Phasing problem of heterodyne-detected two-dimensional infrared spectroscopy

Protein Dynamics by Two-Dimensional Infrared Spectroscopy

Proteins function as ensembles of interconverting structures. The motions span from picosecond bond rotations to millisecond and longer subunit displacements. Characterization of functional dynamics on all spatial and temporal scales remains challenging experimentally. Two-dimensional infrared spectroscopy (2D IR) is maturing as a powerful approach for investigating proteins and their dynamics. We outline the advantages of IR spectroscopy, describe 2D IR and the information it provides, and introduce vibrational groups for protein analysis. We highlight example studies that illustrate the power and versatility of 2D IR for characterizing protein dynamics and conclude with a brief discussion of the outlook for biomolecular 2D IR.

Progress in phase-sensitive sum frequency generation spectroscopy

Sum frequency generation (SFG) spectroscopy is a unique and powerful tool for investigating surfaces and interfaces at the molecular level. Phase-sensitive SFG (PS-SFG) is an upgraded technique that can overcome the inherent drawbacks of conventional SFG. Here we review several methods of PS-SFG developed and reported in 1990-2020. We introduce how and by which group each PS-SFG method was designed and built in terms of interferometer implementation for optical heterodyne detection, with one exception of a recent numerical method that does not rely on interferometry. We also discuss how PS-SFG solved some typical problems for aqueous interfaces that were once left open by conventional SFG. These problems and their solutions are good examples to demonstrate why PS-SFG is essential. In addition, we briefly note a few terminology issues related with PS-SFG to avoid confusion.

Leveraging scatter in two-dimensional spectroscopy: passive phase drift correction enables a global phasing protocol

Phase stability between pulse pairs defining Fourier-transform time delays can limit resolution and complicates development and adoption of multidimensional coherent spectroscopies. We demonstrate a data processing procedure to correct the long-term phase drift of the nonlinear signal during two-dimensional (2D) experiments based on the relative phase between scattered excitation pulses and a global phasing procedure to generate fully absorptive 2D electronic spectra of wafer-scale monolayer MoS₂. Our correction results in a ∼30-fold increase in effective long-term signal phase stability, from ∼λ/2 to ∼λ/70 with negligible extra experimental time and no additional optical components. This scatter-based drift correction should be applicable to other interferometric techniques as well, significantly lowering the practical experimental requirements for this class of measurements.

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.

Hydrophobic Collapse in N-Methylacetamide-Water Mixtures

Aqueous N-methylacetamide solutions were investigated by polarization-resolved pump-probe and 2D infrared spectroscopy (2D IR), using the amide I mode as a reporter. The 2D IR results are compared with molecular dynamics simulations and spectral calculations to gain insight into the molecular structures in the mixture. N-Methylacetamide and water molecules tend to form clusters with "frozen" amide I dynamics. This is driven by a hydrophobic collapse as the methyl groups of the N-methylacetamide molecules cluster in the presence of water. Since the studied system can be considered as a simplified model for the backbone of proteins, the present study forms a convenient basis for understanding the structural and vibrational dynamics in proteins. It is particularly interesting to find out that a hydrophobic collapse as the one driving protein folding is observed in such a simple system.

Interplay between Hydrogen Bonding and Vibrational Coupling in Liquid N-Methylacetamide

Intrinsically disordered proteins play an important role in biology, and unraveling their labile structure presents a vital challenge. However, the dynamical structure of such proteins thwarts their study by standard techniques such as X-ray diffraction and NMR spectroscopy. Here, we use a neat liquid composed of N-methylacetamide molecules as a model system to elucidate dynamical and structural properties similar to those one can expect to see in intrinsically disordered proteins. To examine the structural dynamics in the neat liquid, we combine molecular dynamics, response-function-based spectral simulations, and two-dimensional polarization-resolved infrared spectroscopy in the amide I (CO stretch) region. The two-dimensional spectra reveal a delicate interplay between hydrogen bonding and intermolecular vibrational coupling effects, observed through a fast anisotropy decay. The present study constitutes a general platform for understanding the structure and dynamics of highly disordered proteins.

