Heterodyne-detected stimulated photon echo: applications to optical dynamics in solution

Interconnection between Polarization-Detected and Population-Detected Signals: Theoretical Results and Ab Initio Simulations

Most of spectroscopic signals are specified by the nonlinear laser-induced polarization. In recent years, population-detection of signals becomes a trend in femtosecond spectroscopy. Polarization-detected (PD) and population-detected signals are fundamentally different, because they are determined by photoinduced processes acting on disparate time scales. In this work, we consider the fluorescence-detected (FD) N-wave-mixing (NWM) signal as a representative example of population-detected signals, derive a rigorous expression for this signal, and discuss its approximate variants suitable for numerical simulations. This leads us to the definition of the phenomenological FD (PFD) signal, which contains as a special case all definitions of FD signals available in the literature. Then we formulate and prove the population-polarization equivalence (PPE) theorem, which states that PFD NWM signals produced by (possibly strong) laser pulses can be evaluated as conventional PD signals in which the effective polarization is determined by the PFD transition dipole moment operator. We use the PPE theorem for the construction of the ab initio protocol for the simulation of PFD 4WM signals. As an example, we calculate electronic two-dimensional (2D) PFD spectra of the gas-phase pyrazine and compare them with the corresponding PD 2D spectra.

Two-dimensional fluorescence excitation spectroscopy: A novel technique for monitoring excited-state photophysics of molecular species with high time and frequency resolution

We propose a novel UV/Vis femtosecond spectroscopic technique, two-dimensional fluorescence-excitation (2D-FLEX) spectroscopy, which combines spectral resolution during the excitation process with exclusive monitoring of the excited-state system dynamics at high time and frequency resolution. We discuss the experimental feasibility and realizability of 2D-FLEX, develop the necessary theoretical framework, and demonstrate the high information content of this technique by simulating the 2D-FLEX spectra of a model four-level system and the Fenna-Matthews-Olson antenna complex. We show that the evolution of 2D-FLEX spectra with population time directly monitors energy transfer dynamics and can thus yield direct qualitative insight into the investigated system. This makes 2D-FLEX a highly efficient instrument for real-time monitoring of photophysical processes in polyatomic molecules and molecular aggregates.

Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals

Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.

Fluorescence-Detected Two-Quantum Photon Echoes via Cogwheel Phase Cycling

Two-dimensional (2D) electronic spectroscopy can separate homogeneous and inhomogeneous broadening. While established methods usually probe a photon-echo signal, i.e., a third-order response, to access the homogeneous line width of singly excited states, the homogeneous line width of doubly excited states remained spectroscopically inaccessible. Here we demonstrate the acquisition of two-quantum (2Q) photon echoes using fluorescence-detected 2D spectroscopy. In these eighth-order signals, 2Q coherences are rephased with themselves, leading to line-narrowed 2Q-2Q 2D spectra. By using cogwheel phase cycling, adapted from nuclear magnetic resonance spectroscopy, we isolate the 2Q-2Q 2D spectra of a squaraine dimer and a squaraine polymer and verify the same selectivity of cogwheel phase cycling compared to traditional "nested" phase cycling. The observed difference, between the two systems, in the homogeneous line width of the biexciton can be rationalized as a signature of the interplay of exciton-exciton annihilation, exciton diffusion, and exciton delocalization.

Accurate phase detection in time-domain heterodyne SFG spectroscopy

Heterodyne detection is a ubiquitous tool in spectroscopy for the simultaneous detection of intensity and phase of light. However, the need for phase stability hinders the application of heterodyne detection to electronic spectroscopy. We present an interferometric design for a phase-sensitive electronic sum frequency generation (e-SFG) spectrometer in the time domain with lock-in detection. Our method of continuous phase modulation of one arm of the interferometer affords direct measurement of the phase between SFG and local oscillator fields. Errors in the path length difference caused by drifts in the optics are corrected, offering unprecedented stability. This spectrometer has the added advantage of collinear fundamental beams. The capabilities of the spectrometer are demonstrated with proof-of-principle experiments with GaAs e-SFG spectra, where we see significantly improved signal to noise ratio, spectral accuracy, and lineshapes.

