The control of chemical reactions is a central topic of optimal quantum control and ultrafast laser science. It has always been a dream of chemists and physicists to use laser light in order to steer chemical reactions towards desired targets. In particular the idea of closed-loop quantum control [1] has been a major breakthrough [2,3] in the field. For these early experiments, shaped 800 nm laser pulses were used. Transfer of pulse shaping techniques into the visible [4], mid infrared (MIR) [5] and ultraviolet (UV) [6] (down to 200 nm) wavelength range has already been achieved in the past.

With the pioneering work of shaped-pulse control of high-harmonic generation [7–9] and the technique of coherent soft-x-ray engineering recently introduced [9–11] it now becomes possible for the first time to perform closed-loop learning control experiments in the soft-x-ray spectral range. As we show here, the branching ratios of a photodissociation reaction of sulfur hexafluoride (SF₆) can be controlled by adaptive soft-x-ray spectral shaping. This study can be understood as a demonstration of the versatility and stability of the adaptive coherent soft-x-ray source for this type of experiments. Many applications that directly control and observe the electronic dynamics are expected to follow up on the herein developed technological advance in the future by using a similar experimental configuration. Soft x-rays are particularly useful in this context to obtain selectivity in chemical reactions as they provide a means for site-specific electronic excitation in molecules [12].

The earliest experiments to demonstrate selectivity in chemical reactions by applying shaped optical laser light fields focused on photofragmentation [3,13,14]. This is due to the experimental simplicity to prepare the system and to detect the products. In gas-phase photochemistry, the detection of ionic fragments is particularly simple by using a time-of-flight mass spectrometer.

Sulfur hexafluoride (SF₆) is an interesting, well-known system for the study of photofrag-mentation. When this molecule interacts with light in the soft-x-ray spectral region (ionization potential I_p = 15.32 eV), different positively charged ionic fragments are produced. This can be explained by dissociative photoionization [15–18], which is the dominant fragmentation pro-cess in the soft-x-ray range for many molecules. It means that SF₆ is excited to ionic states embedded in the fragmentation continuum. The potential energy curves for these ionic states can be repulsive for a particular bond, leading to dissociation. In the case of SF₆ this leads to the release of one or more fluorine atoms. In this context of dissociative ionization with soft-x-ray/VUV (vacuum ultraviolet) light, the recent theoretical study by Palacios et al. [19] should be pointed out, where control of dissociative ionization in an H₂ molecule was investigated using moderately intense (10¹² W/cm²) pulses of VUV light.

 

Fig. 1. Setup for the experiments on adaptive control of photochemistry by high-harmonic spectral engineering. The high-harmonic radiation output from the capillary is used to induce dissociative ionization in SF₆ gas. The fragments are detected with a linear time-of-flight mass spectrometer.

Download Full Size | PDF

In our experiment, shaped high-harmonic spectra of coherent soft-x-ray radiation were produced by phase modulation of the driving 800 nm laser pulses prior to high-harmonic generation in an argon-filled capillary. Interaction of these shaped soft x-rays with SF₆ molecules took place in a 1 kHz pulsed valve located after the capillary used for the generation of the high harmonics (see Fig. 1). The harmonic-generation setup is described in more detail in Ref. [9]. A linear time-of-flight (TOF) mass spectrometer of the Wiley-McLaren type [20] was used in order to detect positively charged ions produced by the high-harmonic pulses. The spectrometer used an extraction field for ion collection. The throughput of the mass spectrometer was limited by fine metal meshes used for homogenization of the applied electric fields, resulting in a loss of ion throughput on the order of 40%. A backing pressure of 2 bar was used behind the pulsed valve. The high voltage controlling the opening of the pulsed valve was chosen such that the pressure in the chamber was 2×10^-5 mbar. The pressure was limited to this order of magnitude by the maximum tolerable pressure of the microsphere-plate detector (MSP, manufacturer: El-Mul Technologies) installed in the TOF mass spectrometer.

