Andrew F. Fidler

Single-Shot Gradient-Assisted Photon Echo Electronic Spectroscopy

Two-dimensional electronic spectroscopy (2D ES) maps the electronic structure of complex systems on a femtosecond time scale. While analogous to multidimensional NMR spectroscopy, 2D optical spectroscopy differs significantly in its implementation. Yet, 2D Fourier spectroscopies still require point-by-point sampling of the time delay between two pulses responsible for creating quantum coherence among states. Unlike NMR, achieving the requisite phase stability at optical frequencies between these pulse pairs remains experimentally challenging. Nonetheless, 2D optical spectroscopy has been successfully demonstrated by combining passive and active phase stabilization along with precise control of optical delays and long-term temperature stability, although the widespread adoption of 2D ES has been significantly hampered by these technical challenges. Here, we exploit an analogy to magnetic resonance imaging (MRI) to demonstrate a single-shot method capable of acquiring the entire 2D spectrum in a single laser shot using only conventional optics. Unlike point-by-point sampling protocols typically used to record 2D spectra, this method, which we call GRadient-Assisted Photon Echo (GRAPE) spectroscopy, largely eliminates phase errors while reducing the acquisition time by orders of magnitude. By incorporating a spatiotemporal encoding of the nonlinear polarization along the excitation frequency axis of the 2D spectrum, GRAPE spectroscopy achieves no loss in signal while simultaneously reducing overall noise. Here, we describe the principles of GRAPE spectroscopy and discuss associated experimental considerations.

Dynamic localization of electronic excitation in photosynthetic complexes revealed with chiral two-dimensional spectroscopy

Time-resolved ultrafast optical probes of chiral dynamics provide a new window allowing us to explore how interactions with such structured environments drive electronic dynamics. Incorporating optical activity into time-resolved spectroscopies has proven challenging due to the small signal and large achiral background. Here, we demonstrate that two-dimensional electronic spectroscopy can be adapted to detect chiral signals and that these signals reveal how excitations delocalize and contract following excitation. We dynamically probe the evolution of chiral electronic structure in the light harvesting complex 2 of purple bacteria following photoexcitation by creating a chiral two-dimensional mapping. The dynamics of the chiral two-dimensional signal directly reports on changes in the degree of delocalization of the excitonic state following photoexcitation. The mechanism of energy transfer in this system may enhance transfer probability due to the coherent coupling among chromophores while suppressing fluorescence that arises from populating delocalized states. This generally applicable spectroscopy will provide an incisive tool to probe ultrafast transient molecular fluctuations that are obscured in non-chiral experiments.

Towards a coherent picture of excitonic coherence in the Fenna?Matthews?Olson complex

Observations of long-lived coherence between excited states in several photosynthetic antenna complexes has motivated interest in developing a more detailed understanding of the role of the protein matrix in guiding the underlying dynamics of the system. These experiments suggest that classical rate laws may not provide an adequate description of the energy transfer process and that quantum effects must be taken into account to describe the near unity transfer efficiency in these systems. Recently, it has been shown that coherences between different pairs of excitons dephase at different rates. These details should provide some insight about the underlying electronic structure of the complex and its coupling to the protein bath. Here we show that a simple model can account for the different dephasing rates as well as the most current available experimental evidence of excitonic coherences in the Fenna–Matthews–Olson complex. The differences in dephasing rates can be understood as arising largely from differences in the delocalization and shared character between the underlying electronic states. We also suggest that the anomalously low dephasing rate of the exciton 1–2 coherence is enhanced by non-secular effects.

Signatures of correlated excitonic dynamics in two-dimensional spectroscopy of the Fenna-Matthew-Olson photosynthetic complex

Long-lived excitonic coherence in photosynthetic proteins has become an exciting area of research because it may provide design principles for enhancing the efficiency of energy transfer in a broad range of materials. In this publication, we provide new evidence that long-lived excitonic coherence in the Fenna-Mathew-Olson pigment-protein (FMO) complex is consistent with the assumption of cross correlation in the site basis, indicating that each site shares bath fluctuations. We analyze the structure and character of the beating crosspeak between the two lowest energy excitons in two-dimensional (2D) electronic spectra of the FMO Complex. To isolate this dynamic signature, we use the two-dimensional linear prediction Z-transform as a platform for filtering coherent beating signatures within 2D spectra. By separating signals into components in frequency and decay rate representations, we are able to improve resolution and isolate specific coherences. This strategy permits analysis of the shape, position, character, and phase of these features. Simulations of the crosspeak between excitons 1 and 2 in FMO under different regimes of cross correlation verify that statistically independent site fluctuations do not account for the elongation and persistence of the dynamic crosspeak. To reproduce the experimental results, we invoke near complete correlation in the fluctuations experienced by the sites associated with excitons 1 and 2. This model contradicts ab initio quantum mechanic∕molecular mechanics simulations that observe no correlation between the energies of individual sites. This contradiction suggests that a new physical model for long-lived coherence may be necessary. The data presented here details experimental results that must be reproduced for a physical model of quantum coherence in photosynthetic energy transfer.