Two-dimensional Infrared Spectroscopy Reveals Better Insights of Structure and Dynamics of Protein

Proteins play an important role in biological and biochemical processes taking place in the living system. To uncover these fundamental processes of the living system, it is an absolutely necessary task to understand the structure and dynamics of the protein. Vibrational spectroscopy is an established tool to explore protein structure and dynamics. In particular, two-dimensional infrared (2DIR) spectroscopy has already proven its versatility to explore the protein structure and its ultrafast dynamics, and it has essentially unprecedented time resolutions to observe the vibrational dynamics of the protein. Providing several examples from our theoretical and experimental efforts, it is established here that two-dimensional vibrational spectroscopy provides exceptionally more information than one-dimensional vibrational spectroscopy. The structural information of the protein is encoded in the position, shape, and strength of the peak in 2DIR spectra. The time evolution of the 2DIR spectra allows for the visualisation of molecular motions.

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.

Direct comparison of amplitude and geometric measures of spectral inhomogeneity using phase-cycled 2D-IR spectroscopy

Two-dimensional infrared (2D-IR) spectroscopy provides access to equilibrium dynamics with the extraction of the frequency-fluctuation correlation function (FFCF) from the measured spectra. Several different methods of obtaining the FFCF from experimental spectra, such as the center line slope (CLS), ellipticity, phase slope, and nodal line slope, all depend on the geometrical nature of the 2D line shape and necessarily require spectral extent in order to achieve a measure of the FFCF. Amplitude measures, on the other hand, such as the inhomogeneity index, rely only on signal amplitudes and can, in principle, be computed using just a single point in a 2D spectrum. With a pulse shaper-based 2D-IR spectrometer, in conjunction with phase cycling, we separate the rephasing and nonrephasing signals used to determine the inhomogeneity index. The same measured data provide the absorptive spectrum, needed for the CLS. Both methods are applied to two model molecular systems: tungsten hexacarbonyl (WCO₆) and methylcyclopentadienyl manganese tricarbonyl [Cp'Mn(CO)₃, MCMT]. The three degenerate IR modes of W(CO)₆ lack coherent modulation or noticeable intramolecular vibrational redistribution (IVR) and are used to establish a baseline comparison. The two bands of the MCMT tripod complex include intraband coherences and IVR as well as likely internal torsional motion on a few-picosecond time scale. We find essentially identical spectral diffusion, but faster, non-equilibrium dynamics lead to differences in the FFCFs extracted with the two methods. The inhomogeneity index offers an advantage in cases where spectra are complex and energy transfer can mimic line shape changes due to frequency fluctuations.

Recent advances in multidimensional ultrafast spectroscopy

Multidimensional ultrafast spectroscopies are one of the premier tools to investigate condensed phase dynamics of biological, chemical and functional nanomaterial systems. As they reach maturity, the variety of frequency domains that can be explored has vastly increased, with experimental techniques capable of correlating excitation and emission frequencies from the terahertz through to the ultraviolet. Some of the most recent innovations also include extreme cross-peak spectroscopies that directly correlate the dynamics of electronic and vibrational states. This review article summarizes the key technological advances that have permitted these recent advances, and the insights gained from new multidimensional spectroscopic probes.

Alternative view of two-dimensional spectroscopy

Femtosecond two-dimensional (2D) spectroscopy has become a widely employed method for the investigation of the dynamics of complex chemical and biological systems. In 2D spectroscopy, the sample is excited with three phase-locked femtosecond pulses, and the signal is heterodyned with the local oscillator field. The 2D spectrum is obtained by double Fourier transform with respect to the time delay between the first two pulses and the time delay between the third pulse and the local oscillator field. We show that 2D optical signals can alternatively be measured and computationally simulated as four-wave-mixing signals generated by two femtosecond pulses and two one-sided continuous-wave (CW) pulses. The first femtosecond pulse and one-sided CW pulse create the doorway state, while the second femtosecond pulse and one-sided CW pulse create the window state. This picture relates 2D spectroscopy to other mixed time-frequency-domain techniques, which is useful for the interpretation of the corresponding signals. Moreover, it allows a computationally efficient evaluation of 2D spectra.