The laser pulse energy used for high-harmonic generation was 0.29 mJ after the prism compressor (Fig. 1) at a repetition rate of 1 kHz (Spectra Physics “Spitfire” Ti:sapphire laser system). The prism compressor was manually optimized for maximum high-harmonic efficiency, resulting in highest ion count rates. The pressure in the capillary used for high-harmonic generation was set to 0.1 bar. Due to the setup geometry (see Fig. 1), the harmonic-beam traversed the molecular SF₆ cloud produced by the nozzle and was analyzed by a soft-x-ray spectrometer equipped with a backside-illuminated x-ray CCD camera. Since the beam is only negligibly absorbed in the jet due to the low gas density, this setup is capable of recording the ionic mass spectra and the photon-energy spectra at the same time. This gives the opportunity to compare qualitative changes in the mass spectra—e.g. the changing branching ratios—directly to changes in the soft-x-ray spectra of the light.

 

Fig. 2. Time-of-flight (TOF) cation mass spectra of SF₆ after irradiation with high-harmonic light from a capillary. The molecule undergoes fragmentation, where a number of fluorine atoms are released. The parent ion SF⁺ ₆ at a mass of 146 amu is not observed under our experimental conditions. A characteristic distribution of peak heights for the fragments is recorded where SF⁺ ₅ and SF⁺ ₃ are the most abundant species.

Download Full Size | PDF

In Fig. 2 a typical time-of-flight mass-spectrum is shown for excitation of SF₆ with high-harmonic light present in a wavelength region between 20 and 40 nm (observed with the soft-x-ray spectrometer). No aluminum filter was used between high-harmonic generation and SF₆ target for this recording to obtain a high count rate. This implies that both the fundamental and lower harmonic orders were present in the interaction region. However, it was verified that the ion signal vanished when the HHG capillary was evacuated and therefore no harmonic radiation was produced. Thus, the fundamental laser alone could not be responsible for the fragmentation process. In order to rule out ionization of SF₆ by the laser pulse alone after spectral/temporal modification in the presence of the argon gas in the capillary, we estimated its intensity at the interaction region: the beam diameter of the freely expanding fundamental laser pulse is calculated to increase to ~2 mm after ~0.2 m of propagation from the capillary exit to the SF₆ jet (interaction region). Its intensity is thus >500 times smaller than inside the capillary and therefore can be estimated to be less than 5×10¹¹ W/cm². Since on the order of 9–10 photons need to be absorbed to ionize SF₆, we do not expect significant ionization to be caused by this fundamental light field alone. In order to rule out modifications of the process by the lower harmonic orders and the fundamental light, the experiments described below were carried out with an aluminum filter (0.3 μm thickness) between the capillary exit and the SF₆ gas jet.

The presented results concentrate on the two most dominant fragmentation channels, SF⁺ ₅ and SF⁺ ₃ . As an optimization criterion (fitness function) for the evolutionary algorithm (for details see Ref. [9]) we used the relative yield of ions, i.e. the product branching ratio

where y(SF⁺ _n) denotes the ion yield of SF⁺ _n ions detected with the TOF mass spectrometer, integrated over the entire mass peak. The integrations over the two mass peaks were performed by two boxcar integrators that were read-out by an analog-to-digital converter (ADC) connected to a computer. For each individual of the evolutionary optimization an average of the ion yields of ~1000 laser shots (1s) was acquired. The computer then calculated the product ratio for each individual by dividing the two measured and averaged product yields. One generation of the evolutionary algorithm comprised 50 individuals and the time to acquire the data and perform the ranking, selection, mutation, crossover, and cloning operations on the computer to determine the composition of the next generation was on the order of 80 s. On average, n ≈1000 counts of SF⁺ ₅ and ≈500 counts of SF⁺ ₃ ions were detected in 1 s integration time, leading to a statistical count noise (1/√n) of 3% and 4%, respectively. The instability of the laser-driven high-harmonic source created additional noise, leading to larger standard deviation for the measured branching ratios than expected from the count noise alone (see below).

