The integrated photon echo and solvation dynamics. II. Peak shifts and two-dimensional photon echo of a coupled chromophore system

Quantum diffusion wave-function approach to two-dimensional vibronic spectroscopy

We apply the quantum diffusion wavefunction approach to calculate vibronic two-dimensional (2D) spectra. As an example, we use a system consisting of two electronic states with harmonic oscillator potentials which are coupled to a bath and interact with three time-delayed laser pulses. The first- and second-order perturbative wave functions which enter into the expression for the third-order polarization are determined for a sufficient number of stochastic runs. The wave-packet approach, besides being an alternative technique to calculate the spectra, offers an intuitive insight into the dissipation dynamics and its relation to the 2D vibronic spectra.

Pseudo-rephasing and pseudo-free-induction-decay mechanism in two-color three-pulse photon echo of a binary system

We investigate the two-color three-pulse photon echo peak shift in a (left-right) binary system, where each component consists of a heterodimer. On the basis of the model, we find that the effect of the excitonic asymmetry between two components leads to an additional factor in the peak shift. A pseudo-rephasing and pseudo-free-induction-decay mechanism is proposed to explain the resultant negative peak shift, when the differences between the two left/right components have the opposite sign. In such a case, estimates of the electronic coupling strength via two- and one-color peak shift experiments lead to an underestimate of the coupling magnitude.

Molecular decision trees realized by ultrafast electronic spectroscopy

The outcome of a light-matter interaction depends on both the state of matter and the state of light. It is thus a natural setting for implementing bilinear classical logic. A description of the state of a time-varying system requires measuring an (ideally complete) set of time-dependent observables. Typically, this is prohibitive, but in weak-field spectroscopy we can move toward this goal because only a finite number of levels are accessible. Recent progress in nonlinear spectroscopies means that nontrivial measurements can be implemented and thereby give rise to interesting logic schemes where the outputs are functions of the observables. Lie algebra offers a natural tool for generating the outcome of the bilinear light-matter interaction. We show how to synthesize these ideas by explicitly discussing three-photon spectroscopy of a bichromophoric molecule for which there are four accessible states. Switching logic would use the on-off occupancies of these four states as outcomes. Here, we explore the use of all 16 observables that define the time-evolving state of the bichromophoric system. The bilinear laser-system interaction with the three pulses of the setup of a 2D photon echo spectroscopy experiment can be used to generate a rich parallel logic that corresponds to the implementation of a molecular decision tree. Our simulations allow relaxation by weak coupling to the environment, which adds to the complexity of the logic operations.

Three-pulse photon echo of finite numbers of molecules: single-molecule traces

In conventional bulk nonlinear spectroscopy, the contribution from molecules with different environmental conditions sometimes conceals the properties of interest and prevents the assessment of the heterogeneity of complex systems. This is especially true when exploring mechanisms of coherence loss in multicomponent systems [Ishizaki and Fleming, J. Phys. Chem. B 2011, 115, 6227]. To avoid this drawback of ensemble measurements and evaluate single-molecule behavior, a quantum theory is proposed to study the three-pulse photon echo signal of a two-level system in a bath and reveal the fluctuations inherent to single molecules. The current method takes advantage of the coherent state representation to understand the photon echo experiment in a wave function formalism rather than the reduced density matrix. Information regarding the environmental degrees of freedom (DoF) is explicitly encoded in the initial state of the system plus bath. The thermal fluctuations of the initial states induce variation of the photon echo signal, which is clearly different from the ensemble average echo signal. We use our formalism to demonstrate the recovery of the conventional ensemble response signal from the single-molecule signal.

