Polarization-dependent optical 2D Fourier transform spectroscopy of semiconductors

Two-dimensional spectroscopy beyond the perturbative limit: The influence of finite pulses and detection modes

Ultra-fast and multi-dimensional spectroscopy gives a powerful looking glass into the dynamics of molecular systems. In particular, two-dimensional electronic spectroscopy (2DES) provides a probe of coherence and the flow of energy within quantum systems, which is not possible with more conventional techniques. While heterodyne-detected (HD) 2DES is increasingly common, more recently fluorescence-detected (FD) 2DES offers new opportunities, including single-molecule experiments. However, in both techniques, it can be difficult to unambiguously identify the pathways that dominate the signal. Therefore, the use of numerically modeling of 2DES is vitally important, which, in turn, requires approximating the pulsing scheme to some degree. Here, we employ non-perturbative time evolution to investigate the effects of finite pulse width and amplitude on 2DES signals. In doing so, we identify key differences in the response of HD and FD detection schemes, as well as the regions of parameter space where the signal is obscured by unwanted artifacts in either technique. Mapping out parameter space in this way provides a guide to choosing experimental conditions and also shows in which limits the usual theoretical approximations work well and in which limits more sophisticated approaches are required.

Size-Dependent Hot Carrier Dynamics in Perovskite Nanocrystals Revealed by Two-Dimensional Electronic Spectroscopy

The lifetimes of hot carriers have been predicted to be prolonged in small nanocrystals with an inter-level spacing larger than phonon energy. Nevertheless, whether such a phonon bottleneck is present in perovskite semiconductor nanocrystals remains highly controversial. Here we report compelling evidence of a phonon bottleneck in CsPbI₃ nanocrystals with marked size-dependent relaxation of hot carriers by using broadband two-dimensional electronic spectroscopy (2DES). By combining high resolutions in both the time (<10 fs) and excitation energy domains, 2DES allows the clear disentanglement of the thermalization and cooling processes. The lifetime is over doubled for hot carriers when the average edge length of the nanocrystals decreases from 8.2 nm down to 4.6 nm. The confirmation of the phonon bottleneck effect suggests the feasibility of controlling hot carrier dynamics in perovskite semiconductors with nanocrystal size for potential applications of hot carrier devices.

Evidence for the Dominance of Carrier-Induced Band Gap Renormalization over Biexciton Formation in Cryogenic Ultrafast Experiments on MoS2 Monolayers

Transition-metal dichalcogenides (TMDs) such as MoS₂ display promising electrical and optical properties in the monolayer limit. Due to strong quantum confinement, TMDs provide an ideal environment for exploring excitonic physics using ultrafast spectroscopy. However, the interplay between collective excitation effects on single excitons such as band gap renormalization/exciton binding energy (BGR/EBE) change and multiexciton effects such biexciton formation remains poorly understood. Using two-dimensional electronic spectroscopy, we observe the dominance of single-exciton BGR/EBE signals over optically induced biexciton formation. We make this determination based on a lack of strong PIA features at T = 0 fs in the cryogenic spectra. By means of nodal line slope analysis, we determine that spectral diffusion occurs faster than BGR/EBE change, indicative of distinct processes. These results indicate that at higher sub-Mott limit fluences, collective effects on single excitons dominate biexciton formation.

Determining the Orientation and Vibronic Couplings between Electronic and Vibrational Coordinates with Polarization-Selective Two-Dimensional Vibrational-Electronic Spectroscopy

We experimentally demonstrate polarization-selective two-dimensional (2D) vibrational-electronic (VE) spectroscopy on a transition-metal mixed-valence complex where the cyanide stretching vibrations are coupled to the metal-to-metal charge-transfer transition. A simultaneous fitting of the parallel and crossed polarized 2D VE spectra quantifies the relative vibronic coupling strengths and angles between the charge-transfer transition and three coupled cyanide stretching vibrations in a mode-specific manner. In particular, we find that the bridging vibration, which modulates the distance between the transition-metal centers, is oriented nearly parallel to the charge-transfer axis and is 9 times more strongly coupled to the electronic transition than the radial vibration, which is oriented almost perpendicular to the charge-transfer axis. The results from this experiment allow us to map the spectroscopically observed vibronic coordinates onto the molecular frame providing a general method to spatially resolve vibronic energy transfer on a femtosecond time scale.

