Multiphoton control of the 1,3-cyclohexadiene ring-opening reaction in the presence of competing solvent reactions

Although physical chemistry has often concentrated on the observation and understanding of chemical systems, the defining characteristic of chemistry remains the direction and control of chemical reactivity. Optical control of molecular dynamics, and thus of chemical reactivity provides a path to use photon energy as a smart reagent in a chemical system. In this paper, we discuss recent research in this field in the context of our studies of the multiphoton optical control of the photo-initiated ring-opening reaction of 1,3-cyclohexadiene (CHD) to form 1,3,5- cis-hexatriene (Z-HT). Closed-loop feedback and learning algorithms are able to identify pulses that increase the desired target state by as much as a factor of two. Mechanisms for control are discussed through the influence of the intensity dependence, the nonlinear power spectrum, and the projection of the pulses onto low orders of polynomial phase. Control measurements in neat solvents demonstrate that competing solvent fragmentation reactions must also be considered. In particular, multiphoton excitation of cyclohexane alone is capable of producing hexatriene. Statistical analyses of data sets obtained in learning algorithm searches in neat cyclohexane and for CHD in hexane and cyclohexane highlight the importance of linear and quadratic chirp, while demonstrating that the control features are not so easily defined. Higher order phase components are also important. On the basis of these results the involvement of low-frequency ground-state vibrational modes is proposed. When the population is transferred to the excited state, momentum along the torsional coordinate may keep the wave packet localized as it moves toward the conical intersections controlling the yield of Z-HT.     

Disentangling multidimensional femtosecond spectra of excitons by pulse shaping with coherent control

Sequences of carefully timed and shaped optical pulses provide femtosecond snapshots of molecular structure as well as electronic and vibrational dynamical processes, in analogy with multidimensional NMR. We apply a genetic learning algorithm towards the design of pulse sequences which simplify the multidimensional signals by controlling the relative intensities of various peaks. Numerical simulations demonstrate how poorly resolved weak features may be amplified and observed by using optimized optical pulses, specifically shaped to achieve a desired spectroscopic target.     

Study of the formation of the dispersed phase in aqueous solutions of Cu(II)

The formation of the dispersed phase in aqueous solutions of Cu(II) in the presence of formate and alcohols is studied using the pulse radiolysis method. The incubation time and the half-life for the formation depend on the absorbed dose and on the number of applied pulses as well as on the solution composition itself (Cu concentration, pH, OH-scavenger etc.). With increasing dose per pulse or number of pulses, the incubation time and the half-life for colloid formation decrease. The nature of the colloids formed is discussed.     

Solvent dependent conformational relaxation of cis-1,3,5-hexatriene

Ultrafast transient absorption spectroscopy was used to study the conformational relaxation dynamics of 1,3,5-cis-hexatriene (Z-HT) produced in the photochemical ring-opening reaction of 1,3-cyclohexadiene (CHD) in methanol and n-propanol solvents. The results are compared with earlier investigations performed using cyclohexane and hexadecane solvents [Anderson, N. A.; Pullen, S. H.; Walker II, L. A.; Shiang, J. J.; Sension, R. J.; J. Phys. Chem. A 1998, 102, 10588-10598.]. The conformational relaxation between hot cZc-HT, cZt-HT, and tZt-HT, where the labels c and t designate cis and trans configurations about the single bonds, is much faster in alcohol solvents than in alkane solvents. The hot Z-HT produced in the photochemical ring-opening reaction evolves from the conformationally strained cZc-HT form to the more stable cZt-HT form on a time scale of 2 ps in alcohols compared with 6 ps in alkanes. The overall decay of the internal vibrational temperature of the hot Z-HT is faster in alcohols (5-6 ps) than alkanes (12-20 ps) and is weakly dependent on the specific alcohol or alkane solvent. A small population of cZt-HT (5-10%) is trapped as the solute equilibrates with the surrounding solvent following UV excitation of CHD or direct UV excitation of Z-HT. The influence of solvent on conformational relaxation of Z-HT was investigated further by probing the temperature dependence of the decay of this thermally equilibrated cZt-HT population. The apparent barrier for the cZt --> tZt conformational isomerization is lower in alcohols (17.4 kJ/mol) than in alkanes (23.5 kJ/mol). However the equilibrium Arrhenius prefactor (A(h)) is an order of magnitude smaller for alcohols (ca. 4 x 10(12)) than alkanes (ca. 6 x 10(13)) resulting in an absolute rate of decay that is faster in the alkane than in the alcohol solvents. These results are discussed in the context of transition state theory and Kramers' theory for condensed phase reaction dynamics.     

