Sequences of ultrafast non-resonant multiphoton transitions in a three-electronic level molecule

Non-resonant multiphoton transitions between three electronic states of a molecular system are studied. Based on a projection operator formalism which is formulated in the framework of the so-called time-local as well as the time-nonlocal approach, time-dependent Schrödinger equations are obtained, which include effective couplings to the laser field. For both procedures a slowly varying amplitude approximation can be invoked. The resulting time-local equations are solved in a much more efficient way than the original effective Schrödinger equations. The validity of these approximations is verified numerically for a two-photon process. Furthermore, the effective Schrödinger equations are specified to sequences of two-photon and three-photon transitions. The derived equations are applied to a molecular system consisting of three electronic states with Morse-type potential energy curves. Using different laser pulse scenarios the conditions are discussed under which a sequence of two-photon and three-photon transitions can take place.     

One-color reversible control of photochromic reactions in a diarylethene derivative: three-photon cyclization and two-photon cycloreversion by a near-infrared femtosecond laser pulse at 1.28 μm

One-color control of colorization/decolorization reactions of diarylethene molecules was attained by using nonresonant high-order multiphoton absorption processes with a near-infrared (NIR) femtosecond laser pulse at 1.28 μm with 35 fs full width at half-maximum (fwhm). The intensity of a rather weak laser pulse (<1 nJ/pulse) can induce the simultaneous three-photon absorption leading to the colorization, while much weaker intensity induces two-photon absorption resulting in the decolorization. The spatial patterning concomitant with higher-order multiphoton absorption processes was also demonstrated.     

光电子成像方法研究Xe时间分辨多光子电离过程

利用自行研制的离子成像检测器研究了Xe的飞秒时间分辨双色多光子电离过程.Xe的408nm多光子电离对比实验结果表明,该离子成像检测器与相应的进口产品具有相近的光电子能量分辨率.在272nm飞秒激光作用下,3光子电离产生能量为1.57和0.26eV的光电子,分别对应于Xe+的两个自旋态;在408nm飞秒激光作用下,还观察到第一级阈上电离产生的光电子.在双色飞秒时间分辨实验中,随着两束光相对时间的改变,光电子能谱出现了一系列的变化;随着两束光时间重合程度的增加,由双色多光子电离(3+1'或4'+1)产生的光电子信号逐渐加强;在第二束光的作用下,由第一束单色光产生的光电子出现能量红移,第二束光同时也导致中间态布居数减少.这种光电子能谱的红移现象反映了原子体系中激光场诱导有质动力势的时间分辨动态调制过程.     

Study of IR multiple-photon absorption (MPA) of CF3Br

An extensive numerical analysis of experimental multiple-photon absorption (MPA) data on CF₃Br is presented. The MPA spectra of CF₃Br show several structures which have been identified as multiphoton resonances of different order and evidence has been found for the occurrence of multiphoton transitions starting from the first excited state. Different levels of approximation have been used in modelling the energy states in order to quantitatively reproduce the experimental features. The effect of rotations on the excitation spectra is discussed as well as the inclusion of a thermal distribution over the initial rotational and vibrational states.     

Femtosecond multiphoton ionization of pyrrole

The photoionization dynamics of pyrrole are investigated by using a photoelectron imaging method and a tunable femtosecond laser. Two-photon nonresonant ionization experiments in the wavelength range from 261 to 298 nm indicate that the cation and neutral ground states have similar structures. The main vibrational excitation in the cation ground state is the v(8) mode. Two-photon absorption at 406 nm projects neutral pyrrole into a mixed state comprising the 1B(2) valence and 3p Rydberg states. Ionization from this mixed state mainly results in the overtone excitation of vibrational mode v(8) and v(9) of the cation state. In the wavelength range from 336 to 364 nm, a mixed state comprising the 3d/4s Rydberg and the 4A(1) valence states are populated by the absorption of two photons through vibronic coupling. The partition ratio among these states varies with the excitation wavelength, resulting in dramatic changes in both kinetic energy distributions and angular distributions. As the laser wavelength becomes shorter, from 336 to 314 nm, higher excited states, 3B(2), 5A(1), 6A(1), 7B(1) and 4B(2), can be populated. Photoelectron angular distributions provide supplementary verification of assignments. Our experiments indicate that femtosecond multiphoton ionization and photoelectron imaging methods are powerful tools for investigating short-lived intermediated excited states, which cannot be detected in nanosecond experiments.     

