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.     

Terahertz-laser control of large amplitude vibrational motion in the sub-one-cycle pulse limit

We investigate the control of state-selective population transfer in the THz spectral range generated by sub-one-cycle pulse excitation. To this end we developed a zero-net-force modification of the optimal control algorithm which allows us to extend the algorithm into the ultrashort pulse domain. By combining the analysis of the control landscapes and that of optimal control theory, we were able to formulate a general mechanism suitable for laser control by ultrashort pulses. The strategy consists of a superposition of two pi-pulses with carrier envelope phases of phi = pi/2. The first pulse is effectively in resonance with the targeted transition, while the second one, fired at around the minimum of the first pulse second lobe, removes leaking to the dipole-coupled background state. To compensate for the pulses ultrashort duration, the carrier frequencies of both pulses are red-shifted from the spectroscopic resonance.     

Use of the Gerchberg–Saxton algorithm in optimal coherent anti-Stokes Raman spectroscopy

We are utilizing recent advances in ultrafast laser technology and recent discoveries in optimal shaping of laser pulses to significantly enhance the stand-off detection of explosives via control of molecular processes at the quantum level. Optimal dynamic detection of explosives is a method whereby the selectivity and sensitivity of any of a number of nonlinear spectroscopic methods are enhanced using optimal shaping of ultrafast laser pulses. We have recently investigated the Gerchberg–Saxton algorithm as a method to very quickly estimate the optimal spectral phase for a given analyte from its spontaneous Raman spectrum and the ultrafast laser pulse spectrum. Results for obtaining selective coherent anti-Stokes Raman spectra (CARS) for an analyte in a mixture, while suppressing the CARS signals from the other mixture components, are compared for the Gerchberg–Saxton method versus previously obtained results from closed-loop machine-learning optimization using evolutionary strategies.     

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.     

Spectral phase effects on nonlinear resonant photochemistry of 1,3-cyclohexadiene in solution

We have investigated the ring opening of 1,3-cyclohexadiene to form 1,3,5-cis-hexatriene (Z-HT) using optical pulse shaping to enhance multiphoton excitation. A closed-loop learning algorithm was used to search for an optimal spectral phase function, with the effectiveness or fitness of each optical pulse assessed using the UV absorption spectrum. The learning algorithm was able to identify pulses that increased the formation of Z-HT by as much as a factor of 2 and to identify pulse shapes that decreased solvent fragmentation while leaving the formation of Z-HT essentially unaffected. The highest yields of Z-HT did not occur for the highest peak intensity laser pulses. Rather, negative quadratic phase was identified as an important control parameter in the formation of Z-HT.     

Effective two-photon absorption cross section of heteroaromatic quadrupolar dyes: dependence on measurement technique and laser pulse characteristics

The linear and nonlinear optical properties of the heteroaromatic push-pull-push two-photon absorbing dye N-methyl-2,5-bis[1-(N-methylpyrid-4-yl)ethen-2-yl]-pyrrole ditriflate (PEPEP) are reported. The determination of the two-photon absorption (TPA) cross-section spectrum has been performed with different techniques: femtosecond TPA-white light continuum probe experiments, two-photon-induced fluorescence, and open aperture Z-scan measurements using both nanosecond and femtosecond laser pulses. The measured TPA cross sections and their wavelength dispersion show a marked dependence on the parameters of the laser pulses and on the measurement technique employed. These properties are discussed in terms of the different microscopic mechanisms that can contribute to the multiphoton absorption processes, with different weight depending on the measurement conditions and on the photophysical parameters of the dye.     

