White-Light Optimal Control of Photoinduced Processes - The Journal

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White-Light Optimal Control of Photo-Induced Processes Franz Hagemann, Falko Schwaneberg, Cristina Stanca-Kaposta, and Ludger Woeste J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp510875a • Publication Date (Web): 09 Jan 2015 Downloaded from http://pubs.acs.org on January 13, 2015

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The Journal of Physical Chemistry

White-Light Optimal Control of Photo-Induced Processes Franz Hagemann, Falko Schwaneberg, Cristina Stanca-Kaposta,∗ and Ludger Wöste Institut f¨ ur Experimentalphysik, Freie Universit¨ at Berlin, Arnimallee 14, 14195 Berlin, Germany E-mail: [email protected] Phone: +49 (0)30 83856775. Fax: +49 (0)30 83855567

∗

To whom correspondence should be addressed

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Abstract The photo-fragmentation of Cu3 and Al4 clusters during charge reversal with whitelight pulses is optimized by using an evolutionary algorithm and a pulse shaping setup. By controlling the spectral phase over the full spectral range of the supercontinuum, tailored pulses are generated with the aim of adapting the energetic and temporal structure of the pulse to the characteristic dynamics and electronic manifold of the investigated systems. In this context, maximizing the ratio of the cationic yield of a + selected fragment (Cu+ 2 and Al , respectively) and the parent ion is chosen as an op-

timization target. Significant enhancement factors are achieved, demonstrating a high selectivity in populating specific points on the potential energy surface which facilitates the targeted photo-fragmentation of the investigated systems. The optimal pulse shapes indicate that both vibronic as well as electronic wave packets are probed. Additional laser induced dissociation experiments suggest that fragmentation of the Cu3 clusters occurs in an excited state of the neutral species. Further photo-fragmentation studies of the Cu− 3 anions present a strong wavelength dependence, with the formation of Cu− occurring only when irradiated with wavelengths shorter than 528 nm. No photodissociation is observed for the Al− 4 anions.

Keywords metal cluster, charge reversal, fragmentation, supercontinuum, femtosecond

Introduction Since the invention of the laser in 1960, 1 it has been a dream for many scientists to employ it for state-selective chemistry. However, ultrafast intramolecular vibrational energy redistribution (IVR) processes generally jeopardize the selective excitation of optical transitions, which allows the molecule to be guided to a different configuration of a desired charge, mass, geometry or function. Furthermore, there is a lack of knowledge about the intricate 2


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excited electronic states. Judson and Rabitz 2 proposed a scheme in which pulse shaping techniques in combination with adaptive learning algorithms are employed in a closed loop optimal control experiment to steer the dynamic behavior of a system without prior theoretical knowledge of the system’s Hamiltonian. Numerous experimental demonstrations of this type of control schemes have been successfully performed both in the gas and condensed phase. 3–8 It didn’t take long to realize, that better light sources are required to improve control by accessing more degrees of freedom in the quantum system under investigation. In this sense, carrier-envelope phase control in few-cycle pulses enables the control of electron dynamics during molecular dissociation; 9,10 increasing the available intensity into the strong-field regime raises the chances to achieve resonance by means of stark-shifting of the electronic energy levels. 11–14 Since the typically used liquid crystal spatial light modulators allow the transmission of only visible light, devices for shaping ultraviolet pulses have been developed and employed, for example, for the discrimination of nearly identical flavins. 15 The use of intense, near-arbitrary, shaped white-light laser pulses with few-cycle temporal resolution immensely widens the range of applicable control mechanisms. With the broad range of available wavelengths and tailored sub-pulses comprised of only a fraction of the full bandwidth, excitation of various electronic levels can be performed. Excitation to and superposition of several electronic levels is enabled, creating atomic or molecular electronic wave-packets not only made up from Rydberg states, 16–18 but also from low-lying electronic levels. The temporal resolution is sufficient for addressing even the fastest nuclear dynamics. Here, we present an experimental setup that allows to identify optical pathways, which connect initial molecular configurations via a series of electronically excited states to the desired target state, in the context of a charge reversal process. The experimental configuration is specifically applied to the photo-fragmentation of Cu3 and Al4 gas phase clusters, starting − 19–21 from the linear (Cu− through the 3 ) and rhombic (Al4 ) anionic ground state geometries

neutral and ending up in the cationic state (NeNePo-Negative to Neutral to Positive). 7,22,23 Thus, the charge reversal process is a femtosecond pump and probe technique spanning three

