Niklas Christensson

Origin of Long-Lived Coherences in Light-Harvesting Complexes

A vibronic exciton model is applied to explain the long-lived oscillatory features in the two-dimensional (2D) electronic spectra of the Fenna–Matthews–Olson (FMO) complex. Using experimentally determined parameters and uncorrelated site energy fluctuations, the model predicts oscillations with dephasing times of 1.3 ps at 77 K, which is in a good agreement with the experimental results. These long-lived oscillations originate from the coherent superposition of vibronic exciton states with dominant contributions from vibrational excitations on the same pigment. The oscillations obtain a large amplitude due to excitonic intensity borrowing, which gives transitions with strong vibronic character a significant intensity despite the small Huang–Rhys factor. Purely electronic coherences are found to decay on a 200 fs time scale.

Enhancement of vibronic and ground-state vibrational coherences in 2D spectra of photosynthetic complexes.

A vibronic-exciton model is applied to investigate the recently proposed mechanism of enhancement of coherent oscillations due to mixing of electronic and nuclear degrees of freedom. We study a dimer system to elucidate the role of resonance coupling, site energies, vibrational frequency and energy disorder in the enhancement of vibronic-exciton and ground-state vibrational coherences, and to identify regimes where this enhancement is significant. For a heterodimer representing two coupled bachteriochloropylls of the FMO complex, long-lived vibronic coherences are found to be generated only when the frequency of the mode is in the vicinity of the electronic energy difference. Although the vibronic-exciton coherences exhibit a larger initial amplitude compared to the ground-state vibrational coherences, we conclude that, due to the dephasing of the former, both type of coherences have a similar magnitude at longer population time.

High Frequency Vibrational Modulations in Two-Dimensional Electronic Spectra and Their Resemblance to Electronic Coherence Signatures

In this work we analyze how nuclear coherences modulate diagonal and off-diagonal peaks in two-dimensional electronic spectroscopy. 2D electronic spectra of pinacyanol chloride are measured with 8 fs pulses, which allows coherent excitation of the 1300 cm(-1) vibrational mode. The 2D spectrum reveals both diagonal and off-diagonal peaks related to the vibrational mode. On early time scales, up to 30 fs, coherent dynamics give rise to oscillations in the amplitudes, positions, and shapes of the peaks in the 2D spectrum. We find an anticorrelation between the amplitude and the diagonal width of the two diagonal peaks. The measured data are reproduced with a model incorporating a high frequency mode coupled to an electronic two-level-system. Our results show that these anticorrelated oscillations occur for vibrational wavepackets and not exclusively for electronic coherences as has been assumed previously.

System-Dependent Signatures of Electronic and Vibrational Coherences in Electronic Two-Dimensional Spectra.

In this work, we examine vibrational coherence in a molecular monomer, where time evolution of a nuclear wavepacket gives rise to oscillating diagonal- and off-diagonal peaks in two-dimensional electronic spectra. We find that the peaks oscillate out-of-phase, resulting in a cancellation in the corresponding pump-probe spectra. Our results confirm the unique disposition of two-dimensional electronic spectroscopy (2D-ES) for the study of coherences. The oscillation pattern is in excellent agreement with the diagrammatic analysis of the third-order nonlinear response. We show how 2D-ES can be used to distinguish between ground- and excited-state wavepackets. On the basis of our results, we discuss coherences in coupled molecular aggregates involving both electronic and nuclear degrees of freedom. We conclude that a general distinguishing criterion based on the experimental data alone cannot be devised.

Two-dimensional electronic spectroscopy of beta-carotene.

Two-dimensional electronic spectroscopy (2D) has been applied to beta-carotene in solution to shine new light on the ultrafast energy dissipation network in carotenoids. The ability of 2D to relieve spectral congestion provides new experimental grounds for resolving the rise of the excited state absorption signal between 18,000 and 19,000 cm(-1). In this spectral region, the pump-probe signals from ground state bleach and stimulated emission overlap strongly. Combined modeling of the time-evolution of 2D spectra as well as comparison to published pump-probe data allow us to draw conclusions on both the electronic structure of beta-carotene as well as the spectral densities giving rise to the observed optical lineshapes. To account for the experimental observations on all time scales, we need to include a transition in the visible spectral range from the first optically allowed excited state (S(2)-->S(n2)). We present data from frequency resolved transient grating and pump-probe experiments confirming the importance of this transition. Furthermore, we investigate the role and nature of the S* state, controversially debated in numerous previous studies. On the basis of the analysis of Feynman diagrams, we show that the properties of S*-related signals in chi(3) techniques like pump-probe and 2D can only be accounted for if S* is an excited electronic state. Against this background, we discuss a new interpretation of pump-deplete-probe and intensity-dependent pump-probe experiments.