Coherent control of the isomerization of retinal in bacteriorhodopsin in the high intensity regime

Coherent control protocols provide a direct experimental determination of the relative importance of quantum interference or phase relationships of coupled states along a selected pathway. These effects are most readily observed in the high intensity regime where the field amplitude is sufficient to overcome decoherence effects. The coherent response of retinal photoisomerization in bacteriorhodopsin to the phase of the photoexcitation pulses was examined at fluences of 10(15) - 2.5 ×?10(16) photons per square centimeter, comparable to or higher than the saturation excitation level of the S(0) - S(1) retinal electronic transition. At moderate excitation levels of ～6 ×?10(15) photons/cm(2) (<100 GW/cm(2)), chirping the excitation pulses increases the all-trans to 13-cis isomerization yield by up to 16% relative to transform limited pulses. The reported results extend previous weak-field studies [Prokhorenko et al., Science 313, 1257 (2006)] and further illustrate that quantum coherence effects persist along the reaction coordinate in strong fields even for systems as complex as biological molecules. However, for higher excitation levels of ～200 GW/cm(2), there is a dramatic change in photophysics that leads to multiphoton generated photoproducts unrelated to the target isomerization reaction channel and drastically changes the observed isomerization kinetics that appears, in particular, as a red shift of the transient spectra. These results explain the apparent contradictions of the work by Florean et al. [Proc. Natl. Acad. Sci. U.S.A. 106, 10896 (2009)] in the high intensity regime. We are able to show that the difference in observations and interpretation is due to artifacts associated with additional multiphoton-induced photoproducts. At the proper monitoring wavelengths, coherent control in the high intensity regime is clearly observable. The present work highlights the importance of conducting coherent control experiments in the low intensity regime to access information on quantum interference effects along specific reaction coordinates.     

Coherent control improves biomedical imaging with ultrashort shaped pulses

Although ultrashort pulses are advantageous for multiphoton excitation microscopy, they can be difficult to manipulate and may cause increased sample damage when applied to biological tissue. Here we present a method based on coherent control that corrects phase distortions introduced by high numerical aperture (NA) microscope objectives, thereby achieving the full potential of ultrashort pulses. A number of useful phase functions are recommended to gain selectivity that is similar to that which can be achieved by tuning a longer laser pulse; however this one involves no moving parts and maintains perfect optimization. This capability is used to demonstrate functional imaging by selective two-photon excitation of a pH-sensitive chromophore. Finally, we show that phase functions can also be introduced to minimize multiphoton excitation damage, while maintaining a high efficiency of two-photon excitation.     

Matrix‐assisted laser desorption/ionization by using femtosecond laser pulses in the near‐infrared wavelength regime

We observe a substantial matrix‐assisted laser desorption/ionization (MALDI) signal when irradiating femtosecond laser pulses in the near‐infrared spectral range centered around 800 nm and using standard MALDI matrices with absorption bands in the ultraviolet (UV) regime. The laser pulse energy dependence of this novel phenomenon is investigated in comparison with MALDI with near‐UV laser pulses. Our observations show that multiphoton absorption/ionization could be a major issue among the MALDI processes when the sample is irradiated with ultra‐short laser pulses. Copyright © 2009 John Wiley & Sons, Ltd.     

Multidimensional analytical method based on binary phase shaping of femtosecond pulses

Multidimensional chemical detection and identification based on phase shaped femtosecond laser pulses coupled to mass spectrometry is demonstrated. The method based on binary phase shaping (BPS) takes into account the accuracy and precision standards required by analytical chemistry. It couples multiphoton intrapulse interference of ultrashort laser pulses with time-of-flight mass spectrometry (TOF-MS). We demonstrate that BPS-MS provides a rigorous multidimensional technique for the detection and identification of analogues to chemical agents and mixtures in real time. Experimental results on dimethyl phosphite and pyridine illustrate the new approach toward the real-time accurate detection and identification of chemical compounds including isomers.     

Design of an infrared laser pulse to control the multiphoton dissociation of the Fe-CO bond in CO-heme compounds

Optimal control theory is used to design a laser pulse for the multiphoton dissociation of the Fe-CO bond in the CO-heme compounds. The study uses a hexacoordinated iron-porphyrin-imidazole-CO complex in its ground electronic state as a model for CO liganded to the heme group. The potential energy and dipole moment surfaces for the interaction of the CO ligand with the heme group are calculated using density functional theory. Optimal control theory, combined with a time-dependent quantum dynamical treatment of the laser-molecule interaction, is then used to design a laser pulse capable of efficiently dissociating the CO-heme complex model. The genetic algorithm method is used within the mathematical framework of optimal control theory to perform the optimization process. This method provides good control over the parameters of the laser pulse, allowing optimized pulses with simple time and frequency structures to be designed. The dependence of photodissociation yield on the choice of initial vibrational state and of initial laser field parameters is also investigated. The current work uses a reduced dimensionality model in which only the Fe-C and C-O stretching coordinates are explicitly taken into account in the time-dependent quantum dynamical calculations. The limitations arising from this are discussed in Sec. IV.     