Excited and ground state vibrational dynamics revealed by two-dimensional electronic spectroscopy

Broadband two-dimensional electronic spectroscopy (2DES) can assist in understanding complex electronic and vibrational signatures. In this paper, we use 2DES to examine the electronic structure and dynamics of a long chain cyanine dye (1,1-diethyl-4,4-dicarbocyanine iodide, or DDCI-4), a system with a vibrational progression. Using broadband pulses that span the resonant electronic transition, we measure two-dimensional spectra that show a characteristic six peak pattern from coherently excited ground and excited state vibrational modes. We model these features using a spectral density formalism and the vibronic features are assigned to Feynman pathways. We also examine the dynamics of a particular set of peaks demonstrating anticorrelated peak motion, a signature of oscillatory wavepacket dynamics on the ground and excited states. These dynamics, in concert with the general structure of vibronic two-dimensional spectra, can be used to distinguish between pure electronic and vibrational quantum coherences.

Probing energy transfer events in the light harvesting complex 2 (LH2) of Rhodobacter sphaeroides with two-dimensional spectroscopy

Excitation energy transfer events in the photosynthetic light harvesting complex 2 (LH2) of Rhodobacter sphaeroides are investigated with polarization controlled two-dimensional electronic spectroscopy. A spectrally broadened pulse allows simultaneous measurement of the energy transfer within and between the two absorption bands at 800 nm and 850 nm. The phased all-parallel polarization two-dimensional spectra resolve the initial events of energy transfer by separating the intra-band and inter-band relaxation processes across the two-dimensional map. The internal dynamics of the 800 nm region of the spectra are resolved as a cross peak that grows in on an ultrafast time scale, reflecting energy transfer between higher lying excitations of the B850 chromophores into the B800 states. We utilize a polarization sequence designed to highlight the initial excited state dynamics which uncovers an ultrafast transfer component between the two bands that was not observed in the all-parallel polarization data. We attribute the ultrafast transfer component to energy transfer from higher energy exciton states to lower energy states of the strongly coupled B850 chromophores. Connecting the spectroscopic signature to the molecular structure, we reveal multiple relaxation pathways including a cyclic transfer of energy between the two rings of the complex.

Independent phasing of rephasing and non-rephasing 2D electronic spectra

Assigning absolute phase to two-dimensional (2D) third-order nonlinear optical signals generally requires acquiring both the rephasing and the non-rephasing signals and comparing the sum of the two to spectrally resolved pump-probe spectra. To date, however, Gradient Assisted Photon Echo Spectroscopy (GRAPES) has only been able to acquire rephasing spectra. Such a constraint requires a new phasing protocol. Here, we analytically prove that the rephasing and non-rephasing spectra can be phased independently using pump-probe signal. We verify this result holds even for finite duration pulses by simulation. This relationship holds for all 2D spectroscopies, not only GRAPES. In addition, we present improvements to GRAPES that enable acquisition of rephasing and non-rephasing signals in different phase-matched directions. We employ our phasing protocol to phase the data for laser dye IR-144, leading to reconstruction of purely absorptive 2D spectrum.

Nonlinear Spectroscopic Theory of Displaced Harmonic Oscillators with Differing Curvatures: A Correlation Function Approach

We present a theory for a bath model in which we approximate the adiabatic nuclear potential surfaces on the ground and excited electronic states by displaced harmonic oscillators that differ in curvature. Calculations of the linear and third-order optical response functions employ an effective short-time approximation coupled with the cumulant expansion. In general, all orders of correlation contribute to the optical response, indicating that the solvation process cannot be described as Gaussian within the model. Calculations of the linear absorption and fluorescence spectra resulting from the theory reveal a stronger temperature dependence of the Stokes shift along with a general asymmetry between absorption and fluorescence line shapes, resulting purely from the difference in the phonon side band. We discuss strategies for controlling spectral tuning and energy-transfer dynamics through the manipulation of the excited-state and ground-state curvature. Calculations of the nonlinear response also provide insights into the dynamics of the system-bath interactions and reveal that multidimensional spectroscopies are sensitive to a difference in curvature between the ground- and excited-state adiabatic surfaces. This extension allows for the elucidation of short-time dynamics of dephasing that are accessible in nonlinear spectroscopic methods.

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.

The dependence of exciton transport efficiency on spatial patterns of correlation within the spectral bath

Spatial correlations in spectral bath motions have been proposed to explain long-lived coherence in exciton transport. Systems of interest, ranging from photosynthetic complexes to organic photovoltaics, contain inhomogeneous environments. We consider the possibility that the degree of spatial correlation varies throughout an exciton transport system. We model exciton transport in the Fenna–Matthews–Olson complex (FMO), a photosynthetic light-harvesting complex. Although it remains unclear whether significant spatial correlations exist in FMO, its very high exciton transport efficiency makes it an interesting case for studies of exciton transport. We also simulate a highly symmetric ten-site model system. We use an extension of the environment-assisted quantum transport model to simulate transport, allowing the spatial correlation function to vary throughout the system. We demonstrate both via analysis and via simulation that exciton transport efficiency is most sensitive to changes in correlation between the site coupled to the trap and its neighboring sites. This asymmetry in sensitivity is highly robust and appears irrespective of changes in parameters such as transition dipole orientations and initial conditions. Our results suggest that in the design of exciton transport systems, efforts to increase efficiency by controlling spatial correlation should be focused on the region near the site of exciton trapping.