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Comparison of Electronic and Vibrational Coherence Measured by Two-Dimensional Electronic Spectroscopy Daniel B. Turner,† Krystyna E. Wilk,‡ Paul M. G. Curmi,‡ and Gregory D. Scholes*,† †
Department of Chemistry and Centre for Quantum Information and Quantum Control, 80 Saint George Street, University of Toronto, Toronto, Ontario, M5S 3H6 Canada ‡ School of Physics and Centre for Applied Medical Research, St. Vincent’s Hospital, The University of New South Wales, Sydney, New South Wales 2052, Australia ABSTRACT: The short pulse durations and broad frequency spectra of femtosecond laser pulses allow coherent superpositions of states to be prepared and probed. Two-dimensional electronic spectroscopy (2D ES) has the potential to identify more clearly the origin and evolution of such coherences. In this report we examine how electronic and vibrational coherences can be distinguished by decomposing the total 2D ES signal into rephasing and nonrephasing components. We investigate and identify differences between the cross peak oscillations measured in two laser dyes with those measured in the PC645 lightharvesting antenna protein of the cryptophyte alga Chroomonas sp. strain CCMP270 at ambient temperature. SECTION: Kinetics, Spectroscopy
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hort pulse excitation of superpositions of vibrational states in the ground and electronic excited manifolds allows the evolution of vibrational wavepackets to be monitored.1 7 This allows, for example, the observation of vibrational motions otherwise obscured by line-broadening8 11 or chemical reactions12 14 to be followed. Control of the initial state of the superposition by pulse-shaping can direct the outcome of reactions.15 18 Electronic coherences can also be prepared. In recent work, it has been discovered that electronic coherence in systems of electronically coupled molecules can be surprisingly longlived,19 21 and therefore such effects may appear in energy transfer dynamics (even without coherent short pulse excitation). This observation has important implications for how theories of energy transfer need to be formulated, and, consequently, it impacts the way we think about energy transfer mechanisms and how synthetic light harvesting systems should be designed.22,23 The advance that opened this field was the recognition that two-dimensional electronic spectroscopy (2D ES) can identify electronic coherences by their cross-peak position and oscillation frequency, which is related to the energy difference of the electronic states in superposition.24 These recent reports of electronic coherence in photosynthetic light-harvesting complexes are compelling, but nonetheless it is desirable to be able to differentiate clearly between electronic and vibrational oscillations in 2D ES. To date, electronic coherences have generally been assigned based on knowing the positions of electronic absorption bands or comparison of the experimental results with predictions of dynamics and coherences. Here we compare 2D ES studies of a photosynthetic r 2011 American Chemical Society
light-harvesting complex, PC645 from the cryptophyte alga Chroomonas sp. strain CCMP270, with two laser dyes, one of which exhibits strong vibrational oscillations. A key difference between the spectroscopy of electronic and vibrational manifolds probed by femtosecond pulses is that electronic coherences are formed between electronic excited states, but vibrational coherences are formed and probed in both electronic ground and excited vibronic levels. Therefore, subject to the Franck Condon overlap factors, we anticipate that signatures of vibrational coherences should be more widespread through the 2D electronic spectrum than purely electronic coherences. In Figure 1 we compare a system comprising two electronically coupled molecules that have collective excited states (molecular exciton states25) which we label |Ræ and |βæ with a single molecule whose excited electronic state we label |eæ. In both cases the ground electronic state is labeled |gæ. We consider vibrational levels of the molecule—with frequency separation ν—and assume the Born Oppenheimer approximation so we can write product-state wave functions to designate vibronic levels as shown in Figure 1b. In a 2D ES measurement, four laser beams are incident on the sample, and the pulse timings are varied, leading to three time periods (τ1,τ2, and τ3) between field interactions. One beam is selected as a reference, and the phase matching condition among the other three beams, ksig = ka + kb + kc, leads to signal emitted Received: June 15, 2011 Accepted: July 14, 2011 Published: July 14, 2011 1904
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Figure 1. (a) The electronic coupling case where two electronic states (|Ræ and |βæ) are coupled through a common ground state |gæ. (b) The vibrational coupling case in which vibrational states with frequency separation ν are depicted on the ground |gæ and one electronic |eæ state. (c) Doublesided Feynman diagrams for the diagonal and cross peaks, all with vibrational coherences during time period τ2. The presence of the |gæ|νæ state leads to the emergence of diagrams i and iv.