 

Fig. 3. Control of the branching ratio of SF₆ photofragmentation by shaped soft-x-ray light. The two most dominant fragmentation products SF⁺ ₅ and SF⁺ ₃ as well as the ratio of SF⁺ ₄ versus SF⁺ ₂ were optimized. Both minimization and maximization of product ratios as compared to a reference harmonic spectrum (obtained for the reference setting of our pulse shaper) were achieved.

Download Full Size | PDF

The evolutionary algorithm was programmed to perform a maximization and afterwards a minimization of the product ratio. The results of these experiments are summarized in Fig. 3. The product ratios shown in this figure were obtained by re-applying the optimal pulse shapes found by the algorithm after the optimization was completed. In our experiments, the evolutionary algorithm typically converged after 5–10 generations. The branching ratio could be maximized and minimized by 20–25% with respect to the reference ratio obtained for the unmodulated reference spectrum prior to optimization. The average fitness function values (branching ratios) obtained for the final populations of pulse shapes in the evolutionary algorithm were consistently higher than for the reference spectrum, demonstrating the successive evolution of the algorithm. The error bar of our measurements can be given as 13% (relative to the value of the branching ratio) calculated from the standard deviation of the measured branching ratios obtained for the reference pulse throughout the optimization. The soft-x-ray spectra recorded for the case of maximization and minimization of the ion yield, along with the spectrum before optimization are presented in Fig. 4. Due to the combined effects of absorption by the argon gas used for HHG and the aluminum filter the recorded spectra contain the full spectral intensity information about the light used in the experiment. The spectrum before optimization (unmodulated spectrum) is typical for phase-matched harmonic generation in a capillary. For the maximization case (SF⁺ ₅ versus SF⁺ ₃), a pronounced shift of the overall spectral mean towards lower frequencies is visible. In contrast, the minimization leads to a spectral distribution the spectral mean of which is shifted towards higher soft-x-ray photon energies. Additionally, both optimized spectra exhibit the same amount of (ionization-induced) blueshift of the harmonic peaks with respect to the unmodulated spectrum. The substructure of some harmonic peaks is also modified in the spectra that correspond to different optimization goals. In our experiments, the evolutionary algorithm did not find alternative solutions of optimal soft-x-ray spectral shapes. This could also be explained by the limitations of the accessible soft-x-ray spectral shapes imposed by our pulse shaper and the high-harmonic generation process itself.

 

Fig. 4. Soft-x-ray spectra of shaped harmonic emission employed to optimize photofrag-mentation of SF₆. Optimal harmonic spectra are shown that maximize (dotted lines) or minimize (dashed lines) the two branching ratios SF⁺ ₅ versus SF⁺ ₃ (a) and SF⁺ ₄ versus SF⁺ ₂ (b). The unmodulated reference soft x-ray spectrum before optimization is also given for comparison (solid lines). The integration time for the spectra was ~1 s.

Download Full Size | PDF

The complete mass spectra acquired for the interaction with different soft-x-ray spectra (the unmodulated and the optimized ones) are shown in Fig. 5 for the optimization results on SF⁺ ₅ versus SF⁺ ₃ . The spectra are normalized to the integral ion yield of the entire SF⁺ ₃ peak area, which makes it easier to observe the change in branching ratio by comparing the different yields of the SF⁺ ₅ peak. The shifting of the peaks could be caused by a difference in fragmentation dynamics resulting in different fragment energies. In fact, changes in the distribution of the fragment kinetic energy with XUV pulse duration were also observed in the recent theoretical study by Palacios et al. [19]. In dissociative ionization, the fragments are produced at different kinetic energies, depending on the particular high-lying excited electronic states populated by the soft-x-ray light. Not only the energy can be different but there can also be an angular dependence of ionization with respect to the polarization direction of the linearly polarized high-harmonic light. It is known from earlier studies [16,17] that a pronounced angular anisotropy of the fragmentation process of SF₆ prevails for exciting photon energies in the range of interest here.