Tracking excited state dynamics with coherent control: automated limiting of population transfer in LDS750

Closed loop automated pulse shaping experiments are conducted to investigate population transfer in solutions of the laser dye LDS750 in acetonitrile and ethanol. Guided by a genetic algorithm, the optical phases of broadband noncollinear parametric amplifier pulses are modulated by a micromachined deformable mirror to minimize sample fluorescence. The objectives were to test if nonlinearly chirped pulses could reduce population transfer below levels attained by their linearly chirped analogues, and if so, whether the resulting pulse shapes could be rationalized in terms of the photoinduced molecular dynamics. We further aimed to discover how the optimal solutions depend on the pulse fluence, and on the nature of the solvent. Using frequency resolved optical gating, the optimal field is shown to consist of a transform limited blue portion, which promotes population to the excited state, and a negatively chirped red tail, which follows the Stokes shifting of the excited density and dumps it back down to the ground state through stimulated emission. This is verified by comparing the optimal group delay dispersion with multichannel transient absorption data collected in acetonitrile. The optimal pulse shape was not significantly affected by variation of pulse fluence or by the change of solvent for the two polar liquids investigated. These results are discussed in terms of accumulated insights concerning the photophysics of LDS750 and the capabilities of our learning feedback scheme for quantum control.     

Optimal control of ultrafast selection

Optimal laser control for ultrafast selection of closely lying excited states whose energy separation is smaller than the laser bandwidth is reported on the two-photon transition of atomic cesium; Cs(6S-->7D(J), J=5/2 and 3/2). Selective excitation was carried out by pulse shaping of ultrashort laser pulses which were adaptively modulated in a closed-loop learning system handling eight parameters representing the electric field. Two-color fluorescence from the respective excited states was monitored to measure the selectivity. The fitness used in the learning algorithm was evaluated from the ratio of the fluorescence yields. After fifty generations, a pair of nearly transform-limited pulses were obtained as an optimal pulse shape, proving the effectiveness of the "Ramsey fringes" mechanism. The contrast of the selection ratio was improved by approximately 30% from the simple "Ramsey fringes" experiment.     

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.     

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.     

Wave packet interferometry and quantum state reconstruction by acousto-optic phase modulation

Studies of wave packet dynamics often involve phase-selective measurements of coherent optical signals generated from sequences of ultrashort laser pulses. In wave packet interferometry (WPI), the separation between the temporal envelopes of the pulses must be precisely monitored or maintained. Here we introduce a new (and easy to implement) experimental scheme for phase-selective measurements that combines acousto-optic phase modulation with ultrashort laser excitation to produce an intensity-modulated fluorescence signal. Synchronous detection, with respect to an appropriately constructed reference, allows the signal to be simultaneously measured at two phases differing by 90 degrees. Our method effectively decouples the relative temporal phase from the pulse envelopes of a collinear train of optical pulse pairs. We thus achieve a robust and high signal-to-noise scheme for WPI applications, such as quantum state reconstruction and electronic spectroscopy. The validity of the method is demonstrated, and state reconstruction is performed, on a model quantum system--atomic Rb vapor. Moreover, we show that our measurements recover the correct separation between the absorptive and dispersive contributions to the system susceptibility.     

Femtosecond quantum control of molecular dynamics in the condensed phase

We review the progress in controlling quantum dynamical processes in the condensed phase with femtosecond laser pulses. Due to its high particle density the condensed phase has both high relevance and appeal for chemical synthesis. Thus, in recent years different methods have been developed to manipulate the dynamics of condensed-phase systems by changing one or multiple laser pulse parameters. Single-parameter control is often achieved by variation of the excitation pulse's wavelength, its linear chirp or its temporal subpulse separation in case of pulse sequences. Multiparameter control schemes are more flexible and provide a much larger parameter space for an optimal solution. This is realized in adaptive femtosecond quantum control, in which the optimal solution is iteratively obtained through the combination of an experimental feedback signal and an automated learning algorithm. Several experiments are presented that illustrate the different control concepts and highlight their broad applicability. These fascinating achievements show the continuous progress on the way towards the control of complex quantum reactions in the condensed phase.     

