Letter pubs.acs.org/JPCL
Two-Color Nonlinear Spectroscopy for the Rapid Acquisition of Coherent Dynamics S. Seckin Senlik,† Veronica R. Policht,‡ and Jennifer P. Ogilvie*,† †
Department of Physics, University of Michigan, Ann Arbor, 48109, United States Applied Physics Program, University of Michigan, Ann Arbor, 48109, United States
‡
S Supporting Information *
ABSTRACT: There has been considerable recent interest in the observation of coherent dynamics in photosynthetic systems by 2D electronic spectroscopy (2DES). In particular, coherences that persist during the “waiting time” in a 2DES experiment have been attributed to electronic, vibrational, and vibronic origins in various systems. The typical method for characterizing these coherent dynamics requires the acquisition of 2DES spectra as a function of waiting time, essentially a 3DES measurement. Such experiments require lengthy data acquisition times that degrade the signal-to-noise of the recorded coherent dynamics. We present a rapid and high signal-to-noise pulse-shaping-based approach for the characterization of coherent dynamics. Using chlorophyll a, we demonstrate that this method retains much of the information content of a 3DES measurement and provides insight into the physical origin of the coherent dynamics, distinguishing between ground and excited state coherences. It also enables high resolution determination of ground and excited state frequencies.
C
ization. Several modified versions of 2D experiments have been proposed, which effectively increase (S/N) by either reducing the data acquisition time or by selective excitation of coherence pathways with suppression of extraneous signals. Osborne et al. have developed a modified 2D infrared experiment where they select a particular interpump pulse delay t1, reducing the dimensionality of the experiment to enable rapid and high S/N measurements of the frequency−frequency correlation function.25 Two-color excitation has been used extensively to excite specific Raman coherences in coherent anti-Stokes Raman scattering (CARS) experiments, typically using off-resonant excitation.26,27 The Wright group has developed a frequencydomain approach of tuning excitation wavelengths to excite specific coherence pathways.28 Lee et al. have performed a twocolor photon echo experiment in which they excited a specific coherence and observed the dependence of the integrated echo signal on the two interpulse time delays.13,17 Womick et al. developed a two-color four-wave mixing experiment to excite electronic and nuclear coherences while suppressing population pathways.29 The Davis group has used a similar approach30−32 and has more recently used pulse-shaped excitation33 to excite specific coherence pathways in multidimensional experiments. Wen et al. have also recently used pulse-shaping to enhance exciton and biexciton coherences.34 Here, we present two-color rapid acquisition coherence spectroscopy (T-RACS), which utilizes an ultrafast pulseshaper to shape the pump pulses’ spectra to selectively excite
oherent vibrational dynamics in biological samples on picosecond time scales were first reported in pump− probe spectroscopy studies of the photosynthetic bacterial reaction center by Vos et al.1,2 Over a decade later, twodimensional electronic spectroscopy (2DES) studies performed on the Fenna Matthews Olson (FMO) complex reported coherent dynamics interpreted as electronic in nature,3 stimulating intense interest from both the theoretical and experimental spectroscopy communities. Observations of coherent dynamics by 2DES have now been reported in a wide range of systems, from dye molecules4−6 and aggregates7,8 to photosynthetic antennae9−12 and reaction centers,13−17 quantum dots and organic photovoltaic materials.18,19 In many of these systems, the physical origin and the possible functional role of these coherent dynamics in processes such as energy transfer and charge separation is still being debated.14,15,19−24 A better characterization of these coherences could enrich our understanding of inter- and intramolecular coupling and energy transport and reveal in greater detail the relationship between structure and function in these systems. Recording coherent dynamics with a high signal-to-noise ratio (S/N) is particularly challenging in photosynthetic samples; sample fragility and the risk of exciton−exciton annihilation at high laser fluences limits the S/N and ultimately necessitates extended data acquisition times. These extended data acquisition times degrade the overall S/N due to slow fluctuations of laser amplitude and frequency content that can mask weak coherence signals and introduce errors in fitting the background population kinetics. The desire to obtain rapid, high S/N characterization of coherent dynamics motivates the development of alternative methods to full 2DES character© 2015 American Chemical Society
Received: April 25, 2015 Accepted: June 5, 2015 Published: June 5, 2015 2413
DOI: 10.1021/acs.jpclett.5b00861 J. Phys. Chem. Lett. 2015, 6, 2413−2420
Letter
The Journal of Physical Chemistry Letters specific coherence pathways while simultaneously imposing a fixed interpump pulse time delay, t1. Fixing t1 reduces the dimensionality of the experiment, drastically shortening the time required to record coherent dynamics of interest. To demonstrate T-RACS’s ability to tease out coherent dynamics, we present data acquired via T-RACS alongside broadband and two-color 2DES data from chlorophyll a (Chl a). Chl a is the most abundant chromophore in plant photosynthetic complexes and serves as a good test system for studying and understanding the coherences observed in larger photosynthetic antennae and reaction centers. Probing Coherence with Nonlinear Spectroscopy. Coherences are generated when a light−matter interaction creates a coherent superposition of two states; the system evolves in this coherent state, oscillating at the difference in frequency between the two superposition states. In nonlinear spectroscopies, such coherences are generated and probed by sequences of laser pulses, and the response of the system to these sequences is typically understood using perturbation theory.26 In this perturbative approach, any given nonlinear spectroscopy is analyzed in terms of the possible interactions between the system and the dipole operator, taking into consideration the energy level structure of the system and the details of the spectroscopic measurement. In pump−probe spectroscopy, a pump pulse interacts with the system twice to create populations and coherences that evolve until a third light−matter interaction with the probe pulse some waiting time later. 