Conformation and electronic population transfer in membrane-supported self-assembled porphyrin dimers by 2D fluorescence spectroscopy

Two-dimensional fluorescence spectroscopy (2D FS) is applied to determine the conformation and femtosecond electronic population transfer in a dimer of magnesium meso tetraphenylporphyrin. The dimers are prepared by self-assembly of the monomer within the amphiphilic regions of 1,2-distearoyl-sn-glycero-3-phosphocholine liposomes. A theoretical framework to describe 2D FS experiments is presented, and a direct comparison is made between the observables of this measurement and those of 2D electronic spectroscopy (2D ES). The sensitivity of the method to varying dimer conformation is explored. A global multivariable fitting analysis of linear and 2D FS data indicates that the dimer adopts a "bent T-shaped" conformation. Moreover, the manifold of singly excited excitons undergoes rapid electronic dephasing and downhill population transfer on the time scale of ∼95 fs. The open conformation of the dimer suggests that its self-assembly is favored by an increase in entropy of the local membrane environment.

Two-dimensional vibronic spectroscopy of coherent wave-packet motion

We theoretically study two-dimensional (2D) spectroscopic signals obtained from femtosecond pulse interactions with diatomic molecules. The vibrational wave-packet dynamics is monitored in the signals. During the motion in anharmonic potentials the wave packets exhibit vibrational revivals and fractional revivals which are associated with particular quantum phases. The time-dependent phase changes are identified by inspection of the complex-valued 2D spectra. We use the Na(2) molecule as a numerical example and discuss various pulse sequences which yield information about vibrational level structure and phase relationships in different electronic states.

Two-dimensional spectroscopy can distinguish between decoherence and dephasing of zero-quantum coherences

Recent experiments on a variety of photosynthetic antenna systems have revealed that coherences among electronic states persist longer than previously anticipated. In an ensemble measurement, the observed dephasing of a coherent state can occur because of either disorder across the ensemble or decoherence from interactions with the bath. Distinguishing how much such disorder affects the experimentally observed dephasing rate is paramount for understanding the role that quantum coherence may play in energy transfer through these complexes. Here, we show that two-dimensional electronic spectra can distinguish between the limiting cases of homogeneous dephasing (decoherence) and inhomogeneous dephasing by examining how the quantum beat frequency changes within a cross peak. For the antenna complex LH2 isolated from Rhodobacter sphaeroides , we find that dephasing of the coherence between the B850 and B800 rings arises predominantly from inhomogeneity. In contrast, within the Fenna-Matthews-Olson (FMO) complex from Chlorobium tepidum , dephasing of the coherence between the first two excitons appears quite homogeneous. Thus, the observed dephasing rate sets an upper bound on decoherence for the LH2 complex while establishing both an upper and lower bound for the FMO complex.

Conformation of self-assembled porphyrin dimers in liposome vesicles by phase-modulation 2D fluorescence spectroscopy

By applying a phase-modulation fluorescence approach to 2D electronic spectroscopy, we studied the conformation-dependent exciton coupling of a porphyrin dimer embedded in a phospholipid bilayer membrane. Our measurements specify the relative angle and separation between interacting electronic transition dipole moments and thus provide a detailed characterization of dimer conformation. Phase-modulation 2D fluorescence spectroscopy (PM-2D FS) produces 2D spectra with distinct optical features, similar to those obtained using 2D photon-echo spectroscopy. Specifically, we studied magnesium meso tetraphenylporphyrin dimers, which form in the amphiphilic regions of 1,2-distearoyl-sn-glycero-3-phosphocholine liposomes. Comparison between experimental and simulated spectra show that although a wide range of dimer conformations can be inferred by either the linear absorption spectrum or the 2D spectrum alone, consideration of both types of spectra constrain the possible structures to a "T-shaped" geometry. These experiments establish the PM-2D FS method as an effective approach to elucidate chromophore dimer conformation.

Two-dimensional terahertz correlation spectra of electronic excitations in semiconductor quantum wells

We discuss a novel approach for nonlinear two-dimensional (2D) spectroscopy in the terahertz (THz) frequency range which is based on a collinear interaction geometry of a sequence of THz pulses with the sample. The nonlinear polarization is determined by a phase-resolved measurement of the electric field transmitted through the sample as a function of the delay τ between two phase-locked pulses and the "real" time t. The information provided by a single 2D scan along the τ and t axes is equivalent to that from a noncollinear photon-echo setup equipped with four local oscillators, each interacting with a different diffracted order. We address basic concepts of collinear 2D THz spectroscopy, in particular data analysis and phasing issues. Different rephasing and nonrephasing contributions to the third-order response are separated and 2D correlation spectra derived. As a prototype application, 2D correlation spectra of intersubband excitations of electrons in semiconductor quantum wells are presented.