Fluorescence-detected two-dimensional electronic coherence spectroscopy by acousto-optic phase modulation

Two-dimensional electronic coherence spectroscopy (ECS) is an important method to study the coupling between distinct optical modes of a material system. Such studies often involve excitation using a sequence of phased ultrashort laser pulses. In conventional approaches, the delays between pulse temporal envelopes must be precisely monitored or maintained. Here, we introduce a new experimental scheme for phase-selective nonlinear ECS, which combines acousto-optic phase modulation with ultrashort laser excitation to produce intensity modulated nonlinear fluorescence signals. We isolate specific nonlinear signal contributions by synchronous detection, with respect to appropriately constructed references. Our method effectively decouples the relative temporal phases from the pulse envelopes of a collinear train of four sequential pulses. We thus achieve a robust and high signal-to-noise scheme for phase-selective ECS to investigate the resonant nonlinear optical response of photoluminescent systems. We demonstrate the validity of our method using a model quantum three-level system-atomic Rb vapor. Moreover, we show how our measurements determine the resonant complex-valued third-order susceptibility.     

CIRCADIAN PHASE OF SPARROWS: CONTROL BY LIGHT AND DARK

Abstract— Sparrows ( Passer domesticus ) are day-active birds which exhibit circadian rhythms of perch-hopping activity. The phases of sparrow's circadian rhythms were studied following single 4 h light pulses, single 4 h dark pulses, doublet treatments of light and dark pulses, and a 10 h light pulse.
The sparrows exhibited a phase response curve to 4 h light pulses with maximum phase advances (3.8 h) at CT20 and maximum phase delays(–1.3 h) at CT16. The sparrows also displayed a phase response curve to dark pulses with maximum phase advances (2.2 h) at CT16 and maximum phase delays at CTO(–0.7 h).
The remaining pulses were imposed during the subjective dark-time. The 10 h pulse beginning 1 h after lights-out produced a 2.2 h phase shift. The doublet of 2 h pulses that were the "skeleton" of the 10 h pulse produced a 2.5 h phase shift. The early 2 h pulse, applied by itself resulted in a -0.4 h delay; the late 2 h pulse applied singly produced a 3.1 h advance. When an early 3 h dark pulse was imposed together with a late light pulse, the phase was advanced 3.6 h; singly the pulses produced 1.8 h and 2.7 h advances.     

Complete characterization of molecular vibration using frequency resolved gating

The authors propose a new approach to vibration spectroscopy based on the coherent anti-Stokes Raman scattering of broadband ultrashort laser pulses. The proposed method reveals both the amplitude and the phase of molecular vibrations by utilizing the cross-correlation frequency resolved optical gating (XFROG) technique. The spectrum of the anti-Stokes pulse is measured as a function of the time delay between the laser-induced molecular vibrations and a well characterized broadband femtosecond probe pulse. The iterative XFROG algorithm provides a simultaneous complete characterization of molecular vibrations both in frequency and time domains with high resolution. They demonstrate experimentally the feasibility of the proposed method and show one of its potential applications in disentangling the time behavior of a mixture of vibrationally excited molecules. The technique of femtosecond pulse shaping is used for further improvement of accuracy and stability against noise.     

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.     

Applications of ultrashort shaped pulses in microscopy and for controlling chemical reactions

This article presents a new perspective on laser control based on insights into the effect of spectral phase on nonlinear optical processes. Gaining this understanding requires the systematic evaluation of the molecular response as a function of a series of pre-defined accurately shaped laser pulses. The effort required is rewarded with robust, highly reproducible, results. This approach is illustrated by results on selective two-photon excitation microscopy of biological samples, where higher signal and less photobleaching damage are achieved by accurate phase measurement and elimination of high-order phase distortions from the ultrashort laser pulses. A similar systematic approach applied to laser control of gas phase chemical reactions reveals surprising general trends. Molecular fragmentation pattern is found to be dependent on phase shaping. Differently shaped pulses with similar pulse duration have been found to produce similar fragmentation patterns. This implies that any single parameter that is proportional to the pulse duration, such as second harmonic generation intensity, allows us to predict the molecular fragmentation pattern within the experimental noise. This finding, is illustrated here for a series of isomers. Bond selectivity, coherent photochemistry and their applications are discussed in light of results from these systematic studies.     

Molecular isomerization induced by ultrashort infrared pulses. I. Few-cycle to sub-one-cycle Gaussian pulses and the role of the carrier-envelope phase

Using 550 previously calculated vibrational energy levels and dipole moments we performed simulations of the HCN-->HNC isomerization dynamics induced by sub-one-cycle and few-cycle IR pulses, which we represent as Gaussian pulses with 0.25-2 optical cycles in the pulse width. Starting from vibrationally pre-excited states, isomerization probabilities of up to 50% are obtained for optimized pulses. With decreasing number of optical cycles a strong dependence on the carrier-envelope phase (CEP) emerges. Although the optimized pulse parameters change significantly with the number of optical cycles, the distortion by the Gaussian envelope produces nearly equal fields, with a positive lobe followed by a negative one. The positions and areas of the lobes are also almost unchanged, irrespective of the number of cycles in the half-width. Isomerization proceeds via a pump-dumplike mechanism induced by the sequential lobes. The first lobe prepares a wave packet incorporating many delocalized states above the barrier. It is the motion of this wave packet across the barrier, which determines the timing of the pump and dump lobes. The role of the pulse parameters, and in particular of the CEP, is to produce the correct lobe sequence, size and timing within a continuous pulse.     