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charge states and allowing to probe the wave packet dynamics of mass-selected neutral clusters, on the ground as well as excited state potential energy surfaces. Moreover, through vertical electron photodetachment, the neutral ground as well as excited states can be accessed without limitations by spin and symmetry selection rules. For this purpose we employ shaped white-light laser pulses, which drive the system across a series of temporally opening and closing Franck-Condon windows, to reach the desired target state. The use of such broadband laser pulses opens the access to a high diversity of pathways to reach the target state. The ultrabroadband white-light pulses are extracted from plasma filaments in air at atmospheric pressure. 24 The photo-fragmentation processes are optimized in a feedback loop by means of an evolutionary algorithm. 25 As a result, the multi-photonic transitions become significantly more selective. The method is very promising for reaching any desired point on the potential energy surface, may it be reactive or stable.

Experimental Methods The experiments have been performed in a novel setup composed of a white-light generation and shaping system 24 in combination with a tandem mass spectrometer. 26

Cluster Generation and Tandem Mass Spectrometry − Cu− n and Aln metal cluster anions are generated by sputtering the corresponding metal tar-

gets within a magnetron sputter source, 27 incorporating a commercial sputter head (Kurt J. Lesker) with a DC power supply (DC01 BP, Kurt J. Lesker). Argon gas is used for the sputtering process, which was injected into vacuum via a mass flow controller (1179B, MKS Instruments) leading to an improved signal stability. The generated ions pass a skimmer held at variable potential, are further guided by a radio-frequency (RF) decapole ion-guide and deflected into 90◦ by an electrostatic quadrupole ion-deflector. The ions of interest are mass-selected in a first quadrupole mass filter (Extrel CMS) and focused into a temperature

4


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adjustable hexadecapole ion trap. The trap is continuously filled with helium buffer gas (6.0, Linde AG) at a pressure of 0.03 mbar injected into the trap via a second mass flow controller. During the experiments described here the trap temperature was kept at 20 K by a closed-cycle helium cryostat (CTI-Cryogenics). The irradiation of the thermalized anions with white-light femtosecond laser pulses takes place in the ion trap. Two measurement procedures were followed: a) the anions interact with the white-light laser pulses leading to laser induced dissociation (LID) of the parent anions, or b) the interaction with the white-light laser pulses leads to charge reversal and formation of parent and eventually fragment cations. During the first type of experiments (a) the trap potentials are optimized for a fill/extraction process and in the second type (b) the voltages, optimized for the accumulation of anions, remain unchanged, allowing a continuous extraction of the cations. After extraction from the trap, the ions are again deflected into 90◦ and are mass-filtered by a second quadrupole mass filter. The detection of the ions is performed by a channeltron detector (Burle, Model 4873).

White-Light Pulse Generation and Shaping The laser setup used in these experiments has been described in detail elsewhere. 24 Briefly, a commercial Ti-Sa fs-oscillator and amplifier system (Femtolasers Femtosource Compact Pro, Quantronix Odin C) produces 35 fs laser pulses with an energy of 1 mJ, a central wavelength of 807 nm and 46 nm bandwidth at a repetition rate of 1 kHz. Moderated pulse energies of 450 µJ are used for a mild spectral broadening in the first filamentation stage, by focusing the laser pulses with a spherical mirror (f = 2m). Recollimation and compression to 15 fs FWHM of the spectrally broadenend pulses is realized with a spherical mirror and a pair of chirped mirrors (Layertec). These pulses are again filamented in air by focusing with a concave mirror (f = 1.5 m), leading to a very broad spectrum with a substantial spectral intensity in the visible range down to wavelengths slightly below 500 nm. After the second filamentation stage, the pulses are recollimated by a concave mirror. The dispersion 5