A molecular theory of inhomogeneous broadening,including the correlation between different transitions,in liquids and glasses

Summary We present a molecular theory of the energy distributions for the internal quantum states of a solute in a liquid or glassy solvent. We show that the energy distributions for different states are correlated in a way that depends on the solute-solvent interactions. We show how the theory can be modified easily to describe the transition-energy distributions for different pairs of states, which are of course related to inhomogeneously broadened absorption spectra. We also show that the distributions for different transitions are correlated, and describe how this correlation is measured by nonresonant fluorescence- and phosphorescence-line-narrowing and hole-burning experiments. The theory provides a microscopic framework within which to interpret different phenomenological models. For the case of a Lennard-Jones solute in a Lennard-Jones liquid solvent, we compare our theory to Monte Carlo simulation.     

Femtosecond time-resolved photoelectron-photoion coincidence imaging of multiphoton multichannel photodynamics in NO2

The multiphoton multichannel photodynamics of NO(2) has been studied using femtosecond time-resolved coincidence imaging. A novel photoelectron-photoion coincidence imaging machine was developed at the laboratory in Amsterdam employing velocity map imaging and "slow" charged particle extraction using additional electron and ion optics. The NO(2) photodynamics was studied using a two color pump-probe scheme with femtosecond pulses at 400 and 266 nm. The multiphoton excitation produces both NO(2) (+) parent ions and NO(+) fragment ions. Here we mainly present the time dependent photoelectron images in coincidence with NO(2) (+) or NO(+) and the (NO(+),e) photoelectron versus fragment ion kinetic energy correlations. The coincidence photoelectron spectra and the correlated energy distributions make it possible to assign the different dissociation pathways involved. Nonadiabatic dynamics between the ground state and the A (2)B(2) state after absorption of a 400 nm photon is reflected in the transient photoelectron spectrum of the NO(2) (+) parent ion. Furthermore, Rydberg states are believed to be used as "stepping" states responsible for the rather narrow and well-separated photoelectron spectra in the NO(2) (+) parent ion. Slow statistical and fast direct fragmentation of NO(2) (+) after prompt photoelectron ejection is observed leading to formation of NO(+)+O. Fragmentation from both the ground state and the electronically excited a (3)B(2) and b (3)A(2) states of NO(2) (+) is observed. At short pump probe delay times, the dominant multiphoton pathway for NO(+) formation is a 3x400 nm+1x266 nm excitation. At long delay times (>500 fs) two multiphoton pathways are observed. The dominant pathway is a 1x400 nm+2x266 nm photon excitation giving rise to very slow electrons and ions. A second pathway is a 3x400 nm photon absorption to NO(2) Rydberg states followed by dissociation toward neutral electronically and vibrationally excited NO(A (2)Sigma,v=1) fragments, ionized by one 266 nm photon absorption. As is shown in the present study, even though the pump-probe transients are rather featureless the photoelectron-photoion coincidence images show a complex time varying dynamics in NO(2). We present the potential of our novel coincidence imaging machine to unravel in unprecedented detail the various competing pathways in femtosecond time-resolved multichannel multiphoton dynamics of molecules.     