Ultrafast Spectroscopy with Photocurrent Detection: Watching Excitonic Optoelectronic Systems at Work

While ultrafast spectroscopy with photocurrent detection was almost unknown before 2012, in the last 3 years, a number of research groups from different fields have independently developed ultrafast electric probe approaches and reported promising pilot studies. Here, we discuss these recent advances and provide our perspective on how photocurrent detection successfully overcomes many limitations of all-optical methods, which makes it a technique of choice when device photophysics is concerned. We also highlight compelling existing problems and research questions and suggest ways for further development, outlining the potential breakthroughs to be expected in the near future using photocurrent ultrafast optical probes.

Stabilized phase detection of heterodyne sum frequency generation for interfacial studies

We present a collinear-geometry heterodyne sum frequency generation (HD-SFG) method for interfacial studies. The HD detection is based on a collinear SFG configuration, in which picosecond visible and femtosecond IR beams are used to first produce a strong local oscillator and then to generate weak SFG signals from an interface. A time-delay compensator, consisting of an MgF2 window, is placed before the sample to introduce the time delay between the local oscillator and the interfacial SFG signals for spectral interferometry. Our HD-SFG method exhibits advantages of long-time phase stability. It is not sensitive to sample heights, does not require reflection correction, and is easy to implement.

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.

Ultrafast photochemistry in liquids

Ultrafast photochemical processes can occur in parallel with the relaxation of the optically populated excited state toward equilibrium. The latter involves both intra- and intermolecular modes, namely vibrational and solvent coordinates, and takes place on timescales ranging from a few tens of femtoseconds to up to hundreds of picoseconds, depending on the system. As a consequence, the reaction dynamics can substantially differ from those usually measured with slower photoinduced processes occurring from equilibrated excited states. For example, the decay of the excited-state population may become strongly nonexponential and depend on the excitation wavelength, contrary to the Kasha and Vavilov rules. In this article, we first give a brief account of our current understanding of vibrational and solvent relaxation processes. We then present an overview of important classes of ultrafast photochemical reactions, namely electron and proton transfer as well as isomerization, and illustrate with several examples how nonequilibrium effects can affect their dynamics.

Resolution of the relative phase ambiguity in spectral shearing interferometry of ultrashort pulses

We show that multiple-shear spectral shearing interferometry can overcome the relative phase ambiguity of disjoint spectral components that is present in single-shear approaches. By upconverting the unknown pulse with spatially chirped ancillae, we achieve a shear-to-space mapping that can be acquired on an imaging spectrometer. A subset of this continuous range of shears can be chosen for robust and accurate phase retrieval using a multiple-shear algorithm.

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.

Examination of enzymatic H-tunneling through kinetics and dynamics

In recent years, kinetic measurements of isotope effects of enzyme-catalyzed reactions and their temperature dependence led to the development of theoretical models that were used to rationalize the findings. These models suggested that motions at the femto- to picosecond (fs to ps) time scale modulate the environment of the catalyzed reaction. Due to the fast nature of motions that directly affect the cleavage of a covalent bond, it is challenging to correlate the enzyme kinetics and dynamics related to that step. We report a study of formate dehydrogenase (FDH) that compares the temperature dependence of intrinsic kinetic isotope effects (KIEs) to measurements of the environmental dynamics at the fs-ps time scale (Bandaria et al. J. Am. Chem. Soc. 2008, 130, 22-23). The findings from this comparison of experimental kinetics and dynamics are consistent with models of environmentally coupled H-tunneling models, also known as Marcus-like models. Apparently, at tunneling ready conformations, the donor-acceptor distance, orientation, and fluctuations seems to be well tuned for H-transfer and are not affected by thermal fluctuations slower than 10 ps. This phenomenon has been suggested in the past to be quite general in enzymatic reactions. Here, the kinetics and the dynamics measurements on a single chemical step and on fs-ps time scale, respectively, provide new insight and support for the relevant theoretical models. Furthermore, this methodology could be applied to other systems and be used to examine mutants for which the organization of the donor and acceptor is not ideal, or enzymes with different rigidity and different temperature optimum.