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resulting from the following optical path is pre-compensated by a pair of ultra-broadband chirped mirrors (Layertec). Shaping of the supercontinuum laser pulses is achieved in a 4-f zero dispersion compressor setup incorporating a 640 pixel liquid crystal spatial light modulator (LC-SLM) (SLM 640, Cambridge Research & Instrumentation, Inc.). In order to achieve a flatter intensity profile of the spectral components, the high intensity in the NIR region is attenuated by means of a 66% 800 nm beam splitter. A typical output spectrum is shown in figure 1a). The shaped pulses can be directed either to the vacuum chamber for optimal control experiments or, via a flip mirror, to the home-built transient grating frequency-resolved optical gating (TG-FROG) setup for pulse analysis. 28,29

Figure 1: a) Typical spectrum obtained after two filamentation stages in air at atmospheric pressure and attenuation of the NIR spectral region measured after the pulse shaper setup. b) TG-FROG trace of a typical short pulse compressed for experiments in the ion-trap, measured after propagation through an equivalent air path and vacuum chamber window. The offset phase φof f (ω) written on the LC-SLM for compression of the pulses at the location of the ion trap is slightly readjusted on a daily basis; the pulses are always compressed to 7 fs or less. The main reason for the complicated offset phase φof f (ω) (see figure S1 c) is the wavelength dependent group delay dispersion (GDD) of the ultra-broadband chirped mirrors. Furthermore, small variations in the spectral phase of the pulses can occur every day and have to be compensated. A typical short white-light laser pulse used for experiments performed in the ion trap is shown in figure 1b. The pulse energy was kept at 20 µJ for all experiments presented here, except for the power dependence measurements, 6


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where the attenuation was achieved by means of a wire-grid polarizer (Edmund Optics). The laser pulses are focused into the ion trap with a concave mirror (f = 0.75 m), resulting in an approximate peak intensity of 5 · 1013 W/cm2 .

GDD + GD Pulse Parametrization In order to perform an efficient evolutionary optimization, a routine has been developed that generates only suitable laser pulses with a peak intensity sufficient for producing an acceptable charge reversal cationic signal. At the same time, the routine produces neararbitrary pulses by limiting the number of constraints to the ones which prove necessary. The GDD + GD parametrization routine provides steady phase functions complying with the sampling limit of the pulse shaper setup, by limiting the slope of the phase function such that the phase difference of two adjacent pixels is δφ ≪ π. These phase functions are generated by the following algorithm: the pixel range of the SLM is divided into 30 equal divisions, and two independent parameters, one for group delay (GD) and one for group delay dispersion (GDD), are assigned to each division. Both parameter functions are numerically singly (GD) and doubly (GDD) integrated in order to obtain two steady phase functions, φGD and φGDD , respectively. Summation of both phase functions yields a new phase function that contains information on both the GD and GDD of the output pulse. In order to avoid optimization artifacts stemming from the irregular phase caused by the ultrabroadband chirped mirrors, the offset phase φof f (ω) required for pulse compression is added to each generated phase function (see figure S1). The 60 pulse parameters are optimized using an evolutionary algorithm 25 considering 30 individuals per generation.

Optimized Pulse Electric Field Determination Simulation and understanding of the interaction of the optimized pulses with the molecular systems under investigation requires the knowledge of the optimized pulse’s electric field E(t). The measurement of the electric field E(t) for such complex pulses with nearly octave7



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spanning bandwidths is very difficult. However, due to the proper calibration of the pulse shaper setup, demonstrated by Hagemann et al. 24 and the knowledge of the offset phase φof f (ω), the spectral phase of the optimized pulses φopt (ω) can be calculated. For this purpose, the offset phase φof f (ω) has to be subtracted from the phase written on the LCSLM, φSLM (ω): φopt (ω) = φSLM (ω) − φof f (ω).