Automated polarization-dependent multidimensional coherent spectroscopy phased using transient absorption

An experimental apparatus is described for multidimensional optical spectroscopy with fully automated polarization control, based on liquid crystal variable retarders. Polarization dependence of rephasing two-dimensional coherent spectra are measured in a single scan, with absolute phasing performed for all polarization configurations through a single automated auxiliary measurement at the beginning of the scan. A factor of three improvement in acquisition time is demonstrated, compared to the apparatus without automated polarization control. Results are presented for a GaAs quantum well sample and an InGaAs quantum well embedded in a microcavity.

Ultrafast Charge Carrier Relaxation in Inorganic Halide Perovskite Single Crystals Probed by Two-Dimensional Electronic Spectroscopy

Halide perovskites are promising optoelectronic materials. Despite impressive device performance, especially in photovoltaics, the femtosecond dynamics of elementary optical excitations and their interactions are still debated. Here we combine ultrafast two-dimensional electronic spectroscopy (2DES) and semiconductor Bloch equations (SBEs) to probe the room-temperature dynamics of nonequilibrium excitations in CsPbBr₃ crystals. Experimentally, we distinguish between excitonic and free-carrier transitions, extracting a ∼30 meV exciton binding energy, in agreement with our SBE calculations and with recent experimental studies. The 2DES dynamics indicate remarkably short, <30 fs carrier relaxation at a ∼3 meV/fs rate, much faster than previously anticipated for this material, but similar to that in direct band gap semiconductors such as GaAs. Dynamic screening of excitons by free carriers also develops on a similarly fast <30 fs time scale, emphasizing the role of carrier-carrier interactions for this material's optical properties. Our results suggest that strong electron-phonon couplings lead to ultrafast relaxation of charge carriers, which, in turn may limit halide perovskites' carrier mobilities.

Absolute phase calibration in phase-modulated multidimensional coherent spectroscopy

Establishing the correct phase in multidimensional coherent spectroscopy (MDCS) experiments is critical because the interpretation of quantum pathways is based on the phase of their associated spectral features but is not trivial because the phase introduced by experimental conditions can contaminate the signal. Most phase-modulated MDCS (PM-MDCS) experiments study molecular systems for which the spectra can be phased to produce absorptive lineshapes, but this assumption of absorptive lineshapes can break down in more complicated systems. We present a robust technique for correcting the phase in PM-MDCS experiments and demonstrate accurate spectrum phasing for an anharmonic system.

Deconvolution of optical multidimensional coherent spectra

Optical coherent multidimensional spectroscopy is a powerful technique for unraveling complex and congested spectra by spreading them across multiple dimensions, removing the effects of inhomogeneity, and revealing underlying correlations. As the technique matures, the focus is shifting from understanding the technique itself to using it to probe the underlying dynamics in the system being studied. However, these dynamics can be difficult to discern because they are convolved with the nonlinear optical response of the system. Inspired by methods used to deblur images, we present a method for deconvolving the underlying dynamics from the optical response. To demonstrate the method, we extract the many-particle diffusion Green's functions for excitons in a semiconductor quantum well from two-dimensional coherent spectra.

Biexciton Resonances Reveal Exciton Localization in Stacked Perovskite Quantum Wells

Quasi-two-dimensional lead halide perovskites, MA_n-1Pb_nX_3n+1, are quantum confined materials with an ever-developing range of optoelectronic device applications. Like other semiconductors, the correlated motion of electrons and holes dominates the material's response to optical excitation influencing its electrical and optical properties such as charge formation and mobility. However, the effects of many-particle correlation have been relatively unexplored in perovskite because of the difficultly of probing these states directly. Here, we use double quantum coherence spectroscopy to explore the formation and localization of multiexciton states in these materials. Between the most confined domains, we demonstrate the presence of an interwell, two-exciton excited state. This demonstrates that the four-body Coulomb interaction electronically couples neighboring wells despite weak electron/hole hybridization in these materials. Additionally, in contrast with inorganic semiconductor quantum wells, we demonstrate a rapid decrease in the dephasing time as wells become thicker, indicating that exciton delocalization is not limited by structural inhomogeneity in low-dimensional perovskite.

