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.     

Learning from the acquired optimized pulse shapes about the isotope selective ionization of potassium dimers

Selective optimization of the 39,39K2 and 39,41K2 isotopomers in a three-photon ionization process is presented by applying evolution strategies on shaped fs pulses in a feedback loop. The optimizations at different center wavelengths show considerably large enhancements of one isotope compared to the other and reversed. We compare the acquired optimized pulse shapes for combined phase and amplitude with pure amplitude modulation. Particularly from their spectra we are able to extract information about the optimally chosen differing ionization paths via the involved vibrational states. Furthermore, a comparison of the temporal shape of the optimized pulse forms for combined phase and amplitude with pure phase optimization is given. The presented pulse form analysis demonstrates the potential of restricted optimization to gain insight into the underlying dynamical processes. Our approach reveals how the optimization algorithm precisely addresses the vibrational wave functions both spectrally and temporally.     

Electronic coherence within the semiclassical field-induced surface hopping method: strong field quantum control in K2

We demonstrate that the semiclassical field-induced surface hopping (FISH) method (Mitri?et al., Phys. Rev. A: At., Mol., Opt. Phys., 2009, 79, 053416.) accurately describes the selective coherent control of electronic state populations. With the example of the strong field control in the potassium dimer using phase-coherent double pulse sequences, we present a detailed comparison between FISH simulations and exact quantum dynamics. We show that for short pulses the variation of the time delay between the subpulses allows for a selective population of the desired final state with high efficiency. Furthermore, also for pulses of longer time duration, when substantial nuclear motion takes place during the action of the pulse, optimized pulse shapes can be obtained which lead to selective population transfer. For both types of pulses, the FISH method almost perfectly reproduces the exact quantum mechanical electronic population dynamics, fully taking account of the electronic coherence, and describes the leading features of the nuclear dynamics accurately. Due to the significantly higher computational efficiency of FISH as a trajectory-based method compared to full quantum dynamics simulations, this offers the possibility to theoretically investigate control experiments on realistic systems including all nuclear degrees of freedom.     

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.     

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.     

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.     

Phase-only shaped laser pulses in optimal control theory: application to indirect photofragmentation dynamics in the weak-field limit

We implement phase-only shaped laser pulses within quantum optimal control theory for laser-molecule interaction. This approach is applied to the indirect photofragmentation dynamics of NaI in the weak-field limit. It is shown that optimized phase-modulated pulses with a fixed frequency distribution can substantially modify transient dissociation probabilities as well as the momentum distribution associated with the relative motion of Na and I.     

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.     

Coherent control of the population transfer in complex solvated molecules at weak excitation. An experimental study

We performed a series of successful experiments for the optimization of the population transfer from the ground to the first excited state in a complex solvated molecule (rhodamine 101 in methanol) using shaped excitation pulses at very low intensities (1 absorbed photon per 100-500 molecules per pulse). We found that the population transfer can be controlled and significantly enhanced by applying excitation laser pulses with crafted pulse shapes. The optimal shape was found in feedback-controlled experiments using a genetic search algorithm. The temporal profile of the optimal excitation pulse corresponds to a comb of subpulses regularly spaced by approximately 150 fs, whereas its spectrum consists of a series of well-resolved peaks spaced apart by approximately 6.5 nm corresponding to a frequency of 220 cm(-1). This frequency matches very well with the frequency modulation of the population kinetics (period of approximately 150 fs), observed by excitation with a short (approximately 20 fs) transform-limited laser pulse directly after excitation. In addition, an antioptimization experiment was performed under the same conditions. The difference in the population of the excited state for the optimal and antioptimal pulses reaches approximately 30% even at very weak excitation. The results of optimization are reproducible and have clear physical meaning.     

Chemoselective quantum control of carbonyl bonds in Grignard reactions using shaped laser pulses

Grignard reactants like methylmagnesium chloride are not selective with respect to different carbonyl bonds. We present a theoretical study where shaped laser pulses are utilized to prefer specific bonds in a mixture of more than one carbonyl reactant. A mixture of cyclohexanone and cyclopentanone has been chosen as a representative example. The light pulse is supposed to provide the activation energy and to adopt the function of a protecting group. The control aim is to stretch exclusively the C-O bond of one compound to the length required in the Grignard transition state. To guarantee an experimentally realizable bandwidth for the unshaped pulse, we use our recently developed optimal control theory algorithm, which allows the simultaneous optimization of the light field in the time and frequency domain. Highly selective picosecond control pulses could be optimized in the infrared regime suggesting that laser assisted chemoselectivity is possible to a large extent. To obtain control not only on the final product but also on the excitation mechanism, various initial conditions and frequency restrictions were investigated.     

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.     

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.     

Pulse shaping effect on two-photon excitation efficiency of alpha-perylene crystals and perylene in chloroform solution

We demonstrated that the two-photon excitation efficiency of perylene in chloroform solution as well as that of crystalline perylene was dramatically increased by optimizing the shape of intense femtosecond laser pulses of a regenerative amplifier output. The efficiency was three times higher than for an unshaped single femtosecond pulse with the pulse width of shorter than 50 fs. The pulse shape optimized for the solution sample was a pulse train with a repetition frequency of about 340 cm(-1), and the pulse shape optimized for crystalline perylene was very similar. These results supported our previous findings on alpha-perylene crystals using weak femtosecond pulses from a mode-locked laser oscillator [T. Okada et al. J. Chem. Phys. 121, 6385 (2004)]. Furthermore, it was confirmed that the shaped pulse optimized for the liquid sample could also increase the two-photon excitation efficiency of alpha-perylene crystals and vice versa. We concluded that the mechanism for the increase in excitation efficiency of perylene in chloroform was almost the same as that for alpha-perylene crystal, and that the efficiency increased mainly through intramolecular dynamical processes. Processes involving intermolecular interactions and/or energy states delocalized over the crystal cannot play the major role.     