Mono- and bichromatic electron dynamics: LiH, a test case

This paper describes an electron dynamics method where the time dependence of an external oscillating electric field is the perturbing part of the Hamiltonian. Application of the electric field induces charge movement inside the molecule and electronic transitions between the molecular orbitals. The test system is the neutral LiH molecule. The method is applied to wave functions calculated using the B3LYP (hybrid) density functional, with the STO-3G and the 6-31+G basis sets. The molecule undergoes full population inversion between the HOMO and the LUMO when the electric field is in resonance with the HOMO-LUMO energy gap. The magnitude of the electric field directly affects the rate at which electronic transitions occur and the rate at which charges move between lithium and hydrogen atoms. The method is used to model both monochromatic and bichromatic multiphoton effects in LiH. Monochromatic one-, two- and three-photon transitions occur between the HOMO, LUMO and two other virtual orbitals. There is evidence of both [1+2] direct and [1+1+1] stepwise multiphoton transitions. Bichromatically, two "laser" pulses are applied at different frequencies. Electronic transitions can be fine-tuned to occur via pre-specified pathways of virtual molecular orbitals.     

Comparative study of the photoassociation reaction of He + X+→ HeX+ (X = H,D): Including multiphoton transitions and dissociations

Using the time-dependent quantum wave packet method, the photoassociation (PA) processes of He + H ⁺→ HeH⁺ and He + D ⁺→ HeD⁺, driven by the sin²-shaped femtosecond laser pulse in the electronic ground state, including multiphoton transitions and dissociations, are investigated for a wide range of initial collision momenta spanning from 1 to 4 a.u. (or for the collision energy roughly in the ranges of 0.009∼0.148 eV and 0.006∼0.089 eV for HeH⁺ and HeD⁺ systems, respectively). It is found that, at some collision momenta, multiphoton transitions to deeply bound states are inevitable to occur and can greatly decrease the PA probability of the target state that selected is the vibrational state v = 6. For the dissociation process, the higher-order (two- and three-photon) dissociations, measured from the target state, tend to be significant at relative high collision energies, which implies that above-threshold dissociations may also be an important loss mechanism in the PA process. In addition, it is also shown that the higher-order dissociation is much stronger for HeH⁺ systems than that for HeD⁺ systems at a given collision momentum, and could be enhanced by the strong transitions among deeply bound states.     

Femtosecond time-resolved molecular multiphoton ionization and fragmentation of Na2: experiment and quantum mechanical calculations

We present a comparison between experimental and theoretical results for pump/probe multiphoton ionizing transitions of the sodium dimer, initiated by femtosecond laser pulses. It is shown that the motion of vibrational wave packets in two electronic states is probed simultaneously and their dynamics is reflected in the total Na ₂ ⁺ ion signal which is recorded as a function of the time delay between pump and probe pulse. The time dependent quantum calculations demonstrate that two ionization pathways leading to the same final states of the molecular ion exist: one gives an oscillating contribution to the ion signal, the other yields a constant background. From additional measurements of the Na⁺-transient photofragmentation spectrum it is deduced that another ionization process leading to different final ionic states exists. The process includes the excitation of a doubly excited bound Rydberg state. This conclusion is supported by the theoretical simulation.     

Theory for the optical properties of small Hg n clusters

The static and dynamical polarizabilities of the Hg-dimer are calculated by using a Hubbard Hamiltonian to describe the electronic structure. The Hamiltonian is diagonalized exactly within a subspace of second-quantized electronic states from which only multiply ionized atomic configurations have been excluded. With this approximation we can describe the most important electronic transitions including the effect of charge fluctuations. We analyze the polarizability as a function of the intraatomic Coulomb interaction which represents the repulsion between electrons. We obtain that this interaction results in strong electronic correlations in the excited states and increases the first excitation energy of the dimer by 0.8 eV in comparison to a calculation which neglects correlations, resulting in a better agreement with the experiment.     