Real-time mapping of electronic structure with single-shot two-dimensional electronic spectroscopy

Electronic structure and dynamics determine material properties and behavior. Important time scales for electronic dynamics range from attoseconds to milliseconds. Two-dimensional optical spectroscopy has proven an incisive tool to probe fast spatiotemporal electronic dynamics in complex multichromophoric systems. However, acquiring these spectra requires long point-by-point acquisitions that preclude observations on the millisecond and microsecond time scales. Here we demonstrate that imaging temporally encoded information within a homogeneous sample allows mapping of the evolution of the electronic Hamiltonian with femtosecond temporal resolution in a single-laser-shot, providing real-time maps of electronic coupling. This method, which we call GRadient-Assisted Photon Echo spectroscopy (GRAPE), eliminates phase errors deleterious to Fourier spectroscopies while reducing the acquisition time by orders of magnitude using only conventional optical components. In analogy to MRI in which magnetic field gradients are used to create spatial correlation maps, GRAPE spectroscopy takes advantage of a similar type of spatial encoding to construct electronic correlation maps. Unlike magnetic resonance, however, this spatial encoding of the nonlinear polarization along the excitation frequency axis of the two-dimensional spectrum results in no loss in signal while simultaneously reducing overall noise. Correlating the energy transfer events and electronic coupling occurring in tens of femtoseconds with slow dynamics on the subsecond time scale is fundamentally important in photobiology, solar energy research, nonlinear spectroscopy, and optoelectronic device characterization.

Two-dimensional electronic spectroscopy of molecular aggregates

The properties of molecular aggregates, coupled clusters of small molecules, are often challenging to unravel because of their inherent complexity and disordered environments. Their structure-function relationships are often far from obvious. However, their ability to efficiently channel excitation energy over remarkable distances, as is the case in photosynthetic light harvesting, is a compelling motivation to investigate them. Understanding and subsequently mimicking the processes in photosynthesis, for example, will set the stage for considerable advances in using light harvesting to fuel renewable energy technologies. Two-dimensional (2D) electronic spectroscopy is emerging as a nonlinear optical technique that provides significant insight into the interactions and dynamics of complex molecular systems. In addition to spectrally resolving excitation and emission energies over significant bandwidths with femtosecond resolution, this technique has already enabled discoveries about the structure and dynamics of photosynthetic light-harvesting complexes and other aggregates. Multiple capabilities unique to 2D electronic spectroscopy enable such findings. For example, the spectral resolution of excitation and emission combined with the ability to eliminate the effects of static disorder can reveal the homogeneous line width of a transition and the different dynamic contributions to it. Two dimensional spectroscopy is also sensitive to electronic coherence and has been employed to identify and characterize coherent excitation energy transfer dynamics in photosynthetic systems and conjugated polymers. The presence of cross-peaks, signals for which excitation and emission occur at different wavelengths, provides multiple forms of information. First, it allows the identification of states in congested spectra and reveals correlations between them. Second, we can track excitation energy flow from origin to terminus through multiple channels simultaneously. Finally, 2D electronic spectroscopy is uniquely sensitive to intermolecular electronic coupling through the sign and amplitude of the cross-peaks. This feature makes it possible to reveal spatial molecular configurations by probing electronic transitions. Another means of "resolving" these angstrom-scale arrangements is to manipulate the probing laser pulse polarizations. In this way, we can isolate and modulate specific processes in order to retrieve structural information. In this Account, we demonstrate these capabilities through a close collaboration between experiments and modeling on isolated photosynthetic pigment-protein complexes and also on J-aggregates. Each of the probed systems we describe offers insights that have both increased the utility of 2D electronic spectroscopy and led to discoveries about the molecular aggregates' dynamics and underlying structure.

