Gaining Mechanistic Insight with Control Pulse Slicing: Application to

Article Cite This: J. Phys. Chem. A XXXX, XXX, XXX-XXX

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Gaining Mechanistic Insight with Control Pulse Slicing: Application to the Dissociative Ionization of CH2BrI Xi Xing, Roberto Rey-de-Castro, and Herschel Rabitz* Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States S Supporting Information *

ABSTRACT: In quantum control experiments with shaped femtosecond laser pulses, adaptive feedback control is often used to identify pulse shapes that can optimally steer the quantum system toward the desired outcome. However, gaining mechanistic information can pose a challenge due to the varied structural features of the control pulses and/or the often complex nature of the associated simulations of the experiments. In this article, we introduce control pulse slicing (CPS) as an easyto-implement experimental analysis tool that can be employed directly in the laboratory without the need for modeling, to gain mechanistic insights about control experiments, regardless of whether the pulse is optimal or chosen by other means. As an illustration, we apply CPS to dissociative ionization of CH2BrI with mass spectral detection, where two pulses with similar intensities are investigated, with each capable of distinctively controlling the ratio of Br+/CH2Br+. These two control pulses were, respectively, first identified with closed loop and open loop procedures, and then the multispecies experimental data was analyzed with CPS. By comparing the dynamical evolution of the observed multiple fragment ion yields upon slicing scans of the two distinct pulses, we were able to reveal insights about the control mechanism for manipulating the objective ratio. In addition, we also identified the relationship between the temporal structures of the control pulses and the associated key reaction pathways involved in ionic as well as neutral electronic states, in spite of the signals only directly being from the ionic species. The CPS technique is not limited to controlled fragmentation mass spectrometry, and it may be applied to gain mechanistic insights in any control experiment, reflected in the nature of the recorded signal.

1. INTRODUCTION With advances in ultrafast lasers1,2 and pulse shaping3−5 technologies, experimental control of quantum systems has enjoyed growing success in recent years; similar statements apply to controlled quantum dynamics with other electromagnetic resources.6,7 The implementation of closed-loop adaptive feedback control (AFC)8,9 provides a practical means to find an optimal pulse for a posed goal even without prior detailed knowledge about the system Hamiltonian. A number of experiments have utilized AFC to explore the control of chemical reactions, including molecular fragmentation, ionization, isomerization and etc., in both the gas and solid phases10−21 as well as in other atomic and molecular applications.22−24 Although, finding an optimal solution typically can be readily achieved with the aid of a global search algorithm (e.g., genetic algorithm (GA)) linked to an objective fitness function, extracting insights about the ensuing control mechanism often calls for additional effort. There have been only a few cases where a good understanding of the control mechanism was gained from the optimal solutions alone.25,26 The challenge involved arises due to the common situation of operating with a large number of control variables and the nonlinearity of the dynamics with respect to the field. The optimal pulses may contain rich pulse structures, making it a challenge to characterize the embedded features in the time © XXXX American Chemical Society

and/or frequency domain of a pulse and identify their linkages to the control mechanism. In addition, the procedure of utilizing the observed control in a simulation of the experiment is often hindered by the complexity of the dynamics and uncertainties in the Hamiltonian. Thus, far, there is a paucity of general experimental analysis tools that are tailored to extract mechanistic insights directly from suitable laboratory data to avoid the latter companion modeling complexities. However, some efforts have been focused at gaining control mechanistic insights involving electron and nuclear wavepacket dynamics in the strong laser field ionization. In particular, some studies have used various pump−probe techniques, photoelectron spectroscopic methods,27,28 and/or velocity map imaging (VMI) measurements of photoelectrons in coincidence with photoions,29−31 in combination with electronic structure calculations32 and quantum dynamical simulations,17,33 which have provided rich information on control mechanisms. These studies often call for sophisticated apparatus and detailed additional knowledge about the system in order to understand the physics. The present work aims at introducing general experimental tools that can be universally used in conjunction Received: September 11, 2017 Revised: October 25, 2017 Published: October 26, 2017 A

DOI: 10.1021/acs.jpca.7b08835 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

multiple portions of the pulse may be simultaneously sliced out) can provide further mechanistic insights. The remainder of the paper is organized as follows: Section 2 describes the general basis and procedure for performing the CPS method along with simulations as a guide to its utility. Section 3 presents an implementation of CPS to the experimentally controlled dissociative ionization of CH2BrI, including an interpretation of the CPS results. Section 4 provides a conclusion and an outlook on future directions for exploiting CPS capabilities.

