2D ES Research Articles

Ultrabroadband two-dimensional electronic spectroscopy in the pump-probe geometry using conventional optics.

We report ultrabroadband two-dimensional electronic spectroscopy (2D ES) measurements obtained in the pump-probe geometry using conventional optics. A phase-stabilized Michelson interferometer provides the pump-pulse delay interval, τ1, necessary to obtain the excitation-frequency dimension. Spectral resolution of the probe beam provides the detection-frequency dimension, ω3. The interferometer incorporates active phase stabilization via a piezo stage and feedback from interference of a continuous-wave reference laser detected in quadrature. To demonstrate the method, we measured a well-characterized laser dye sample and obtained the known peak structure. The vibronic peaks are modulated as a function of the waiting time, τ2, by vibrational wave packets. The interferometer simplifies ultrabroadband 2D ES measurements and analysis.

Interference among Multiple Vibronic Modes in Two-Dimensional Electronic Spectroscopy

Vibronic coupling between electronic and vibrational states in molecules plays a critical role in most photo-induced phenomena. Many key details about a molecule’s vibronic coupling are hidden in linear spectroscopic measurements, and therefore nonlinear optical spectroscopy methods such as two-dimensional electronic spectroscopy (2D ES) have become more broadly adopted. A single vibrational mode of a molecule leads to a Franck–Condon progression of peaks in a 2D spectrum. Each peak oscillates as a function of the waiting time, and Fourier transformation can produce a spectral slice known as a ‘beating map’ at the oscillation frequency. The single vibrational mode produces a characteristic peak structure in the beating map. Studies of single modes have limited utility, however, because most molecules have numerous vibrational modes that couple to the electronic transition. Interactions or interference among the modes may lead to complicated peak patterns in each beating map. Here, we use lineshape-function theory to simulate 2D ES arising from a system having multiple vibrational modes. The simulations reveal that the peaks in each beating map are affected by all of the vibrational modes and therefore do not isolate a single mode, which was anticipated.

Two-Dimensional Electronic Spectroscopy Reveals the Spectral Dynamics of Förster Resonance Energy Transfer

Summary Two-dimensional electronic spectroscopy (2D ES) probes the energies of chromophores and their coupling, and therefore, the technique is now widely used for studying excitation-energy-transfer mechanisms. The ubiquity and importance of Forster resonance energy transfer (FRET) demand a thorough study of its signatures in 2D ES. Here, using principles from noisy-light spectroscopy to account for the spontaneous transfer event, we describe a model of the signals that arise from FRET in 2D ES. This model yields three theoretical results regarding the energy-transfer peak, which are consistent with our laboratory measurements. A second unanticipated finding is that the solvation processes that give rise to the dynamic Stokes shift of the acceptor signal also induce a relatively slower redshift of the energy-transfer signal, revealing a fundamental difference in solvation relaxation between photoexcited and FRET-excited acceptor molecules. The signatures derived from the model serve as a benchmark for ongoing work on energy-transfer mechanisms. Here, Turner and colleagues develop a noisy-light-inspired model of FRET in 2D ES to account for the vibrations that activate it. Crucially, they reveal several unreported features that distinguish FRET from other signals. These signatures are fundamental and immediately applicable to ongoing work on photosynthetic complexes, solar nanomaterials, and other renewable energy focal points. Future interdisciplinary work ranging from studies of energy transfer in organisms to medically applicable bio-imaging methodologies will take advantage of these spectral and temporal signatures.

Resolving the Fluorescence Quenching Mechanism of an Oxazine Dye Using Ultrabroadband Two-Dimensional Electronic Spectroscopy.

The design and optimization of fluorescent labels and fluorogenic probes rely heavily on their ability to distinguish among multiple competing fluorescence quenching mechanisms. Cresyl violet, a member of the 1,4-oxazine family of dyes, has generally been regarded as an exemplary fluorescent probe; however, recent ultrafast experiments revealed an excited-state decay kinetic of 1.2 ps, suggesting the presence of a transient photochemical state. Here, we present ultrabroadband two-dimensional electronic spectroscopy (2D ES) measurements of cresyl violet in the presence of the fluorescence quenching agent 3,6-di(2-hydroxyethyl)-1,2,4,5-tetrazine. The broad spectral bandwidth allows for the evaluation of multiple fluorescence quenching mechanisms such as exciton formation, photoinduced electron transfer, resonance energy transfer, and excited-state proton transfer. The 2D electronic spectra in the presence and absence of the quencher suggest that excited-state proton transfer drives the system's excited-state dynamics and leads to a cresyl violet tautomer involved in fluorescence quenching. The invocation of the tautomeric form of cresyl violet neatly resolves longstanding inconsistencies in the photophysics of oxazine dyes more generally. Although still under development, the application of ultrabroadband 2D ES to a molecular system represents a compelling demonstration of the technique's future role in the study of photochemical reaction mechanisms.