Strong Quantum Coherence between Fermi Liquid Mahan Excitons

In modulation doped quantum wells, the excitons are formed as a result of the interactions of the charged holes with the electrons at the Fermi edge in the conduction band, leading to the so-called "Mahan excitons." The binding energy of Mahan excitons is expected to be greatly reduced and any quantum coherence destroyed as a result of the screening and electron-electron interactions. Surprisingly, we observe strong quantum coherence between the heavy hole and light hole excitons. Such correlations are revealed by the dominating cross-diagonal peaks in both one-quantum and two-quantum two-dimensional Fourier transform spectra. Theoretical simulations based on the optical Bloch equations where many-body effects are included phenomenologically reproduce well the experimental spectra. Time-dependent density functional theory calculations provide insight into the underlying physics and attribute the observed strong quantum coherence to a significantly reduced screening length and collective excitations of the many-electron system.

Optical three dimensional coherent spectroscopy

Optical multdimensional coherent spectroscopy has recently been the subject of significant activity. While two-dimensional spectroscopy is most common, it is possible to extend the method into three dimensions. This perspective reviews the different approaches to three-dimensional spectroscopy and the systems that have been studied with it. The advantages of adding an additional dimension are discussed and compared to the resulting experimental challenges.

Analytical calculation of two-dimensional spectra

We demonstrate an analytical calculation of two-dimensional (2D) coherent spectra of electronic or vibrational resonances. Starting with the solution to the optical Bloch equations for a two-level system in the 2D time domain, we show that a fully analytical 2D Fourier transform can be performed if the projection-slice and Fourier-shift theorems of Fourier transforms are applied. Results can be fit to experimental 2D coherent spectra of resonances with arbitrary inhomogeneity.

Isolating quantum coherence using coherent multi-dimensional spectroscopy with spectrally shaped pulses

We demonstrate how spectral shaping in coherent multidimensional spectroscopy can isolate specific signal pathways and directly access quantitative details. By selectively exciting pathways involving a coherent superposition of exciton states we are able to identify, isolate and analyse weak coherent coupling between spatially separated excitons in an asymmetric double quantum well. Analysis of the isolated signal elucidates details of the coherent interactions between the spatially separated excitons. With a dynamic range exceeding 10(4) in electric field amplitude, this approach facilitates quantitative comparisons of different signal pathways and a comprehensive description of the electronic states and their interactions.

Temperature-dependent conformations of a membrane supported zinc porphyrin tweezer by 2D fluorescence spectroscopy

We studied the equilibrium conformations of a zinc porphyrin tweezer composed of two carboxylphenyl-functionalized zinc tetraphenyl porphyrin subunits connected by a 1,4-butyndiol spacer, which was suspended inside the amphiphilic regions of 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC) liposomes. By combining phase-modulation two-dimensional fluorescence spectroscopy (2D FS) with linear absorbance and fluorimetry, we determined that the zinc porphyrin tweezer adopts a mixture of folded and extended conformations in the membrane. By fitting an exciton-coupling model to a series of data sets recorded over a range of temperatures (17-85 °C) and at different laser center wavelengths, we determined that the folded form of the tweezer is stabilized by a favorable change in the entropy of the local membrane environment. Our results provide insights toward understanding the balance of thermodynamic factors that govern molecular assembly in membranes.

Continuously tunable optical multidimensional Fourier-transform spectrometer

A multidimensional optical nonlinear spectrometer (MONSTR) is a robust, ultrastable platform consisting of nested and folded Michelson interferometers that can be actively phase stabilized. The MONSTR provides output pulses for nonlinear excitation of materials and phase-stabilized reference pulses for heterodyne detection of the induced signal. This platform generates a square of identical laser pulses that can be adjusted to have arbitrary time delays between them while maintaining phase stability. This arrangement is ideal for performing coherent optical experiments, such as multidimensional Fourier-transform spectroscopy. The present work reports on overcoming some important limitations on the original design of the MONSTR apparatus. One important advantage of the MONSTR is the fact that it is a closed platform, which provides the high stability. Once the optical alignment is performed, it is desirable to maintain the alignment over long periods of time. The previous design of the MONSTR was limited to a narrow spectral range defined by the optical coating of the beam splitters. In order to achieve tunability over a broad spectral range the internal optics needed to be changed. By using broadband coated and wedged beam splitters and compensator plates, combined with modifications of the beam paths, continuous tunability can be achieved from 520 nm to 1100 nm without changing any optics or performing alignment of the internal components of the MONSTR. Furthermore, in order to achieve continuous tunability in the spectral region between 520 nm and 720 nm, crucially important for studies on numerous biological molecules, a single longitudinal mode laser at 488.5 nm was identified and used as a metrology laser. The shorter wavelength of the metrology laser as compared to the usual HeNe laser has also increased the phase stability of the system. Finally, in order to perform experiments in the reflection geometry, a simple method to achieve active phase stabilization between the signal and the reference beams has been developed.