with control pulses discovered by AFC or other means in order to gain insights into the induced mechanism even with minimal knowledge of the underlying molecular physics. With this general goal in mind, we have recently proposed and implemented a set of new tools, including Hamiltonian encoding-observable decoding (HE-OD),34 landscape Hessian analysis (LHA)35 and control pulse slicing (CPS). The CPS concept was only briefly considered in a previous paper.36 In this article, we will present CPS in detail and provide results of its implementation in the study of controlling dissociative ionization of CH2BrI in order to demonstrate its utility in revealing control mechanisms with complex pulses and dynamical scenarios. The CPS method may be viewed as analogous to pump− probe spectroscopy where the time delay between two pulses is varied and the molecular dynamics is probed. However, while pump−probe spectroscopy is often limited to containing two transform limited pulses or fixed-shaped pulses, CPS is tailored to the particular waveform in the control field itself to specifically learn about the dynamics driven by the control pulse. Therefore, CPS is a special pulse shaping-based technique exploiting both phase and amplitude modulation, which is employed af ter obtaining the original control pulse. Although CPS does not rely on quantum dynamical simulations, its operating principle is parallel to common practice employed in simulations. In particular, in many simulations the goal is to meet the physical objective at time T, and the simulations are stopped at any desired time τ, where τ < T, in order to observe the intermediate yields in the target objective or possibly other ancillary products. Such producttime plots are routinely employed in almost all simulation studies to provide valuable mechanistic insights by observing the dynamical evolution of the system over τ < T, thereby revealing correlations between different state populations or other dynamical features as well as yielding information about the role of pulse temporal structures. In quantum control experiments, information is typically only available at the final outcome at time T(i.e., even T → ∞ in some cases). For example, in controlled fragmentation studies using a time-of-flight mass spectrometer (TOF-MS), the mass spectrum resulting from a particular laser pulse is only observed at the end of the flight time after the laser-molecule interaction is long over. In such circumstances, what has happened in between the start and completion of the pulse, as well as possibly postpulse dynamics, is not explicitly known. Thus, readily performed experimental real time system monitoring of the evolution over the pulse interaction would be very valuable, just as it is in simulations.37−39 With the aid of pulse shaping, the CPS method, presented in detail in this article, provides a means to address this need. However, even the added details provided by CPS in the laboratory, or like information from intermittently stopped simulations, still leaves hidden intimate details about interfering quantum amplitudes; HE-OD can provide additional complementary insights about interfering amplitudes,34 although it is not used in the present work. Briefly, CPS operates by applying a series of special pulse shapes to the system using phase and amplitude modulation, where each application of CPS correspondingly removesa selective portion of the original pulse in time (i.e., pulse slicing) in a systematic fashion. The resultant array of CPS driven measurements can reveal key aspects of the evolution of the system, and alternative variants of pulse slicing (e.g.,

2. CPS METHOD The time-dependent electric field of a laser pulse can be written as ⎡ 1 E(t ) = Re⎢ ⎣ 2π

+∞

∫−∞

⎤ E(ω) exp( −iωt ) dω⎥ ⎦

= A(t ) cos[ωt + ϕ(t )]

(1)

where the temporal field E(t) has amplitude A(t) ⩾ 0 and real phase ϕ(t) while corresponding spectral field E(ω) = A(ω) exp[iϕ(ω)] is a function of the spectral amplitude A(ω) ⩾ 0 and real spectral phase ϕ(ω). Consider a heaviside step function h(τ − t) such that h(τ − t) = 1 for t ≤ τ and h(τ − t) = 0 for t > τ. The time truncated field E(t,τ) can expressed as36 E(t , τ ) = E(t ) × h(τ − t )

(2)

In computational simulations, the formality of this operation is rarely, if ever, expressed as commanding the simulation to stop at time τ in a trivial procedure. However, in the laboratory, especially with ultrafast pulses, there is no direct access to taking such a time slice out of the nominal field E(t). Nevertheless, the pulse is available in the frequency domain, and we may exploit that to achieve the same result, yet indirectly. In particular, in the frequency domain, we have the Fourier transform of E(t,τ) → E(ω,τ) as a convolution. +∞

E (ω , τ ) =

∫−∞

E(ω′) × Hτ(ω − ω′) dω′

(3)

where E(ω) and Hτ(ω) are the Fourier transforms of E(t) and h(τ − t), respectively. Because of the finite laser bandwidth available in the laboratory there is a limit to how fast the field can be turned off (i.e., truncated in the time domain). Thus, in practice, h(τ − t) has to be taken as a smooth function of time. So, in the experiment, instead of using the step function, we apply the slicing function h(τ − t ) =

1 erfc(t /Δt ) 2

(4)

where erfc is the complementary error function and Δt defines the turn-off time, or CPS resolution In practical laboratory implementation, the truncated field is represented at discretized frequencies, given by N

E(ωj , τ ) ≈

∑ E(ωk)Hτ(ωj − ωk) k=1

(5)

where N is the number of spectral components. Therefore, given the control field E(ω) in the frequency domain with the known spectral phase ϕ(ω) and amplitude A(ω) as well as the error function at cutting time τ, one can use eq 5 as an approximation to eq 3 to calculate a particular desired truncated field denoted as E(ω)′ ≡ E(ω, τ) with B