2DES uses a series of three light pulses: two pump pulses separated by variable time delay, t1, followed by a probe some waiting time, t2, later (Figure 1a). In 2DES each pump pulse contributes a single interaction to create populations and coherences that evolve during t2. 2DES signal is typically recorded as a function of the delays t1 and t2, whereas the t3 dependence is often detected directly in the frequency domain to yield ω3. Fourier transforming the 2DES data with respect to t1 produces a twodimensional (ω1, ω3) spectrum for a given t2. Information about how individual transitions behave is mapped along the diagonal (ω1 = ω3), whereas off-diagonal cross peaks describe couplings and coherences in the system.3,10,35,36 By looking at the two-dimensional (ω1, ω3) distribution of the coherence amplitude we can gain considerable insight into the physical origin and dynamics of the system. This can be achieved by Fourier-transforming with respect to t2 (essentially performing 3DES) to create a 3D frequency solid that can be “sliced” to observe the 2D distribution of particular ω2 modes of interest in what are called coherence or Fourier maps (Figure 2b).8,14,37 These Fourier maps have been presented as metrics for determining the physical origin of coherences in 3DES signals in a large body of theoretical work; there are several simplified model systems proposed to assign electronic, vibrational, and vibronic coherence origin.22,37−43 Here, we focus on the displaced oscillator model39,42 for vibrational coherences to explain observed coherent dynamics in Chl a. Comparing the Fourier maps for the displaced oscillator with experimental data enables the assignment of vibrational origin and distinction between ground and excited state vibrational coherence. This distinction has been achieved previously in pump−probe spectroscopy using phase arguments,1,2 whereas in 2DES comparisons of rephasing and nonrephasing amplitudes and phases, as well as Fourier map distributions, have been used.39,40,42,44−47 Two-Color Rapid Acquisition Coherence Spectroscopy (T-RACS). We seek a method that selectively excites particular coherence
Figure 1. Pulse-ordering diagrams for two-dimensional electronic spectroscopy (2DES) and two-color rapid acquisition coherence spectroscopy (T-RACS). (a) Broadband 2DES pulse sequence uses two identical broadband pump pulses (black) followed by a third broadband probe pulse (blue, dot-dash). (b) Absorption spectrum of chlorophyll a in an isopropanol/glycerol mixture at 77 K (brown, short-dash); peak absorption of the Qy band is at 14 925 cm−1 (670 nm). Laser spectra used in broadband 2DES experiments: pump (black, solid) and probe (blue, dot-dashed) spectra; for T-RACS experiments different pairs of the three Gaussian spectra were used as pumps (orange, dash; red, long dash; green, dotted), followed by a broadband probe (blue, dot-dashed). (c)−(e) T-RACS pulse sequences employing the respective pump spectra shown in panel b. T-RACS sequence in panel c selectively probes excited-state vibrational coherences, whereas panel d selectively probes groundstate vibrational coherences and panel e probes a mixture of ground and excited state coherence pathways.
pathways and enables rapid characterization of the coherences with a high S/N while retaining much of the information content of a full 3DES measurement. To achieve this goal, we adopt a two-color excitation scheme where the two pump pulses have no spectral overlap and possess the appropriate frequency difference to excite the coherence of interest. The probe pulse remains unshaped and broadband. We fix the t1 delay to ensure the desired pulse-ordering (avoiding substantial pulse overlap), and we record the coherence signal as a function of t2 and ω3. The pulse sequences for different T-RACS experiments are shown in Figure 1c−e. We note that our approach is similar to that of Womick et al., who performed two-color four-wave mixing experiments with a fixed t1 = 0.29 Here, we separate the rephasing and nonrephasing signals and use different color orders to selectively excite particular coherences and probe their physical and ground/excited state origin. To understand how T-RACS excites and records coherent dynamics and to compare the information it provides with what is obtained by 3DES, we consider a displaced oscillator system 2414
DOI: 10.1021/acs.jpclett.5b00861 J. Phys. Chem. Lett. 2015, 6, 2413−2420
Letter
The Journal of Physical Chemistry Letters
Figure 2. (a) Displaced oscillator model featuring electronic transition energy E and vibrational level transition frequency Ω. (b) Cartoon rephasing Fourier map for the displaced oscillator model at ω2 = Ω, displaying the characteristic “chair” pattern of the displaced oscillator model. The corresponding Feynman diagrams are detailed in the Supporting Information. Of particular interest are signals located at the blue triangle and orange star that correspond to excited and ground state vibrational coherences, respectively. All other signatures correspond to a mixture of ground and excited electronic state pathways. (c)−(e) Cartoon rephasing Fourier maps for the respective two-color pulse sequences shown in Figure 1c−e. Each two-color experiment selects a subset of the coherent signals detected in the rephasing Fourier map from a broadband 3DES experiment (shown in panel b). Signals in panel c are exclusively excited-state vibrational coherences, whereas panel d selectively probes ground-state vibrational coherences and panel e probes a mixture of excited and ground state contributions as discussed in Supporting Information Figure S1.