(1)

Hence, together with the measurement of the spectrum I(ω), the electric field of the optimized pulse in the frequency domain E˜ + (ω) can be calculated by: 30 E˜ + (ω) =

r

π p I(ω) e−iφopt (ω) . ε0 c n

(2)

The temporal electric field E + (t) can be obtained by Fourier transforming E˜ + (ω) according to: 1 E (t) = 2π +

Z

∞

E˜ + (ω)eiωt dω .

(3)

−∞

As plots of E(t) are very vague in showing the occurrence of different light frequencies over time, these are not shown here. Rather, the calculated intensity I(t) = E(t)E ∗ (t) and calculated TG-XFROG traces 31 of the optimized pulses are shown. To obtain the latter, the electric field E + (t) is multiplied with a gate function G(t − τ ), Fourier transformed, and the square of the absolute value is calculated to obtain the spectrum I(ω, τ ) at time τ : Z I(ω, τ ) =

∞ +

E (t) · G(t − τ )e

−iωt

−∞

2 dt .

(4)

In order to resolve the short features of the optimized pulses, a Gaussian function with a FWHM duration of 8 fs was chosen as the gate function G(t − τ ).

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Results and Discussion Copper Trimer The charge reversal experiments on Cu− 3 anions were performed by irradiating the trapped and thermalized ions with short as well as shaped white-light pulses. For all the charge reversal experiments on the Cu− 3 anion, wavelengths shorter than 540 nm were blocked to avoid photo-fragmentation of the parent anions into Cu− (see discussion later in text). A typical cationic mass spectrum obtained by irradiating the trapped Cu− 3 anions with 7 fs short white-light laser pulses is shown in figure 2. The strongest mass peak is observed for − the Cu+ 3 cations generated through direct charge reversal of the Cu3 anions. Significant + signal intensities are also observed for the Cu+ 2 and Cu fragment cations resulting from the

photodissociation of the trimer. For exploring the fragmentation mechanism, a linear chirp scan, where φ′′ was scanned

Figure 2: Mass spectrum of the Cu+ n (n = 1-3) cations produced in a charge reversal experiment, starting from Cu− anions which were irradiated with 20 µJ, 7 fs white-light laser 3 pulses. from -400 fs2 to 400 fs2 while monitoring all three cationic photo-product signals, was performed and is depicted in figure 3. As the charge reversal is a highly nonlinear process (the 32 vertical detachment energy, VDE, for Cu− and the ionization potential, IP, for 3 = 2.37 eV

Cu3 = 5.8 eV 33 ), the strongest ion yield is observed for φ′′ = 0 fs2 where the peak intensity

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Figure 3: Cu3 charge reversal linear chirp scan from -400 fs2 to +400 fs2 . The Cu+ 3 (red + line with square symbols), Cu+ (blue line with circles) and Cu (green line with triangles) 2 cation yields are monitored. of the pulses is highest and decreases with ascending negative and positive chirp, owing to + the lower peak intensities. Interestingly, the (Cu+ 2 /Cu3 ) ratio changes considerably with the

chirp. As observed in figure 3, for φ′′ = 0 fs2 this ratio equals 0.6 and it changes to 1.0 for negative chirps larger than φ′′ = -70 fs2 , while the ion yield remains on a fairly high level. + 2 A similar (Cu+ 2 /Cu3 ) ratio of 1.0 is observed also for positive chirps larger than 100 fs . + Hence, maximizing the (Cu+ 2 / Cu3 ) ratio was chosen as target for an optimization using + the GDD+GD parametrization. During the optimization, the ion yield of Cu+ 2 and Cu3 was

measured for each individual pulse and the fitness F of the pulses was determined either by the formula: + + F = (Cu+ 2 − Cu3 ) · (Cu2 )