in the reference direction. In a 2D ES measurement, time period τ1 (the time between fields ka and kb) is scanned while the emitted signal is detected using a spectrometer for a selected τ2 value. During a rephasing measurement, field ka is incident on the sample first (τ1 > 0) and a photon echo can occur during the emission time period, τ3. For nonrephasing measurements, field ka is incident second (τ1 < 0), and no echo occurs. Together the rephasing and nonrephasing spectra form a complete signal that, after Fourier transformation, can lead to fully absorptive lineshapes in the real part of the 2D ES.26 Signals involving interactions between a material and the electric fields provided by a series of femtosecond pulses can be conveniently explained in terms of the evolution of the system density matrix, where a set of double-sided Feynman diagrams can account for all possible pulse time orderings and all possible interactions with the system eigenstates.27,28 It has been established that oscillations in the 2D ES signal amplitude as a function of τ2 for a system like that sketched in Figure 1a arise from oscillations in the rephasing contribution to the cross peak and oscillations in the nonrephasing contribution to the diagonal peak.20,29,30 However, in the case of vibrational coherences for the system indicated in Figure 1b, diagonal as well as off-diagonal oscillations are anticipated in both rephasing and nonrephasing spectra,31 33 as suggested by the representative double-sided Feynman diagrams presented in Figure 1c. As a first step to comparing electronic and vibrational quantum beats in 2D ES, we needed to improve the quality of the 2D ES data. We made a series of technological upgrades, which simultaneously lowered the data acquisition time, increased the signal-to-noise ratio, increased the pulse bandwidth, and improved the pulse compression. Details are reported in the
Figure 2. Linear absorption (solid black lines) and pulse spectra (dashed red lines) for R6G (a), CV (b), and PC645 (c).
Methods section; briefly, we accomplished the above by decreasing the pulse propagation distance, using as few transmissive optics as possible, and by incorporating a 2D diffractive optic. 1905
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Figure 3. (a) 2D ES spectra of PC645 at the indicated τ2 values. Contours are linearly spaced at 3% intervals. The cross peak (X) has a negative amplitude, and it does not reappear at later τ2 times. (b) The values extracted from the 2D ES (blue), nonrephasing (black), and rephasing (red) spectra. The oscillations in the 2D ES are dominated by the rephasing component.
Data quality improved to the point that we did not need to apply filters, apodization functions, or phase-flattening routines that are commonly used to reduce noise during analysis of the 2D ES data sets. (The only filter used is the Heaviside filter required in the spectral interferometry algorithm to enforce causality.34) We measured the laser dyes Rhodamine 6G (R6G) and cresyl violet perchlorate (CV) in addition to the antenna protein phycocyanin 645 (PC645), all at room temperature (298 K). Dye samples were solvated in methanol to an optical density of ∼0.3 in a 1 mm path-length cuvette. The protein sample was diluted—using a potassium phosphate buffer at a pH of 6.8—to also have an OD of ∼0.3; it was flowed via a 1 mm flow-cell cuvette at a rate of 0.05 mL/min to eliminate slow photobleaching. The linear absorption spectra and the laser pulse spectra are illustrated in Figure 2. The peak absorption of R6G appears at 567 THz (529 nm); R6G has a 46 THz (1520 cm 1) vibrational mode due to an aromatic C C stretch.35,36 The peak absorption of CV appears at 505 THz (594 nm), and its strong vibrational mode—attributed to an orthogonal aromatic stretching motion in the central ring37,38—has a frequency of 18 THz (595 cm 1). The vibrational modes of the dye molecules lead to the vibronic progression of additional peaks in the absorption spectra that are blue-shifted from the lowest-frequency absorption feature. R6G (CV) has a vibronic shoulder at about 610 THz (525 THz). PC645 is a light-harvesting protein that contains eight bilin chromophores held in a protein lattice. The absorption spectrum of PC645 therefore involves eight electronic peaks20,39 that are spectrally broad due to both sample inhomogeneity and rapid dephasing, and there is significant overlap among the eight
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transitions. Previous studies suggest that a modestly coupled dihydrobiliverdin (DBV) chromophore pair has absorption maxima at 510 THz (588 nm) and 529 THz (567 nm), and a minimally coupled mesobiliverdin (MBV) chromophore pair has absorption maxima at 499 THz (601 nm) and 496 THz (604 nm). Raman spectra of related proteins show several discrete vibrational modes within our spectral bandwidth.40 The 2D ES spectra for PC645 are shown in Figure 3a. With the signal-to-noise ratio and repeatability attainable with the experimental setup, we see rich dynamics throughout the 2D spectrum for the full τ2 time period of 300 fs. The focus of this work is the cross peak dynamics in the first 100 fs; other dynamics will be presented and analyzed in future studies. The negative-amplitude cross peak (X) appears at an absorption frequency value of 522 THz (2.16 eV) and emission frequency value of 498 THz (2.06 eV); the clear peak in the contour plot does not reappear at τ2 times greater than 100 fs. The frequency coordinates of X suggest coupling between the DBV+ at 525 THz and the MBV at 499 THz, which would be consistent with previous studies.20,39 However, we advise caution in trying to relate these frequencies to any underlying individual chromophore pair since the spectrum contains contributions from four underlying levels near the cross peak coordinates (the DBV pair and the MBV pair), and the strong, broad diagonal peak could easily obscure higher frequency contributions to X. We examine the dynamics of the cross peak in Figure 3b, where error bars