Population inversion,temperature, and photon distributions of the generalized fermionic Ising ferromagnetic model: Path‐integral representation of the spin system

The quantum partition function and the emerging energy of a fermionic Ising ferromagnetic model involving all possible interactions (generalized Ising model) are obtained from an appropriate tracing of the analytic propagator path integral over Grassmann variable coherent nonorthogonal states in the imaginary time domain. The dynamics derived from the interaction of this system with a single‐mode cavity field in the rotating wave approximation is investigated for nonresonant states within the framework of the Jaynes–Cummings two‐level model consisting of the vacuum state and a thermally averaged manifold of excited states. Time evolution of the population inversion is computed in the nanosecond time scale, assuming that the initial coherent state of the field is given by a Poisson distribution. The limit of high temperatures characterizing the manifold of excited states becomes chaotic with rapid oscillations, whereas the ground state is described correctly in the thermodynamic limit by the vacuum state. A breakup is seen in the photon distribution into a series of peaks because of the detuning between the spin system and the field. However, this structure is smeared out, and the general shape is preserved in the computation emerging from the Laplace transform of the photon distribution. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Electronic spectroscopy and ultrafast energy relaxation pathways in the lowest Rydberg States of trimethylamine

Resonance-enhanced multiphoton ionization photoelectron spectroscopy has been applied to study the electronic spectroscopy and relaxation pathways among the 3p and 3s Rydberg states of trimethylamine. The experiments used femtosecond and picosecond duration laser pulses at wavelengths of 416, 266, and 208 nm and employed two-photon and three-photon ionization schemes. The binding energy of the 3s Rydberg state was found to be 3.087 +/- 0.005 eV. The degenerate 3p x, y states have binding energies of 2.251 +/- 0.005 eV, and 3p z is at 2.204 +/- 0.005 eV. Using picosecond and femtosecond time-resolved experiments we spectrally and temporally resolved an intricate sequence of energy relaxation pathways leading from the 3p states to the 3s state. With excitation at 5.96 eV, trimethylamine is found to decay from the 3p z state to 3p x, y in 539 fs. The decay to 3s from all the 3p states takes place with a 2.9 ps time constant. On these time scales, trimethylamine does not fragment at the given internal energies, which range from 0.42 to 1.54 eV depending on the excitation wavelength and electronic state.     

Optical control of the singlet-triplet transition in Rb2

By controlling nonresonant dynamic Stark shifts it is possible to effectively decouple the intramolecular couplings of simple molecules. We have illustrated this effect in the 1 (1)Sigma(u)-->1 (3)Pi(u) transition in Rb(2). The laser scheme implies two important control knobs: the laser frequency, which must be chosen to avoid both single and multiphoton resonances and to select different electronic environments for the singlet and triplet states, and the pulse intensity, which must amplify the asymmetry in the dynamic polarizabilities that allows the decoupling, avoiding undesired strong-pulse effects. The mechanism of the scheme implies not only brute-force energy shifts but also light-induced reshaping of the potentials to avoid the undesired crossings. Quantitative aspects of the method are analyzed by using molecular models of increasing complexity for Rb(2).     

Optimal control of ultrafast laser driven many-electron dynamics in a polyatomic molecule: N-methyl-6-quinolone

We report time-dependent configuration interaction singles calculations for the ultrafast laser driven many-electron dynamics in a polyatomic molecule, N-methyl-6-quinolone. We employ optimal control theory to achieve a nearly state-selective excitation from the S(0) to the S(1) state, on a time scale of a few ( approximately 6) femtoseconds. The optimal control scheme is shown to correct for effects opposing a state-selective transition, such as multiphoton transitions and other, nonlinear phenomena, which are induced by the ultrashort and intense laser fields. In contrast, simple two-level pi pulses are not effective in state-selective excitations when very short pulses are used. Also, the dependence of multiphoton and nonlinear effects on the number of states included in the dynamical simulations is investigated.     

Effective Hamiltonian for femtosecond vibrational dynamics

Time propagation of zero-order states of an effective spectroscopic Hamiltonian is tested against femtosecond time dependent dynamics of adiabatic wavepackets evolving on a model potential energy surface for two coupled modes of the radical HO(2) with multiple potential wells and above barrier motion. A generalized Hamiltonian which breaks the usual conserved polyad action by including extra resonance couplings (V(2:1) and V(3:1)) successfully describes the time evolution after the further addition of two "ultrafast" couplings. These new couplings are a nonresonant coupling a(1)a(2)+a(1)(?)a(2)(?) and a resonant coupling V(1:1) that functions as an ultrafast term because the system is far from 1:1 frequency resonance.     