with a single vibrational level of frequency Ω on the ground and excited electronic states separated by energy E (Figure 2a). Turner et al. have detailed the double-sided Feynman diagrams that illustrate how intraband coherence on the ground or excited electronic state of the displaced oscillator can be generated by a 2DES rephasing pulse sequence.42 Within the displaced oscillator model, the rephasing Fourier map has a characteristic “chair” shape,39 and excited and ground state coherences can be clearly separated as shown in Figure 2b with a triangle and star, respectively. T-RACS experiments can be designed to excite a subset of the “chair” signals of the displaced oscillator system. As long as the bandwidth of the individual pump pulses is less than Ω, the choice of pump pulse spectra and their relative ordering determine which set of coherence pathways will be excited. Figure 2c−e shows the subset of specific coherence pathways for a displaced oscillator that are excited by different rephasing T-RACS experiments (respective pulse-sequences shown in Figure 1c−e). The corresponding double-sided Feynman diagrams are detailed in the Supporting Information, along with the nonrephasing signals. For a given T-RACS pulse sequence, the first pump pulse creates a coherence between ground and excited states that must oscillate at a frequency contained within its bandwidth (neglecting coherence transfer events). Thus, the bandwidth of the first pulse effectively windows the coherence signals along the ω1 axis. The bandwidth and central frequency of the second pump pulse determines which intraband coherences will be excited and evolve at ω2. Because T-RACS resolves ω3, and rephasing and nonrephasing signals can be readily separated, T-
RACS can readily resolve the different coherent signals present in a 3DES-derived Fourier map as depicted in Figure 2c−e. Thus, it can be used to assign the physical origin of the observed coherence. In the case of vibrational coherence, it also enables identification of ground and excited state contributions and their respective frequencies. Observations of Coherence in Chl a by 3DES and T-RACS. To demonstrate the ability to selectively excite and study particular coherences with T-RACS, we perform studies of Chl a in isopropanol/glycerol solution. These studies also enable a comparison of the relative speed, information content, and signal-to-noise ratio (S/N) of the 3DES and T-RACS methods. The pulse spectra for both the 3DES and T-RACS experiments are shown in Figure 1b. The pump-pulse spectra for the TRACS experiments have been chosen to selectively excite coherence at ω2 ≅ 740 cm−1 to match a vibrational mode reported in resonance Raman,48−51 fluorescence line-narrowing49 and pump−probe52 experiments and also observed in our recent study of the photosystem II reaction center.14 The t2-dependent signals for broadband 3DES and T-RACS (for pulse sequence in Figure 1e) are shown in Figure 3a and c, respectively, for t1 = 0 fs. The rephasing (red, solid) and nonrephasing (blue, dashed) 3DES signal (Figure 3a) are dominated by population dynamics that must be fit and subtracted out in order to analyze the overlaid coherent oscillations that appear as a weakly periodic amplitude modulation. The Frobenius spectrum (taken by summing the square of the signal amplitude over dimensions ω1 and ω3 and then taking the square root) of the rephasing signal from the 2415
DOI: 10.1021/acs.jpclett.5b00861 J. Phys. Chem. Lett. 2015, 6, 2413−2420
Letter
The Journal of Physical Chemistry Letters
increase of S/N of the T-RACS method over 3DES can be attributed to the substantial reduction in data acquisition time that reduces laser power and spectral fluctuations. As expected the two-color excitation of T-RACS imparts spectral selectivity compared to the broadband 2DES technique. This is demonstrated by the ratio of the selected coherence to the next largest peak amplitude in the Frobenius spectrum (Figure 3d). The amplitude of the 742 cm−1 (738 cm−1) peak in the rephasing (nonrephasing) signal is 21 (23) times larger than the next largest peak in the T-RACS experiments, whereas the same ratio for the largest peak within 640 ≤ ω2 ≤ 840 cm−1 in the rephasing (nonrephasing) broadband 2DES technique is only 3 (2.5). We note that in the present example the ∼740 cm−1 coherence is relatively isolated from other modes; the case of selectively exciting one out of several coherences within a few tens of wavenumbers of one another has not been tested here. Information Content of T-RACS. To investigate the ability of the T-RACS method to selectively excite specific coherences and to discern their physical origin, we present Chl a data from broadband 3DES, spectrally shaped two-color 3DES, and TRACS measurements in Figure 4. Figure 4a shows the Fourier map for ω2 = 747 cm−1 derived from the rephasing broadband 3DES data. This Fourier map displays the characteristic chair pattern expected for a displaced oscillator. In Figure 4c−e, we show Fourier maps and T-RACS data for the corresponding pulse sequences shown in Figure 1c−e. The Fourier maps require scanning t1 (as in standard 2DES and 3DES measurements), whereas the T-RACS data was recorded for set t1 = 60 fs. The Fourier maps resemble the expected maps for a displaced oscillator shown in Figure 2c−e, demonstrating that the use of two-color excitation and color order selects the expected subset of the coherence signals produced by broadband excitation. Fourier maps derived from broadband 3DES data reveal the overall distribution of coherence amplitude as a function of (ω1, ω3), which is particularly useful for initial coherence studies in systems where little is known about the physical origin of the coherences or the frequencies to be expected. In contrast, Fourier maps generated from the pulse-shaped two-color 3DES feature a subset of the signals within the broadband 3DES Fourier map, where the spectral amplitude of the first pump pulse essentially applies a filter to the ω1 axis of the broadband 3DES Fourier map. The frequency of the second pulse and the choice of phase-matching (rephasing or nonrephasing) selects the subset of coherence signals to be resolved along ω3. Although T-RACS does not resolve the ω1 axis, it is clear from Figure 4c−e that the T-RACS data contains similar information to the Fourier maps recorded with the pulseshaped two-color pump spectra. By resolving the ω3 axis, the TRACS data shows the same distinct signals separated by Ω; there is little additional information to be gained by resolving ω1 when relatively narrowband two-color excitation is used. The reduced acquisition time and higher S/N compared to 3DES make T-RACS an attractive alternative that retains the information content that can be used to assign the physical origin of the coherence (for example, ground or excited state vibrational coherence). Chlorophyll a has been well studied by resonance Raman,48,49 fluorescence line narrowing (FLN),49,51,50 holeburning,57 and pump−probe52 spectroscopies. Although here we have focused on the ∼740 cm−1 mode to demonstrate the T-RACS approach, we have observed other modes as well and
Figure 3. Waiting time, t2, traces for the real part of rephasing (red) and nonrephasing (blue, dashed) signals and their corresponding Frobenius spectra for the broadband 3DES (a,b) and a T-RACS (c,d) experiment, which used the pulse sequence in Figure 1e. All the waiting time traces are taken with t1 = 0 fs to highlight the increased contrast of the oscillations when population kinetics are suppressed by using two-color excitation.