representing one standard deviation are due to the statistics of three consecutive measurements. The 2D ES displayed in Figure 3a are selected from one of the three measurements. The trace was made by integrating the absorption dimension from 521 THz to 524 THz and the emission dimension from 497 THz to 498 THz; this is illustrated by the semitransparent green box in the τ2 = 55 fs 2D spectrum. Using the upper-left section of the peak retains the cross peak dynamics but reduces potential contributions from overlap with the broad diagonal peak. As shown in Figure 3b, the oscillations in the 2D ES trace (blue) are dominated by the rephasing contribution (red). At first glance, it appears that the nonrephasing contribution (black) does not oscillate, supporting the notion that the cross peak does not involve vibrational coherences. Upon close inspection, there seems to be an oscillation in the nonrephasing component at about 50 fs. Unfortunately, since the apparent valley is contained within the error of the measurement, conclusively showing the presence or complete absence of nonrephasing oscillations is problematic even with the vastly improved signal-to-noise. The curves in Figure 3b have the same scale but are displaced vertically to ease viewing. The periodicity of the oscillations is about 30 fs. Given the τ2 time steps of 5 fs and the unavoidable difficulty in locating the cross peak coordinates accurately, the periodicity seems reasonably close to the value (41 fs) anticipated by the frequency coordinates of the peak. We present the frequency resolved transient grating (TG) spectra for the two dyes in Figure 4a. Oscillations in TG signals can be described as the evolution of the nuclear wavepacket on the electronic surface; as the wavepacket moves, the electronic polarizability changes. After the initial (∼15 fs) nonresonant solvent response, CV shows several oscillations at its 18 THz vibrational mode. R6G, meanwhile, shows only one oscillation at its vibrational frequency; the weak oscillations after τ2∼50 fs might be signatures of the other weak, low-frequency modes of the molecule.41 1906
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Figure 4. (a) Frequency-resolved TG spectra of R6G and CV. (b) 2D ES spectra of R6G (top row) and CV (bottom row) at the indicated τ2 values. Contours are linearly spaced at 6% intervals. The diagonal (cross) peak is labeled D (X). (c) Plots of D (black curve) and X (red curve) extracted from the real part of the 2D ES spectra for R6G (i) and CV (ii). (d) We further analyzed the behavior of X in CV by extracting traces from the 2D ES (blue), rephasing (red), and nonrephasing (black) spectra. Both the rephasing and nonrephasing traces show oscillations as expected for vibrational coherences.
Representative 2D ES for the two dye molecules are presented in Figure 4b. Using two different dyes allows us to highlight the difference between strong and weak spectral modulations due to a molecular vibrational mode. R6G has been intensely studied and is thus an ideal chromophore for assessing the spectroscopic apparatus. It serves as a reference for line shape analysis, since the 2D ES for the other two samples contain strong modulations due to other close-lying levels. 2D spectra before τ2 values of 15 fs contain limited but nonzero nonresonant responses in addition to the dye response and are therefore not displayed. The R6G spectra display two features. The stronger feature (D) absorbs at
a frequency of 565 THz and is centered about the diagonal. Its initial inhomogeneity—as manifest in the diagonal elongation42— is due to varying solvent environments; dissipation at longer τ2 times is due to bath relaxation.43 The weaker feature (X) appears to be a vibrational cross peak; the amplitude of the feature is positive. One of the pathways leading to this shoulder involves a |g1æÆg0| vibrational coherence during τ2, but it is clear from the TG spectrum that at most one period of oscillation is expected. The peak decays rapidly so that by 25 fs it remains as only a slight asymmetry to D. The remaining cross peak signal can be described by diagrams containing populations, not coherences, 1907
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The Journal of Physical Chemistry Letters during τ2. Figure 4c(i) contains a trace of the value of the two peaks through all τ2 time points. These observations are in accord with the dynamics measured in the TG experiment. The 2D ES of CV display several peaks that overlap and oscillate as a function of τ2. In principle it would be useful to create a three-dimensional (3D) spectral solid44,45 to separate oscillatory signals from nonoscillatory signals, but the limited τ2 window prohibits scanning until the oscillations have ceased. The rectangular shape of the spectrum is due to four strong peaks: two diagonal peaks and two cross peaks. Due to rapid dephasing of the optical coherences, the peaks are rather broad. That, in addition to the minimal splitting due to the low value of the vibrational frequency, causes the peaks to overlap significantly. All four peaks oscillate throughout τ2. At τ2 of 15 fs, we observe a strong cross peak above the diagonal; its oscillations are indicative of nuclear vibrational coherences during τ2. At τ2 values of 20 and 100 fs, the diagonal peaks are more pronounced than the cross peaks, and at τ2 values of 75 and 300 fs, the cross peaks are stronger than the diagonal peaks. The dynamics of the two peaks marked in the CV spectra are displayed in Figure 4c(ii). The trace for peak X was created by integrating from 506 to 509 THz in absorption and 521 to 523 THz in emission; peak D was created by integrating from 506 to 509 THz in both absorption and emission. Since the traces are from a single scan, we do not display error bars for this data set. Given that X and D oscillate out of phase with each other in the 2D ES, it is unexpected that their traces show in-phase oscillations. This apparent discrepancy is due to an unequal number of signal pathways for each peak that contain