Two-Dimensional Electronic Spectroscopy Reveals the Spectral Dynamics of Förster Resonance Energy Transfer

Two-dimensional electronic spectroscopy (2D ES) probes the energies of chromophores and their coupling, and therefore the technique is now widely used for studying excitation energy-transfer mechanisms. The ubiquity and importance ofForster Resonance Energy Transfer (FRET) demand a thorough study of its signatures in 2D ES. Here, using principles from noisy-light spectroscopy to account for the spontaneous transfer event, we describe a model that explicitly includes the intramolecular vibrational modes necessary to activate FRET. Our laboratory measurements of carbocyanine dyes are consistent with three theoretical results regarding the location, shape, and spectral dynamics of the energy-transfer peak. The signatures derived from the vibronic FRET model serve as a benchmark for ongoing work on energy-transfer mechanisms.

Coherent Two-Quantum Two-Dimensional Electronic Spectroscopy Using Incoherent Light.

Two-quantum two-dimensional electronic spectroscopy (2Q 2D ES) may provide a measure of electron-correlation energies in molecules. Attempts to obtain this profound but elusive signal have relied on experimental implementations using femtosecond laser pulses, which induce an overwhelming background signal of nonresonant response. Here we explore theoretically the signatures of electron correlation in coherent 2Q 2D ES measurements that use spectrally incoherent light, I(4) 2Q 2D ES. One can use such fields to suppress nonresonant response, and therefore this method may better isolate the desired signature of electron correlation. Using an appropriate treatment of the multilevel Bloch electronic system, we find that I(4) 2Q 2D ES presents an opportunity to measure electron-correlation energies in molecules.

Probing Homogeneous Line Broadening in CdSe Nanocrystals Using Multidimensional Electronic Spectroscopy.

The finite spectral line width of an ensemble of CdSe nanocrystals arises from size and shape inhomogeneity and the single-nanocrystal spectrum itself. This line width directly limits the performance of nanocrystal-based devices, yet most optical measurements cannot resolve the underlying contributions. We use two-dimensional electronic spectroscopy (2D ES) to measure the line width of the band-edge exciton of CdSe nanocrystals as a function of radii and surface chemistry. We find that the homogeneous width decreases for increasing nanocrystal radius and that surface chemistry plays a critical role in controlling this line width. To explore the hypothesis that unpassivated trap states serve to broaden the homogeneous line width and to explain its size-dependence, we use 3D ES to identify the spectral signatures of exciton-phonon coupling to optical and acoustic phonons. We find enhanced coupling to optical phonon modes for nanocrystals that lack electron-passivating ligands, suggesting that localized surface charges enhance exciton-phonon coupling via the Fröhlich interaction. Lastly, the data reveal that spectral diffusion contributes negligibly to the homogeneous line width on subnanosecond time scales.

Time-Resolved Twisting Dynamics in a Porphyrin Dimer Characterized by Two-Dimensional Electronic Spectroscopy.

Molecular conformational changes in electronic excited states play a key role in numerous light-activated processes. In the case of porphyrin oligomers intramolecular twisting influences energy and charge transport dynamics. Here we address the twisting reaction in both ground and excited states in a model porphyrin dimer, employing two-dimensional electronic spectroscopy (2D ES). By spreading the information over excitation and detection frequencies, cross-peaks reveal the twisting reaction in both the ground and excited states unambiguously and distinctly from other dynamics. A quasi-barrierless planarization reaction is observed in the excited state on a tens of picoseconds time scale. This is accompanied by a spectral narrowing, indicative of a reduction in conformational disorder. The reverse reaction is suppressed in the excited state due to a steep activation energy barrier. However, in the ground state the barrier is within the thermal energy distribution, and therefore contributions from reverse and forward reactions could be observed on the subnanosecond time scale. Crucially 2D ES enables simultaneous assessment of ground and excited state reactions through analysis of different spectral regions on the 2D spectral maps.