Two-dimensional double-quantum spectra reveal collective resonances in an atomic vapor

We report the observation of double-quantum coherence signals in a gas of potassium atoms at twice the frequency of the one-quantum coherences. Since a single atom does not have a state at the corresponding energy, this observation must be attributed to a collective resonance involving multiple atoms. These resonances are induced by weak interatomic dipole-dipole interactions, which means that the atoms cannot be treated in isolation, even at a low density of 10(12)  cm(-3).

Coherent Vibronic Coupling in Light-Harvesting Complexes from Photosynthetic Marine Algae

Observations of long-lived coherences in photosynthetic light-harvesting complexes utilize short pulses with broad spectral bandwidths to coherently excite multiple transitions and coherent superpositions. In order to identify the role that such quantum effects might play in efficient energy transfer, however, an alternative approach is required. We have developed a technique for two-color photon echo spectroscopy to selectively excite the pathway of interest and measure its evolution in the absence of any other excitation. We use this technique to excite a coherence pathway in phycocyanin-645 from cryptophyte algae and measure the dynamics of this coherence. A decoherence time of 500 fs was measured, and clear signatures for strong coupling between the electronic states and phonon modes were observed, allowing coherent coupling between otherwise nonresonant transitions. This provides detailed experimental evidence of the long-lived coherences and the nature of the quantum mechanical interactions between electronic states and phonon modes in phycocyanin-645 from cryptophyte marine algae.

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.

Invited article: The coherent optical laser beam recombination technique (COLBERT) spectrometer: coherent multidimensional spectroscopy made easier

We have developed an efficient spectrometer capable of performing a wide variety of coherent multidimensional measurements at optical wavelengths. The two major components of the largely automated device are a spatial beam shaper which controls the beam geometry and a spatiotemporal pulse shaper which controls the temporal waveform of the femtosecond pulse in each beam. We describe how to construct, calibrate, and operate the device, and we discuss its limitations. We use the exciton states of a semiconductor nanostructure as a working example. A series of complex multidimensional spectra-displayed in amplitude and real parts-reveals increasingly intricate correlations among the excitons.

Ultrafast double-quantum-coherence spectroscopy of excitons with entangled photons

We calculate the four-wave-mixing signal of excitons generated at k(4) = k(1) + k(2) - k(3) by two pulsed entangled photon pairs (k(1), k(2))and(k(3), k(4)), where all four modes are chronologically ordered. Entangled photons offer an unusual combination of bandwidths and temporal resolution not possible by classical beams. Contributions from different resonances can be selected by varying the parameters of the photon wave function. The signal scales linearly rather than quadratically with the laser field intensity, which allows performance of the measurements at low powers.

Two-quantum many-body coherences in two-dimensional fourier-transform spectra of exciton resonances in semiconductor quantum wells

We present experimental coherent two-dimensional Fourier-transform spectra of Wannier exciton resonances in semiconductor quantum wells generated by a pulse sequence that isolates two-quantum coherences. By measuring the real part of the signals, we determine that the spectra are dominated by two-quantum coherences due to mean-field many-body interactions, rather than bound biexcitons. Simulations performed using dynamics controlled truncation agree with the experiments.

Three-dimensional electronic spectroscopy of excitons in GaAs quantum wells

We demonstrate three-dimensional (3D) electronic Fourier transform spectroscopy of GaAs quantum wells using four fully phase-coherent, noncollinear optical fields. Since the full complex signal field is measured as a function of all three time intervals, nearly every peak in the resulting 3D spectral solid arises from a distinguishable sequence of transitions represented by a single Feynman pathway. We use the 3D spectral peaks to separate two pathways involving weakly bound mixed biexcitons generated in different time orders. In the process, we reveal a peak that was previously obscured by a correlated but unbound exciton pair coherence. We also demonstrate a calibration procedure for the carrier frequency which yields biexciton binding energy values with high accuracy.

