Control of molecular fragmentation using shaped femtosecond pulses

The possibility that chemical reactions may be controlled by tailored femtosecond laser pulses has inspired recent studies that take advantage of their short pulse duration, comparable to intramolecular dynamics, and high peak intensity to fragment and ionize molecules. In this article, we present an experimental quest to control the chemical reactions that take place when isolated molecules interact with shaped near-infrared laser pulses with peak intensities ranging from 1013 to 1016 W/cm2. Through the exhaustive evaluation of hundreds of thousands of experiments, we methodically evaluated the molecular response of 16 compounds, including isomers, to the tailored light fields, as monitored by time-of-flight mass spectrometry. Analysis of the experimental data, taking into account its statistical significance, leads us to uncover important trends regarding the interaction of isolated molecules with an intense laser field. Despite the energetics involved in fragmentation and ionization, the integrated second-harmonic generation of a given laser pulse (ISHG), which was recorded as an independent diagnostic parameter, was found to be linearly proportional to the total ion yield (IMS) generated by that pulse in all of our pulse shaping measurements. Order of magnitude laser control over the relative yields of different fragment ions was observed for most of the molecules studied; the fragmentation yields were found to vary monotonically with IMS and/or ISHG. When the extensive changes in fragmentation yields as a function of IMS were compared for different phase functions, we found essentially identical results. This observation implies that fragmentation depends on a parameter that is responsible for IMS and independent from the particular time-frequency structure of the shaped laser pulse. With additional experiments, we found that individual ion yields depend only on the average pulse duration, implying that coherence does not play a role in the observed changes in yield as a function of pulse shaping. These findings were consistently observed for all molecules studied (p-, m-, o-nitrotoluene, 2,4-dinitrotoluene, benzene, toluene, naphthalene, azulene, acetone, acetyl chloride, acetophenone, p-chrolobenzonitrile, N,N-dimethylformamide, dimethyl phosphate, 2-chloroethyl ethyl sulfide, and tricarbonyl-[eta5-1-methyl-2,4-cyclopentadien-1-yl]-manganese). The exception to our conclusion is that the yield of small singly-charged fragments resulting from a multiple ionization process in a subset of molecules, were found to be highly sensitive to the phase structure of the intense pulses. This coherent process plays a minimal role in photofragmentation; therefore, we consider it an exception rather than a rule. Changes in the fragmentation process are dependent on molecular structure, as evidenced in a number of isomers, therefore femtosecond laser fragmentation could provide a practical dimension to analytical chemistry techniques.     

Gaining mechanistic insight from closed loop learning control: the importance of basis in searching the phase space

This paper discusses different routes to gaining insight from closed loop learning control experiments. We focus on the role of the basis in which pulse shapes are encoded and the algorithmic search is performed. We demonstrate that a physically motivated, nonlinear basis change can reduce the dimensionality of the phase space to one or two degrees of freedom. The dependence of the control goal on the most important degrees of freedom can then be mapped out in detail, leading toward a better understanding of the control mechanism. We discuss simulations and experiments in selective molecular fragmentation using shaped ultrafast laser pulses.     

Optimal control methods applied on the ionization processes of alkali dimers

We present two novel optimization methods by employing shaped fs-laser pulses in a closed feedback loop. The first describes control pulse cleaning where extraneous features were removed by applying genetic pressure on certain pulse components. The second reports parametric optimization with intuitive parameters such as subpulse distances, chirps, phase differences, and spectral peak patterns. These methods were conducted on the ionization process of alkali dimers produced in a molecular beam and improved the performances of the optimized pulses compared with short pulses at the same pulse energy. Moreover, we attempt to analyze the obtained pulse shapes regarding the underlying optimized processes. Further investigations concerning isotope selective fragmentation and optimal control of excitation processes of ultracold rubidium dimers in a magneto-optical trap (MOT) are also shown.     