Generation of DNA photolesions by two-photon absorption of a frequency-doubled Ti:sapphire laser

The formation of spatially localized regions of DNA damage by multiphoton absorption of light is an attractive tool for investigating DNA repair. Although this method has been applied in cells, little information is available about the formation of lesions by multiphoton absorption in the absence of exogenous or endogenous sensitizing agents. Therefore, we have investigated DNA damage induced in vitro by direct two-photon absorption of frequency-doubled femtosecond pulses from a Ti:sapphire laser. We first developed a quantitative polymerase chain reaction assay to measure DNA damage, and determined that the quantum yield of lesions formed by one-photon absorption of 254 nm light is 7.86×10(-4). We then measured the yield of lesions resulting from exposure to the visible femtosecond laser pulses, which exhibited a quadratic intensity dependence. The two-photon absorption cross section of DNA has a value (per nucleotide) of 2.6 GM at 425 nm, 2.4 GM at 450 nm, and 1.9 GM at 475 nm. A comparison of these in vitro results to several in vivo studies of multiphoton photodamage indicates that the onset of DNA damage occurs at lower intensities in vivo; we suggest possible explanations for this discrepancy.     

Supersonic Jet/Time-of-flight mass spectrometry of adenine using nanosecond and femtosecond lasers

Mass spectra and ionization efficiencies of adenine were measured with nanosecond (15 ns) and femtosecond (500 fs) laser pulses at identical energy levels. A molecular ion is clearly observed in both spectra, but the efficiency is improved 10-fold when a femtosecond laser is used, indicating the distinct advantage of ultrashort laser pulses for multiphoton ionization of nucleobases in supersonic jet spectrometry.     

Far-UV photochemical bond cleavage of n-amyl nitrite: bypassing a repulsive surface

We have investigated the deep-UV photoinduced, homolytic bond cleavage of amyl nitrite to form NO and pentoxy radicals. One-color multiphoton ionization with ultrashort laser pulses through the S(2) state resonance gives rise to photoelectron spectra that reflect ionization from the S(1) state. Time-resolved pump-probe photoionization measurements show that upon excitation at 207 nm, the generation of NO in the v = 2 state is delayed, with a rise time of 283 (16) fs. The time-resolved mass spectrum shows the NO to be expelled with a kinetic energy of 1.0 eV, which is consistent with dissociation on the S(1) state potential energy surface. Combined, these observations show that the first step of the dissociation reaction involves an internal conversion from the S(2) to the S(1) state, which is followed by the ejection of the NO radical on the predissociative S(1) state potential energy surface.     

Multiphoton near-infrared femtosecond laser pulse-induced DNA damage with and without the photosensitizer proflavine