(5)

or by the routine: if

Cu+ 2 > T

+ F = Cu+ 2 / Cu3

else F =

(Cu+ 2

(6)

/ Cu+ 3 )/10 ,

with the threshold T set to 700 or 800 counts. The fitness functions F were chosen such + that not only a higher (Cu+ 2 / Cu3 ) ratio is favored, but also a higher total signal level

(especially with the first fitness function), such that the signal to noise ratio is sufficient 10


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for a successful optimization. The optimizations were usually terminated after about 30 generations, determined by a very small mutation parameter indicating the infeasibility of significant further optimization. Best optimization factors of 2.7 to 3.0 with respect to the short laser pulse (1.64 to 1.82 with respect to the -100 fs2 chirped pulse, where the same ion yields are measured as with the optimal pulse) were achieved. Figure 4 shows the Cu+ 3 and Cu+ 2 ion yields while switching between the optimized and the short white-light pulses as well as the corresponding calculated TG-XFROG traces and intensity profiles of the optimal pulses obtained from the four best optimization runs. As observed from figure 4, the optimization algorithm does not lead to the compression of the supercontinuum to one few-cycle white-light laser pulse. The non-trivial optimal pulse shapes obtained here suggest a complicated excitation mechanism involving a multitude of electronic states, in which the sub-pulses act in a cooperative manner, such that a higher fragmentation ratio is achieved. Analysis of the four optimized pulses reveals a very complex structure with several discrete short sub-pulses of variable intensities and wavelengths, with some sub-pulses spanning over the entire spectrum from the visible to NIR range. All four optimal pulses feature similar but also individual characteristics; common to all is a sequence of intense short sub-pulses with descending wavelength at the leading edge followed by less intense pulses with longer wavelengths at later times. However, the timings, the bandwidths and the number of sub-pulses vary. Considering only the sub-pulses with fair enough intensity, the temporal delay between sub-pulses ranges from approximately 10 fs (figure 4 d and f) to 115 fs (figure 4 f) and the number of sub-pulses from three (figure 4 f) to four or more (figure 4 d). The trailing sequence of NIR pulses also features different numbers of sub-pulses and endures for 150 fs (figure 4 b) to about 250 fs (fig. 4 f). In order to be able to elucidate the molecular reaction pathway effected by an optimal pulse, it is important to consider the intensity of each individual sub-pulse which might result in a certain non-linearity degree as well as the time delays within the pulse sequence with regard to the dynamic response of the Cu3 cluster. For an optimal excitation, dissociation

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+ Figure 4: Optimization of the (Cu+ 2 /Cu3 ) ratio. left: Comparison of the ion yields obtained by switching between the optimized pulses and a short pulse (red line with square symbols + for Cu+ 3 and blue line with circles for Cu2 ). right: Corresponding calculated TG-XFROG traces (top) and calculated intensities (bottom) of the optimized pulses. The results were obtained from four different optimization runs measured on three different days. For the first optimization (figures a and b) the fitness was determined using formula (5), whereas for the other three optimizations the routine (6) was employed.

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and ionization pathway, the occurrence of the sub-pulses in the optimized laser pulse has to be synchronized with the dynamics of the molecular system. 34 The broad bandwidth of the white-light pulses allows for the resonant excitation of many different electronic states lying at the available photon energies or their multiples. Furthermore, simultaneous excitation of several electronically excited states leading to the formation of electronic wave packets is possible. 35 Thus, both vibronic as well as electronic wave packets might play a role for the effective excitation and ionization of the desired fragment. The time-delays between the subpulses which range from ten up to a few hundred femtoseconds are too short to be addressing only vibrational dynamics, 36 which for the triangular neutral Cu3 feature periods between 115 and 284 fs. 19,37 Thus, the short sub-pulse delays likely are the signature of electronic wave packets. 38 Such intramolecular electronic wave packets, formed by the simultaneous excitation of energetically close lying excited states, have been observed previously 16,17 and more recently by means of attosecond pulses. 38 A more in-depth interpretation of the observed pulse shapes requires theoretical calculations and we hope that these results will stimulate some attention in this regard. In a qualitative manner, it can be stated that the complex pulse shapes in figure 4 suggest a stepwise excitation mechanism along various electronic states or their superpositions, with femtosecond time delays between the sub-pulses such that beneficial Franck-Condon windows and wave-packet interferences for the excitation are met, leading to the highly selective formation of Cu+ 2 fragment ions and minimization of the energetically more favorable direct photoionization of the Cu3 trimer. To gain more insight into the fragmentation mechanism, LID experiments on the Cu− 3 anion and the Cu+ 3 cation were conducted by irradiating the trapped ions with 7 fs short white-light pulses or one of the four optimized pulses shown in figure 4 for which λ < 540 nm were blocked. The parent ion and the fragmentation products were monitored with the − second quadrupole mass spectrometer. No fragmentation of the Cu+ 3 cations or Cu3 anions