vibrational coherences during time period τ2. Close inspection of the traces reveals that while the oscillations are indeed in phase, the relative amplitudes are such that at some times, such as τ2 = 100 fs, the black line (D) is greater than the red line (X), indicating D will appear stronger than X, and at other times, such as τ2 = 75 fs, the situation is reversed with X at higher amplitude than D. We extracted the nonrephasing and rephasing contributions to X and plotted them in Figure 4d to verify that we are measuring a vibrational coherence. Indeed, the nonrephasing component of the signal clearly oscillates, indicating that vibrational coherences are, at least in part, responsible for the cross peak. Unlike the PC645 measurement, the oscillations in the two components have nearly equal amplitudes in the CV measurement. There is one additional difference between the PC645 spectra and the spectra of the two dyes worth mentioning. The cross peak amplitudes in the dye molecules are always positive, whereas in PC645 the peak oscillates between positive and negative amplitude values. Although it warrants further investigation, this could suggest another method of differentiating between the two types of coupling. Viewing the vibrational coherence as oscillations of a wavepacket, the Franck Condon overlap cannot be negative, and thus the amplitude of the peak is positive or zero. On the other hand, the coherent superposition between two electronic states will simply evolve its phase during τ2, and the real part of the cross peak amplitude can cycle through both positive and negative values. The question has arisen lately as to how to verify that the cross peak(s) in 2D ES of photosynthetic proteins are caused by electronic coupling, not vibrational modulations. In this report we have described and demonstrated a method that can be used to detect contributions from vibrations. When the relative contribution is zero, we can conclude that the cross peak is due
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solely to electronic coupling. However, this protocol cannot differentiate between the two types of couplings in all cases. For example, in a system that has both electronic and vibronic contributions, it is possible that the nonrephasing component will oscillate but part of the rephasing oscillations will be due to electronic couplings. In other words, the lack of oscillations in the nonrephasing contribution to the cross peak is sufficient to demonstrate the absence of vibrational coherences, and, in this analysis, was required to show the existence of electronic coherences. If nonrephasing oscillations are present, this confirms there is some contribution from vibrational coherences, but does not immediately imply the absence of electronic coherences. This protocol also relies on the absence of other physical processes that could cause oscillations in the cross peaks. To a first approximation, the PC645 experiment seemed to be a case of pure electronic coupling. Upon closer examination, enabled by the quality of data we can obtain with the new experimental setup described in this report, it is clear that there are rich dynamics detected throughout the 2D spectrum. With the spectrally broad pulses used in the measurements report here, these dynamics may include contributions from underlying vibrational coherences. Future analyses and measurements using polarized 2D ES46,47 or changing the sample temperature21 will undoubtedly lead to additional insights.
’ METHODS Tunable Laser Source. A 5 kHz repetition rate regenerative amplifier seeded by a Ti:sapphire oscillator produces 150 fs duration pulses centered at 800 nm with about 0.6 mJ of energy. About 0.15 mJ seeds a home-built noncollinear optical parametric amplifier (NOPA).48 The all-reflective-optics design allows the NOPA to amplify the entire visible spectrum if desired.49 Typically, we place a 3 mm thick, uncoated UV fused silica window in the white light to reduce the spectral fwhm to about 60 nm, which can then be tuned to the appropriate central frequency. The NOPA converts about 15% of the 10 μJ, 400 nm pump to the desired output using a 1 mm thick β-barium borate (BBO) mixing crystal. The spatial mode is nearly TEM00 with almost no angular dispersion as observed by translating a pinhole lateral to the beam propagation direction at the focal plane created in the sample position; shot-to-shot intensity fluctuations are 1 2% as measured using a 1 ns rise-time photodiode with intrinsic noise below this level. All mirrors used for visible beams throughout the experiment are coated with protected silver. We use the combination of a folded 4-f grating compressor and a single-prism prism compressor50 to compress the pulse.51 The pulse for the R6G (CV/PC645) experiment is 12 fs (14 fs) full width at half-maximum (fwhm) in duration, where pulse compression is monitored using the nonresonant third-order response from methanol in the sample position. The beam is attenuated by the combination of a broadband half-waveplate and a 0.7 mm thick wire-grid polarizer before entering the fourwave-mixing (FWM) setup. FWM Apparatus. The FWM setup is similar to a previous design.52 The beam first encounters a 50 cm focal length spherical mirror. At the focal plane of this mirror is a 2 mm thick phase mask (UV fused silica substrate) that is etched in a 2D crosshatched pattern with 10 μm-wide features at a depth optimized for first-order diffraction of 500 nm incident wavelength. The four first-order diffraction beams, each about 12% of the input power, are arranged in the BOXCARS configuration. They are 1908
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Figure 5. All-optical phasing using spectral interference patterns between the LO and, individually, each excitation beam. (a) Data from a scan in which the interference pattern from the stationary beam has been subtracted from a scanned beam. (b) Spectrally integrated trace for the above pattern. The subcycle timing offset is about 0.25 fs and needs to be corrected.