The control experiment was repeated for the branching ratio between two different photofrag-ment ions, namely SF⁺ ₄ versus SF⁺ ₂ . The fitness function used here was defined as

 

Fig. 5. Time-of-flight mass spectra resulting from the interaction of SF₆ with tailored soft x-ray light for the case of maximization and minimization of the SF⁺ ₅ versus SF⁺ ₃ branching ratio. The two mass-spectra are normalized to the integral ion yield (integrated over entire mass peak) of the SF⁺ ₃ peak area to visualize the relative changes on the SF⁺ ₅ peak. The changing fine structure of the peaks are indicative of differences in the fragmentation dynamics. (b) is an enlarged view of (a) in the region of interest.

Download Full Size | PDF

The results of the maximization and minimization are also shown in Fig. 3. The branching ratio of SF⁺ ₄ versus SF⁺ ₂ ion yields turns out to be more rigid and cannot be changed to the same degree as the ratio of SF⁺ ₅ versus SF⁺ ₃ in this control experiment. Maximization resulted in an increase of the ratio by 15%, whereas minimization by 10% was achieved. It is important to note that the short- and long-term stability (on the <1-minute and 10-minute timescales for consistency within one generation and the entire progression of the algorithm, respectively) of the shaped coherent soft-x-ray light from the high-harmonic generation process is high enough to allow the evolutionary algorithm to find an optimal set of control parameters even though the branching ratio can only be slightly changed. This demonstrates the technical versatility of the presented method to perform in principle any optimal control experiment in the soft-x-ray spectral region.

The origin of control of this photodissociation reaction cannot immediately be determined. The spectral amplitude changes significantly for the different control tasks. In fact, it was shown in earlier studies [16]—although in a slightly different spectral regime (14–29 eV, i.e. 43– 89 nm wavelength)—that the yields of photofragments of SF₆ depend on the photon energy used. These studies were performed with spectrally incoherent soft x-rays from a synchrotron facility. Further investigations will show how the spectral coherence (short pulsed nature) of the soft x-rays in the optimal control experiments above affects the process of dissociative ionization. The development of harmonic fine structure in the optimized spectra could be an indicator of these additional effects.

In the future one can now consider using this technique for a new type of quantum control experiments including inner valence/core electronic states to achieve site specificity [12]. By using a sufficiently broad (multi-eV) coherent spectrum in the soft-x-ray region, one could imagine the creation of a coherent superposition of electronic excited states from a lower-lying bound state, resulting in a time-dependent electronic wavefunction that changes on an ultrafast (possibly attosecond) time scale. If the soft-x-ray intensity is high enough or a strong infrared/visible laser field is present, this dynamic wavefunction can be transferred to a dissociative molecular state depending on the instantaneous shape of the electronic wavefunction. For a detailed analysis, a pump—probe experiment has to be performed.

The spectral variability of the used XUV source allows for a variety of different coherent soft-x-ray spectral distributions. However, using laser systems with controlled carrier- envelope phase [21], more sophisticated pulse-shaping devices (e.g. to realize spatial [10 , 11], spatio-temporal [22], and polarization shaping [23]) and multi-color high-harmonic control schemes [24] will lead to enhanced spectral shaping capability in the soft-x-ray region.

In summary, the first experiment on optimal control in the soft-x-ray spectral region was performed using the technique of high-harmonic spectral engineering. Photofragmentation yields of the SF₆ molecule were controlled by the application of shaped coherent soft-x-ray light. In one case the branching ratio SF⁺ ₅ versus SF⁺ ₃ could be changed by 25%. This result demonstrates sufficient stability of the shaped soft-x-ray light for optimal control experiments. The optimal soft-x-ray spectral distribution changed significantly for different control objectives such as maximization and minimization. The presented experiment is the first demonstration of optimal control of molecular dynamics with tailored soft-x-ray light. In the future, quantum control will not only be applied to control of molecular motion and vibrational dynamics but will also include the control of electronic dynamics in atomic and molecular systems.