Exciton-exciton correlations revealed by two-quantum, two-dimensional fourier transform optical spectroscopy

The Coulomb correlations between photoexcited charged particles in materials such as photosynthetic complexes, conjugated polymer systems, J-aggregates, and bulk or nanostructured semiconductors produce a hierarchy of collective electronic excitations, for example, excitons, and biexcitons, which may be harnessed for applications in quantum optics, light-harvesting, or quantum information technologies. These excitations represent correlations among successively greater numbers of electrons and holes, and their associated multiple-quantum coherences could reveal detailed information about complex many-body interactions and dynamics. However, unlike single-quantum coherences involving excitons, multiple-quantum coherences do not radiate; consequently, they have largely eluded direct observation and characterization. In this Account, we present a novel optical technique, two-quantum, two-dimensional Fourier transform optical spectroscopy (2Q 2D FTOPT), which allows direct observation of the dynamics of multiple exciton states that reflect the correlations of their constituent electrons and holes. The approach is based on closely analogous methods in NMR, in which multiple phase-coherent fields are used to drive successive transitions such that multiple-quantum coherences can be accessed and probed. In 2Q 2D FTOPT, a spatiotemporal femtosecond pulse-shaping technique has been used to overcome the challenge of control over multiple, noncollinear, phase-coherent optical fields in experimental geometries used to isolate selected signal contributions through wavevector matching. We present results from a prototype GaAs quantum well system, which reveal distinct coherences of biexcitons that are formed from two identical excitons or from two excitons that have holes in different spin sublevels ("heavy-hole" and "light-hole" excitons). The biexciton binding energies and dephasing dynamics are determined, and changes in the dephasing rates as a function of the excitation density are observed, revealing still higher order correlations due to exciton-biexciton interactions. Two-quantum coherences due to four-particle correlations that do not involve bound biexciton states but that influence the exciton properties are also observed and characterized. The 2Q 2D FTOPT technique allows many-body interactions that cannot be treated with a mean-field approximation to be studied in detail; the pulse-shaping approach simplifies greatly what would have otherwise been daunting measurements. This spectroscopic tool might soon offer insight into specific applications, for example, in detailing the interactions that affect how electronic energy moves within the strata of organic photovoltaic cells.

Optical two-dimensional fourier transform spectroscopy of semiconductor quantum wells

Coherent light-matter interactions of direct-gap semiconductor nanostructures provide a great test system for fundamental research into quantum electronics and many-body physics. The understanding gained from studying these interactions can facilitate the design of optoelectronic devices. Recently, we have used optical two-dimensional Fourier-transform spectroscopy to explore coherent light-matter interactions in semiconductor quantum wells. Using three laser pulses to generate a four-wave-mixing signal, we acquire spectra by tracking the phase of the signal with respect to two time axes and then Fourier transforming them. In this Account, we show several two-dimensional projections and demonstrate techniques to isolate different contributions to the coherent response of semiconductors. The low-temperature spectrum of semiconductor quantum wells is dominated by excitons, which are electron-hole pairs bound through Coulombic interactions. Excitons are sensitive to their electronic and structural environment, which influences their optical resonance energies and line widths. In near perfect quantum wells, a small fluctuation of the quantum well thickness leads to spatial localization of the center-of-mass wave function of the excitons and inhomogeneous broadening of the optical resonance. The inhomogeneous broadening often masks the homogeneous line widths associated with the scattering of the excitons. In addition to forming excitons, Coulombic correlations also form excitonic molecules, called biexcitons. Therefore, the coherent response of the quantum wells encompasses the intra-action and interaction of both excitons and biexcitons in the presence of inhomogeneous broadening. Transient four-wave-mixing studies combined with microscopic theories have determined that many-body interactions dominate the strong coherent response from quantum wells. Although the numerous competing interactions cannot be easily separated in either the spectral or temporal domains, they can be separated using two-dimensional Fourier transform spectroscopy. The most common two-dimensional Fourier spectra are S(I)(omega(tau),T,omega(t)) in which the second time period is held fixed. The result is a spectrum that unfolds congested one-dimensional spectra, separates excitonic pathways, and shows which excitons are coherently coupled. This method also separates the biexciton contributions and isolates the homogeneous and inhomogeneous line widths. For semiconductor excitons, the line shape in the real part of the spectrum is sensitive to the many-body interactions, which we can suppress by exploiting polarization selection rules. In an alternative two-dimensional projection, S(I)(tau,omega(Tau),omega(t)), the nonradiative Raman coherent interactions are isolated. Finally, we show S(III)(tau,omega(Tau),omega(t)) spectra that isolate the two-quantum coherences associated with the biexciton. These spectra reveal previously unobserved many-body correlations.

