1. Introduction

Coherent effects in biology have been extensively discussed in the context of efficient energy and electron transfer in photosynthetic systems [1, 2]. A short laser pulse excitation creates a superposition of energy eigenstates of the system, which can in principle allow for the coherent energy or electron transfer. Thus, the coherent transfer hypothesis relies on the existence of coherent electronic superpositions on the time scale of energy transfer. In femtosecond spectroscopy experiments various types of coherences are readily observed as signal amplitude and phase oscillations. Long-lived oscillatory features have been observed for more than two decades in pump probe (PP) experiments and more recently in two-dimensional electronic spectroscopy (2DES) measurements of all studied photosynthetic pigment-protein complexes [3–10].

The origin of the observed oscillations can be very different in nature. Apart from the collective motions of electrons (electronic coherences), excitation can also initiate coherent oscillations of nuclei, giving rise to vibrational coherences in the form of vibrational wave packets in the ground and excited electronic states. Since electrons are three orders of magnitude lighter than nuclei and interact with the environment strongly, electronic coherences are expected to dephase within ~100 fs at least at physiological temperatures. Whereas vibrational coherences can last for picoseconds [11]. Photosynthetic pigments have rich vibrational structure, which is readily observable in resonance Raman (RR) or fluorescence line-narrowing experiments [12, 13]. Therefore, vibrational coherences are expected to be present in photosynthetic complexes and interfere with the electronic coherences [14]. Recently, vibronic mixing between electronic and vibrational degrees of freedom was proposed to play a crucial role in the observed coherences, and coherences excited through vibronically mixed states were identified in 2D spectra [15–19].

It is thus highly important to distinguish between the vibrational, electronic and vibronically mixed coherences before drawing conclusions about the mechanisms of energy and/or electron transfer [45]. Theoretical [14, 20] and analytical [21] tools were developed to this end. Using these ideas, and employing analysis of oscillation maps, three different types of coherences in a large nanoring molecule, featuring well separated multiple transitions were unraveled in a recent 2DES study [22]. Additionally, polarization control in 2DES [23, 24] can in principle lead to the complete suppression of the intramolecular vibrational coherences and thus greatly facilitate separation of coherences [18, 19].

Polarization-controlled 2DES pulse sequences have been applied to a number of light-harvesting systems [7,17–19,25]. It can be seen in these reports that oscillatory features usually have longer lifetimes than the achievable experimental scans, which are usually limited by the sample and/or laser stability [6,7,10,18,19]. Insufficiently long sampling of the coherence oscillations in 2DES leads to a sub-optimal frequency resolution and rather complicated extraction of the dephasing times [18,19]. It is worth noting that alternative schemes of modified 2DES experiments with extended population time scans have been employed to extract specific parts of the nonlinear response (see [26] and references therein).

On the other hand, PP spectroscopy does not require coherence time scanning, and thus allows for much faster acquisition. PP anisotropy measurements have proven valuable for analysis of the coherence oscillations in the past [3, 4, 27]. However, since only two pulses are available for polarization control, PP does not provide complete suppression of the undesirable signals (for example population decays), which is needed for the unambiguous identification of coherences.

To combine the fast PP data acquisition with the flexibility of the polarization control afforded by 2DES, we turned to transient grating (TG) spectroscopy. In this technique three noncollinear excitation pulses are employed, and signal field is emitted in the phase-matched direction, which makes TG, unlike PP, a background-free method [28, 29]. The polarization control of the two excitation pulses in the homodyne TG experiments was implemented already in the eighties [30], and later was used to study dephasing of ground state coherences in sodium flames [31]. In more recent heterodyne-detected TG experiments appropriately attenuated ffourth, so called local oscillator (LO) pulse was introduced to measure spectral interferograms between the signal and LO to improve signal-to-noise ratio, and to enable for the phase-sensitive detection [32, 33, 46]. Such optical arrangement, implemented with a diffractive optics element [32], is at the core of the wide-spread 2DES implementation using boxcar geometry [34].

In this work we implemented an advanced polarization control to the heterodyne-detected TG spectroscopy by manipulating polarization of all four pulses and performing polarization filtering of the signal. Specifically, we used the double-crossed (DC) polarization scheme, previously employed in the 2DES experiments (DC-2D) [7, 25], in the transient grating mode (DC-TG) to separate intermolecular coherences from the intramolecular vibrational ones. In addition to simpler and faster data acquisition (than in the 2DES experiment), we gained high frequency resolution of the beatings and were able to accurately estimate dephasing times, which eluded us before [18].