Ultrafast photo-induced charge transfer unveiled by two-dimensional electronic spectroscopy

The interaction of exciton and charge transfer (CT) states plays a central role in photo-induced CT processes in chemistry, biology, and physics. In this work, we use a combination of two-dimensional electronic spectroscopy (2D-ES), pump-probe measurements, and quantum chemistry to investigate the ultrafast CT dynamics in a lutetium bisphthalocyanine dimer in different oxidation states. It is found that in the anionic form, the combination of strong CT-exciton interaction and electronic asymmetry induced by a counter-ion enables CT between the two macrocycles of the complex on a 30 fs timescale. Following optical excitation, a chain of electron and hole transfer steps gives rise to characteristic cross-peak dynamics in the electronic 2D spectra, and we monitor how the excited state charge density ultimately localizes on the macrocycle closest to the counter-ion within 100 fs. A comparison with the dynamics in the radical species further elucidates how CT states modulate the electronic structure and tune fs-reaction dynamics. Our experiments demonstrate the unique capability of 2D-ES in combination with other methods to decipher ultrafast CT dynamics.

Double-quantum two-dimensional electronic spectroscopy of a three-level system: Experiments and simulations

Double-quantum coherence two-dimensional (2Q2D) electronic spectroscopy is utilized to probe the dynamic fluctuations of electronic states in a solvated molecule at approximately twice the energy of the ground state bleach transition. The 2Q2D spectrum gives insight into the energetic position and spectral fluctuations (system-bath interaction) of the probed excited states. Combining it with single-quantum two-dimensional (1Q2D) electronic spectroscopy enables one to determine the strength of the excited state absorption transition and the relative detuning of electronic states, as well as the dynamics of the single-quantum coherence. To investigate the correlation of spectral fluctuations in different electronically excited states, we have carried out experiments on a solvated dye (Rhodamine 6G) with 23 fs pulses centered at the maximum of the linear absorption spectrum. The 2Q2D spectrum reveals three peaks of alternating signs with the major negative peak located at higher frequencies along the emission axis compared to the single positive peak. The 1Q2D spectrum, on the other hand, shows a negative peak stemming from excited state absorption at lower frequencies along the emission axis. Analysis of the signal in the homogeneous limit fails to account for this observation as well as the number of peaks in the 2Q2D spectrum. Employing a three-level model in which all time correlations of the third-order response function are accounted for via second-order cumulant expansion gives good agreement with both the 1Q2D and 2Q2D data. Furthermore, the analysis shows that the fluctuations of the probed electronic states are highly correlated, reflecting the modulation by a common nuclear bath and similarities in the nature of the electronic transitions.

Electronic Double-Quantum Coherences and Their Impact on Ultrafast Spectroscopy: The Example of β-Carotene

The energy level structure and dynamics of biomolecules are important for understanding their photoinduced function. In particular, the role of carotenoids in light-harvesting is heavily studied, yet not fully understood. The conventional approach to investigate these processes involves analysis of the third-order optical polarization in one spectral dimension. Here, we record two-dimensional correlation spectra for different time-orderings to characterize all components of the transient molecular polarization and the optical signal. Single- and double-quantum two-dimensional experiments provide insight into the energy level structure as well as the ultrafast dynamics of solvated β-carotene. By analysis of the lineshapes, we obtain the transition energy and characterize the potential energy surfaces of the involved states. We obtain direct experimental proof for an excited state absorption transition in the visible (S2→Sn2). The signatures of this transition in pump−probe transients are shown to lead to strongly damped oscillations with characteristic pump and probe frequency dependence.

Appearance of intramolecular high-frequency vibrations in two-dimensional, time-integrated three-pulse photon echo data

An alternative experimental outline to measure homodyne detected three-pulse photon-echo data is presented. The novel experimental approach allowing for online monitoring and correction of experimental timing and stability is discussed in detail using the paradigm system of Nile blue in alcohol solution. It is shown that excellent signal-to-noise ratios together with high reproducibility of the data can be routinely achieved. We report in detail on the appearance of high-frequency intramolecular vibrations in the two-dimensional three-pulse photon-echo data and suggest that besides the conventionally discussed three-pulse photon-echo peak-shift the width of the integrated echo signal as a function of population time contains identical and easily accessible information on high-frequency intramolecular vibrations. A comparison of experimental data with theoretical modeling is performed showing that the observed echo-width oscillations are in line with predictions of the Brownian oscillator model.

Probing the strength of the system-bath interaction by three-pulse photon echoes

We explore how the width of the three-pulse photon echo signal at long population times can be used to determine the strength of the system-bath interaction. Using simulation with finite pulses we show that a simple relation exist between the width of the echo signal, the coupling strength, and the pulse autocorrelation. The derived model is applied to Rhodamine 6G in alcoholic solution, a paradigm system for the study of solvation dynamics, and the results are compared to conventional methods. The independently determined coupling strength forms the basis for a computationally inexpensive route to determine the entire spectral density, the key parameter when considering system-bath interactions. Our method allows us to accurately estimate the relative amplitude of fast and slow components in the correlation function using only impulsive limit simulations. We show that the peak shift significantly overestimates the amplitude of the fastest decay component for our experimental data. Changing solvent from methanol to 1-hexanol we observe a narrowing of the width of the echo profile. The changes in the echo width allow us to estimate the changes of the coupling strength in various solvents.