A versatile ultrastable platform for optical multidimensional Fourier-transform spectroscopy

The JILA multidimensional optical nonlinear spectrometer (JILA-MONSTR) is a robust, ultrastable platform consisting of nested and folded Michelson interferometers that can be actively phase stabilized. This platform generates a square of identical laser pulses that can be adjusted to have arbitrary time delay between them while maintaining phase stability. The JILA-MONSTR provides output pulses for nonlinear excitation of materials and phase-stabilized reference pulses for heterodyne detection of the induced signal. This arrangement is ideal for performing coherent optical experiments, such as multidimensional Fourier-transform spectroscopy, which records the phase of the nonlinear signal as a function of the time delay between several of the excitation pulses. The resulting multidimensional spectrum is obtained from a Fourier transform. This spectrum can resolve, separate, and isolate coherent contributions to the light-matter interactions associated with electronic excitation at optical frequencies. To show the versatility of the JILA-MONSTR, several demonstrations of two-dimensional Fourier-transform spectroscopy are presented, including an example of a phase-cycling scheme that reduces noise. Also shown is a spectrum that accesses two-quantum coherences, where all excitation pulses require phase locking for detection of the signal.

Two-quantum 2D FT electronic spectroscopy of biexcitons in GaAs quantum wells

The motions of electrons in solids may be highly correlated by strong, long-range Coulomb interactions. Correlated electron-hole pairs (excitons) are accessed spectroscopically through their allowed single-quantum transitions, but higher-order correlations that may strongly influence electronic and optical properties have been far more elusive to study. Here we report direct observation of bound exciton pairs (biexcitons) that provide incisive signatures of four-body correlations among electrons and holes in gallium arsenide (GaAs) quantum wells. Four distinct, mutually coherent, ultrashort optical pulses were used to create coherent exciton states, transform these successively into coherent biexciton states and then new radiative exciton states, and finally to read out the radiated signals, yielding biexciton binding energies through a technique closely analogous to multiple-quantum two-dimensional Fourier transform (2D FT) nuclear magnetic resonance spectroscopy. A measured variation of the biexciton dephasing rate indicated still higher-order correlations.

Isolating excitonic Raman coherence in semiconductors using two-dimensional correlation spectroscopy

We present the experimental and simulation results of two-dimensional optical coherent correlation spectroscopy signals along the phase-matching direction k(I) = -k(1) + k(2) + k(3) projected on the two-dimensional (2D) (Omega(3),Omega(2)) plane corresponding to the second and third delay periods. Overlapping Raman coherences in the conventional (Omega(3),Omega(1)) 2D projection may now be clearly resolved. The linewidths of the heavy-hole (HH) and light-hole (LH) excitonic Raman coherence peaks are obtained. Further insights on the higher-order (beyond time-dependent Hartree-Fock) correlation effects among mixed (HH and LH) two excitons can be gained by using a cocircular pulse polarization configuration.

Instantaneous mapping of coherently coupled electronic transitions and energy transfers in a photosynthetic complex using angle-resolved coherent optical wave-mixing

Understanding the role of coherent electronic motion is expected to resolve general questions of importance in macromolecular energy transfer. We demonstrate a novel nonlinear optical method, angle-resolved coherent wave mixing, that separates out coherently coupled electronic transitions and energy transfers in an instantaneous two-dimensional mapping. Angular resolution of the signal is achieved by using millimeter laser beam waists at the sample and by signal relay to the far field; for this we use a high energy, ultrabroadband hollow fiber laser source. We reveal quantum electronic beating with a time-ordered selection of transition energies in a photosynthetic complex.