could be observed for any of these pulses. As already shown by Jarrold et al., 39 fragmentation of internally cold Cu+ 3 cations requires wavelengths shorter than 440 nm which are not

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Figure 5: Measurement of the laser induced decomposition of Cu− 3 anions with 7 fs short white-light pulses versus cutoff wavelength of the laser pulse spectrum. The Cu− 3 parent ion − (red line with square symbols) as well as the Cu2 (blue line with circles) and Cu− (green line with triangles) fragment ion channels were monitored. The red arrow marks the onset of the Cu− anion signal at λ > 535 nm. available in the experiments presented here. Interestingly, Cu− fragments are detected when Cu− 3 anions are irradiated with 7 fs short pulses that contain wavelengths shorter than 540 nm as shown in figure 5, where the shorter − − wavelengths were gradually unblocked while monitoring the Cu− 3 , Cu2 , and Cu ion yields.

At a cutoff wavelength of 535 nm Cu− anions start to appear. The fragment ion signal shows 32 an edge at 528 nm (2.35 eV), a value which is very close to the VDE of Cu− 3 (2.37 eV),

and remains steady for cutoff wavelengths below 520 nm. No Cu− 2 anions could be detected even when irradiating with full bandwidth laser pulses. The Cu− 3 parent ion signal shows a constant depletion of about 500 counts independent of the cutoff wavelength, suggesting that the Cu− fragment anions arise from the photo-depleted, neutralized portion. Although 40 CID measurements on Cu− reveal the loss of Cu2 , and thus the formation 3 of Spasov et al.,

of Cu− , as the favored fragmentation channel, this cannot be the case here, due to the wavelength independent photodepletion of the parent ion. Cu− fragment anions could thus result from the photodissociation on an excited state of the neutral Cu3 cluster, for example a Cu− Cu+ 2 ion pair state, or alternatively from the fragmentation of neutral Cu3 into Cu2 and Cu followed by an electron capture of the latter, facilitated by the enhanced generation

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of photoelectrons caused by the single photonic photodetachment of Cu− 3. The fact that neither Cu3 cations nor anions fragment when irradiated with the short or optimized laser pulses with wavelengths below 540 nm blocked, suggests that the fragmentation into Cu+ 2 during the charge reversal process has to occur in an excited state of the neutral Cu3 cluster. Power dependence measurements for the Cu− 3 charge reversal conducted with 7 fs laser 3.3 dependence for Cu+ pulses indicate a I2.9 dependence for the formation of Cu+ 2. 3 and a I 33 Since the VDE for Cu− 3 is 2.37 eV and the ionization potentials for Cu3 and Cu2 are 5.8 eV

and 7.9 eV, 41 a minimum of four and five 600 nm photons (six and seven photons at 800 nm) + are necessary for the ionization of Cu+ 3 or the formation of Cu2 cations, respectively. Con-

sidering also the dissociation energy for the loss of Cu from neutral Cu3 of approximately 1 eV, 19 one additional photon might be required for the formation of Cu+ 2 . The fact that the power dependence observed in the experiment is lower indicates that at least one resonant intermediate state, most probably an excited state of the neutral species, is involved in the charge reversal process. A deeper understanding of the photo-induced fragmentation process presented here, which is coded in the optimal pulse shapes obtained, requires however, a rigorous analysis by theory.