Lineshape analysis of coherent multidimensional optical spectroscopy using incoherent light.

Coherent two-dimensional electronic spectroscopy using incoherent (noisy) light, I((4)) 2D ES, holds intriguing challenges and opportunities. One challenge is to determine how I((4)) 2D ES compares to femtosecond 2D ES. Here, we merge the sophisticated energy-gap Hamiltonian formalism that is often used to model femtosecond 2D ES with the factorized time-correlation formalism that is needed to describe I((4)) 2D ES. The analysis reveals that in certain cases the energy-gap Hamiltonian is insufficient to model the spectroscopic technique correctly. The results using a modified energy-gap Hamiltonian show that I((4)) 2D ES can reveal detailed lineshape information, but, contrary to prior reports, does not reveal dynamics during the waiting time.

The separation of vibrational coherence from ground- and excited-electronic states in P3HT film

Concurrence of the vibrational coherence and ultrafast electron transfer has been observed in polymer/fullerene blends. However, it is difficult to experimentally investigate the role that the excited-state vibrational coherence plays during the electron transfer process since vibrational coherence from the ground- and excited-electronic states is usually temporally and spectrally overlapped. Here, we performed 2-dimensional electronic spectroscopy (2D ES) measurements on poly(3-hexylthiophene) (P3HT) films. By Fourier transforming the whole 2D ES datasets (S(λ1,T̃2,λ3)) along the population time (T̃2) axis, we develop and propose a protocol capable of separating vibrational coherence from the ground- and excited-electronic states in 3D rephasing and nonrephasing beating maps (S(λ1,ν̃2,λ3)). We found that the vibrational coherence from pure excited electronic states appears at positive frequency (+ν̃2) in the rephasing beating map and at negative frequency (-ν̃2) in the nonrephasing beating map. Furthermore, we also found that vibrational coherence from excited electronic state had a long dephasing time of 244 fs. The long-lived excited-state vibrational coherence indicates that coherence may be involved in the electron transfer process. Our findings not only shed light on the mechanism of ultrafast electron transfer in organic photovoltaics but also are beneficial for the study of the coherence effect on photoexcited dynamics in other systems.

Single-residue insertion switches the quaternary structure and exciton states of cryptophyte light-harvesting proteins.

Observation of coherent oscillations in the 2D electronic spectra (2D ES) of photosynthetic proteins has led researchers to ask whether nontrivial quantum phenomena are biologically significant. Coherent oscillations have been reported for the soluble light-harvesting phycobiliprotein (PBP) antenna isolated from cryptophyte algae. To probe the link between spectral properties and protein structure, we determined crystal structures of three PBP light-harvesting complexes isolated from different species. Each PBP is a dimer of αβ subunits in which the structure of the αβ monomer is conserved. However, we discovered two dramatically distinct quaternary conformations, one of which is specific to the genus Hemiselmis. Because of steric effects emerging from the insertion of a single amino acid, the two αβ monomers are rotated by ∼73° to an "open" configuration in contrast to the "closed" configuration of other cryptophyte PBPs. This structural change is significant for the light-harvesting function because it disrupts the strong excitonic coupling between two central chromophores in the closed form. The 2D ES show marked cross-peak oscillations assigned to electronic and vibrational coherences in the closed-form PC645. However, such features appear to be reduced, or perhaps absent, in the open structures. Thus cryptophytes have evolved a structural switch controlled by an amino acid insertion to modulate excitonic interactions and therefore the mechanisms used for light harvesting.

Two-Dimensional Electronic Spectroscopy Using Incoherent Light: Theoretical Analysis

Electronic energy transfer in photosynthesis occurs over a range of time scales and under a variety of intermolecular coupling conditions. Recent work has shown that electronic coupling between chromophores can lead to coherent oscillations in two-dimensional electronic spectroscopy measurements of pigment-protein complexes measured with femtosecond laser pulses. A persistent issue in the field is to reconcile the results of measurements performed using femtosecond laser pulses with physiological illumination conditions. Noisy-light spectroscopy can begin to address this question. In this work we present the theoretical analysis of incoherent two-dimensional electronic spectroscopy, I((4)) 2D ES. Simulations reveal diagonal peaks, cross peaks, and coherent oscillations similar to those observed in femtosecond two-dimensional electronic spectroscopy experiments. The results also expose fundamental differences between the femtosecond-pulse and noisy-light techniques; the differences lead to new challenges and new opportunities.

