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Mapping Excited-State Dynamics by Coherent Control of a Dendrimer’s Photoemission Efficiency

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Science  09 Oct 2009:
Vol. 326, Issue 5950, pp. 263-267
DOI: 10.1126/science.1176524

Abstract

Adaptive laser pulse shaping has enabled impressive control over photophysical processes in complex molecules. However, the optimal pulse shape that emerges rarely offers straightforward insight into the excited-state properties being manipulated. We have shown that the emission quantum yield of a donor-acceptor macromolecule (a phenylene ethynylene dendrimer tethered to perylene) can be enhanced by 15% through iterative phase modulation of the excitation pulse. Furthermore, by analyzing the pulse optimization process and optimal pulse features, we successfully isolated the dominant elements underlying the control mechanism. We demonstrated that a step function in the spectral phase directs the postexcitation dynamics of the donor moiety, thus characterizing the coherent nature of the donor excited state. An accompanying pump-probe experiment implicates a 2+1 photon control pathway, in which the optimal pulse promotes a delayed excitation to a second excited state through favorable quantum interference.

Since ancient times, humans have been trying to control the transformation of matter. For more than a century, absorption of light has been used to initiate photochemical reactions. It is only in the past 20 years, however, that researchers have devised techniques to steer the ensuing dynamics through modulation of the optical excitation field. Such quantum, or coherent, control schemes (13) use laser-derived electric fields to direct the motion of wave packets along excited-state potential energy surfaces (46). In principle, the phases and amplitudes in the applied field necessary to achieve a given outcome can be obtained from the field’s coupling to the molecular Hamiltonian. In practice, rational design of the requisite pulse shapes remains an insurmountable problem for large molecules in condensed phase: The complete Hamiltonian is either unknown or too complex to be used in electric field calculations. Instead, researchers have relied on empirical methods whereby pulse shapes are determined through iterative optimization using the desired product (e.g., fluorescence quantum yield) as a feedback parameter (7). Thus, photoinduced processes can be actively manipulated without previous knowledge of the Hamiltonian and the light-matter couplings (811).

This closed-loop feedback technique has proven powerfully versatile. For example, modulation of isomerization yield in the natural photoreceptor bacteriorhodopsin (11), and control of quantum efficiency in both natural and artificial photosynthetic antennae by tuning spectral amplitude and phase in resonant linear excitation (9, 12), were shown. Nonetheless, very few closed-loop experiments have yielded optimal pulse shapes that can be directly explained in terms of known molecular properties of the system under investigation (9, 11, 1315). Major hindrances to attain such insight are the often intricate relationship between the variables to be optimized and the molecular response; the large number of parameters used for the generation of arbitrarily modulated pulses; and the often arbitrary, random pathways to optimization generated by the iteration algorithms. A major goal in the field is thus to develop a procedure for gleaning molecular insight from coherent control, especially in systems where the photophysical or photochemical pathways are presently unknown. For example, using optimal control, Branderhorst et al. (15) were able to identify wave packets with minimum position variance as candidates to minimize coupling to the bath and thus increase coherence robustness.

Our approach toward this end is to search for a confined set of parameters that directly govern the optimization. The idea is to express all the independent electric field parameters obtained from the collection of closed-loop optimization data as a combined set, filtering out those variables with redundant or negligible effects on the molecular response (1620). Ideally, it ought to be more straightforward to associate these fewer parameters with a physical property.

We apply this approach to coherent control studies of the emissive properties of the phenylene ethynylene dendrimer 2G2-m-Per (Fig. 1) (21), designed to mimic natural light harvesting systems (22). Phenylene ethynylene dendrimers are rigid macromolecules with a high quantum yield for energy transfer from donor to acceptor moieties (2224). They present a folded geometry with the dendritic branches packed in a bouquet-like spatial arrangement (23). The donor consists of two indistinguishable monodendrons attached to a central phenyl ring at meta positions, disrupting the π conjugation between the two branches. In each monodendron, phenylene ethynylene units are connected in ortho and para substitution, creating extended π conjugated systems with broad absorption bands (23). Upon ultraviolet-visible absorption, the excitation is delocalized within each monodendron, from where energy can migrate to an acceptor—in this case, a perylene moiety mutually meta to both donors on the central phenyl ring (23). To better characterize the excited state dynamics, we also probed the acceptorless system 2G2-m-OH and acceptor perylene separately.