broadband 2DES experiment (Figure 3b) features many coherences. Several of these (ω2 = 265, 348, and 747 cm−1) are prominent above the noise floor. In contrast to the broadband 3DES experiment, the T-RACS trace in Figure 3c is dominated by a single frequency oscillation with no obvious exponential dependence, indicating that the two-color pump pulse sequence selects the desired coherence and suppresses contributions from population pathways. The Frobenius spectrum in Figure 3d features one large amplitude peak near ω2 = 742 cm−1; all the other modes present in the broadband 3DES case have been effectively suppressed. Here, we show the rephasing and nonrephasing signals for t1 = 0 fs in order to highlight the population dynamics during t2 present in the 3DES data. T-RACS experiments with t1 > 0 have lower S/ N as shown in Supporting Information Figure S2 but have welldefined pulse-ordering when t1 is greater than the pump pulse duration, enabling cleaner separation of coherent pathways. Speed, Signal-to-Noise Ratio, and Selectivity. The coherences extracted from the broadband 3DES experiments shown in Figure 3b required 110 min of data acquisition time. In contrast, the T-RACS experiments, scanned over the same number of t2 points with the same averaging required only 7 min, more than 15 times shorter. We note that the use of a pulse-shaper, which enables data acquisition in the rotatingframe,53,54 significantly reduces the number of t1 points required to resolve the ω1 frequency axis. Without this sampling reduction, 2DES experiments that do not acquire data in the rotating frame typically record several hundred t1 points.55,56 In this case T-RACS offers approximately 2 orders of magnitude faster acquisition of coherent dynamics than 3DES. We also note that the rapid acquisition enabled by TRACS makes scanning longer t2 delays straightforward should increased spectral resolution of the coherence frequency be desired. The rephasing (nonrephasing) Frobenius spectrum (Figure 3d) of the T-RACS experiment boasts a S/N that is 32 (29) times higher than that acquired by 3DES (Figure 3b). The 2416
DOI: 10.1021/acs.jpclett.5b00861 J. Phys. Chem. Lett. 2015, 6, 2413−2420
Letter
The Journal of Physical Chemistry Letters
Figure 4. (a) Rephasing Fourier map for ω2 = 747 cm−1, derived from the broadband 3DES data, showing the characteristic chair pattern for a displaced oscillator. (b) Expected signals contributing to the rephasing Fourier map within the displaced oscillator model. Of particular interest are the excited state (blue triangle) and ground state (orange star) coherence signals. Corresponding double-sided Feynman diagrams are given in the Supporting Information (Figure S1). (c)−(e) Rephasing Fourier maps from two-color 3DES and corresponding T-RACS signals for the respective pulse sequences shown in Figure 1c−e. Dotted lines indicate ω1,ω3 = (E − ℏΩ)/ℏ and (E + ℏΩ)/ℏ, solid lines indicate ω1,ω3 = E/ℏ; in ω3, these lines indicate the position of the blue triangle and orange star that (within the displaced oscillator model) correspond to excited state and ground state coherence, respectively. The coherence frequency (ω2) for two-color 3DES (T-RACS) for pulse-sequences in (c)−(e) were determined to be (c) 736 cm−1 (740 cm−1), (d) 748 cm−1 (746 cm−1), (e) 742 cm−1 (742 cm−1). Contours are plotted in increments of 10% (a) and 5% for (c)−(e), starting from 4% of the maximum intensity.
Figure 5. (a) T-RACS rephasing signal at t1 = 60 fs, ω3 = 15673 cm−1 for the excited state pulse sequence of Figure 1c. (b) T-RACS rephasing signal at t1 = 60 fs, ω3 = 14285 cm−1 for the ground state pulse sequence of Figure 1d. (c) Rephasing Frobenius spectra of the excited state (red solid) and ground state (blue dashed) T-RACS data.