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Figure 1. Simulated demonstration of the time slicing procedure. The laser spectrum is assumed here to be a Gaussian centered at 800 nm and with 40 nm fwhm. (a) Initial field’s temporal amplitude (blue) and phase (red). (b) Initial field’s spectral amplitude (blue) and phase (red). (c) Temporal amplitude (blue) and phase (red) from a sliced field at τ = 200 fs and Δt = 100 fs. (d) Spectral amplitude (blue) and phase (red) for the sliced field at τ = 200 fs and Δt = 100 fs. The dotted green curve in part d represents the ideal spectral amplitude to be applied, which is out of the SLM maximum amplitude limit. The dotted curves in part c correspond to the temporal amplitude and phase of the ideal pulse, which is compared to the practical ones in solid curves. (see details in text).

associated phase ϕ′(ω) and amplitude A′(ω), where E(ω)′ = A′(ω)exp[iϕ′ (ω)]. The transmittance T(ω) = [A′ (ω) /A(ω)]2, as determined by the SLM amplitude mask will often in practice be limited to being ⩽1 for each spectral component ωk. However, it can occur that, more than the full SLM amplitude of the original field (e.g., T (ωk) > 1) at certain frequencies ωk is needed in order to create the desired sliced pulse, especially when small Δt (i.e., a sharp cut) is applied. Similarly, additional laser bandwidth or pulse energy may be needed. These circumstances can arise due to the oscillations of the spectral amplitude modulation arising from the Fourier transform of the error function at small values of Δt. Thus, Δt can have a lower bound, which is related to the duration of the transform limited pulse. However, the temporal structure of the truncated field E(t, τ) is mostly affected by the spectral phase rather than the spectral amplitude so that forcing A′ (ωk) = A (ωk) when A′ (ωk) > A(ωk) can be treated as an approximation, which often only results in negligible errors in the amplitude of E(t, τ) (e.g., see simulation in Figure 1, below). This issue would also not arise if the original control pulse had a sufficient reduced upper limit on the spectral amplitude to start with (i.e., using less than the full spectral amplitude available for the original control field). We also point out that the CPS procedure actually determines the field leaving the pulse shaper, and distortion could further occur on the way to the control sample; this situation applies to the control field itself as well and calls for due care under virtually all laser circumstances. In practice the value of Δt must be adapted to the particular experimental needs. In cases when high temporal resolution is desired, Δt can take it is minimum value given by the pulse bandwidth. In these cases, as mentioned above, the initial field

must be obtained at a lower laser power for generating accurate sliced fields. In other situations it may be advantageous to increase the value of Δt in order to reduce the requirements for higher laser powers over the original field at some spectral components. In our experiments, increasing Δt to ∼3 times the bandwidth-allowed minimum value resulted in small distortions such that acceptable sliced fields could be generated using the same laser power as in the original field. Figure 1 shows a computer simulation demonstrating the CPS method on a randomly generated pulse (i.e., via a randomly chosen spectral phase ϕ′(ω) at fixed spectral amplitude A(ω). The laser spectrum used in the simulation is a Gaussian centered at 800 nm and with 40 nm fwhm. Figure 1a shows the initial field in the time domain (temporal amplitude A(t) ⩾ 0 in blue and phase ϕ(t) red) obtained by applying the spatial light modulator (SLM) masks shown in Figure 1b with full amplitudes and arbitrary phases on the SLM (range between 0 and 2π). The dotted curves in Figure 1c depict a smoothly sliced ideal field at time τ = 200 fs calculated with Δt = 100 fs in eq 4. The Fourier transform back to the frequency domain for the sliced pulse is shown as dotted curves in Figure 1d. However, it is noted that, the spectral amplitude in part d exceeds the full (i.e., accessible) amplitude of the Gaussian envolope in Figure 1b for certain frequency components for this ideally sliced pulse, which would not be attainable in the experimental implementation. A simple treatment of thresholding the SLM transmittance to 100% without changing the spectral phase is applied to the SLM mask and the resulting spectrum is shown as the blue solid curve in Figure 1d. The corresponding field in time domain after this treatment is plotted as the solid blue curve in Figure 1c, whose C


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Figure 2. Schematic of the time slicing procedure for CPS(+) and CPS(−). (a) Error functions h(τ − t) for CPS(+) with the increasing slicing time τ marked by the black arrow. (b) Error functions h̃(τ − t) for CPS(−) also with the increasing slicing time τ (τ = −1,0,1 ps for illustration). The dotted curves with the sequencially filled areas in parts c and d represent the sliced fields in the corresponding cases as compared to the original fields represented by the red curves.