Instantaneous mapping of coherently coupled electronic transitions and energy transfers in a photosynthetic complex using angle-resolved coherent optical wave-mixing

Understanding the role of coherent electronic motion is expected to resolve general questions of importance in macromolecular energy transfer. We demonstrate a novel nonlinear optical method, angle-resolved coherent wave mixing, that separates out coherently coupled electronic transitions and energy transfers in an instantaneous two-dimensional mapping. Angular resolution of the signal is achieved by using millimeter laser beam waists at the sample and by signal relay to the far field; for this we use a high energy, ultrabroadband hollow fiber laser source. We reveal quantum electronic beating with a time-ordered selection of transition energies in a photosynthetic complex.

Coherent multidimensional vibrational spectroscopy of biomolecules: concepts, simulations, and challenges

The response of complex molecules to sequences of femtosecond infrared pulses provides a unique window into their structure, dynamics, and fluctuating environments. Herein we survey the basic principles of modern two-dimensional infrared (2DIR) spectroscopy, which analogous to those of multidimensional NMR spectroscopy. The perturbative approach for computing the nonlinear optical response of coupled localized chromophores is introduced and applied to the amide backbone transitions of proteins, liquid water, membrane lipids, and amyloid fibrils. The signals are analyzed using classical molecular dynamics simulations combined with an effective fluctuating Hamiltonian for coupled localized anharmonic vibrations whose dependence on the local electrostatic environment is parameterized by an ab initio map. Several simulation methods, (cumulant expansion of Gaussian fluctuation, quasiparticle scattering, the stochastic Liouville equations, direct numerical propagation) are surveyed. Chirality-induced techniques which dramatically enhance the resolution are demonstrated. Signatures of conformational and hydrogen-bonding fluctuations, protein folding, and chemical-exchange processes are discussed.

All-optical retrieval of the global phase for two-dimensional Fourier-transform spectroscopy

A combination of spatial interference patterns and spectral interferometry are used to find the global phase for non-collinear two-dimensional Fourier-transform (2DFT) spectra. Results are compared with those using the spectrally resolved transient absorption (STRA) method to find the global phase when excitation is with co-linear polarization. Additionally cross-linear polarized 2DFT spectra are correctly "phased" using the all-optical technique, where the SRTA is not applicable.

Noninterferometric two-dimensional fourier-transform spectroscopy of multilevel systems

We demonstrate a technique that determines the phase of the photon-echo emission from spectrally resolved intensity data without requiring phase-stabilized input pulses. The full complex polarization of the emission is determined from spectral intensity measurements. The validity of this technique is demonstrated using simulated data, and is then applied to the analysis of two-color data obtained from the light-harvesting molecule lycopene.

Visualization of excitonic structure in the Fenna-Matthews-Olson photosynthetic complex by polarization-dependent two-dimensional electronic spectroscopy

Photosynthetic light-harvesting proceeds by the collection and highly efficient transfer of energy through a network of pigment-protein complexes. Interchromophore electronic couplings and interactions between pigments and the surrounding protein determine energy levels of excitonic states, and dictate the mechanism of energy flow. The excitonic structure (orientation of excitonic transition dipoles) of pigment-protein complexes is generally deduced indirectly from x-ray crystallography, in combination with predictions of transition energies and couplings in the chromophore site basis. We demonstrate that coarse-grained, excitonic, structural information in the form of projection angles between transition dipole moments can be obtained from the polarization-dependent, two-dimensional electronic spectroscopy of an isotropic sample, particularly when the nonrephasing or free polarization decay signal, rather than the photon echo signal, is considered. This method provides an experimental link between atomic and electronic structure, and accesses dynamical information with femtosecond time resolution. In an investigation of the Fenna-Matthews-Olson complex from green sulfur bacteria, the energy transfer connecting two particular exciton states in the protein was isolated as the primary contributor to a crosspeak in the nonrephasing two-dimensional spectrum at 400 femtoseconds under a specific sequence of polarized excitation pulses. The results suggest the possibility of designing experiments using combinations of tailored polarization sequences to separate and monitor individual relaxation pathways.