3DES) exhibit signal at both the “triangle” and the “star” position, indicating excited and ground state contributions in agreement with Du et al.52 The same conclusion can be drawn
will discuss their physical origin in a subsequent publication. The rephasing Fourier maps for the ∼740 cm−1 mode (shown in Figure 4a,c,d as derived from broadband and two-color 2417
DOI: 10.1021/acs.jpclett.5b00861 J. Phys. Chem. Lett. 2015, 6, 2413−2420
Letter
The Journal of Physical Chemistry Letters
range. In systems where coherent dynamics have not previously been studied, a combination of 3DES and T-RACS may be most effective. Broadband 3DES serves well to survey the Frobenius spectrum of all coherent modes, whereas T-RACS could be used to perform rapid, higher S/N studies of selected coherent dynamics of interest. We have used both 2DES and TRACS to demonstrate that Chl a exhibits clear coherent dynamics. Using T-RACS we have studied the ∼740 cm−1 mode in detail, showing that T-RACS can separate ground and excited state coherences and determine their frequencies and dephasing times. We note that our observations of strong coherent dynamics in Chl a are in contrast to recent reports of only weak coherent signatures in 2DES studies of bacteriochlorophyll a.58 The ease with which coherent dynamics can be characterized by T-RACS should make it a valuable tool to address current open questions about the role of coherence and electronic−vibrational coupling in energy transfer and charge separation in natural and artificial light-harvesting materials. Experimental Methods. All experiments performed here used a hybrid pulse-shaping/diffractive optics method discussed previously.59 The pump and probe spectra for both the broadband 3DES and T-RACS experiments are shown in Figure 1b and are produced by two home-built NOPAs. We used Chlorophyll a (Chl a) samples derived from Anacystis nidulans algae purchased from Sigma-Aldrich. Our sample was prepared in a solvent of isopropanol and glycerol at a 1:1 ratio. We measured a sample optical density OD = 0.23 in a 380 μm thick custom sample cell that was loaded into a cryostat and held at 77 K.
from the T-RACS data in Figure 4c,d. Comparing the frequencies obtained in the rephasing T-RACS data and Fourier maps for the excited-state coherence pulse sequence (Figure 2c) with those of the ground-state coherence pulse sequence (Figure 2d), we find a consistent red shift of the excited state coherence frequency with respect to the ground state value. Comparing Ground and Excited State Dephasing. To resolve differences in ground and excited state coherence frequencies and compare their relative dephasing times we performed higher resolution T-RACS scans. The improved S/N and speed of T-RACS enables high frequency resolution measurements since long t2 scans can be readily made. The excited and ground state signals were recorded using the pulse sequences shown in Figure 1c and 1d, respectively, at t1 = 60 fs. Representative rephasing time domain data showing the excited and ground state coherences are plotted in Figure 5a and b respectively, at ω3 values that were selected for their high S/N. Figure 5c shows the corresponding Frobenius spectra for the excited and ground state coherences. The higher resolution of the 5 ps scan reveals an additional small amplitude vibrational mode to the blue side of the main peak in both the excited and ground state data. For the excited state data, we find frequencies of 738 ± 3 cm−1 and 748 ± 3 cm−1 for the dominant and smaller modes, respectively, which compare well with the reported frequencies of 740 ± 4 cm−1 and 750 ± 4 cm−1 from FLN experiments.50 On the ground state, we find frequencies of 743 ± 3 cm−1 and 754 ± 3 cm−1, which also compare well with the reported frequencies of 744 ± 2 cm−1 and 750 ± 2 cm−1 from the same FLN experiments.50 Assuming Lorentzian lineshapes, the excited and ground state dominant modes have similar dephasing times of 1420 ± 200 fs and 1490 ± 200 fs, respectively. For the T-RACs experiment that reports mixed ground and excited state coherence (Figure 2e), we find an intermediate value of 742 ± 4 cm−1 in the rephasing T-RACS data, consistent with our expectations for a mixture of ground and excited state. These frequencies were also consistent with the results obtained by two-color 3DES as reported in Figure 4c−d and with the nonrephasing T-RACS data presented in Supporting Information Figure S3. We note that although the use of the displaced oscillator model works well for the ∼740 cm−1 mode, there are aspects of the data that cannot be well accounted for by this simple model. These aspects are discussed in the Supporting Information (Figures S4−5). In conclusion, we have demonstrated a rapid and high S/N pulse-shaping-based approach for recording coherent dynamics. Compared to recording coherences using broadband 3DES, TRACS offers enhanced S/N and a significant reduction in data acquisition time: 15-fold compared to 3DES methods that operate in the rotating-frame, and approximately two orders of magnitude reduction compared to standard 3DES methods. This method is most easily implemented with a pulse-shaper, though we note that this approach could also be applied with other methods of spectral amplitude control. Although TRACS is a reduced dimensionality experiment, through the appropriate choice of pulse-sequence and resolution of the ω3dependence of the signal, it retains much of the information about the physical origin of the coherence that is available from 3DES measurements, such as the ability to distinguish excitedstate and ground-state coherence. It can also be used to determine the excited and ground state coherence frequencies with high spectral resolution and high S/N and has the benefit over FLN of enabling measurements over a broad temperature
■
ASSOCIATED CONTENT
S Supporting Information *
Further details about the experimental methods and data analysis as well as the double-sided Feynman diagrams showing how the different pulse-orderings in T-RACS generate different coherent states within the displaced oscillator model. Additional experimental data is also shown and discussed. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.5b00861.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS S.S.S. and V.R.P. acknowledge support from the National Science Foundation (grant no. PHY-1305450). J.P.O. acknowledges support from the Office of Basic Energy Sciences, the U.S. Department of Energy (grant no. DE-FG02-07ER15904).