arrows. CPS(+) has an intuitive interpretation as removing later portions of the field and thereby assess the impact on the subsequent recorded system response. In contrast, the dynamical response to CPS(−) provides insights into the role of the initial portion of the control (i.e., by cutting it out while leaving the later portion unaffected). The two complementary CPS methods will be applied in the experimental illustration below.

temporal structure does not differ much from the desired one (dotted green), except for some modest temporal amplitude variations and evident low amplitude ringing right after the slicing time τ = 200 fs for the modified field. The dotted and solid traces shown in parts c and d of Figure 1 are illustrative of the small discrepancies in our experiment between the ideal and actually applied sliced fields. The discrepancies were small in part due to our choice of a smoother decay during the slicing procedure with Δt = 100 fs instead of the Δt = 30 fs sustainable by our laser bandwidth. The same treatment is applied in the experimental sections below, where the SLM transmittance is bounded by 1. In order to obtain more precisely sliced pulses, the initial field must be obtained at a reduced laser power with spectral amplitude modulation in the SLM such that, in the pulse slicing experiments, it is possible to produce higher spectral amplitude than the initial ones while still being experimentally accessible. As explained above, when h(τ − t) in eq 4 is applied, the rear portion (i.e., the domain t > τ) of the original pulse is sliced off at time τ. As τ is scanned over the entire pulse duration starting from the very beginning of the pulse, portions of the original temporal field are successively added in with increasing τ. We refer to this procedure as “additive-CPS” or CPS(+). When the step function is defined as h̃(τ − t) = 1 − h(τ − t) = h(t−τ), the f ront portion (i.e., the domain t < τ) of the original pulse is sliced off at time τ instead, and the corresponding scan of increasing values of τ successively removes more of the front portion of the original pulse, which is referred to as “subtractive-CPS” or CPS(−). The schematics of CPS(+) and CPS(−) are shown in Figure 2, where, the original pulse is represented by the red curves in parts c and d and the sliced pulses truncated at τ = −1, 0, 1 ps are highlighted by the sequential filled areas under the dotted curves in the corresponding cases. Parts a and b Figure 2 show the slicing functions h(τ − t) and h̃(τ − t) corresponding to CPS(+) and CPS(−), respectively. The slicing time τ is scanned with increasing τ values in both cases, as denoted by the black

3. EXPERIMENTAL DETERMINATION OF CONTROL PULSES FOR SUBSEQUENT CPS ANALYSIS The experiment employing CPS entails controlled dissociative ionization olyx f CH2BrI with shaped laser pulses. The experimental setup has been described in detail elsewhere.40,41 Briefly, we employed a femtosecond Ti: Sapphire laser system consisting of an oscillator and a multipass amplifier (KMlab, Dragon) to produce pulses at a repetition rate of 3 kHz with ∼25 fs pulse width and an averaged output of 1 mJ centered at ∼785 nm. The laser pulses are shaped with a dual-mask liquid crystal SLM containing 640 pixels (CRI, SLM-640), capable of simultaneous phase and amplitude modulation. The shaped laser pulses are focused with a fused silica lens of f = 20 cm into a vacuum chamber, to a spot size of radius ∼50 μm with ∼0.35 mJ pulse energy and an estimated maximum peak intensity of 8 × 1014 W/cm2. A linear time-of-flight mass spectrometer (Jordan TOF) is used to detect the laser-induced ionic fragments. Samples are introduced into the vacuum chamber (base pressure ∼1 × 10−8 Torr) through an effusive leak value to maintain a constant pressure of 1 × 10−6 Torr during the experiment. Ion signals are collected and amplified with a 40 mm microchannel plate which is coupled to a fast digital oscilloscope (Lecroy 104MXi) for signal averaging and processing. A personal computer equipped with a genetic algorithm (GA) is used to control the SLM for running and synchronizing the AFC experiment. A reference phase mask for the transform limited (TL) pulse is identified by optimizing the two-photon diode absorption (TPA) signal, which was used to D


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Figure 3. Time-of-flight mass spectra of CH2BrI resulting from (a) pulse A: TL pulse giving the lowest objective yield of Br+/CH2Br+ ∼ 0.2. (b) Pulse B: a shaped pulse that maximizes the ratio of Br+/CH2Br+ to ∼2.5. (c) Pulse C: a shaped pulse with a significantly reduced ratio of Br+/CH2Br+ but with a similar pulse intensity as that of pulse B; the procedure for finding pulse C avoids the TL pulse and provides an interesting mechanistic comparison between pulse B and pulse C for CPS control mechanism analysis (see the text and Figure 4 for further discussion on how pulse C was determined).