Fig. 1

Chemical structures (top from left to right) of donor-acceptor (2G2-m-Per), acceptor (Per), and donor (2G2-m-OH) molecules. The energy-level diagram for 2G2-m-Per shows two energy transfer pathways. Solid lines correspond to the cascade pathway (τ1~500 fs, τ2~750 fs), the dashed line to a not yet fully understood direct pathway (τ3 ~ 400 fs) investigated in single-photon excitation experiments (23). Initial excitation energy is 3.14 eV (dendritic backbone), and detection is in the 2.6- to 2.1-eV range (perylene or backbone emission).

Previous time-resolved spectroscopy showed that upon single-photon absorption, energy migrates toward the acceptor through two different pathways (23). One pathway (contributing to ~60% of the energy transfer yield) involves multistep exciton migration within the dendrimer backbone followed by transfer to the acceptor. This is an incoherent mechanism driven by an energy gradient. A parallel path (~40% contribution) appears to involve direct exciton migration from donor to acceptor (Fig. 1) (23). The possibility of coherence preservation in this latter process makes these macromolecules a compelling target for quantum control schemes.

Our experimental setup (fig. S1) comprises a femtosecond laser source, a pulse shaper to produce arbitrary phase and/or amplitude modulation, and a detection system to reveal the molecular response to excitation with tailored pulses (25). These molecules absorb linearly in the blue visible region only, lacking any one-photon absorption at λ > 495 nm. In the presence of an ~800-nm pulse, they are excited through two-photon absorption under the weak field limit (25). The samples consisted of dilute solutions of 2G2-m-Per (donor-acceptor) and 2G2-m-OH (donor) and perylene (acceptor) dissolved in dichloromethane (26).

We began with a closed-loop optimization run directed toward maximizing two-photon absorption (TPA) by the 2G2-m-Per dendrimers. Specifically, we iteratively applied a set of phase-modulated pulses to the sample and then fed the results (in this case, overall emission intensity) into a customized genetic algorithm that in turn produced a new generation of pulses for further testing (25). We simultaneously measured two-photon induced current (TPIC) when the tailored pulses were focused onto a GaAsP photodiode. For a two-photon excitation process, the number of excited molecules should scale linearly with the TPIC. Thus, a relative quantum yield can be obtained by measuring or evaluating the ratio of fluorescence intensity to TPIC signal. When the objective was to increase emission intensity, this ratio reached its maximum value early on (less than ~20 generations) and then remained unchanged. Analysis of the optimization revealed that overall emission increased in parallel with TPIC [constant quantum yield (QY), Fig. 2A, green line] as pulse duration decreased. Hence, there was no coherent control over QY; shortening the pulses simply raised the two-photon absorption probability (27, 28). The optimal pulse shape was the trivial transform limited (TL) case with full width at half maximum of 45 fs.

Fig. 2

Closed-loop experiments. (A) Green and red traces show optimization with the objective of maximizing overall emission or relative emission QY, respectively, in photoexcited 2G2-m-Per. The best individuals for each generation are plotted against a two-photon induced diode response (TPIC). Relative to a TPIC value of 1 for the optimal pulse, the first optimization yields a QY of 0.95, the second a QY of 1.13 for the same absorptivity (dashed line). (B) FROG image for a transform limited pulse (top) and the optimal pulse (bottom). Note the different time scales for the two pulses. (C) Second-order spectra (left) and the corresponding autocorrelations (right) of excitation pulses measured at different stages of the QY optimization procedure. From top to bottom: TL, generation 1 (random phase), 10, 20, 50, 100, and 200. The autocorrelations are plotted on a logarithmic scale to highlight the transformation of the long initial randomly phased pulse into the optimal pulse shape: a short spike with longer (1.5 ps) wings.