Pigment organization and energy level structure in light-harvesting complex 4: insights from two-dimensional electronic spectroscopy

Photosynthetic light-harvesting antennae direct energy collected from sunlight to reaction centers with remarkable efficiency and rapidity. Despite their common function, the pigment-protein complexes that make up antenna systems in different types of photosynthetic organisms exhibit a wide variety of structural forms. Some individual organisms express different types of complexes depending on growth conditions. For example, purple photosynthetic bacteria Rp. palustris preferentially synthesize light-harvesting complex 4 (LH4), a structural variant of the more common and widely studied LH2, when grown under low-light conditions. Here, we investigate the ultrafast dynamics and energy level structure of LH4 using two-dimensional (2D) electronic spectroscopy in combination with theoretical simulations. The experimental data reveal dynamics on two distinct time scales, consistent with coherent dephasing within approximately the first 100 fs, followed by relaxation of population into lower-energy states on a picosecond time scale. We observe excited state absorption (ESA) features marking the existence of high-energy dark states, which suggest that the strongest dipole-dipole coupling in the complex occurs between bacteriochlorophyll transition dipole moments in an in-line geometry. The results help to refine the current understanding of the pigment organization in the LH4 complex, for which a high-resolution crystal structure is not yet available.

Dynamics of light harvesting in photosynthesis

We review recent theoretical and experimental advances in the elucidation of the dynamics of light harvesting in photosynthesis, focusing on recent theoretical developments in structure-based modeling of electronic excitations in photosynthetic complexes and critically examining theoretical models for excitation energy transfer. We then briefly describe two-dimensional electronic spectroscopy and its application to the study of photosynthetic complexes, in particular the Fenna-Matthews-Olson complex from green sulfur bacteria. This review emphasizes recent experimental observations of long-lasting quantum coherence in photosynthetic systems and the implications of quantum coherence in natural photosynthesis.

Fluorescence-detected two-dimensional electronic coherence spectroscopy by acousto-optic phase modulation

Two-dimensional electronic coherence spectroscopy (ECS) is an important method to study the coupling between distinct optical modes of a material system. Such studies often involve excitation using a sequence of phased ultrashort laser pulses. In conventional approaches, the delays between pulse temporal envelopes must be precisely monitored or maintained. Here, we introduce a new experimental scheme for phase-selective nonlinear ECS, which combines acousto-optic phase modulation with ultrashort laser excitation to produce intensity modulated nonlinear fluorescence signals. We isolate specific nonlinear signal contributions by synchronous detection, with respect to appropriately constructed references. Our method effectively decouples the relative temporal phases from the pulse envelopes of a collinear train of four sequential pulses. We thus achieve a robust and high signal-to-noise scheme for phase-selective ECS to investigate the resonant nonlinear optical response of photoluminescent systems. We demonstrate the validity of our method using a model quantum three-level system-atomic Rb vapor. Moreover, we show how our measurements determine the resonant complex-valued third-order susceptibility.

Adiabatic Passage in a Three-State System with Non-Markovian Relaxation: The Role of Excited-State Absorption and Two-Exciton Processes

The influence of excited-state absorption (ESA) and two-exciton processes on a coherent population transfer with intense ultrashort chirped pulses in molecular systems in solution has been studied. A unified treatment of adiabatic rapid passage (ARP) in such systems has been developed using a three-state electronic system with relaxation treated as a diffusion on electronic potential energy surfaces. We have shown that ESA has a profound effect on coherent population transfer in large molecules that necessitates a more accurate interpretation of experimental data. A simple and physically clear model for ARP in molecules with three electronic states in solution has been developed by extending the Landau-Zener calculations putting in a third level to random crossing of levels. A method for quantum control of two-exciton states in molecular complexes has been proposed.