pulses B and C operating within the same pulse intensity region provides an interesting control scenario to mechanistically assess with CPS. Note that, Br has two isotopes (i.e., 79Br and 81 Br) with nearly 1:1 abundance, resulting in the appearance of double peaks for Br+ (mass 79, 81) and CH2Br+ (mass 93, 95), respectively. Since the peak of CH279Br+ overlaps with the minor species of C81Br+ at mass 93, we picked the integrated signals from the single peaks of CH281Br+ and 81Br+ (marked as * in Figure 3.1) instead of both isotopes to avoid compexities due to this additional circumstance. The existence of C81Br+ is evident from observing a small peak of C79Br+ at mass 91 and C79HBr+ at mass 92. In the remainder of the paper, we simply use Br+ to imply recording the selected isotope 81Br+ and similarly CH281Br+ is used to denote CH2Br+. From Figure 3, we see clearly that the mass spectra arising from the three different shaped pulses show quite distinct patterns, with the objective ratio of Br+/CH2Br+ ranging from 0.2 for pulse A, to 2.5 for pulse B, and 0.6 for pulse C. The detailed procedures for identifying pulses B and C are described below. Using a GA, we first performed phase-only optimizations with 80 pixel bundles (i.e., 8 neighboring pixels in each bundle) at full amplitude to both maximize and minimize the objective ratio of Br+/CH2Br+. However, with this procedure, minimization simply gives back the TL pulse A, yielding the ratio ∼0.2, while maximization produces an optimal pulse that enhances the ratio by more than a factor of 10 to ∼2.5 (pulse B in Figure 3b). The TPA signal is monitored and recorded during the optimization procedures. Figure 4 shows the full history of data recorded during the ratio maximization for identifying pulse B. The red dots in the main plot record the correlation of the objective ratio versus the TPA signal for every shaped pulse utilized during the GA search, which starts from a

correct for the high order dispersion from the amplifier output. The two photon signal is also used to characterize the integrated pulse intensity for each shaped pulse. The mass spectrum of CH2BrI upon strong field ionization contains multiple fragmentation species, including CH2Br+, CH2I+, Br+, I+, CH2+, I2+,CH2BrI+, etc. Among all these species, we choose to only focus on the four major fragments (i.e., CH2Br+, CH2I+, Br+, I+) in this study, which correspond to ionic products arising from breaking the C−Br and C−I bonds. Figure 3a shows the mass spectra of CH2BrI resulting from the transform limited pulse (TL labeled as pulse A), while Figure 3b and (c) show the mass spectra from two selected shaped pulses (labeled as pulse B and pulse C, respectively). Pulse B is identified through closed-loop optimization with the target set to maximize the ratio of Br+/CH2Br+; in contrast, pulse C is picked from an open-loop procedure, which significantly reduces the same ratio, while operating in the same intensity regime as B. The procedure of finding pulse C is similar to that in reference41 and will be described in detail in Supporting Information. Here, we define the control objective as the fragment ratio of Br+/CH2Br+, which corresponds to breaking the strongest bond versus the weakest carbon−halogen bond. These objectives are chosen for demonstration purposes, and any other measurable objective could be used as well for subsequent CPS analysis. All the mass spectra are normalized to the highest peak of each spectrum, although the absolute yield from the unshaped TL pulse A is much higher than achieved by the shaped pulses (B and C). The integrated pulse intensities for the latter two pulses (B and C) are similar, by first performing AFC to find pulse B that maximizes Br+/CH2Br+ and then using an open-loop manual search for pulse C that gives a small value for the ratio at essentially the same TPA value as for pulse B. The distinct objective yields achieved with E


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TL pulse at the right bottom corner and ends up with an optimal pulse B marked by the arrow at the left top. The insert plot in Figure 4 shows the optimization of the fitness over 75 generations, exhibiting a significant enhancement of the ratio achieved through optimization. The overall yield (i.e., the integrated total MS signal) from pulse B is significantly lower than that from pulse A. The resulting optimal pulse B is found to be much lower in peak intensity compared to pulse A by observing their TPA signals; the role of intensity is well-known in highly nonlinear optical processes, such as the dissociative ionization events. Thus, in choosing pulse C for comparison mechanistically with the action of the optimal pulse B, we confine the choice of pulse C to give a very similar TPA signal. There are alternative means to make interesting mechanistic comparisons while minimizing field intensity effects (e.g., modifying the control objective fitness functions in AFC by adding weight or penalty functions including the absolute yields of one or more species to bias the fitness function). Here, we adopt an open-loop procedure for finding pulse C, which starts from filling the control landscape with a large number of polynomial phase sampling pulses followed by picking a desired pulse C that meets our requirement from the resultant pulse library; see Supporting Information for details. Pulse C, identified using this procedure, has the objective ratio of ∼0.6. Pulses B and C have distinctly different yield ratios, while their integrated pulse intensities are nearly identical as measured by TPA. Therefore, pulse B and pulse C form a pair of dynamical interest, with the intensity effect removed.