Aluminum Tetramer To substantiate the general applicability of the experimental technique, the controlled photofragmentation of Al4 clusters during the charge reversal process was additionally studied. Initial LID investigations on the Al− 4 anions indicated no photo-fragmentation into anionic products even when the anions were irradiated with the entire spectrum of the white-light pulses. For this reason, the optimal control experiments were performed by using the entire spectrum of the white-light laser pulses. A typical cationic mass spectrum obtained upon the irradiation of the trapped and thermalized Al− 4 anions with 7 fs white-light pulses in the 15



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context of a charge reversal process is shown in figure 6. The highest cationic yield is observed

Figure 6: Mass spectrum of the cations produced in a charge reversal experiment by irradiating the Al− 4 anions with 20 µJ, 7 fs short white-light pulses. for Al+ 4 generated by multiphotonic excitation and ionization of the parent anions, followed + by strong Al+ , Al+ 3 , and Al2 photo-fragment signals. Even a small amount of Argon tagged

Al+ ions (67 amu) is detected. Although such weakly bound complexes formed via three body collisions have already been observed in low temperature ion traps, 42 the formation of the Al+ ·Ar in this experiment is surprising and indicates that the Al+ photo-fragments have sufficient time in the trap to thermalize and bind an Ar atom prior to their extraction. The Ar atoms required for tagging enter the trap through diffusion from the ion source region, where high amounts are used for the sputtering process. In order to investigate the influence of the spectral phase of the pulses on the photofragmentation process upon charge reversal, a linear chirp scan between φ” = − 300 fs2 and φ” = +300 fs2 was first performed while monitoring the parent and the photo-fragment cation yields, as shown in figure 7. As can be observed from figure 7, for φ” = 0 the Al+ 4 ion signal is higher than for the Al+ photo-fragment, while this ratio strongly changes for stronger positive and negative chirps where the Al+ yield is highest. The ion yields for the other two fragments are very low and are not considered further. Hence, maximizing the (Al+ /Al+ 4 ) ratio was chosen as an objective for optimization. Due to the low signals observed for the Al cluster cations, the fitness F of the pulses was determined only by using formula 16


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(5), which favors the signal level increase more than the routine (6). Figure 8 shows the

Figure 7: Laser pulse linear chirp scan for the charge reversal of Al− 4 anions between -300 + + 2 2 fs and 300 fs . Al4 (red line with square symbols), Al3 (black line with downward-oriented + triangles), Al+ 2 (green line with upward-oriented triangles), and Al (blue line with circles) are monitored. calculated TG-XFROG traces and intensity profiles of the optimal pulses obtained in the four best optimization runs and the comparison of the Al+ and Al+ 4 cation yields for the optimal and the short laser pulses. Optimization factors of 2.7 up to 3.4 relative to the short + + 7 fs pulse were obtained for the (Al+ /Al+ 4 ) ratio. An improvement of the (Al /Al4 ) ratio is

also observed during the linear chirp scan (see figure 7), with the highest ratio at -175 fs2 . The optimization factors calculated relative to a pulse with a chirp of -175 fs2 are between 1.25 and 1.75. By analyzing the optimal pulse traces, a considerable difference is observed between the first and the other three traces. While the first optimized pulse features a sequence of many short pulses with descending wavelengths, the other three present sequences of short pulses with ascending wavelengths. This difference is attributed to two very different pathways which result, however, in similar optimization factors. All four optimal pulses feature very short sub-pulse delays on the order of 10 fs. As in the case of Cu3 , such short sub-pulse delays cannot account solely for vibrational dynamics, which for neutral rhombic Al4 feature periods between 99 and 498 fs, 43 and thus likely are a signature of electronic wave packet propagation as well.