Post-processing phase-correction algorithm in two-dimensional electronic spectroscopy

In a typical two-dimensional electronic spectroscopy (2DES) experiment, the timing errors of the coherence and emission time when determining the absolute time zeros usually introduce extraneous spectral phase slopes and distort the 2D spectrum. In this work, a phase-correction method that merely relies on the data post-processing algorithm is proposed. The method allows reconstructing the spectrum by simply subtracting the artificial linear spectral-phase slopes from the phase component of the 2D spectrum along both coherence and emission frequency axes. The new method has the advantages of ease of implementation and no need for the supplementary experiments and iterative fitting algorithm as commonly-used phasing methods, which may improve the phasing issue in 2DES and serve as a cross-check of now available phasing methods.

Intrinsic phasing of heterodyne-detected multidimensional infrared spectra

We show that it is possible to phase multidimensional infrared spectra generated by a boxcars geometry four-wave mixing spectrometer directly from the signal generated by the molecular vibration of interest, without the need for auxiliary phasing measurements. For isolated vibrations, the phase profile of the 2D response smoothly varies between fixed phase limits, allowing for a general target for phasing independent of the degree of anharmonicity exhibited between the ground and excited state. As a proof of principle, the 2D response of the ∼2155 cm^-1 thiocyanate stretch vibration of MeSCN, a system exhibiting anharmonicity such that the 0-1 and 1-2 transitions are spectrally isolated, is successfuly phased directly from the experimental spectra. The methodology is also applied to correctly phase extremely weak signals of the unnatural amino acid azidohomoalanine following background subtraction.

Precise phase determination with the built-in spectral interferometry in two-dimensional electronic spectroscopy

A new method determining the precise phase of pulse sequences in two-dimensional electronic spectroscopy (2DES) is proposed merely using the already built-in spectral interferometry. The approach is easily implemented without the supplementary instrumental construction, only at the expense of a few additional scanning and data-fitting processes. This method is executed with the sample in place, effectively avoiding the phase ambiguities of the beam propagation in samples, thus calibrating the absolute phase at the exact interaction region. The new proposed method is expected to improve the phasing procedure in 2DES in a more convenient way.

Line shape analysis of two-dimensional infrared spectra

Ultrafast two-dimensional infrared (2D IR) spectroscopy probes femtosecond to picosecond time scale dynamics ranging from solvation to protein motions. The frequency-frequency correlation function (FFCF) is the quantitative measure of the spectral diffusion that reports those dynamics and, within certain approximations, can be extracted directly from 2D IR line shapes. A variety of methods have been developed to extract the FFCF from 2D IR spectra, which, in principle, should give the same FFCF parameters, but the complexity of real experimental systems will affect the results of these analyses differently. Here, we compare five common analysis methods using both simulated and experimental 2D IR spectra to understand the effects of apodization, anharmonicity, phasing errors, and finite signal-to-noise ratios on the results of each of these analyses. Our results show that although all of the methods can, in principle, yield the FFCF under idealized circumstances, under more realistic experimental conditions they behave quite differently, and we find that the centerline slope analysis yields the best compromise between the effects we test and is most robust to the distortions that they cause.

Experimental implementations of two-dimensional fourier transform electronic spectroscopy

Two-dimensional electronic spectroscopy (2DES) reveals connections between an optical excitation at a given frequency and the signals it creates over a wide range of frequencies. These connections, manifested as cross-peak locations and their lineshapes, reflect the underlying electronic and vibrational structure of the system under study. How these spectroscopic signatures evolve in time reveals the system dynamics and provides a detailed picture of coherent and incoherent processes. 2DES is rapidly maturing and has already found numerous applications, including studies of photosynthetic energy transfer and photochemical reactions and many-body interactions in nanostructured materials. Many systems of interest contain electronic transitions spanning the ultraviolet to the near infrared and beyond. Most 2DES measurements to date have explored a relatively small frequency range. We discuss the challenges of implementing 2DES and compare and contrast different approaches in terms of their information content, ease of implementation, and potential for broadband measurements.