In contrast, when the QY was directly used as the feedback functional, the control process moved beyond modulation of the TPA (Fig. 2A, red line). Brixner et al. showed a similar response for the two-photon excitation of [Ru(dpb)3]2+ (29). For 2G2-m-Per, in the early generations the optimization pathway largely resembled that of the TPA-maximization experiment. The QY rose dramatically from a relative value of 0.6 (for the starting set of pulses with random phase) to a value of ~0.95 with a concomitant rise in the TPIC (indicative of increased absorption). Beyond that point, the results of each experiment differ, driven by distinct phase parametrizations leading to distinct optimal outcomes. In the QY-optimization case (Fig. 2A, red line), QY continued to grow with essentially no further accompanying increase in TPIC. Thus, the optimally shaped pulse raised the number of photons emitted without significantly changing the number of molecules excited. Specifically, the pulse induced 25% of the absorption observed with a TL pulse while improving the QY by 15% (reaching a maximum value of 1.13; dashed vertical line in Fig. 2A). The QY optimization yields an excitation pulse quite different from the TL pulse, as the optimal pulse includes information regarding the excited state and its dynamics after excitation (Fig. 2B).

To understand the changes occurring during the optimization process, we measured the second harmonic spectra and autocorrelations of the best excitation pulses in each generation of the closed-loop experiment (Fig. 2C). The greatest changes occur during the first 20 generations, ultimately yielding a second-order spectrum resembling that of the TL pulse. In later generations, the spectrum remains centered at ~403 nm (indicating the absence of spectral selectivity during optimization) and shows only a slight flattening of its profile. Interestingly, this spectral broadening does not correlate with a decrease in pulse duration. Instead, the autocorrelation traces for the corresponding pulses show a narrow central peak with additional structure on its wings. These changes are consistent with the QY/TPIC correlation observed in Fig. 2A, where optimization of quantum yield proceeded first by uncovering the phase distribution necessary to maximize excitation and then subsequently by tuning the excited-state dynamics independent of the absorption probability.

As is often the case in closed-loop coherent control studies, the optimal pulse that emerged from our genetic algorithm exhibited a rather complex electric field (Fig. 2B, bottom panel) that offered limited direct insight into straightforward molecular properties. Our goal is to go beyond the optimization process and learn specific information about the molecular properties (18). We therefore sought to extract the essential parameters of the optimal pulse in the hope of attaining a simplified picture of the control process.

We applied partial least squares regression methods (25) to correlate spectral phase features with the improvement in quantum yield at each stage of the optimization. This statistical analysis uncovered two components crucial for reaching the final objective. One component accounts for the changes on pulse shape (G1 to G20 in Fig. 2C) improving two-photon absorption. It morphs the initial random phases into a flat spectral phase to create a short excitation pulse. The other component involves spectral steps; it has a significant contribution in explaining fitness evolution and accounts for the improvement on QY (25). Additionally, using the SHG-FROG (second-harmonic generation frequency resolved optical gating) technique, we retrieved the electric field for the experimental optimal pulse. It presents an asymmetric temporal profile with two distinguishable features: a ~50-fs spike followed by a ~1-ps-long tail (fig. S4B). The retrieved spectral phase function presents steps (fig. S4A) comparable to those associated with the second component identified in the statistical analysis (fig. S3).

Based on the foregoing analysis, we reduced the excitation pulse shape to its two most significant features: a short time component and a spectral phase with a steplike signature. Because we essentially understood the role of the short pulse component in optimizing excitation, we focused our attention on the meaning of the steplike signature observed in the spectral phase. We aimed to demonstrate that information extracted from the closed-loop experiment could be harnessed to control the excited-state dynamics without a priori knowledge of the molecular Hamiltonian, thereby offering insight into the control mechanism. To this end, we modulated the excitation pulses with a steplike phase function varied in sizes between 0 and 2π in steps of 0.1π. These (open-loop) experiments were performed without a feedback signal for optimization.