directed by a small steering mirror toward a 3 in. diameter, 50 cm focal length mirror. The steering mirror allows us to use the large spherical mirror at an angle of exactly zero degrees. The large spherical mirror collimates and makes parallel the four beams, which then pass above, below, and to the sides of the steering mirror. Three of the beams traverse antiparallel pairs of 1, uncoated UV fused silica glass wedges for pulse delays.53 One wedge from each pair is mounted on a computer-controlled delay stage (Newport VP-25XL). The stage accuracy sets the step accuracy, which we measured to be ∼850 zs. The pulse that serves as the final excitation field interaction is chopped at a frequency of 25 Hz; the chopper also triggers the detector, which acquires signal for 20 ms (100 laser shots). The fourth beam—a reference known as the local oscillator (LO) for spectral interferometry34—is attenuated by 104 and interacts with the sample ∼250 fs before the final excitation field. The four pulses then encounter a second 3 in. diameter spherical mirror used at zero degrees, but with a focal length of 20 cm. The pulses focus and cross in the sample plane after encountering another small steering mirror. The focused beam waist diameter is about 50 μm, and the spatial interference periodicity (Λ), as given by Λ = λ/(2 sin (θ/2)), where θ is the angle at which two beams cross, is about 2 μm. The signal and LO are collimated by a 20 cm focal length curved mirror and are directed to an imaging spectrometer (f = 16.3 cm) coupled to a charge-coupled device (CCD) detector. The resolution is about 0.2 nm, and it has 1024 pixels in the dispersed dimension. The spectrometer is calibrated using a Hg/Ar lamp. One 2D ES scan for a given τ2 value takes about 3 min. Due to sturdy mounts, boxes around the optics, and compact construction, the phase stability of the apparatus52,54 is about λ/350 short-term (5 min) and λ/200 long-term (2 h). All
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2D ES experiments are performed with pulse energies of e5 nJ. 2D ES are created by scanning τ1—at a given τ2 value—from 0 to 45 fs in 0.15 fs steps for rephasing and nonrephasing time orderings. The optical coherences during time period τ1 have fully decayed by about (25 fs due to the large spectral bandwidth and concomitant short pulse duration. Time period τ2 is incremented in 5 fs steps. Subcycle Timing Adjustment. Finding the relative optical phase offsets among the four pulses has been a concern for 2D spectroscopy since the technique was pioneered.55 The procedure for finding the global phase offset (colloquially, “phasing”) typically involves invoking the projection-slice theorem and then comparing to the frequency-resolved pump probe spectrum. This is burdensome and in some cases not possible; thus other phasing methods were developed. One group has used the abilities of a pulse shaper,56 while other groups have monitored spatial fringe patterns.57,58 Our procedure is based on the latter technique, except we use spectral, not spatial, fringe patterns to find the subcycle timing offsets. After compressing the pulses, we place a 25 μm diameter pinhole at the sample location. We then block two of the excitation beams and let the LO and one excitation beam pass through the pinhole. Since the LO and any of the excitation beams are separated temporally by hundreds of femtoseconds, no spatial interference occurs at the sample plane that would lead to spatiotemporal modulations58 of the resultant diffraction. Therefore, a large pinhole can be used, unlike the spatial fringe approach. We verified this by using a 1 ( 0.5 μm diameter pinhole and measuring identical 2D ES spectra. We then isolate the LO direction and measure the spectral interference pattern between the two temporally separated pulses (the LO and an excitation beam) using the spectrometer that is already in place for the 2D measurements. One excitation beam is selected as the stationary reference; we measure, record, and store its spectral interference pattern. Then, the stationary excitation beam is blocked, and a second excitation beam is allowed to interfere with the LO. We scan this second excitation beam temporally for several optical cycles, and the set of spectral interference patterns (one for each time delay) is recorded. To find the subcycle time point at which the scanned excitation beam has the same phase as the stationary excitation beam, we subtract the stored interference pattern of the stationary excitation beam from the set of interference patterns created by the scanned excitation