Effect of diatomic molecular properties on binary laser pulse optimizations of quantum gate operations

The importance of the ro-vibrational state energies on the ability to produce high fidelity binary shaped laser pulses for quantum logic gates is investigated. The single frequency 2-qubit ACNOT(1) and double frequency 2-qubit NOT(2) quantum gates are used as test cases to examine this behaviour. A range of diatomics is sampled. The laser pulses are optimized using a genetic algorithm for binary (two amplitude and two phase parameter) variation on a discretized frequency spectrum. The resulting trends in the fidelities were attributed to the intrinsic molecular properties and not the choice of method: a discretized frequency spectrum with genetic algorithm optimization. This is verified by using other common laser pulse optimization methods (including iterative optimal control theory), which result in the same qualitative trends in fidelity. The results differ from other studies that used vibrational state energies only. Moreover, appropriate choice of diatomic (relative ro-vibrational state arrangement) is critical for producing high fidelity optimized quantum logic gates. It is also suggested that global phase alignment imposes a significant restriction on obtaining high fidelity regions within the parameter search space. Overall, this indicates a complexity in the ability to provide appropriate binary laser pulse control of diatomics for molecular quantum computing.     

Efficient and robust strong-field control of population transfer in sensitizer dyes with designed femtosecond laser pulses

We demonstrate control of electronic population transfer in molecules with the help of appropriately shaped femtosecond laser pulses. To this end we investigate two photosensitizer dyes in solution being prepared in the triplet ground state. Excitation within the triplet system is followed by intersystem crossing and the corresponding singlet fluorescence is monitored as a measure of population transfer in the triplet system. We record control landscapes with respect to the fluorescence intensity on both dyes by a systematic variation of laser pulse shapes combining second order and third order dispersion. In the strong-field regime we find highly structured topologies with large areas of maximum or minimum population transfer being insensitive over a certain range of applied laser intensities thus demonstrating robustness. We then compare our experimental results with simulations on generic molecular potentials by solving the time-dependent Schr?dinger equation for excitation with shaped pulses. Control landscapes with respect to population transfer confirm the general trends from experiments. An analysis of regions with maximum or minimum population transfer indicates that coherent processes are responsible for the outcome of our excitation process. The physical mechanisms of joint motion of ground and excited state wave packets or population of a vibrational eigenstate in the excited state permit us to discuss the molecular dynamics in an atom-like picture.     

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.     

Isotope selective photoionization of NaK by optimal control: theory and experiment

We present a joint theoretical and experimental study of the maximization of the isotopomer ratio (23)Na(39)K(23)Na(41)K using tailored phase-only as well as amplitude and phase modulated femtosecond laser fields obtained in the framework of optimal control theory and closed loop learning (CLL) technique. A good agreement between theoretically and experimentally optimized pulse shapes is achieved which allows to assign the optimized processes directly to the pulse shapes obtained by the experimental isotopomer selective CLL approach. By analyzing the dynamics induced by the optimized pulses we show that the mechanism involving the dephasing of the wave packets between the isotopomers (23)Na (39)K and (23)Na (41)K on the first excited state is responsible for high isotope selective ionization. Amplitude and phase modulated pulses, moreover, allow to establish the connection between the spectral components of the pulse and corresponding occupied vibronic states. It will be also shown that the leading features of the theoretically shaped pulses are independent from the initial conditions. Since the underlying processes can be assigned to the individual features of the shaped pulses, we show that optimal control can be used as a tool for analysis.     

Fragmentation dynamics of methane by few-cycle femtosecond laser pulses

The fragmentation pattern of CH4 was experimentally studied at an intensity of approximately 10(14) W/cm2 with laser durations varying from 8 to 110 fs. When the laser duration was 8 fs, only the primarily fragmental CH3+ ion was observed in addition to the parent CH4+ ion. When the laser duration was 30 fs, small fragmental CH2+ and H+ ions appeared. When the laser duration was 110 fs, some doubly charged ions were also observed in addition to the abundant singly charged ions. The large mass spectra difference demonstrated that the pulse duration had a strong effect on the fragmentation of the parent ion produced in the single ionization. The effect of laser intensity on the fragmentation of CH4+ was also studied for few-cycle femtosecond laser pulses. The results demonstrated that the first-return recollision between the rescattered electron and the parent ion played a significant role in the fragmentation dynamics of the parent ion. Depending on the ion-electron impact energy, the recollision excited the parent ion to a dissociated state or doubly charged state. The experimentally observed singly charged fragmental ions resulted from the recollision-induced dissociation of CH4+ or the Coulomb explosion of CH(4)2+.     