Optical control of two-photon excitation efficiency of alpha-perylene crystal by pulse shaping

Optimized pulse shaping experiments were carried out on the control of two-photon excitation efficiency of an alpha-perylene crystal in the temperature region from 30 to 290 K. It was found that a pulse train with a pulse interval of 90 fs and an alternately reversing phase relation increased the excitation efficiency by a factor of 2 for the whole temperature region. The pulse shape characteristic for effective efficiency increase was reduced by double pulse experiments in which the dependence of the emission intensity on the pulse interval and relative phase between pulses were measured. The mechanism of the efficiency increase is briefly discussed using a sliding-window Fourier transform of the pulse shape.     

Understanding optimal control results by reducing the complexity

Deciphering control mechanisms from control pulse structures found in closed-loop learning experiments is often complicated due to the complexity of the pulse structure. Simplification of pulse forms is demonstrated by systematically reducing the complexity of the search space, applied on the model-like multi-photon ionization of NaK. Reducing the pulse complexity leads to the exclusion of participating excited states, thereby restricting the involved pathways. The phase function is parameterized by a sinusoidal spectral phase modulation, whose parameters are investigated with respect to the yield and the obtained optimal field. By progressively reducing the number of parameters and thereby the complexity of the phase modulation, control pulses are generated which are more and more reduced to the molecule’s primary dynamical properties. This enables to find optimized control pulses that can be subject to a simple intuitive interpretation.     

Optical Kerr effect spectroscopy using time-delayed pairs of pump pulses with orthogonal polarizations

We characterize in detail a recently introduced technique in which perpendicularly polarized pulses with controllable intensities and timing are used for the excitation step in optical Kerr effect spectroscopy. We examine the ratio of pump pulse intensities required to cancel the contribution of reorientational diffusion or of a Raman-active intramolecular vibration to the signal as a function of the delay time between excitation pulses. These results indicate that the signal can be described well as arising from the sum of independent third-order responses initiated by each pump pulse. This conclusion is further supported by using data obtained with a single pump pulse to model decays obtained with two pump pulses.     

An ultrafast time-resolved fluorescence spectroscopy system for metal ion complexation studies with organic ligands

A dedicated spectrofluorimeter using ultrashort laser pulses as an excitation source was developed to measure the fluorescence properties of organic ligands for metal ion complexation with organic ligands. The laser system consists of an oscillator system for generation of femtosecond laser pulses, an amplifier system to increase the pulse energy of the generated pulses to about 2 mJ and an optical parametrical amplifier system to provide tunable laser pulses over a wide wavelength range (280 nm-10 microm). The laser pulses were applied to the sample and the emitted fluorescence was detected using a fast-gating intensified CCD camera-based spectrometer. To verify the performance of the laser, the well-known protonation constant [Pure Appl. Chem. 69 (1997) 329] of 2,3-dihydroxybenzoic acid was determined. The fluorescence lifetime of the excited species was determined as 375+/-32 ps in the pH range from 1.0 to 6.0, having a fluorescence emission maximum at 438 nm. The first protonation constant was determined from fluorescence data as log K(3)=3.17+/-0.05 at an ionic strength of 0.1 M and at 294 K exploiting the Stern-Volmer mechanism. The agreement of the protonation constant with literature data (log K(3)=3.10+/-0.20, I=0.1 M, T=298 K [Bull. Soc. Jpn. 44 (1971) 3459]) demonstrates the excellent performance of our system. Furthermore, we determined the complex formation constant log K(1)=-3.11+/-0.16 by measuring the fluorescence properties of the ligand for the 1:1 uranyldihydroxobenzoate complex in the pH range from 3.0 to 4.5 at ionic strength of 0.1 M and at 294 K. We also determined the complex formation constant via the fluorescence emission of the metal ion uranium(VI). The fluorescence of the uranyl ion is influenced by dynamic quenching of the non-dissociated ligand and by static quenching due to the complex formation. After correction of these effects using the determined fluorescence lifetime, the complex formation constant was calculated to be log K(1)=-3.99+/-0.44. A 1:1 metal:ligand stoichiometry was determined with both measurement methods. However, the difference of the obtained formation constants and the derived standard deviations indicate a superimposition of effects with the excited-state reactions of the ligand.