■
REFERENCES
(1) Vos, M. H.; Jones, M. R.; Hunter, C. N.; Breton, J.; Martin, J. L. Coherent Nuclear-Dynamics At Room-Temperature In Bacterial Reaction Centers. Proc. Natl. Acad. Sci. U.S.A. 1994, 91, 12701−12705. (2) Vos, M. H.; Rappaport, F.; Lambry, J. C.; Breton, J.; Martin, J. L. Visualization Of Coherent Nuclear Motion In A Membrane-Protein By Femtosecond Spectroscopy. Nature 1993, 363, 320−325. (3) Engel, G. S.; Calhoun, T. R.; Read, E. L.; Ahn, T. K.; Mancal, T.; Cheng, Y. C.; Blankenship, R. E.; Fleming, G. R. Evidence For Wavelike Energy Transfer Through Quantum Coherence in Photosynthetic Systems. Nature 2007, 446, 782−786.
2418
DOI: 10.1021/acs.jpclett.5b00861 J. Phys. Chem. Lett. 2015, 6, 2413−2420
Letter
The Journal of Physical Chemistry Letters (4) Tekavec, P. F.; Myers, J. A.; Lewis, K. L. M.; Ogilvie, J. P. Two Dimensional Electronic Spectroscopy with a Continuum Probe. Opt. Lett. 2009, 34, 1390−1392. (5) Nemeth, A.; Milota, F.; Mancal, T.; Lukes, V.; Hauer, J.; Kauffmann, H. F.; Sperling, J. Vibrational Wave Packet Induced Oscillations in Two-Dimensional Electronic Spectra. I. Experiments. J. Chem. Phys. 2010, 132, 184514. (6) Mancal, T.; Nemeth, A.; Milota, F.; Lukes, V.; Kauffmann, H. F.; Sperling, J. Vibrational Wave Packet Induced Oscillations in TwoDimensional Electronic Spectra. II. Theory. J. Chem. Phys. 2010, 132, 184515. (7) Halpin, A.; Johnson, P. J. M.; Tempelaar, R.; Murphy, R. S.; Knoester, J.; Jansen, T. L. C.; Miller, R. J. D. Two-Dimensional Spectroscopy of a Molecular Dimer Unveils the Effects of Vibronic Coupling on Exciton Coherences. Nat. Chem. 2014, 6, 196−201. (8) Milota, F.; Prokhorenko, V. I.; Mancal, T.; von Berlepsch, H.; Bixner, O.; Kauffmann, H. F.; Hauer, J. Vibronic and Vibrational Coherences in Two-Dimensional Electronic Spectra of Supramolecular J-Aggregates. J. Phys. Chem. A 2013, 117, 6007−6014. (9) Schlau-Cohen, G. S.; Calhoun, T. R.; Ginsberg, N. S.; Read, E. L.; Ballottari, M.; Bassi, R.; van Grondelle, R.; Fleming, G. R. Pathways of Energy Flow in LHCII from Two-Dimensional Electronic Spectroscopy. J. Phys. Chem. B 2009, 113, 15352−15363. (10) Read, E. L.; Engel, G. S.; Calhoun, T. R.; Mancal, T.; Ahn, T. K.; Blankenship, R. E.; Fleming, G. R. Cross-Peak-Specific TwoDimensional Electronic Spectroscopy. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 14203−14208. (11) Scholes, G. D.; Fleming, G. R.; Olaya-Castro, A.; van Grondelle, R. Lessons from Nature about Solar Light Harvesting. Nat. Chem. 2011, 3, 763−774. (12) Collini, E.; Wong, C. Y.; Wilk, K. E.; Curmi, P. M. G.; Brumer, P.; Scholes, G. D. Coherently Wired Light-Harvesting in Photosynthetic Marine Algae at Ambient Temperature. Nature 2010, 463, 644−647. (13) Lee, H.; Cheng, Y. C.; Fleming, G. R. Coherence Dynamics in Photosynthesis: Protein Protection of Excitonic Coherence. Science 2007, 316, 1462−1465. (14) Fuller, F. D.; Pan, J.; Butkus, V.; Gelzinis, A.; Senlik, S.; Wilcox, D. E.; Yocum, C. F.; Valkunas, L.; Abramavicius, D.; Ogilvie, J. P. Vibronic Coherence in Oxygenic Photosynthesis. Nat. Chem. 2014, 6, 706−711. (15) Romero, E.; Augulis, R.; Novoderezhkin, V. I.; Ferretti, M.; Thieme, J.; Zigmantas, D.; van Grondelle, R. Quantum Coherence in Photosynthesis for Efficient Solar-Energy Conversion. Nat. Phys. 2014, 10, 676−682. (16) Westenhoff, S.; Palecek, D.; Edlund, P.; Smith, P. W. E.; Zigmantas, D. Coherent Picosecond Exciton Dynamics in a Photosynthetic Reaction Center. J. Am. Chem. Soc. 2012, 134, 16484−16487. (17) Ryu, I. S.; Dong, H.; Fleming, G. R. Role of ElectronicVibrational Mixing in Enhancing Vibrational Coherences in the Ground Electronic States of Photosynthetic Bacterial Reaction Center. J. Phys. Chem. B 2014, 118, 1381−1388. (18) Collini, E.; Scholes, G. D. Coherent Intrachain Energy Migration in a Conjugated Polymer at Room Temperature. Science 2009, 323, 369−373. (19) Song, Y.; Clafton, S. N.; Pensack, R. D.; Kee, T. W.; Scholes, G. D. Vibrational Coherence Probes the Mechanism of Ultrafast Electron Transfer in Polymer-Fullerene Blends. Nat. Commun. 2014, 5, 4933. (20) Tiwari, V.; Peters, W. K.; Jonas, D. M. Electronic Resonance with Anticorrelated Pigment Vibrations Drives Photosynthetic Energy Transfer Outside the Adiabatic Framework. Proc. Natl. Acad. Sci. U.S.A. 2013, 110, 1203−1208. (21) Kolli, A.; O’Reilly, E. J.; Scholes, G. D.; Olaya-Castro, A. The Fundamental Role of Quantized Vibrations in Coherent Light Harvesting by Cryptophyte Algae. J. Chem. Phys. 2012, 137, 174109. (22) Chenu, A.; Christensson, N.; Kauffmann, H. F.; Mancal, T. Enhancement of Vibronic and Ground-State Vibrational Coherences in 2D Spectra of Photosynthetic Complexes. Sci. Rep. 2013, 3, 2029.