Dissociative ionization of methane by chirped pulses of intense laser light

Measurements have been made of optical field-induced ionization and fragmentation of methane molecules at laser intensities in the 10(16) W cm(-2) range using near transform limited pulses of 100 fs duration as well as with chirped pulses whose temporal profiles extend up to 1500 fs. Data is taken both in constant-intensity and constant-energy modes. The temporal profile of the chirped laser pulse is found to affect the morphology of the fragmentation pattern that is measured. Besides, the sign of the chirp also affects the yield of fragments like C2+, H+, and H2+ that originate from methane dications that are formed by optical field-induced double ionization.     

Control goal selection through anticorrelation analysis in the detection space

A statistical method is reported to determine the pairs of fragment ions in a mass spectrum that are most susceptible to control by adaptive optimization of the laser pulse shapes in the strong-field regime. The proposed method is based on covariance analysis of the mass spectral fragmentation patterns generated by a set of randomly shaped pulses. The pairs of fragment ions that have higher negative covariances possess a correspondingly higher degree of controllability in an adaptive control experiment, whereas the pairs that have higher positive covariances possess correspondingly lower controllability.     

Phase control over decaying molecular states in intense laser pulses

A time-dependent approach to study phase control over molecular photoabsorption, provided by intense laser pulses, is elaborate. The method allows for the decay linewidth of molecular states and frequency bandwidth of the controlling laser field, and can be applied in weak and strong laser fields where the perturbation theory is invalid. It is shown that a frequency mismatch between the fundamental laser wave and its third harmonic can destroy control. For the example of the one-photon versus three-photon control a simple picture of interference from two monochromatic absorption pathways is not enough to explain phase control and one needs to consider a nonlinear temporal interference of multiquantum transitions. In the perturbation-theory limit an elegant generalization of the famous Shapiro-Hepburn-Brumer equation for the one-photon versus three-photon control is derived. Various numerical calculations illustrate the dependence of phase control on molecular linewidth, fundamental laser wavelength, pulse duration, and peak intensity. It is obtained, that the one-photon versus three-photon control is productive if the molecular state populations, individually produced by each laser wave, have beats of approximately the same frequency. The calculations demonstrate that an enough intense optical pulse can suppress molecular decay and may be used in order to keep stable the state population of a decaying molecule for a long time. The available experimental results for the one-photon versus three-photon control over simple and large polyatomic molecules are analyzed and recommendations for the experimental improvement of control are formulated.     

Simulations of quantum computation with a molecular ion

The capabilities of a new system for coherent control—intense terahertz light pulses acting on trapped, gas phase D₃O⁺ molecules—are investigated using realistic molecular and pulse parameters. Computer simulations show that a set of three shaped pulses can be used to perform four level (two qubit) quantum computational gates on the inversion–rotation energy levels and read-out the result using degenerate four-wave mixing. Two pulse shaping techniques are employed, one directly shaping a terahertz pulse, and another shaping a visible laser pulse that is rectified by a terahertz antenna. Both are found to be effective for control. Methods for initializing the inversion–rotation wavepacket, making the pulse robust against power variations, maximizing its fidelity to a unitary gate transformation and addressing limitations of energy level connectivity are discussed.     

Vibrational molecular quantum computing: basis set independence and theoretical realization of the Deutsch-Jozsa algorithm

The phase of quantum gates is one key issue for the implementation of quantum algorithms. In this paper we first investigate the phase evolution of global molecular quantum gates, which are realized by optimally shaped femtosecond laser pulses. The specific laser fields are calculated using the multitarget optimal control algorithm, our modification of the optimal control theory relevant for application in quantum computing. As qubit system we use vibrational modes of polyatomic molecules, here the two IR-active modes of acetylene. Exemplarily, we present our results for a Pi gate, which shows a strong dependence on the phase, leading to a significant decrease in quantum yield. To correct for this unwanted behavior we include pressure on the quantum phase in our multitarget approach. In addition the accuracy of these phase corrected global quantum gates is enhanced. Furthermore we could show that in our molecular approach phase corrected quantum gates and basis set independence are directly linked. Basis set independence is also another property highly required for the performance of quantum algorithms. By realizing the Deutsch-Jozsa algorithm in our two qubit molecular model system, we demonstrate the good performance of our phase corrected and basis set independent quantum gates.     

Interpreting closed-loop learning control of molecular fragmentation in terms of wave-packet dynamics and enhanced molecular ionization

We interpret a molecular fragmentation experiment using shaped, ultrafast laser pulses in terms of enhanced molecular ionization during dissociation. A closed-loop learning control experiment was performed to maximize the CF3+CH3+ production ratio in the dissociative ionization of CH3COCF3. Using ab inito molecular structure calculations and quasistatic molecular ionization calculations along with data from pump-probe experiments, we identify the primary control mechanism which is quite general and should be applicable to a broad class of molecules.     