The excitation of pBr322 supercoiled plasmid DNA with intense near-IR 810 nm fs laser pulses by a simultaneous multiphoton absorption mechanism results in single-strand breaks after treatment of the irradiated samples with Micrococcus luteus UV endonuclease. This enzyme cleaves DNA strands at sites of cyclobutane dimers that are formed by the simultaneous absorption of three (or more) 810 nm IR photons (pulse width approximately 140 fs, 76 MHz pulse repetition, average power output focused through 10x microscope objective is approximately 1.2 MW/cm2). Direct single-strand breaks (without treatment with M. luteus) were not observed under these conditions. However, in the presence of 6 microM of the intercalator proflavine (PF), both direct single- and double-strand breaks are observed under conditions where substantial fractions of undamaged supercoiled DNA molecules are still present. The fraction of direct double-strand breaks is 30 +/- 5% of all measurable strand cleavage events, is independent of dosage (up to 6.4 GJ/cm2) and is proportional to In, where I is the average power/area of the 810 nm fs laser pulses, and n = 3 +/- 1. The nicking of two DNA strands in the immediate vicinity of the excited PF molecules gives rise to this double-strand cleavage. In contrast, excitation of the same samples under low-power, single-photon absorption conditions (approximately 400-500 nm) gives rise predominantly to single-strand breaks, but some double-strand breaks are observed at the higher dosages. Thus, single-photon excitation with 400-500 nm light and multiphoton activation of PF by near-IR fs laser pulses produces different distributions of single- and double-strand breaks. These results suggest that DNA strand cleavage originates from unrelaxed, higher excited states when PF is excited by simultaneous IR multiphoton absorption processes.     

Multiphoton ionization of molecules: A comparison between femtosecond and nanosecond laser pulse ionization efficiency

Multiphoton ionization mass spectra of nonvolatile molecules laser desorbed into a supersonic beam are recorded. It is shown by indirect measurements that the laser desorption of neutrals is not mass limited, but lead to the formation of neutrals with intesities large enough for intense signals. To investigate the efficiency of the multiphoton ionization process with varying laser pulse durations, simultaneous laser pulses of 500 fs and 5 ns or 100 fs and 5 ns have been applied to the neutral beam. The energies of both femtosecond and nanosecond laser pulses are held in a comparable magnitude, and thus produce, in the resulting ion intensity, very large differences up to 4 orders of magnitude. For larger evaporated molecules (> 500 u) the ionization efficiency from nanosecond laser pulses drops significantly in comparison to femtosecond laser pulse excitation. A variety of possible reasons for the different ionization and dissociation behavior in femtosecond and nanosecond laser pulse excitations are discussed in this paper. It is rationalized that even with very short laser pulses and large molecules the “ladder switching model” for ionization and fragmentation is valid.     

Two-photon induced uncaging of a reactive intermediate. Multiphoton in situ detection of a potentially valuable label for biological applications

[reaction: see text] Two-photon induced Wolff rearrangement of a terphenyl diazoketone 1 was achieved by using focused laser pulses of 532 nm from a Q-switched Nd:YAG laser. The nonfluorescent terphenyl diazoketone 1 was transformed into a fluorescent ester derivative 4, which can be detected in situ using the focused laser pulses at 532 nm. Laser power dependence studies show that the Wolff rearrangement is induced by two-photon absorption of the terphenyl diazoketone 1, but suggests that more than two photons of 532 nm are involved (a multiphoton process) in excitation of the ester derivative 4.     

Photobleaching of reduced nicotinamide adenine dinucleotide and the development of highly fluorescent lesions in rat basophilic leukemia cells during multiphoton microscopy

Endogenous reduced nicotinamide adenine dinucleotide (NADH) fluorescence provides an intrinsic indicator of the cellular metabolic state, but prolonged monitoring is limited by photobleaching and/or phototoxicity. Multiphoton excitation of NADH by ultrashort, 740-nm laser pulses provides a significant improvement over UV excitation by eliminating peripheral photobleaching; however, molecules within the subfemtoliter excitation volume remain susceptible. We have investigated the photophysical mechanisms responsible for multiphoton photobleaching of NADH in living cells to permit the imaging technique to be optimized. The loss of fluorescence because of multiphoton photobleaching was measured by repetitively imaging individual planes within rat basophilic leukemia cells. The photobleaching rate was proportional to the fourth power of the laser intensity. Based on these measurements, we propose a double-biphotonic, four-photon photobleaching mechanism and estimate the quantum yield of photobleaching of intracellular NADH to be 0.0073 +/- 0.0002 by this mechanism. In addition to photobleaching, the development of bright, punctate fluorescent lesions can also be observed. The frequency of lesion formation also increased approximately as the fourth power of the laser intensity after an intensity-dependent threshold number of images had been exceeded. The consequences for two-photon metabolic imaging are discussed.     

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.