Practical aspects of ROESY experiments for identification of bound waters in the cyclic tetrasaccharide

ROESY pulse sequences are presented and evaluated to identify bound waters in the cyclic tetrasaccharide. The first experiment incorporated the double-pulsed field gradient spin-echo (DPFGSE) for selective water excitation at the initial portion of the pulse sequence. Although long, shaped pulses were used in DPFGSE to achieve the highly selective excitation of water resonance that is very close to resonances of the cyclic tetrasaccharide, the approach was not effective because of the loss of sensitivity. Concomitant use of long delays and moderate length of shaped pulses in the portion of DPFGSE gained more sensitivity. A simple approach incorporating spin-echo with long delays instead of DPFGSE also afforded a sensitive spectrum. Practical aspects of these ROESY experiments are illustrated using the cyclic tetrasaccharide cyclo-{-->6}-alpha-D-Glcp-(1-->3)-alpha-D-Glcp-(1-->6)-alpha-D-Glcp-(1-->3)-alpha-D-Glcp-(1-->).     

Coherent control of the ultrafast dissociative ionization dynamics of bromochloroalkanes

We report on the coherent control of the ultrafast ionization and fragmentation dynamics of the bromochloroalkanes C(2)H(4)BrCl and C(3)H(6)BrCl using shaped femtosecond laser pulses. In closed-loop control experiments on bromochloropropane (C(3)H(6)BrCl) the fragment ion yields of CH(2)Cl(+), CH(2)Br(+), and C(3)H(3)(+) are optimized with respect to that of the parent cation C(3)H(6)BrCl(+). The fragment ion yields are recorded in additional experiments in order to reveal the energetics of cation fragmentation, where laser-produced plasma radiation is used as a tunable pulsed nanosecond vacuum ultraviolet radiation source along with photoionization mass spectrometry. The time structure of the optimized femtosecond laser pulses leads to a depletion of the parent ion and an enhancement of the fragment ions, where a characteristic sequence of pulses is required. Specifically, an intense pump pulse is followed by a less intense probe pulse where the delay is 0.5 ps. Similarly optimized pulse shapes are obtained from closed-loop control experiments on bromochloroethane (C(2)H(4)BrCl), where the fragment ion yield of CH(2)Br(+) is optimized with respect to that of C(2)H(4)BrCl(+) as well as the fragment ion ratios C(2)H(2)(+)/CH(2)Br(+) and C(2)H(3)(+)/C(2)H(4)Cl(+). The assignment of the underlying control mechanism is derived from one-color 804 nm pump-probe experiments, where the yields of the parent cation and several fragments show broad dynamic resonances with a maximum at Δt = 0.5 ps. The experimental findings are rationalized in terms of dynamic ionic resonances leading to an enhanced dissociation of the parent cation and some primary fragment ions.     

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.     

J-modulated ADEQUATE experiments using different kinds of refocusing pulses

Owing to the recent developments concerning residual dipolar couplings (RDCs), the interest in methods for the accurate determination of coupling constants is renascenting. We intended to use the J-modulated ADEQUATE experiment by K?vér et al. for the measurement of (13)C - (13)C coupling constants at natural abundance. The use of adiabatic composite chirp pulses instead of the conventional 180 degrees pulses, which compensate for the offset dependence of (13)C 180 degrees pulses, led to irregularities of the line shapes in the indirect dimension causing deviations of the extracted coupling constants. This behaviour was attributed to coupling evolution, during the time of the adiabatic pulse (2 ms), in the J-modulation spin echo. The replacement of this pulse by different kinds of refocusing pulses indicated that a pair of BIPs (broadband inversion pulses), which behave only partially adiabatic, leads to correct line shapes and coupling constants conserving the good sensitivity obtained with adiabatic pulses.     

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.     

Quantum control of molecular vibrational and rotational excitations in a homonuclear diatomic molecule: a full three-dimensional treatment with polarization forces

The optimal control of the vibrational excitation of the hydrogen molecule [Balint-Kurti et al., J. Chem. Phys. 122, 084110 (2005)] utilizing polarization forces is extended to three dimensions. The polarizability of the molecule, to first and higher orders, is accounted for using explicit ab initio calculations of the molecular electronic energy in the presence of an electric field. Optimal control theory is then used to design infrared laser pulses that selectively excite the molecule to preselected vibrational-rotational states. The amplitude of the electric field of the optimized pulses is restricted so that there is no significant ionization during the process, and a new frequency sifting method is used to simplify the frequency spectrum of the pulse. The frequency spectra of the optimized laser pulses for processes involving rotational excitation are more complex than those relating to processes involving only vibrational excitation.     

Singlet versus triplet dynamics of β-carotene studied by quantum control spectroscopy

Biomolecules very often present complex energy deactivation networks with overlapping electronic absorption bands, making their study a difficult task. This can be especially true in transient absorption spectroscopy when signals from bleach, excited state absorption and stimulated emission contribute to the signal. However, quantum control spectroscopy can be used to discriminate specific electronic states of interest by applying specifically designed laser pulses. Recently, we have shown the control of energy flow in bacterial light-harvesting using shaped pump pulses in the visible and the selective population of pathways in carotenoids using an additional depletion pulse in the transient absorption technique. Here, we apply a closed-loop optimization approach to β-carotene using a spatial light modulator to decipher the energy flow network after a multiphoton excitation with a shaped ultrashort pulse in the near-IR. After excitation, two overlapping bands were detected and identified as the S₁ state and the first triplet state T₁. Using the transient absorption signal at a specific probe delay as feedback, the triplet signal could be optimized over the singlet contribution.