The two-photon induced absorption signal measured with the GaAsP photodiode (Fig. 3A, top panel) yielded a symmetric well and was modeled (solid line) considering two-photon absorption with phase-modulated pulses, assuming a step phase function and a small residual cubic phase (30). The measured QY from a solution containing only the acceptor molecule (perylene) showed a similarly symmetric phase dependence and did not improve relative to the response induced by a TL pulse (25). The response observed for the 2G2-m-OH (donor) and 2G2-m-Per (donor-acceptor) samples (Fig. 3A, middle panel) was strikingly different. Excitation with pulses modulated by a spectral phase step function with step sizes between 1.2π and 1.8π enhanced emission QY relative to the TL pulse (phase of 0 or 2π) response. The maximum ratio, at 1.4π for both samples, represents a 10% and 5% increase for 2G2-m-Per and 2G2-m-OH, respectively. The spectral step function recovers more than half of the QY improvement induced by the optimal pulse (QY for optimal pulse is 1.13 and for the 1.4π pulse is 1.09). The response from these macromolecules does not follow the model of two-photon absorption with phase-modulated pulses, implicating a mechanism in which the excited-state dynamics (as distinct from the excitation process) are purely controlled by phase.

Fig. 3

Single-parameter experiments. Effect of varying the spectral phase step size applied to the excitation pulse (centered at ~800 nm) on [(A) top panel] two-photon induced diode response and [(A), middle panel] emission QY measured for solutions of donor 2G2-m-OH (blue) and donor-acceptor 2G2-m-Per (red). The QY values show a maximum at 1.4π. [(A), bottom panel] Ratio of red to blue curves. (B) QY of 2G2-m-Per after two-photon excitation with a pair of pulses (~800 nm). Each pair is modulated with 0 (green) and π (magenta) relative phase. The 70-fs delay (green curve maximum) corresponds well to the double-pulse separation in pulses shaped by a spectral phase step of 1.4π radians. (C) Transient absorption experiment performed on 2G2-m-OH (blue) and 2G2-m-Per (red) with 400-nm pump and 800-nm probe pulses. Photoinduced absorption in both molecules reveals a second excited state accessible by 800-nm absorption, confirming the possibility of a 2+1 mechanism for the coherent control.

We can further analyze the impact of the steplike spectral phase on energy transfer by comparing the results with the pure donor (2G2-m-OH) to those with the donor-acceptor molecule (2G2-m-Per). In 2G2-m-OH, the dendritic backbone acts as both absorber and emitter, whereas in 2G2-m-Per, the perylene trap emits after the energy transfer process (under steady-state conditions, less than 1% of the fluorescence arises from the donor when the perylene is present) (23). Variation of the 2G2-m-Per/2G2-m-OH QY ratio with spectral phase step size shows that the energy transfer process itself is phase sensitive (Fig. 3A, bottom panel). For steps with phases between 0 and ~π/2, the relative QY remains unchanged, which implies that only the donor excited state is being controlled. For larger steps, the QY ratio becomes phase sensitive, peaking at a step size of π. At that point (π spectral phase step), the QY of 2G2-m-Per is 8% larger than 2G2-m-OH; hence, the energy transfer yield was increased.

In the time domain, the impact of applying a step in the spectral phase function is to create a double pulse (fig. S6) with the relative timing and intensity of the subpulses dependent on the step size (25). Modulation with a 0.6π step pushes most of the intensity into the late component, whereas a 1.4π step creates the mirror image in time, with most of the intensity in the early component. The second-order spectra for both excitation pulses are identical (fig S6, second and third rows), but their induced emission quantum yields change from 0.73 to 1.09 (Fig. 3A at π ± 0.4π), a 35% difference. This observation rules out a substantial role of phase modulation in shifting the second-order spectrum to match the two-photon absorption and drive the QY enhancement (25).