(23) Huelga, S. F.; Plenio, M. B. Vibrations, Quanta and Biology. Contemp. Phys. 2013, 54, 181−207. (24) Falke, S. M.; Rozzi, C. A.; Brida, D.; Maiuri, M.; Amato, M.; Sommer, E.; De Sio, A.; Rubio, A.; Cerullo, G.; Molinari, E.; Lienau, C. Coherent Ultrafast Charge Transfer in an Organic Photovoltaic Blend. Science 2014, 344, 1001−1005. (25) Osborne, D. G.; Kubarych, K. J. Rapid and Accurate Measurement of the Frequency-Frequency Correlation Function. J. Phys. Chem. A 2013, 117, 5891−5898. (26) Mukamel, S. Principles of Nonlinear Optics and Spectroscopy; Oxford University Press: Oxford, 1995. (27) Butcher, P. N.; Cotter, D. The Elements of Nonlinear Optics; Cambridge University Press: Cambridge, 2003; Vol. 9. (28) Wright, J. C. Multiresonant Coherent Multidimensional Spectroscopy. In Annual Review of Physical Chemistry; Leone, S. R., Cremer, P. S., Groves, J. T., Johnson, M. A., Eds.; 2011; Vol. 62, pp 209−230. (29) Womick, J. M.; Miller, S. A.; Moran, A. M. Toward the Origin of Exciton Electronic Structure in Phycobiliproteins. J. Chem. Phys. 2010, 133, 024507. (30) Richards, G. H.; Wilk, K. E.; Curmi, P. M. G.; Davis, J. A. Disentangling Electronic and Vibrational Coherence in the Phycocyanin-645 Light-Harvesting Complex. J. Phys. Chem. Lett. 2014, 5, 43− 49. (31) Richards, G. H.; Wilk, K. E.; Curmi, P. M. G.; Quiney, H. M.; Davis, J. A. Excited State Coherent Dynamics in Light-Harvesting Complexes from Photosynthetic Marine Algae. J. Phys. B: At., Mol. Opt. Phys. 2012, 45, 154015. (32) Richards, G. H.; Wilk, K. E.; Curmi, P. M. G.; Quiney, H. M.; Davis, J. A. Coherent Vibronic Coupling in Light-Harvesting Complexes from Photosynthetic Marine Algae. J. Phys. Chem. Lett. 2012, 3, 272−277. (33) Tollerud, J. O.; Hall, C. R.; Davis, J. A. Isolating Quantum Coherence Using Coherent Multi-Dimensional Spectroscopy with Spectrally Shaped Pulses. Opt. Express 2014, 22, 6719−6733. (34) Wen, P.; Nelson, K. A. Selective Enhancements in 2D Fourier Transform Optical Spectroscopy with Tailored Pulse Shapes. J. Phys. Chem. A 2013, 117, 6380−6387. (35) Jonas, D. M. Two-Dimensional Femtosecond Spectroscopy. Annu. Rev. Phys. Chem. 2003, 54, 425−463. (36) Lewis, K. L. M.; Ogilvie, J. P. Probing Photosynthetic Energy and Charge Transfer with Two-Dimensional Electronic Spectroscopy. J. Phys. Chem. Lett. 2012, 3, 503−510. (37) Butkus, V.; Zigmantas, D.; Abramavicius, D.; Valkunas, L. Distinctive Character of Electronic and Vibrational Coherences in Disordered Molecular Aggregates. Chem. Phys. Lett. 2013, 587, 93−98. (38) Butkus, V.; Valkunas, L.; Abramavicius, D. Vibronic Phenomena and Exciton-Vibrational Interference in Two-Dimensional Spectra of Molecular Aggregates. J. Chem. Phys. 2014, 140, 034306. (39) Butkus, V.; Zigmantas, D.; Valkunas, L.; Abramavicius, D. Vibrational vs. Electronic Coherences in 2D Spectrum of Molecular Systems. Chem. Phys. Lett. 2012, 545, 40−43. (40) Egorova, D. Self-Analysis of Coherent Oscillations in TimeResolved Optical Signals. J. Phys. Chem. A 2014, 118, 10259−10267. (41) Egorova, D. Detection of Electronic and Vibrational Coherences in Molecular Systems by 2D Electronic Photon Echo Spectroscopy. Chem. Phys. 2008, 347, 166−176. (42) Turner, D. B.; Dinshaw, R.; Lee, K. K.; Belsley, M. S.; Wilk, K. E.; Curmi, P. M. G.; Scholes, G. D. Quantitative Investigations of Quantum Coherence for a Light-Harvesting Protein at Conditions Simulating Photosynthesis. Phys. Chem. Chem. Phys. 2012, 14, 4857− 4874. (43) Christensson, N.; Kauffmann, H. F.; Pullerits, T.; Mancal, T. Origin of Long-Lived Coherences in Light-Harvesting Complexes. J. Phys. Chem. B 2012, 116, 7449−7454. (44) Turner, D. B.; Wilk, K. E.; Curmi, P. M. G.; Scholes, G. D. Comparison of Electronic and Vibrational Coherence Measured by Two-Dimensional Electronic Spectroscopy. J. Phys. Chem. Lett. 2011, 2, 1904−1911. 2419