Figure 4. Correlation of the objective yield for the fragment ratio: Br+/ CH2Br+ versus the normalized two photon absorption (TPA) signal of each laser pulse. The black dots denote the objective ratio of Br+/ CH2Br+ obtained from systematically scanning the chirp parameters of a polynomial phase expansion (second, third and fourth order chirp). The red circles denote the full record of the objective yields from a GA optimization of the ratio Br+/CH2Br+ starting with the TL pulse A at TPA signal 1 and finally yielding pulse B. Among the black dots pulse C was chosen to give a reduced yield for the ratio while operating at the same intensity (TPA signal) as pulse B. See Supporting Information for a detailed description of how pulse C was chosen and for further discussion of the TPA signals. Pulses B and C form a pulse pair of interest for CPS control mechanism analysis.

Figure 5. Dynamical evolution of the fragment yields for Br+, CH2Br+, I+ and CH2I+ upon CPS applied to pulses B and C: (a) CPS(+) on pulse B; (b) CPS(−) on pulse B; (c) CPS(+) on pulse C; (d) CPS(−) on pulse C. The temporal amplitude structures A(t) of the control pulses B and C are shown as the gray background. The slicing time in CPS(+) at which the fragment ions just start to appear is denoted as τ0, as highlighted by the vertical dashed lines. The red dotted region highlights the main portion of the pulse that induces dissociative ionization with intensities just above the threshold. The black dotted region indicates the portion of the pulse that induces the dynamics occurring on the ionic surface, which is distinct for pulse B and C, as shown in parts a and c. The dynamics occurring on the neutral surface is dark in CPS(+) as no ion signals are observed, but is evident in CPS(−) ((b) and (d)) by the yield differences at τ0 and an earlier time τ1 (τ1 < τ0). F


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which has a clear contribution from controlling the secondary dissociation channel of CH2Br+ after the dissociative ionization is initiated. A similar comment applies to maximizing I+/CH2I+ with pulse B, althougth this ratio was not directly targeted as the goal of the optimization. In analyzing the dissociative ionization products, there often remains an open question about whether neutral excitations play a role in the ultimately detected ion yields. Indeed, any neutral excitations arising from the weak initial portion of the pulse are “dark” to the CPS(+) scans as no ion signals can be observed in the early stage of the scan until the pulse intensity reaches a threshold. In the following, it is shown how CPS(−) scans provide a means to address the role of neutral excitation, in an indirect fashion. Figures 5b and (d) show the fragment yields upon CPS(−) with pulse B and pulse C, respectively. The ion signals at the starting point of the CPS(−) scans (i.e.,τ = −2000 fs) correspond to the original pulses without slicing, which should be equal to those at the end of CPS(+) scans (i.e.,τ = 2000 fs). Any small differences for some species arise from the experimental noise. The CPS(−) plots may be interpreted by comparing the fragment ion yields arising from a sliced pulse at τ0 to that with a pulse sliced at an arbitrary earlier time τ1, in order to determine whether the portion of the pulse in between τ0 and τ1 plays any roles (e.g., in altering the neutral initial state populations). As highlighted by the red solid circles in parts b and d of Figure 5, the fragment yields for Br+ and I+, are both lower at τ0 than at τ1, which implies that, the portion of the pulse in between τ0 and τ1 contributes to the enhancement of the yields in Br+ and I+ through neutral pathways, even though the nature of the neutral states are not revealed here. In contrast, the yield differences in CH2Br+ and CH2I+ are not obvious within the same slicing time frame as highlighted by solid blue circles in Figure 5, parts b and d. Althought, neutral excitations to the dissociate states of CH2Br and CH2I should occur more easily, this behavior possibly arises because CH2Br+ and CH2I+ are predominately created from direct dissociative ionization with lower-lying energy states, while Br+ and I+ are much more difficult to create, with their dissociative ionization states lying higher. Therefore, the indirect pathways involving neutral excitaion become more important for creating Br+ and I+. Therefore, the yields in Br+ and I+ are significantly more affected by the early time part of the pulse before any ion products are formed. The important part for the early time dynamics on neutrals is addressed by the different response of the halogens and methyl halides in CPS(−). The collective observations in CPS(+) and CPS(−) suggest that, while the early portion of the pulse plays a role in the ultimate yield enhancement of Br + and I + involving intermediate neutral dynamics, the late portion of the pulse is responsible for the reduced yields in CH2Br+ and CH2I+ involving dynamics on the ionic surface.42 Further examining the temporal structure of the full control pulses B and C shown in the background of Figure 5, it is evident that pulse B, which maximizes the objective ratio of Br+/CH2Br+, contains complex pulse structure over its entire temporal range; in contrast, pulse C, which produces a lower product ratio, is almost free of late-pulse features beyond ∼500 fs. Examination of these pulses further supports the CPS interpretation that, the late-pulse structure plays a central role in controlling the objective yield of Br+/CH2Br+. For pulse B the ratio denominator (i.e., the CH2Br+ yield) can be greatly reduced by opening up the secondary dissociation channel

Our goal is to understand the distinctions in the control mechanisms from these two pulses that are capable of distinctively controlling the fragment ratio of Br+/CH2Br+ in the dissociative ionization of CH2BrI. Thus, we want to address why these two pulses with analogous pulse intensities are able to alter the ratio of Br+/CH2Br+ by more than a factor of 2. With this objective in mind, we will also demonstrate that CPS is a useful tool for gaining control mechanistic insights with arbitrarily shaped control pulses.