beam and then integrate spectrally. An example subtracted 2D spectral interference pattern is shown in Figure 5a, and its spectrally integrated trace is shown in Figure 5b. We adjust the time of the scanned excitation beam such that the difference is zero. For the example data, the subcycle temporal overlap occurs at about 0.25 fs. To finish the procedure, this operation is repeated for the other nonstationary excitation beam. In short, we measure, one at a time, the spectral fringe pattern created by the light scattered from the LO and each of the three input beams. Using one spectral fringe pattern as a stationary reference, we make subcycle timing adjustments to the two remaining beams so that the fringe patterns match exactly. This procedure is permitted for FWM setups in which the pulse fronts of all beams are parallel, not crossed, in the focal plane.52,56 Because the pulse fronts are parallel in the focal plane, the timing of a pulse across the plane is identical.59 Since wedges adjust only the envelope, not phase, of a pulse,60 we can set time zero with subcycle accuracy to within (0.03 fs, which corresponds to a phase of about (5 degrees.58 1909
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The Journal of Physical Chemistry Letters Finally, we find the delay between the LO and the signal by Fourier transformation of the interference pattern created by a third-order nonresonant signal at τ1 = τ2 = 0 with the LO.54,57 The procedure satisfied two important verifications. First of all, the 2D ES of several samples after many laser alignments have conformed to both theoretical expectations and to previous 2D ES measurements. Second, the projection of the 2D ES onto the emission axis qualitatively matches the frequency-resolved pump probe spectrum. Although the match between the 2D ES projection and the pump probe was not quantitative, using the traditional fitting approach did not provide a better match. The discrepancy is still being studied.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT We thank Michael Belsley, Rayomond Dinshaw, Alexei Halpin, J€urgen Hauer, Philip Johnson, and Kyung-Koo Lee for helpful discussions and the Keith Nelson group for assistance in procuring the 2D diffractive optic. We thank DARPA for funding under the QuBE program. The United States Air Force Office of Scientific Research under contract number FA9550-10-1-0260 and the Natural Sciences and Engineering Research Council of Canada are also acknowledged for financial support. ’ REFERENCES (1) Heller, E. J. The Semiclassical Way to Molecular Spectroscopy. Acc. Chem. Res. 1981, 14, 368–375. (2) Ruhman, S.; Joly, A. G.; Nelson, K. A. Time-Resolved Observations of Coherent Molecular Vibrational Motion and the General Occurrence of Impulsive Stimulated Scattering. J. Chem. Phys. 1987, 86, 6563. (3) Chesnoy, J.; Mokhtari, A. Resonant Impulsive-Stimulated Raman Scattering on Malachite Green. Phys. Rev. A 1988, 38, 3566–3576. (4) Fragnito, H. L.; J.-Y., B.; Becker, P. C.; Shank, C. V. Evolution of the Vibronic Absorption Spectrum in a Molecule Following Impulsive Excitation with a 6 fs Optical Pulse. Chem. Phys. Lett. 1989, 160, 101–104. (5) Pollard, W. T.; Fragnito, H. L.; J.-Y., B.; Shank, C. V.; Mathies, R. A. Quantum-Mechanical Theory for 6 fs Dynamic Absorption Spectroscopy and its Application to Nile Blue. Chem. Phys. Lett. 1990, 168, 239–245. (6) Elsaesser, T.; Kaiser, W. Vibrational and Vibronic Relaxation of Large Polyatomic Molecules in Liquids. Annu. Rev. Phys. Chem. 1991, 42, 83–107. (7) Jonas, D. M.; Fleming, G. R. In Ultrafast Processes in Ultrafast Processes in Chemistry and Photobiology; El-Sayed, M. A., Tanaka, I., Molin, Y., Eds.; Chemistry for the 21st Century; Blackwell Scientific Publications: Oxford, 1995; p 225. (8) Yan, Y. J.; Mukamel, S. Semiclassical Dynamics in Liouville Space: Application to Molecular Electronic Spectroscopy. J. Chem. Phys. 1988, 88, 5735–5748. (9) Cina, J. A.; Smith, T. J. Impulsive Effects of Phase-Locked Pulse Pairs on Nuclear Motion in the Electronic Ground State. J. Chem. Phys. 1993, 98, 9211–924. (10) Vos, M. H.; Rappaport, F.; Lambry, J.-C.; Breton, J.; Martin, J.-L. Visulization of Coherent Nuclear Motion in a Membrane Protein by Femtosecond Spectroscopy. Nature 1993, 363, 320–325. (11) Shen, Y.-C.; Cina, J. A. What Can Short-Pulse Pump-Probe Spectroscopy Tell Us About Franck-Condon Dynamics?. J. Chem. Phys. 1999, 110, 9793–9806. (12) Dantus, M.; Rosker, M. J.; Zewail, A. H. Real-Time Femtosecond Probing of “Transition States” in Chemical Reactions. J. Chem. Phys. 1987, 87, 2395–2397.