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Figure 8: Optimization of the (Al+ /Al+ 4 ) ratio. left: Comparison of the ion yields obtained by irradiating the trapped ions with the optimized pulses vs. irradiation with a short pulse + (Al+ - blue line with circles, Al+ 2 - green line with upward-oriented triangles, Al3 - black line with downward-oriented triangles and Al+ 4 - red line with squares). right: Corresponding calculated TG-XFROG traces (top) and calculated intensities (bottom) of the optimized pulses. The results were obtained from four different optimization runs measured on different days. Due to the low ion signal, the first fitness function (5) was used for all the four measurements presented here. 18 ACS Paragon Plus Environment

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The vertical electron affinity of Al− 4 extracted from photoelectron spectra is approximately 2.0 eV. 44–47 Hence, single-photonic photodetachment is possible with the employed laser spectrum. As both the anion and the neutral clusters have similar rhombus geometries (D2h symmetry 43 ) resulting in close values for the vertical and adiabatic electron affinities, the Al4 clusters could be present in their neutral electronic ground state after electron photodetachment. 20,21,43,48 Thus, fragmentation during the charge reversal probably occurs in an excited state of the neutral cluster. Power dependence measurements with 7 fs short white-light laser pulses yield a power dependence of I3.3 for Al+ and I2.9 for Al+ 4 . With the above mentioned vertical detachment energy for Al− 4 and the ionization potentials of 6.0 eV and 6.5 eV for Al and Al4 , respectively, 49 more than four (600 nm) to six (800 nm) photons are needed for the charge reversal process and fragmentation into Al+ . Considering also the dissociation energy of ground state neutral Al4 into Al of approximately 2.0 eV, 43 an even higher number of photons might be required for the formation of Al+ . As for Cu− 3, the smaller observed power dependence indicates that at least one resonant intermediate electronic state is involved.

Conclusion The white-light optimal control of Cu3 and Al4 photo-fragmentation processes in the context of a charge reversal process is demonstrated for the first time by using an evolutionary algorithm and a pulse shaping setup. The use of shaped supercontinuum white-light pulses in our laboratory is unique and allows us to address not only a series of vibrationally but also a multitude of electronically excited states for the investigated molecules, opening access to a high diversity of pathways to reach the target state. For an efficient optimization, a parametrization routine is presented, which generates only suitable laser pulses with peak intensities sufficient to produce acceptable charge reversal cationic signals. Optimization factors for the fragment to parent ratios of up to 3.0 for Cu3 and 3.4 for Al4 relative to the short 7 fs white-light pulses are achieved. Such optimization factors demonstrate the 19



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high selectivity in populating specific points on the potential energy surface for markedly different systems, attainable by the presented method. Investigation of the optimal pulse profiles suggests that not only vibronic, but also electronic wave packets are probed. The power dependent measurements performed with short white-light pulses indicate that at least one step must be resonant for the formation of both parent and fragment cations. A deep understanding of the pathway taken by the two investigated systems during the optimization process requires a rigorous treatment from theory which will hopefully be stimulated by these experiments. The results presented in this paper nourish the hope, that shaped white-light pulses combined with the charge reversal process might be generalized to a tool with the ability to populate a large spectrum of desired states for a high diversity of molecular systems. Given the ability to probe specific states, the presented method could be further tested in this regard.

Acknowledgement The authors gratefully acknowledge the generous funding support provided by the Collaborative Research Center SFB 546 ”Structure, Dynamics and Reactivity of Aggregates of Transition Metal Oxides” of the German Science Foundations (DFG). F. S. acknowledges the Evangelische Studienwerk Villigst for financial support. The authors express their greatest thanks to Prof. Dr. John Maier (Basel), Alexander von Humbold fellow at the Freie Universität Berlin, for helpful and stimulating discussions.

Supporting Information Available Example for the generation of a phase function with the GDD+GD-algorithm.(Figure S1) This material is available free of charge via the Internet at http://pubs.acs.org/.

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