2. Results

Our implementation of heterodyne-detected TG uses the same experimental scheme as 2DES with only difference being that t₁ delay between the first two excitation pulses is kept constant at zero during the population scans. It has been shown that a projection (integration) of the 2DES signal along the ω₁ frequency (Fourier conjugate of the t₁ delay) in the complex plain corresponds to the heterodyne-detected TG [35]. On the other hand the PP signal corresponds to the projection of the real part of the 2DES signal only [35], and therefore the phase information is inaccessible in the PP experiment.

We demonstrate the heterodyne-detected DC-TG implementation by performing experiments on the photosynthetic reaction centers from purple bacteria Rhodobacter sphaeroides (RC_sph). Coherence signals in RC_sph have been extensively studied, since it represents a model system for energy transfer in a weakly coupled excitonic system, as well as for the charge separation in photosynthesis [3, 4, 7, 18, 36–38]. The RC_sph protein embeds two strongly coupled bacteriochlorophylls a, two accessory bacteriochlorophylls a and two bacteriopheophytins a, all arranged in two nearly symmetric branches [39]. Together they form three excitonic bands denoted P, B and H. The excitation energy is funneled along both branches from H through B towards P, where charge separation is initiated. The reaction centers used in our experiments were chemically oxidized by removing the electron from P. Blocking the electron transfer in this way allowed us to investigate energy transfer dynamics between H, B and oxidized P exclusively [7,18].

In order to access the coherence response only, population-related dynamics were subtracted, and purely oscillating residuals were Fourier transformed to obtain coherence frequencies, which can be compared to the RR spectra [12]. When polarizations of all four pulses are oriented parallel to each other and match the orientation of the linear polarizer placed in the signal, TG — similarly to PP or 2DES — does not provide any selectivity of the contributing oscillatory pathways. Fig. 1 shows a comparison between TG-, RR- and 2DES-extracted frequencies associated with the B excitonic band of RC_sph. We observe very rich spectra with a good match between the frequencies obtained from RR and time-domain TG measurements. Certain modes are even better resolved in TG than in RR (Fig. 1, see e.g. 382 and 402 cm⁻¹ modes). Because of a limited scan range of the population time t₂ in 2DES the obtained spectral lines show substantial broadening. The noticeable relative decrease of the spectral line amplitudes with increasing frequency of the 2DES- and TG-extracted modes in comparison to RR is mainly caused by the limited laser spectrum used in the time-domain experiments [40, 41], but there could also be some effect of the directional filtering [42].

 

Fig. 1 Comparison of the frequency modes associated with the B band (integrated over the whole band) of RC_sph. The resonant Raman spectrum was reproduced from Ref. [12] (dashed line). Similar information about Raman frequencies can be extracted from 2DES, however typically with lower resolution (dotted line). Performing a long scan in TG experiment (solid line) improves the frequency resolution, making it similar to RR. The lower amplitude of the higher-frequency modes in all-parallel polarization 2DES and TG experiments is mainly caused by the spectrally limited pulses.

Download Full Size | PDF

The superior frequency resolution of the coherence signals in the TG experiment is effectively a result of the faster acquisition, which allowed for longer population scans as compared to 2DES experiments. For example, in our previous RC_sph experiments at 77 K [7], a data set consisting of 100 2D spectra typically required 13 hours of data acquisition. Such long acquisition limits the feasible population scan, because of unavoidable instabilities of the laser system. Compared to the 2DES experiments each population time point in TG experiments was measured ~40 times faster (12 s) including 5 averages per data point. The large difference in the scan speed is achieved, because t₁ delay is not scanned in the TG experiment.

We would like to remark here on some differences between the PP and TG measurements. First, heterodyne-detected TG provides signal phase information, thereby allowing for complex Fourier transform over t₂, resulting in separation of the coherence beatings with negative and positive frequencies [20, 21]. In this way, it is possible to fully or partially separate ground state and excited state contributions [19, 22, 40]. Second, it is possible to set t₁ > 0 to measure only rephasing response which is furthermore useful for disentangling contributions from different coherences [14, 26, 43]. However, TG, just like PP, does not provide the resolution along the excitation frequency, and thus oscillating signals at cross-peaks (as seen in 2DES measurements) are mixed in the TG measurements with the oscillating signals at diagonal peaks, which can result in all kind of signal interferences [19, 35].