Efficient Simulation of Three-Pulse Photon-Echo Signals with Application to the Determination of Electronic Coupling in a Bacterial Photosynthetic Reaction Center

A time-nonlocal quantum master equation coupled with a perturbative scheme to evaluate the third-order polarization in the phase-matching direction k(s) = -k(1) + k(2) + k(3) is used to efficiently simulate three-pulse photon-echo signals. The present method is capable of describing photon-echo peak shifts including pulse overlap and bath memory effects. In addition, the method treats the non-Markovian evolution of the density matrix and the third-order polarization in a consistent manner, thus is expected to be useful in systems with rapid and complex dynamics. We apply the theoretical method to describe one- and two-color three-pulse photon-echo peak shift experiments performed on a bacterial photosynthetic reaction center and demonstrate that, by properly incorporating the pulse overlap effects, the method can be used to describe simultaneously all peak shift experiments and determine the electronic coupling between the localized Q(y) excitations on the bacteriopheophytin (BPhy) and accessory bateriochlorophyll (BChl) in the reaction center. A value of J = 250 cm(-1) is found for the coupling between BPhy and BChl.

Cross-peak-specific two-dimensional electronic spectroscopy

Intermolecular electronic coupling dictates the optical properties of molecular aggregate systems. Of particular interest are photosynthetic pigment-protein complexes that absorb sunlight then efficiently direct energy toward the photosynthetic reaction center. Two-dimensional (2D) ultrafast spectroscopy has been used widely in the infrared (IR) and increasingly in the visible to probe excitonic couplings and observe dynamics, but the off-diagonal spectral signatures of coupling are often obscured by broad diagonal peaks, especially in the visible regime. Rotating the polarizations of the laser pulses exciting the sample can highlight certain spectral features, and the use of polarized pulse sequences to elucidate cross-peaks in 2D spectra has been demonstrated in the IR for vibrational transitions. Here we develop 2D electronic spectroscopy using cross-peak-specific pulse polarization conditions in an investigation of the Fenna-Matthews-Olson light harvesting complex from green photosynthetic bacteria. Our measurements successfully highlight off-diagonal features of the 2D spectra and, in combination with an analysis based on the signs of features arising from particular energy level pathways and theoretical simulation, we characterize the dominant response pathways responsible for the spectral features. Cross-peak-specific 2D electronic spectroscopy provides insight into the interchromophore couplings, as well as into the energetic pathways giving rise to the signal. With femtosecond resolution, we also observe dynamical processes that depend on these couplings and interactions with the protein environment.

Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems

Photosynthetic complexes are exquisitely tuned to capture solar light efficiently, and then transmit the excitation energy to reaction centres, where long term energy storage is initiated. The energy transfer mechanism is often described by semiclassical models that invoke 'hopping' of excited-state populations along discrete energy levels. Two-dimensional Fourier transform electronic spectroscopy has mapped these energy levels and their coupling in the Fenna-Matthews-Olson (FMO) bacteriochlorophyll complex, which is found in green sulphur bacteria and acts as an energy 'wire' connecting a large peripheral light-harvesting antenna, the chlorosome, to the reaction centre. The spectroscopic data clearly document the dependence of the dominant energy transport pathways on the spatial properties of the excited-state wavefunctions of the whole bacteriochlorophyll complex. But the intricate dynamics of quantum coherence, which has no classical analogue, was largely neglected in the analyses-even though electronic energy transfer involving oscillatory populations of donors and acceptors was first discussed more than 70 years ago, and electronic quantum beats arising from quantum coherence in photosynthetic complexes have been predicted and indirectly observed. Here we extend previous two-dimensional electronic spectroscopy investigations of the FMO bacteriochlorophyll complex, and obtain direct evidence for remarkably long-lived electronic quantum coherence playing an important part in energy transfer processes within this system. The quantum coherence manifests itself in characteristic, directly observable quantum beating signals among the excitons within the Chlorobium tepidum FMO complex at 77 K. This wavelike characteristic of the energy transfer within the photosynthetic complex can explain its extreme efficiency, in that it allows the complexes to sample vast areas of phase space to find the most efficient path.