Systematic control of nonlinear optical processes using optimally shaped femtosecond pulses.

This article reviews experimental efforts to control multiphoton transitions using shaped femtosecond laser pulses, and it lays out the systematic study being followed by us for elucidating the effect of phase on nonlinear optical laser-molecule interactions. Starting with a brief review of nonlinear optics and how nonlinear optical processes depend on the electric field inducing them, a number of conclusions can be drawn directly from analytical solutions of the equations. From a Taylor expansion of the phase in the frequency domain, we learn that nonlinear optical processes are affected only by the second- and higher-order terms. This simple result has significant implications on how pulse-shaping experiments are to be designed. If the phase is allowed to vary arbitrarily as a continuous function, then an infinite redundancy that arises from the addition of a linear phase function across the spectrum with arbitrary offset and slope could prevent us from carrying out a closed-loop optimization experiment. The early results illustrate how the outcome of a nonlinear optical transition depends on the cooperative action of all frequencies in the bandwidth of a laser pulse. Maximum constructive or destructive interference can be achieved by programming the phase using only two phase values, 0 and pi. This assertion has been confirmed experimentally, where binary phase shaping (BPS) was shown to outperform other alternative functions, sometimes by at least on order of magnitude, in controlling multiphoton processes. Here we discuss the solution of a number of nonlinear problems that range from narrowing the second harmonic spectrum of a laser pulse to optimizing the competition between two- and three-photon transitions. This Review explores some present and future applications of pulse shaping and coherent control.     

Two-photon spectroscopy of dipole-forbidden transitions

We have investigated the applicability of CNDO/S-type methods for the calculation of optical spectra of molecules with the special implication that the calculations should not only describe the intense, dipole-allowed transitions which dominate the one-photon absorption spectrum but also those transitions which are one-photon forbidden in first-order approximation. We show that such a method is well suited to predict dipole allowed and dipole forbidden transitions at a similar level of accuracy if double excited configurations are taken into account. In spite of the lack of perfect pairing in NDO methods there are still two types of states which exhibit a different sensitivity towards correlation effects. Therefore, the approximation by which we describe the R-dependence of the Coulomb repulsion gains much more importance than in cases where mainly dipole allowed transitions are of interest. These findings confirm results obtained earlier from theories for which the pairing theorem is valid. The calculated data show an excellent stability with respect to further increase of the number of configurations if at least about 200 energy selected configurations are taken into account.     

Control of nitromethane photoionization efficiency with shaped femtosecond pulses

The applicability of adaptive femtosecond pulse shaping is studied for achieving selectivity in the photoionization of low-density polyatomic targets. In particular, optimal dynamic discrimination (ODD) techniques exploit intermediate molecular electronic resonances that allow a significant increase in the photoionization efficiency of nitromethane with shaped near-infrared femtosecond pulses. The intensity bias typical of high-photon number, nonresonant ionization is accounted for by reference to a strictly intensity-dependent process. Closed-loop adaptive learning is then able to discover a pulse form that increases the ionization efficiency of nitromethane by ～150%. The optimally induced molecular dynamics result from entry into a region of parameter space inaccessible with intensity-only control. Finally, the discovered pulse shape is demonstrated to interact with the molecular system in a coherent fashion as assessed from the asymmetry between the response to the optimal field and its time-reversed counterpart.     

Sequential versus direct multiphoton absorption

We present results of exact calculations on a three-level Morse oscillator modeling HF which suggest that multiphoton absorption proceeds by sequential single-level transitions, transitions arising from coupling between non-adjacent states being dynamically negligible. The time-dependent Schrödinger equation is integrated in the Floquet formalism.