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(13) Scherer, N.; Jonas, D. M.; Fleming, G. R. Femtosecond Wave Packet and Chemical Reaction Dynamics of Iodine in Solution: Tunable Probe Study of Motion Along the Reaction Coordinate. J. Chem. Phys. 1993, 99, 153–168. (14) Wang, Q.; Schoenlein, R. W.; Peteanu, L. A.; Mathies, R. A.; Shank, C. V. Vibrationally Coherent Photochemistry in the Femtosecond Primary Event of Vision. Science 1994, 266, 422–424. (15) Bartana, A.; Kosloff, R.; Tannor, D. J. Laser Cooling of Molecular Internal Degrees of Freedom by a Series of Shaped Pulses. J. Chem. Phys. 1993, 99, 196. (16) Assion, A.; Baumert, T.; Bergt, M.; Brixner, T.; Kiefer, B.; Seyfried, V.; Strehle, M.; Gerber, G. Control of Chemical Reactions by Feedback-Optimized Phase-Shaped Femtosecond Pulses. Science 1998, 282, 919–922. (17) Herek, J. L.; Wohlleben, W.; Cogdell, R. J.; Dirk, Z.; Motzkus, M. Quantum Control of Energy Flow in Light Harvesting. Nature 2002, 417, 533–535. (18) Prokhorenko, V. I.; Nagy, A. M.; Waschuk, S. A.; Brown, L. S.; Birge, R. R.; Miller, R. J. D. Coherent Control of Retinal Isomerization in Bacteriorhodopsin. Science 2006, 313, 1257–1261. (19) 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, 782–6. (20) 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, 644–7. (21) Panitchayangkoon, G.; Hayes, D.; Fransted, K. A.; Caram, J. R.; Harel, E.; Wen, J.; Blankenship, R. E.; Engel, G. S. Long-Lived Quantum Coherence in Photosynthetic Complexes at Physiological Temperature. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 12766–12770. (22) Scholes, G. D. Quantum-Coherent Electronic Energy Transfer: Did Nature Think of It First?. J. Phys Chem. Lett. 2010, 1, 2–8. (23) Scholes, G. D. Coherence in Photosynthesis. Nat. Phys. 2011, 7, 448–449. (24) Cheng, Y.-C.; Fleming, G. R. Dynamics of Light Harvesting in Photosynthesis. Annu. Rev. Phys. Chem. 2009, 60, 241–262. (25) Scholes, G. D.; Rumbles, G. Excitons in Nanoscale Systems. Nat. Mater. 2006, 5, 683–696. (26) Demird€oven, N.; Khalil, M.; Tokmakoff, A. Correlated Vibrational Dynamics Revealed by Two-Dimensional Infrared Spectroscopy. Phys. Rev. Lett. 2002, 89, 237401. (27) Mukamel, S. Multidimensional Femtosecond Correlation Spectroscopies of Electronic and Vibrational Excitations. Annu. Rev. Phys. Chem. 2000, 51, 691–729. (28) Cho, M. Coherent Two-Dimensional Optical Spectroscopy. Chem. Rev. 2008, 108, 1331–418. (29) Cheng, Y.-C.; Fleming, G. R. Coherence Quantum Beats in Two-Dimensional Electronic Spectroscopy. J. Phys. Chem. A 2008, 112, 4254–4260. (30) Calhoun, T. R.; Ginsberg, N. S.; Schlau-Cohen, G.; Cheng, Y.C.; Ballottari, M.; Bassi, R.; Fleming, G. R. Quantum Coherence Enabled Determination of the Energy Landscape in Light-Harvesting Complex II. J. Phys. Chem. B 2009, 113, 16291–16295. (31) Egorova, D. Detection of Electronic and Vibrational Coherences in Molecular Systems by 2D Electronic Photon Echo Spectroscopy. Chem. Phys. 2008, 347, 166. (32) 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. (33) Christensson, N.; Milota, F.; Hauer, J.; Sperling, J.; Bixner, O.; Nemeth, A.; Kauffmann, H. F. High Frequency Vibrational Modulations in Two-Dimensional Electronic Spectra and Their Resemblance to Electronic Coherence Signatures. J. Phys. Chem. B 2011, 115, 5383–5391. (34) Lepetit, L.; Cheriaux, G.; Joffre, M. Linear Techniques of Phase Measurement by Femtosecond Spectral Interferometry for Application in Spectroscopy. J. Opt. Soc. Am. B 1995, 12, 2467–2474. 1910
dx.doi.org/10.1021/jz200811p |J. Phys. Chem. Lett. 2011, 2, 1904–1911
The Journal of Physical Chemistry Letters (35) Hildebrandt, P.; Stockburger, M. Surface-Enhanced Resonance Raman Spectroscopy of Rhodamine 6G Adsorbed on Colloidal Silver. J. Phys. Chem. 1984, 88, 5935–5944. (36) Lucassen, G. W.; do Boeij, W. P.; Greve, J. Polarization-Sensitive CARS of Excited-State Rhodamine 6G: Induced Anisotropy Effects on Depolarization Ratios. Appl. Spectrosc. 1993, 47, 1975–1988. (37) Vogel, E.; Gbureck, A.; Kiefer, W. Vibrational Spectroscopic Studies on the Dyes Cresyl Violet and Coumarin 152. J. Mol. Struct. 