One- and Two-Color Photon Echo Peak Shift Studies of Photosystem I

Wavelength-dependent one- and two-color photon echo peak shift spectroscopy was performed on the chlorophyll Qy band of trimeric photosystem I from Thermosynechococcus elongatus. Sub-100 fs energy transfer steps were observed in addition to longer time scales previously measured by others. In the main PSI absorption peak (675-700 nm), the peak shift decays more slowly with increasing wavelength, implying that energy transfer between pigments of similar excitation energy is slower for pigments with lower site energies. In the far-red region (715 nm), the decay of the peak shift is more rapid and is complete by 1 ps, a consequence of the strong electron-phonon coupling present in this spectral region. Two-color photon echo peak shift data show strong excitonic coupling between pigments absorbing at 675 nm and those absorbing at 700 nm. The one- and two-color peak shifts were simulated using the previously developed energy transfer model (J. Phys. Chem. B 2002, 106, 10251; Biophysical Journal 2003, 85, 140). The simulations agree well with the experimental data. Two-color photon echo peak shift is shown to be far more sensitive to variations in the molecular Hamiltonian than one-color photon echo peak shift spectroscopy.

Two-dimensional optical three-pulse photon echo spectroscopy. II. Signatures of coherent electronic motion and exciton population transfer in dimer two-dimensional spectra

Using the nonperturbative approach to the calculation of nonlinear optical spectra developed in a foregoing paper [Mancal et al., J. Chem. Phys. 124, 234504 (2006), preceding paper], calculations of two-dimensional electronic spectra of an excitonically coupled dimer model system are presented. The dissipative exciton transfer dynamics is treated within the Redfield theory and energetic disorder within the molecular ensemble is taken into account. The manner in which the two-dimensional spectra reveal electronic couplings in the aggregate system and the evolution of the spectra in time is studied in detail. Changes in the intensity and shape of the peaks in the two-dimensional relaxation spectra are related to the coherent and dissipative dynamics of the system. It is shown that coherent electronic motion, an electronic analog of a vibrational wave packet, can manifest itself in two-dimensional optical spectra of molecular aggregate systems as a periodic modulation of both the diagonal and off-diagonal peaks.

Two-dimensional electronic spectra of symmetric dimers: Intermolecular coupling and conformational states

We study the information content of two-dimensional (2D) electronic photon-echo (PE) spectra, with special emphasis on their potential to distinguish, for waiting times T=0, between different conformations of electronically coupled symmetric dimers. The analysis is performed on the basis of an analytical formula for the frequency-domain 2D PE signal. The symmetric dimers are modeled in terms of two identical, energy-degenerate, excitonically coupled pairs of electronic states in the site representation. The spectra of conformationally weighted ensembles, composed of either two or four dimers, are compared with their one-dimensional linear absorption counterparts. In order to provide a realistic coupling pattern for the ensemble consisting of four dimers, excitonic couplings are estimated on the basis of optimized geometries and site-transition dipole moments, calculated by standard semiempirical methods for the bridged bithiophene structure 1,2-bithiophene-2-yl-ethane-1,2-dion (T2[CO]2). In the framework of our model, the highly readable 2D PE spectra can unambiguously identify spectral doublets, by relating peak heights and positions with mutual orientations of site-localized transition dipoles.

Anti-Correlated Spectral Motion in Bisphthalocyanines: Evidence for Vibrational Modulation of Electronic Mixing

We exploit a coherently excited nuclear wave packet to study nuclear motion modulation of electronic structure in a metal bridged phthalocyanine dimer, lutetium bisphthalocyanine, which displays two visible absorption bands. We find that the nuclear coordinate influences the energies of the underlying exciton and charge resonance states as well as their interaction; the interplay of the various couplings creates unusual anti-correlated spectral motion in the two bands. Excited state relaxation dynamics are the same regardless of which transition is pumped, with decay time constants of 1.5 and 11 ps. The dynamics are analyzed using a three-state kinetic model after relaxation from one or two additional states faster than the experimental time resolution of 50-100 fs.