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.

Exciton Superposition States in CdSe Nanocrystals Measured Using Broadband Two-Dimensional Electronic Spectroscopy

Coherent superpositions among eigenstates are of interest in fields as diverse as photosynthesis and quantum computation. In this report, we used two-dimensional electronic spectroscopy (2D ES) to measure the decoherence time of a superposition of the two lowest-energy excitons in colloidal CdSe nanocrystals (cubic phase) in solution at room temperature. In the electron-hole representation, the quantum coherence is, remarkably, a twelve-particle correlation. By comparing the measured 2D ES to simulations, we also explored the effects of inhomogeneous broadening and examined the spectroscopic signatures of biexcitons.

Quantitative investigations of quantum coherence for a light-harvesting protein at conditions simulating photosynthesis

Recent measurements using two-dimensional electronic spectroscopy (2D ES) have shown that the initial dynamic response of photosynthetic proteins can involve quantum coherence. We show how electronic coherence can be differentiated from vibrational coherence in 2D ES. On that basis we conclude that both electronic and vibrational coherences are observed in the phycobiliprotein light-harvesting complex PC645 from Chroomonas sp. CCMP270 at ambient temperature. These light-harvesting antenna proteins of the cryptophyte algae are suspended in the lumen, where the pH drops significantly under sustained illumination by sunlight. Here we measured 2D ES of PC645 at increasing levels of acidity to determine if the change in pH affects the quantum coherence; quantitative analysis reveals that the dynamics are insensitive to the pH change.

Comparison of Electronic and Vibrational Coherence Measured by Two-Dimensional Electronic Spectroscopy

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 light-harvesting antenna protein of the cryptophyte alga Chroomonas sp. strain CCMP270 at ambient temperature.

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.

Comparison of magnetotransport in two-dimensional arrays of quantum dots and antidots.

The longitudinal and Hall conductivities and resistivities are compared for two-dimensional (2D) square arrays of quantum dots and antidots in 2D electronic systems (ES's). The effects on the magnetotransport from the bound and coherent collimated states are explained. The energy eigenvalue spectra are obtained as a function of the magnetic field. The wave-vector dispersion of the energy eigenvalues is also calculated for the two systems. For antidots, there is a threshold magnetic field above which the system behaves like a homogeneous 2D ES. This threshold and the quenching of the Hall effect for antidots and the insulating behavior and Aharonov-Bohm quantum oscillations in a quantum-dot array are the main findings in this paper.

Heat-capacity study of two-dimensional electrons in GaAs/AlxGa1-xAs multiple-quantum-well structures in high magnetic fields: Spin-split Landau levels.

Using an earlier developed ac calorimetric technique, we measure the heat capacity of the two-dimensional electron system (2D ES) in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As multiple-quantum-well structures with relatively low density and high mobility (${\mathit{n}}_{2\mathrm{D}}$\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}${10}^{11}$/${\mathrm{cm}}^{2}$; \ensuremath{\mu}\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}${10}^{5}$ ${\mathrm{cm}}^{2}$/V s). Sweeping the magnetic field B up to \ensuremath{\sim}10 T below 1 K, we have observed the heat capacity, and thereby the equilibrium density of states (DOS) of a 2D ES in the spin-split lowest Landau levels. Analyzing the 2D ES DOS derived from our data, we find that many-body interactions within the 2D ES must be considered in order to explain the B dependence of both the spin splitting and broadening of the Landau levels. In optimal fits to our data, the g factor of Landau-level spin splitting is enhanced more than 10 times over the value at B=0, in agreement with results from analyses of the 2D ES transport. The Landau-level broadening oscillates versus 1/B, consistent with earlier results for the heat capacity of higher-density 2D ES samples.

Determination of energy spectrum parameters for two-dimensional carriers from the quantum oscillation beating pattern.

Recent experimental results of Das et al. and of Luo et al. on the Shubnikov--de Haas oscillation beatings in two-dimensional electron systems (2D ES) are quantitatively described in terms of a model based on the energy spectrum of a 2D ES with strong spin-orbit coupling. Values of the energy spectrum parameters, including the g factor, are obtained for two-dimensional electrons in ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As/${\mathrm{In}}_{0.52}$${\mathrm{Al}}_{0.48}$As (x\ensuremath{\simeq}0.6) heterostructures.