2000, 550 551, 177–190. (38) Fuji, T.; Saito, T.; Kobayashi, T. Dynamical Observation of Duschinksy Rotation by Sub-5-fs Real-Time Spectroscopy. Chem. Phys. Lett. 2000, 332, 324–330. (39) Huo, P.; Coker, D. F. Theoretical Study of Coherent Excitation Energy Transfer in Cryptophyte Phycocyanin 645 at Physiological Temperature. J. Phys. Chem. Lett. 2011, 2, 825–833. (40) Kneip, C.; Parbel, A.; Foerstendorf, H.; Scheer, H.; Seibert, F.; Hildebrandt, P. Fourier Transform Near-Infrared Resonance Raman Spectroscopy Study of the Alpha-Subunit of Phycoerythrocyanin and Phycocyanin from the Cyanobacterium Mastigocladus laminosus. J. Raman Spectrosc. 1998, 29, 939–944. (41) Shim, S.; Stuart, C. M.; Mathies, R. A. Resonance Raman CrossSections and Vibronic Analysis of Rhodamine 6G from Broadband Stimulated Raman Spectroscopy. ChemPhysChem 2008, 9, 697–699. (42) Tokmakoff, A. Two-Dimensional Line Shapes Derived from Coherent Third-Order Nonlinear Spectroscopy. J. Phys. Chem. A 2000, 104, 4247–4255. (43) Mukamel, S. Principles of Nonlinear Optical Spectroscopy; Oxford University Press: New York, 1995. (44) Turner, D. B.; Stone, K. W.; Gundogdu, K.; Nelson, K. A. Three-Dimensional Electronic Spectroscopy of Excitons in GaAs Quantum Wells. J. Chem. Phys. 2009, 131, 144510. (45) Fidler, A. F.; Harel, E.; Engel, G. S. Dissecting Hidden Couplings Using Fifth-Order Three-Dimensional Electronic Spectroscopy. J. Phys. Chem. Lett. 2010, 1, 2876–2880. (46) Ginsberg, N. S.; Davis, J. A.; Ballottari, M.; Cheng, Y.-C.; Bassi, R.; Fleming, G. R. Solving Structure in the CP29 Light Harvesting Complex With Polarization-Phased 2D Electronic Spectroscopy. Proc. Natl. Acad. Sci. U.S.A. 2011, 108, 3848–3853. (47) Bristow, A. D.; Karaiskaj, D.; Dai, X.; Mirin, R. P.; Cundiff, S. T. Polarization Dependence of Semiconductor Exciton and Biexciton Contributions to Phase-Resolved Optical Two-Dimensional FourierTransform Spectra. Phys. Rev. B 2009, 79, 161305(R). (48) Wilhelm, T.; Piel, J.; Riedle, E. Sub-20-fs Pulses Tunable Across the Visible from a Blue-Pumped Single-Pass Noncollinear Parametric Converter. Opt. Lett. 1997, 22, 1494–1497. (49) Johnson, P. J. M.; Prokhorenko, V. I.; Miller, R. J. D. Enhanced Bandwidth Noncollinear Optical Parametric Amplification with a Narrowband Anamorphic Pump. Opt. Lett. 2011, 36, 2170–2072. (50) Akturk, S.; Gu, X.; Kimmel, M.; Trebino, R. Extremely Simple SinglePrism Ultrashort-Pulse Compressor. Opt. Express 2006, 14, 10101–10108. (51) Fork, R. L.; Brito Cruz, C. H.; Becker, P. C.; Shank, C. V. Compression of Optical Pulses to Six Femtoseconds by Using Cubic Phase Compensation. Opt. Lett. 1987, 12, 483–485. (52) Nemeth, A.; Sperling, J.; Hauer, J.; Kauffmann, H. F.; Milota, F. Compact Phase-Stable Design for Single- and Double-Quantum TwoDimensional Electronic Spectroscopy. Opt. Lett. 2009, 34, 3301–3303. (53) Brixner, T.; Mancal, T.; Stiopkin, I. V.; Fleming, G. R. PhaseStabilized Two-Dimensional Electronic Spectroscopy. J. Chem. Phys. 2004, 121, 4221–36. (54) Prokhorenko, V. I.; Halpin, A.; Miller, R. J. D. CoherentlyControlled Two-Dimensional Photon Echo Electronic Spectroscopy. Opt. Express 2009, 17, 9764–79. (55) Hybl, J. D.; Albrecht, A. W.; Gallagher Faeder, S. M.; Jonas, D. M. Two-Dimensional Electronic Spectroscopy. Chem. Phys. Lett. 1998, 297, 307–313. (56) Turner, D. B.; Stone, K. W.; Gundogdu, K.; Nelson, K. A. Invited Article: The COLBERT Spectrometer: Coherent Multidimensional Spectroscopy Made Easier. Rev. Sci. Instrum. 2011, in press.
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(57) Bristow, A. D.; Karaiskaj, D.; Dai, X.; Cundiff, S. T. All-Optical Retrieval of the Global Phase for Two-Dimensional Fourier-Transform Spectroscopy. Opt. Express 2008, 16, 18017–27. (58) Backus, E. H. G.; Garrett-Roe, S.; Hamm, P. Phasing Problem of Heterodyne-Detected Two-Dimensional Infrared Spectroscopy. Opt. Lett. 2008, 33, 2665–7. (59) Maznev, A. A.; Crimmins, T. F.; Nelson, K. A. How to Make Femtosecond Pulses Overlap. Opt. Lett. 1998, 23, 1378–80. (60) Albrecht, A. W.; Hybl, J. D.; Gallagher Faeder, S. M.; Jonas, D. M. Experimental Distinction Between Phase Shifts and Time Delays: Implications for Femtosecond Spectroscopy and Coherent Control of Chemical Reactions. J. Chem. Phys. 1999, 111, 10934–10956.
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