4. EXPERIMENTAL CPS MECHANISM ANALYSIS This section applies the CPS technique described in section 2 to pulses B and C obtained above. It is expected that distinct control mechanisms are involved in these two cases due to the different nature of these pulses, which can be revealed by monitoring and comparing the dynamical yield changes of the fragments with CPS scans. Figure 5 shows the dynamical evolution of the fragment yields for Br+ and CH2Br+ upon control pulse slicing at time τ operated on pulse B and pulse C, using the schematics of both CPS(+) and CPS(−) as described in Figure 2. The resulting yields for I+ and CH2I+ are also plotted, generated by the same pulses B and C, as additional information to compare with Br+ and CH2Br+. The temporal structures of pulse B and C are calculated from the spectral phases and amplitudes of the associated SLM masks, and the temporal amplitudes are shown as the background in Figure 5. In CPS(+) plots a and c, the slicing time at which fragment ions just about to appear is −600 fs for pulse B and −400 fs for pulse C. We denote this slicing time as τ0 with vertical dashed lines, before which, no fragment ions are observed with the head portion of the pulse. After τ0, the sliced pulse will include a main portion of the pulse with peak intensities above a threshold to induce ionization and fragmentation, and the ion yields start to rise as highlighted by the red dotted regions. With more late portions of the pulse added in, the yield of the fragment ions undergoes further changes as highlighted by the black dotted regions. Notice that, the red and black dotted boxes are for illustration purposes as there should be no clear demarcation between the two identified regions, in practice. As shown in Figure 5a, after τ0 at −600 fs, the yields of CH2Br+ and CH2I+ both increase with the main portion of the pulse followed by a decrease starting at τ ∼ 0 fs as the late portion of the pulse arrives. In contrast, the yields of Br+ and I+ both increase with the main portion of the pulse and continue to do so until the completion of the pulse. As highlighted by the black dotted box in Figure 5a, after the dissociative ionization is initiated, the yields of CH2Br+ (CH2I+) and Br+ (I+) are anticorrelated, indicating that the products CH2Br+ and CH2I+ initially created appear to dissociate with continued arrival of the remainder of the pulse, likely undergoing secondary dissociation into Br+ and I+, respectively. Thus, the increase of the Br+ or I+ yields is expected to at least be partially due to these processes. In contrast, the CPS(+) of pulse C in Figure 5c shows a completely different dynamical process. All the four fragments rise and then stay constant at their maximum yield with the incoming pulse scan beyond τ ≃ 500 fs. No decrease of the CH2Br+ and CH2I+ fragments is observed, indicating that the secondary dissociation channel, which is observed for pulse B, is not activated by pulse C. Pulse B contains much richer structure than pulse C at late times, which is responsible for the distinctly different behavior of the Br+/CH2Br+ ratio. In summary, the CPS(+) scan in Figure 5a with pulse B explains the capability of maximizing the objective ratio Br+/CH2Br+, G


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scans applied to pulses B and C indicates that, the secondary dissociation pathway of CH2Br+ on the ionic surface after initial ionization can be controlled to manipulate the yield of CH2Br+, and therefore the ratio of Br+/CH2Br+, by exploiting the special late-pulse structures in B, or the lack of them in C. This effect appears to dominate the control mechanisms for the desired control objective. In addition, the signatures in the CPS(−) signals also interestingly indicate the presence of neutral states arising from weak prepulses before ionization occurs, which appears to help enhance the yield of Br+ (and I+). The ancillary behavior of I+/CH2I+ is also interestingly revealed by CPS. In particular, although this is an example of breaking the weak/ strong bonds, it also exhibits a nontrivial contribution due to secondary fragmentation of CH2I+ to form I+ as evident in Figure 5a. This demonstration case study with CH2BrI utilized both CPS(+) and CPS(−) techniques generically shown in Figure 2, which provide complementary information regarding the control mechanisms. While the “bright” portion of the control pulses (effective after ionization) can be analyzed with CPS(+), in contrast, the “dark” portion of the pulse (before ionization occurs) may be analyzed with CPS(−). Furthermore, CPS is not only limited to these two types of scans. The same general procedures can be adapted (with suitably created step-like cutoff functions) to leave just the middle portion of the pulse or even multiple pieces of a pulse as desired to assess how different portions of a pulse interact to affect the product. The unique feature of CPS make it a special tool for postanalysis of AFC especially for complex pulses interacting with complex systems. CPS, as with any pulse probing techniques, is limited by the time slicing resolution, typically >50−100 fs (Δt in eq 2.4) with Ti:saphire laser systems in order to achieve a desired cut. It is also important to note that, the temporal changes of the observations induced by a time slicing scan is not equivalent to the instantaneous observation of that event as the system evolves after τ to the time of observation, which is effectively at infinite time in the present cases of time-of-flight mass spectral detection. However, one can envision other forms of probing/ detection that are performed at the sliced time when they are technologically feasible to perform. Nevertheless, even within a time-of-flight configuration we showed that CPS scans can reveal valuable information about the nature of various portions of the pulse upon examining the response of the ion signals. In general, the knowledge gained about the system response from CPS data may possibly be further used to guide or design new pulses with altered structures to achieve (avoid) special mechanistic features that would otherwise be inaccessible from traditional control experiments that only measure the final signal. We hope that the combined ease of performing CPS with the significant gain in mechanistic information it fosters will stimulate routine use of the tool.