DOI: 10.1021/acs.jpclett.5b00861 J. Phys. Chem. Lett. 2015, 6, 2413−2420
Letter
The Journal of Physical Chemistry Letters (45) Song, Y.; Hellman, C.; Stingelin, N.; Scholes, G. D. The Separation of Vibrational Coherence From Ground- and Excitedelectronic States in P3HT Film. J. Chem. Phys. 2015, 142, 212410. (46) Caram, J. R.; Fidler, A. F.; Engel, G. S. Excited and Ground State Vibrational Dynamics Revealed by Two-Dimensional Electronic Spectroscopy. J. Chem. Phys. 2012, 137, 024507. (47) Seibt, J.; Pullerits, T. Beating Signals in 2D Spectroscopy: Electronic or Nuclear Coherences? Application to a Quantum Dot Model System. J. Phys. Chem. C 2013, 117, 18728−18737. (48) Lutz, M. Resonance Raman Spectra of Chlorophyll in Solution. J. Raman Spectrosc. 1974, 2, 497−516. (49) Telfer, A.; Pascal, A. A.; Bordes, L.; Barber, J.; Robert, B. Fluorescence Line Narrowing Studies on Isolated Chlorophyll Molecules. J. Phys. Chem. B 2010, 114, 2255−2260. (50) Peterman, E. J. G.; Wenk, S. O.; Pullerits, T.; Palsson, L. O.; van Grondelle, R.; Dekker, J. P.; Rogner, M.; van Amerongen, H. Fluorescence and Absorption Spectroscopy of the Weakly Fluorescent Chlorophyll a in Cytochrome b(6)f of Synechocystis PCC6803. Biophys. J. 1998, 75, 389−398. (51) Ratsep, M.; Linnanto, J.; Freiberg, A. Mirror Symmetry and Vibrational Structure in Optical Spectra of Chlorophyll a. J. Chem. Phys. 2009, 130, 194501. (52) Du, J.; Teramoto, T.; Nakata, K.; Tokunaga, E.; Kobayashi, T. Real-Time Vibrational Dynamics in Chlorophyll a Studied with a FewCycle Pulse Laser. Biophys. J. 2011, 101, 995−1003. (53) Gundogdu, K.; Stone, K. W.; Turner, D. B.; Nelson, K. A. Multidimensional Coherent Spectroscopy Made Easy. Chem. Phys. 2007, 341, 89−94. (54) Shim, S. H.; Zanni, M. T. How to Turn Your Pump-Probe Instrument into a Multidimensional Spectrometer: 2D IR and Vis Spectroscopies via Pulse Shaping. Phys. Chem. Chem. Phys. 2009, 11, 748−761. (55) Cowan, M. L.; Ogilvie, J. P.; Miller, R. J. D. Two-Dimensional Spectroscopy Using Diffractive Optics Based Phased-Locked Photon Echoes. Chem. Phys. Lett. 2004, 386, 184−189. (56) Brixner, T.; Mancal, T.; Stiopkin, I. V.; Fleming, G. R. PhaseStabilized Two-Dimensional Electronic Spectroscopy. J. Chem. Phys. 2004, 121, 4221−4236. (57) Gillie, J. K.; Small, G. J.; Golbeck, J. H. Nonphotochemical Hole-Burning of the Native Antenna Complex of Photosystem-I (PSI200). J. Phys. Chem. 1989, 93, 1620−1627. (58) Fransted, K. A.; Caram, J. R.; Hayes, D.; Engel, G. S. TwoDimensional Electronic Spectroscopy of Bacteriochlorophyll a in Solution: Elucidating the Coherence Dynamics of the Fenna− Matthews−Olson Complex Using Its Chromophore as a Control. J. Chem. Phys. 2012, 137, 125101. (59) Fuller, F. D.; Wilcox, D. E.; Ogilvie, J. P. Pulse Shaping Based Two-Dimensional Electronic Spectroscopy in a Background Free Geometry. Opt. Express 2014, 22, 1018−1027.
2420
DOI: 10.1021/acs.jpclett.5b00861 J. Phys. Chem. Lett. 2015, 6, 2413−2420