Testing for memory-free spectroscopic coordinates by 3D IR exchange spectroscopy

Using 3D infrared (IR) exchange spectroscopy, the ultrafast hydrogen-bond forming and breaking (i.e., complexation) kinetics of phenol to benzene in a benzene/CCl4 mixture is investigated. By introducing a third time point at which the hydrogen-bonding state of phenol is measured (in comparison with 2D IR exchange spectroscopy), the spectroscopic method can serve as a critical test of whether the spectroscopic coordinate used to observe the exchange process is a memory-free, or Markovian, coordinate. For the system under investigation, the 3D IR results suggest that this is not the case. This conclusion is reconfirmed by accompanying molecular dynamics simulations, which furthermore reveal that the non-Markovian kinetics is caused by the heterogeneous structure of the mixed solvent.

2D IR spectroscopy with phase-locked pulse pairs from a birefringent delay line

We introduce a new scheme for two-dimensional IR spectroscopy in the partially collinear pump-probe geometry. Translating birefringent wedges allow generating phase-locked pump pulses with exceptional phase stability, in a simple and compact setup. A He-Ne tracking scheme permits to scan continuously the acquisition time. For a proof-of-principle demonstration we use lithium niobate, which allows operation up to 5 μm. Exploiting the inherent perpendicular polarizations of the two pump pulses, we also demonstrate signal enhancement and scattering suppression.

Multidimensional coherent photocurrent spectroscopy of a semiconductor nanostructure

Multidimensional Coherent Optical Photocurrent Spectroscopy (MD-COPS) is implemented using unstabilized interferometers. Photocurrent from a semiconductor sample is generated using a sequence of four excitation pulses in a collinear geometry. Each pulse is frequency shifted by a unique radio frequency through acousto-optical modulation; the Four-Wave Mixing (FWM) signal is then selected in the frequency domain. The interference of an auxiliary continuous wave laser, which is sent through the same interferometers as the excitation pulses, is used to synthesize reference frequencies for lock-in detection of the photocurrent FWM signal. This scheme enables the partial compensation of mechanical fluctuations in the setup, achieving sufficient phase stability without the need for active stabilization. The method intrinsically provides both the real and imaginary parts of the FWM signal as a function of inter-pulse delays. This signal is subsequently Fourier transformed to create a multi-dimensional spectrum. Measurements made on the excitonic resonance in a double InGaAs quantum well embedded in a p-i-n diode demonstrate the technique.

2D IR spectroscopy using four-wave mixing, pulse shaping, and IR upconversion: a quantitative comparison

Recent technological advances have led to major changes in the apparatuses used to collect 2D IR spectra. Pulse shaping offers several advantages including rapid data collection, inherent phase stability, and phase-cycling capabilities. Visible array detection via upconversion allows the use of visible detectors that are cheaper, faster, more sensitive, and less noisy than IR detectors. However, despite these advantages, many researchers are reluctant to implement these technologies. Here we present a quantitative study of the S/N of 2D IR spectra collected with a traditional four-wave mixing (FWM) apparatus, with a pulse shaping apparatus, and with visible detection via upconversion to address the question of whether weak chromophores at low concentrations are still accessible with such an apparatus. We find that the enhanced averaging capability of the pulse shaping apparatus enables the detection of small signals that would be challenging to measure even with the traditional FWM apparatus, and we demonstrate this ability on a sample of cyanylated dihydrofolate reductase.

Two-dimensional electronic spectroscopy for mapping molecular photophysics

We demonstrate the ability of two-dimensional electronic spectroscopy (2DES) to map ultrafast energy transfer and dynamics in two systems: the pigment–protein complex photosystem I (PSI) and aggregates of the conjugated polymer poly(3-hexylthiophene) (P3HT). A detailed description of our experimental set-up and data processing procedure is also given.

