron motion can occur in electron wavepackets created by nonadiabatic interactions at avoided crossings near conical intersections or by asec photoexcitation. It is found that the MHOHG spectra can monitor electron localization on asec time scale.     

Long-range energy transfer and ionization in extended quantum systems driven by ultrashort spatially shaped laser pulses

The processes of ionization and energy transfer in a quantum system composed of two distant H atoms with an initial internuclear separation of 100 atomic units (5.29 nm) have been studied by the numerical solution of the time-dependent Schr?dinger equation beyond the Born-Oppenheimer approximation. Thereby it has been assumed that only one of the two H atoms was excited by temporally and spatially shaped laser pulses at various laser carrier frequencies. The quantum dynamics of the extended H-H system, which was taken to be initially either in an unentangled or an entangled ground state, has been explored within a linear three-dimensional model, including the two z coordinates of the electrons and the internuclear distance R. An efficient energy transfer from the laser-excited H atom (atom A) to the other H atom (atom B) and the ionization of the latter have been found. It has been shown that the physical mechanisms of the energy transfer as well as of the ionization of atom B are the Coulomb attraction of the laser driven electron of atom A by the proton of atom B and a short-range Coulomb repulsion of the two electrons when their wave functions strongly overlap in the domain of atom B.     

Spectral Asymptotics for Higher-Order Ordinary Differential Equations

This paper gives one-term componentwise asymptotics for theM and spectral matrices of a self-adjoint realisation of aneven-order ordinary differential expression. The underlyinginterval is assumed to have at least one regular endpoint, andthe boundary conditions are supposed to be separated. Furthermore,the weight function and the reciprocal of the highest-ordercoefficient are supposed to be of regular variation at the regularendpoint, in the sense of Bingham, Goldie and Teugels. 1991Mathematics Subject Classification: 34B24, 34E05.     

Laser phase control of high-order harmonic generation at large internuclear distance: the H+ -H2+ system

Exact (Born-Oppenheimer) 3-D numerical solutions of the time-dependent Schr?dinger equation are obtained for the one electron linear H+-H2+ atom-molecule system at large internuclear distance R in interaction with two-cycles intense (I>10(14) W cm(-2)) 800 nm laser pulses. High-order harmonic generation (HHG) spectra are obtained with an energy cutoff larger than the atomic maximum of I(p)+3U(p), where I(p) is the ionization potential and U(p) is the ponderomotive energy. At large R, this extended cutoff is shown to be related to the nature of electron transfer, whose direction is shown to depend critically on the carrier-envelope phase (CEP) of the ultrashort pulse. Constructive and destructive interferences in the HHG spectrum resulting from coherent superpositions of electronic states in the H+-H2+ system are interpreted in terms of multiple electron trajectories extracted from a time profile analysis.