To address the question which of the observed coherences have intermolecular origin (purely electronic or vibronic coherences, delocalized over two or more molecules, as well as ground state coherences, excited via vibronically coupled excited states [16]), and to separate them from the intramolecular vibrational coherences, the DC pulse sequence is used in 2DES, where polarizations of the four individual pulses are set to (45°, −45°, 90°, 0°). These experiments allow for almost complete suppression of intramolecular vibrations in the isotropically oriented samples. In the 2DES experiments on reaction centers we have achieved a suppression of ~80 times of the intramolecular vibrational coherences and population related signals, and thus only weak oscillating residues stemming mostrly from intermolecular coherences remained [7, 18]. Coherence modes which "survive" the DC pulse sequence have energy close to the splitting between the B and H excitonic bands (∼620 cm⁻¹), which is a prerequisite for vibronically mixed intermolecular coherence. Full account of the photophysical mechanism underlying these long-lived intermolecular coherences is given elsewhere [18]. Here we focus on the question as to whether heterodyne-detected polarization-controlled TG has the same selectivity for intermolecular coherences.

To this end we carried out heterodyne-detected TG measurements with the same polarization settings of all four beams as in DC-2D (Fig. 2A). In Fig. 2B the DC-TG kinetic trace at the detection frequency corresponding to the H band is compared to the DC-2D kinetic trace at the upper cross-peak, with excitation frequency ω₁ = 12500 cm⁻¹ and detection frequency ω₃ = 13100 cm⁻¹, where the B transition is excited and the H transition is probed. This region has been identified as the most unambiguous for exploring mixed vibrational/electronic coherences [40]. Even though the two signals obtained from DC-TG and DC-2D experiments do not have exact correspondence in their origin, as mentioned above, there is almost a perfect match between extracted coherence traces. The relative oscillation amplitudes of the modes in both measurements, as seen in the Fourier amplitude spectra (Fig. 2C), show a good agreement, whereas DC-TG data provides dramatically increased frequency resolution. The accurately determined major frequencies are thus 563 cm⁻¹ and 651 cm⁻¹, whereas they were estimated to be ∼560 cm⁻¹ and ∼650 cm⁻¹, respectively from the 2DES experiment [18].

 

Fig. 2 DC-TG compared to the corresponding DC-2D signal. (A) DC-TG kinetic scan at detection frequency ω₃ = 13100 cm⁻¹ matching the H excitonic transition. (B) Comparison of the DC-TG (solid line) with the DC-2D kinetic trace from the upper B-H cross-peak (dashed line) demonstrates the correspondence between the two. (C) Amplitudes of Fourier transforms carried out on the traces (A, B) identify the coherences excited via vibronically coupled states.

Download Full Size | PDF

Moreover, from the complex fit of the full population time range of the DC-TG data, we were able to extract the lifetimes of the two strongest modes (563 cm⁻¹ and 651 cm⁻¹) as 1.4 ± 0.1 and 2.5 ± 0.1 ps, respectively. These are typical dephasing times for vibrational coherences and are much longer than any expected electronic coherence time. The photophysical explanation of these long-lived coherences has been provided by “energy transfer-induced coherence shift” mechanism [18].

3. Conclusions

We have demonstrated that the heterodyne-detected transient grating technique improves the frequency resolution of oscillatory features (coherences) as compared to 2DES and allows for accurate extraction of their dephasing times. Implementation of the full polarization control in TG experiment allows for identifying electronic coherences or vibrational coherences excited via vibronically coupled states. The demonstrated technique should provide a valuable addition to the spectroscopist’s toolbox, especially in the field of light-harvesting, as the presence of coherences accessed by vibronic mixing points to the importance of vibronic coupling for efficient light-capture [17–19, 44].

4. Methods

The experimental setup has been described in detail previously [7, 47, 48]. Briefly, a compressed output of the lab-built noncollinear optical parametric amplifier working at 20 kHz repetition rate was split into four replicas by use of a plate beamsplitter and dispersive optics element [47]. The first two pulses overlapped in time and created TG, where the third pulse, delayed by the population time t₂, was scattered in the phase matching direction (collinear to the attenuated fourth pulse, LO). The interferograms between the third order signal and LO were measured in a spectrometer. Polarizations of all four pulses were individually set by a quarter-wave plate and wire grid polarizers (contrast ratio ∼800). Dual frequency lock-in detection was used to filter out signal from scattering [47]. Pulses, compressed to ~17 fs, were centered at 770 nm with FWHM ∼1500 cm⁻¹, and were focused to a 160 μm spot. Pulse energies were 2 nJ and 4 nJ per pulse for all-parallel and double-crossed polarization measurements, respectively. TG scans were measured up to 7000 fs with the 5 fs step.

RC_sph were chemically oxidized using potassium hexacyanoferrate (150 mM), mixed with glycerol (65 % v/v ratio), cooled down to 77 K in 0.5 mm fused silica cell to yield maximum absorption of < 0.3 OD at 800 nm [7].