Two-Dimensional Electronic Spectroscopy Reveals Ultrafast Downhill Energy Transfer in Photosystem I Trimers of the Cyanobacterium Thermosynechococcus elongatus

Two-dimensional electronic spectroscopy (2DES) was used to investigate the ultrafast energy-transfer dynamics of trimeric photosystem I of the cyanobacterium Thermosynechococcus elongatus. We demonstrate the ability of 2DES to resolve dynamics in a large pigment-protein complex containing ∼300 chromophores with both high frequency and time resolution. Monitoring the waiting-time-dependent changes of the line shape of the inhomogeneously broadened Qy(0-0) transition, we directly observe downhill energy equilibration on the 50 fs time scale.

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.

Three-dimensional infrared spectroscopy of isotope-substituted liquid water reveals heterogeneous dynamics

The dynamics of the hydrogen bond network of isotopically substituted liquid water are investigated with a new ultrafast nonlinear vibrational spectroscopy, three-dimensional infrared spectroscopy (3D-IR). The 3D-IR spectroscopy is sensitive to three-point frequency fluctuation correlation functions, and the measurements reveal heterogeneous structural relaxation dynamics. We interpret these results as subensembles of water which do not interconvert on a half picosecond time scale. We connect the experimental results to molecular dynamics (MD) simulations, performing a line shape analysis as well as complex network analysis.

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.

Heterodyne-detected dispersed vibrational echo spectroscopy

We develop heterodyned dispersed vibrational echo spectroscopy (HDVE) and demonstrate the new capabilities in biophysical applications. HDVE is a robust ultrafast technique that provides a characterization of the real and imaginary components of third-order nonlinear signals with high sensitivity and single-laser-shot capability and can be used to extract dispersed pump-probe and dispersed vibrational echo spectra. Four methods for acquiring HDVE phase and amplitude spectra were compared: Fourier transform spectral interferometry, a new phase modulation spectral interferometry technique, and combination schemes. These extraction techniques were demonstrated in the context of protein amide I spectroscopy. Experimental HDVE and heterodyned free induction decay amide I spectra were explicitly compared to conventional dispersed pump-probe, dispersed vibrational echo, and absorption spectra. The new capabilities of HDVE were demonstrated by acquiring single-shot spectra and melting curves of ubiquitin and concentration-dependent spectra of insulin suitable for extracting the binding constant for dimerization. The introduced techniques will prove particularly useful in transient experiments, studying irreversible reactions, and micromolar concentration studies of small proteins.

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.

Unobtrusive interferometer tracking by path length oscillation for multidimensional spectroscopy

We track the path difference between interferometer arms with few-nanometer accuracy without adding optics to the beam path. We measure the interference of a helium-neon beam that copropagates through the interferometer with midinfrared pulses used for multidimensional spectroscopy. This can indicate motion, but not direction. By oscillating the path length of one arm with a mirror on a piezoelectric stack and monitoring the oscillations of the recombined helium-neon beam, the direction can be calculated, and the path delay can be continuously tracked.

Purely absorptive three-dimensional infrared spectroscopy

We demonstrate a method to collect purely absorptive three-dimensional (3D) fifth-order vibrational spectra on the model system CO(2) in H(2)O. The six beam interferometer is described, as well as a method to experimentally determine the phase of the 3D spectrum. The measured spectra agree very well with simulations of the data based on the cumulant expansion. There are five peaks corresponding to different paths up and down the vibrational ladder. The positions, signs, and amplitudes of the peaks agree with theoretical predictions, and the intensities of the peaks scale linearly with concentration. Based on the concentration dependence and agreement between the simulations and measurements, we conclude that cascaded lower order signals contribute negligibly to the observed signal.

Coherently-controlled two-dimensional photon echo electronic spectroscopy

Optical two-dimensional photon-echo spectroscopy is realized with shaped excitation pulses, allowing coherent control of twodimensional spectra. This development enables probing of state-selective quantum decoherence and phase/time sensitive couplings between states. The coherently-controlled two-dimensional photon-echo spectrometer with two pulse shapers is based on a passively stabilized four-beam interferometer with diffractive optic, and allows heterodyne detection of signals with a long-term phase stability of approximately Lambda/100. The two-dimensional spectra of Rhodamine 101 in a methanol solution, measured with unshaped and shaped pulses, exhibit significant differences. We observe in particular, the appearance of fine structure in the spectra obtained using shaped excitation pulses.