It is important to emphasize that the results do not depend solely on the time delay between the excitation double pulses or on their relative intensities. Figure 3B shows the effect of varying the time delay between two equally intense pulses that have distinct relative phases. For the double pulses with zero relative spectral phase (green curve), the 2G2-m-Per QY increases above the value observed for a TL pulse, yielding the greatest enhancement for a delay of ~70 fs. This delay coincides with the delay calculated from the phase-stepped pulse that maximized QY (1.4π) (fig. S6). Experiments with 2G2-m-OH yielded a similar response. In contrast, when the relative phase of the subpulses was shifted to π (magenta), no enhancement relative to a TL pulse was observed, regardless of delay time. As expected for two-photon excitation, the QY signals decreased as the pair of pulses arrived at the sample with delays larger than their pulse width.

The sensitivity of emission yield to the relative phase between the two temporal components of the excitation pulse is a clear consequence of the quantum nature of the excited state formed. The optimum spectral phase evidently facilitates interference processes to modify the excited-state dynamics, which suppresses the coupling to undesired internal conversion pathways (31). One possible physical mechanism is that at ~70 fs, a new light-matter interaction occurs, moving the excited-state wave packet away from regions on the excited potential surface prone to nonradiative relaxation pathways. To explore this hypothesis, we performed a pump-probe experiment in which the sample was resonantly excited at ~400 nm (equivalent in frequency to the two-photon excitation at 800 nm) and probed at 800 nm. We sought with this experiment to uncover a second excited state that might further interact with the laser field after the initial excitation event. Indeed, Fig. 3C indicates that both the pure donor and donor-acceptor molecules have a strong photoinduced absorption around 800 nm, which grows within the instrument response time. A small decay was observed in 2G2-m-Per because of energy transfer to the acceptor.

Hence, there is an auxiliary excited state in the donor moiety that can be resonantly accessed by a briefly delayed 800-nm pulse in the quantum control experiment. For the right phase and temporal tuning, this process is enhanced, diminishing nonradiative decay and thus increasing overall QY. In the energy transfer process (23), only the direct pathway would be controllable by phase-modulated pulses; thus, the fraction of excited molecules that can undergo this 2+1 mechanism is limited and cannot be measured by a power dependence study.

This mechanism is bolstered by closed-loop experiments directed toward minimizing the emission quantum yield. The iteration cycle yielded only a smooth, long pulse, implying that absorption efficiency was reduced and thus that the excited state dynamics could not be actively manipulated (25).

Since the initial experiments on coherent control of light-matter interactions, several phase/amplitude sensitive mechanisms have been found to influence photoinduced processes (3234). Here, we affirm that the control is exerted on the dynamics of the excited state. We therefore need to assess the possibility of contributions from intensity dependence of the two-photon absorption (Fig. 2) (19, 35, 36); spectral control; uniqueness of the phase function; direct excitation of the acceptor; and a mechanism of optimally “dumping” from the excited state, to the overall optimization. Evaluation of all these mechanisms are detailed in (25).

Through a succession of closed and open-loop optimization studies, we have discovered that a simple step function applied to the spectral phase of a photoexcitation pulse can enhance the emission quantum yield of a complex donor-acceptor molecule.

Closed-loop experiments taught us about an optimization based on different components: population transfer and excited-state dynamics control. We identified and manipulated previously unappreciated coherences in the donor-localized excited state of the molecule. Interferences on the excited state of the donor activate a delayed excitation, changing the overall coupling into nonradiative pathways. This mechanism affords a methodology to explore dynamical processes.

Supporting Online Material

www.sciencemag.org/cgi/content/full/326/5950/263/DC1

Materials and Methods

SOM Text

Figs. S1 to S11

References

  • * Present address: Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104–6323, USA.

  • On leave from Raja Ramanna. Centre for Advanced Technology, Indore, India.

References and Notes

  1. 2G2-m-Per is a second-generation dendrimer with two monodendrons on meta positions and an ethynylene perylene trap.
  2. Materials and methods are available as supporting material on Science Online.
  3. This work was supported by the NSF, CHE-0239120.

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