utilizing the late pulse structure, while the weak prepulse can also enhance the objective ratio via neutral excitation, but only giving rise to mild enhancement of Br+ relative to CH2Br+. Therefore, we may also understand why the TL pulse, which is free of pre- and late-pulse features, gives a minimum value in the objective ratio (note the ratio shown in Figure 3a), while appropriate broadening the TL pulse, in either direction, can enhance the ratio due to the two mechanisms described above. The pre- and late- pulse features play distinct roles on the objective ratio, giving rise to the large difference in yield ratios reflected in pulse B and C. This distinction is further emphasized from the comparative behavior of the action of control pulses B and C with approximately the same intensities. Additional insights may be gained from further analysis of the CPS signals. Both CPS(+) scans show that, after a turn-on threshold that initiates dissociative ionization, nearly all the fragment species start to rise simultaneously, as shown in Figure 5a at ∼ −600 fs and Figure 5c at ∼ −400 fs, even thought the individual species appearance energies (AE) are nominally distinct. It is known that, CH2Br+ has the lowest AE, followed by CH2I+ and I+,while Br+ has the highest AE.30 Since the ionic dissociative states that lead to the lower AE species should be more easily accessed than the higher ones, we would expect the distribution of the fragmentation yields to follow the ordering of AE, which is the case for pulse B (i.e., [CH2Br+] > [CH2I+] > [I+] > [Br+]) during the initial rising edge of the window around −500 fs to −400 fs. At this initial stage, this ordering of the fragment yield agrees well with that of a TL pulse (not shown), for which, the ratio Br+/CH2Br+ is minimum. But, the complex structure of pulse B produces additional dynamics occurring on the ionic and neutral surfaces making significant changes to the relative yields of the species, as discussed earlier. However, for pulse C in Figure 5c, we observed [I+] > [CH2Br+] > [Br+] > [CH2I+] at this initial stage instead, with both Br+ and I+ being relatively enhanced when compared to the yield ordering with pulse B. This observation, combined with the results from CPS(−) scan of pulse C in Figure 5d, further supports that, the prepulses induce neutral excitations to facilitate access to higher ionic states and thereby enhance the yields of the nominally harder to ionize species: Br+ and I+. In summary, the implementation of CPS in this example shows the advantages of utilizing CPS(+) and CPS(−) observations along the full pulse evolution to gain mechanistic insights, especially when the control pulse has complex temporal structure.

5. CONCLUSION In this article, we introduce the general experimental CPS tool, which may be routinely employed in conjunction with AFC experiments to aid in gaining control mechanism insights. CPS may be just as well applied to any chosen pulse, whether optimal or deduced by other means, to gain insight into the associated mechanism. The CPS tool is not limited to control in any particular spectral regime or to the ratio of two recorded product signals. As an illustration of CPS, weprovide an experimental demonstration of its utility in revealing the mechanisms involved in controlling the fragment ratio of Br+/ CH2Br+ from the dissociative ionization of CH2BrI along with an examination of the accompanying related ions I+ and CH2I+. Two pulses, respectively B and C were, identified with closed loop and open loop procedures, respectively, where C was chosen to have the same intensity as B but with a distinctly lower objective fragment ratio of Br+/CH2Br+. The CPS(+)

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b08835. Details on the open-loop procedure for finding pulse C in Figure 4 of the main text as well as the control landscape for the fragmentation ratio of Br+/CH2Br+ in the polynomial phase space (PDF) H


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AUTHOR INFORMATION

Corresponding Author

*(H.R.) E-mail: [email protected]. ORCID

Herschel Rabitz: 0000-0002-4433-6142 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the support from (H.R.) the ARO (W911NF16-1-0014), (R.R.-d.-C.) the NSF (CHE-1464569), and (X.X.) the DOE (DE-FG02-02ER15344).

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Gaining Mechanistic Insight with Control Pulse Slicing: Application to

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