Optimal control in a dissipative system: vibrational excitation of CO/Cu(100) by IR pulses

The question as to whether state-selective population of molecular vibrational levels by shaped infrared laser pulses is possible in a condensed phase environment is of central importance for such diverse fields as time-resolved spectroscopy, quantum computing, or "vibrationally mediated chemistry." This question is addressed here for a model system, representing carbon monoxide adsorbed on a Cu(100) surface. Three of the six vibrational modes are considered explicitly, namely, the CO stretch vibration, the CO-surface vibration, and a frustrated translation. Optimized infrared pulses for state-selective excitation of "bright" and "dark" vibrational levels are designed by optimal control theory in the framework of a Markovian open-system density matrix approach, with energy flow to substrate electrons and phonons, phase relaxation, and finite temperature accounted for. The pulses are analyzed by their Husimi "quasiprobability" distribution in time-energy space.     

分子动力学模拟飞秒激光对C60光裂解反应机理的影响

基于半经典分子动力学方法模拟超快激光诱导的C60光裂解反应.选择能量为2.0eV,半峰全宽(FWHM)分别为40和500fs的激光作用于C60分子,调节脉冲强度使其发生裂解反应,比较长短脉宽飞秒激光对C60裂解反应机理的影响.通过分析产物分布、原子平衡指数、温度以及吸收能量(包括动能、势能和电子能量),证实飞秒激光脉冲下C60的光裂解主要由电子激发态控制,非热力学效应在该反应中起重要作用.激光场的作用时间和强度均影响光裂解反应过程,而电子吸收能量饱和后光场强度的作用则变得不明显.     

The use of intense femtosecond laser pulses for the fragmentation of chitosan

The use of ultrashort laser pulses for the fragmentation of chitosan was investigated. Femtosecond Ti-saphire laser pulses were focused into a flask containing 1.0% chitosan in 0.1 M acetic acid. The effects of the pulse energy (between 0.1 and 0.82 mJ) and the focal length on the laser-induced fragmentation were followed by viscometry and size exclusion chromatography. The chemical structure and degree of acetylation of chitosan and its fragments were studied using elemental analysis, IR and ¹H NMR spectroscopy. The experimental results showed that (i) Ti-saphire laser irradiation induced chain scission in the chitosan macromolecules, (ii) the chemical structure, including the degree of acetylation, did not change significantly upon laser irradiation, (iii) the number of chain scission dependence on laser energy suggests that fragmentation was a two-photon process, and (iv) at constant pulse energy, the molecular weight dropped to a minimum as a function of the focal length (between 45 and 330 mm), indicating that the efficiency of fragmentation was very sensitive to the geometry of the laser beam.     

Isomeric identification by laser control mass spectrometry

The influence shaped femtosecond laser pulses have on molecular photofragmentation and ionization, coupled with the intrinsic sensitivity of mass spectrometry, results in a powerful tool for fast, accurate, reproducible and quantitative isomeric identification. Complex phase functions are introduced to enhance differences during the laser-molecule interactions, which depend on geometric structure, resulting in different fragmentation fingerprints. A full account is given on the setup and results leading to a technique that can be used to distinguish between compounds normally indistinguishable by conventional electron ionization mass spectrometry. We demonstrate geometric and structural isomer identification of cis-/trans-3-heptene, cis-/trans-4-methyl-2-pentene, o-/p-cresol and o-/p-xylene. For the positional isomers of xylene we present a complete dataset consisting of 1024 different phases to explore phase complexity. A selection of two phases from that data can then be used to achieve quantitative identification in mixtures of xylene isomers. Finally, we evaluate receiver operational curves obtained from our experimental data to demonstrate the reliability that can be achieved by femtosecond laser control mass spectrometry.     

Charge-transfer as a mechanism for controlling molecular fragmentation

We investigate control over molecular fragmentation in the halogen substituted acetone 1,1-dibromo-3,3,3-trifluoroacetone using shaped ultrafast laser pulses. Following insight gained from closed-loop learning control experiments, further tests reveal that control over the CF₃⁺/CHBr₂⁺ ratio exploits a charge-transfer mechanism. We interpret the control in terms of adiabatic rapid passage.