How to turn your pump-probe instrument into a multidimensional spectrometer: 2D IR and Vis spectroscopies via pulse shaping

We have recently developed a new and simple way of collecting 2D infrared and visible spectra that utilizes a pulse shaper and a partly collinear beam geometry. 2D IR and Vis spectroscopies are powerful tools for studying molecular structures and their dynamics. They can be used to correlate vibrational or electronic eigenstates, measure energy transfer rates, and quantify the dynamics of lineshapes, for instance, all with femtosecond time-resolution. As a result, they are finding use in systems that exhibit fast dynamics, such as sub-millisecond chemical and biological dynamics, and in hard-to-study environments, such as in membranes. While powerful, these techniques have been difficult to implement because they require a series of femtosecond pulses to be spatially and temporally overlapped with precise time-resolution and interferometric phase stability. However, many of the difficulties associated with implementing 2D spectroscopies are eliminated by using a pulse shaper and a simple beam geometry, which substantially lowers the technical barriers required for researchers to enter this exciting field while simultaneously providing many new capabilities. The aim of this paper is to provide an overview of the methods for collecting 2D spectra so that an outsider considering using 2D spectroscopy in their own research can judge which approach would be most suitable for their research aims. This paper focuses primarily on 2D IR spectroscopy, but also includes our recent work on adapting this technology to collecting 2D Vis spectra. We review work that has already been published as well as cover several topics that we have not reported previously, including phase cycling methods to remove background signals, eliminate unwanted scatter, and shift data collection into the rotating frame.

Two-color two-dimensional Fourier transform electronic spectroscopy with a pulse-shaper

We report two-color two-dimensional Fourier transform electronic spectroscopy obtained using an acousto-optic pulse-shaper in a pump-probe geometry. The two-color setup will facilitate the study of energy transfer between electronic transitions that are widely separated in energy. We demonstrate the method at visible wavelengths on the laser dye LDS750 in acetonitrile. We discuss phase-cycling and polarization schemes to optimize the signal-to-noise ratio in the pump-probe geometry. We also demonstrate that phase-cycling can be used to separate rephasing and nonrephasing signal components.

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

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

Nonlinear wave-packet interferometry and molecular state reconstruction in a vibrating and rotating diatomic molecule

We formulate two-color nonlinear wave-packet interferometry (WPI) for application to a diatomic molecule in the gas phase and show that this form of heterodyne-detected multidimensional electronic spectroscopy will permit the reconstruction of photoinduced rovibrational wave packets from experimental data. Using two phase-locked pulse pairs, each resonant with a different electronic transition, nonlinear WPI detects the quadrilinear interference contributions to the population of an excited electronic state. Combining measurements taken with different phase-locking angles isolates various quadrilinear interference terms. One such term gives the complex overlap between a propagated one-pulse target wave packet and a variable three-pulse reference wave packet. The two-dimensional interferogram in the time domain specifies the complex-valued overlap of the given target state with a collection of variable reference states. An inversion procedure based on singular-value decomposition enables reconstruction of the target wave packet from the interferogram without prior detailed characterization of the nuclear Hamiltonian under which the target propagates. With numerically calculated nonlinear WPI signals subject to Gaussian noise, we demonstrate the reconstruction of a rovibrational wave packet launched from the A state and propagated in the E state of Li2.

Automated 2D IR spectroscopy using a mid-IR pulse shaper and application of this technology to the human islet amyloid polypeptide

The capability of 2D IR spectroscopy to elucidate time-evolving structures is enhanced by a programmable mid-IR pulse shaper that greatly improves the ease, speed, and accuracy of data collection. Traditional ways of collecting 2D IR spectra are difficult to implement, cause distorted peak shapes, and result in poor time resolution and/or phase problems. We report on several methods for collecting 2D IR spectra by using a computer-controlled germanium acoustooptic modulator that overcomes the above problems. The accuracy and resolution of each method is evaluated by using model metal carbonyl compounds that have well defined lineshapes. Furthermore, phase cycling can now be employed to largely alleviate background scatter from heterogeneous samples. With these methods in hand, we apply 2D IR spectroscopy to study the structural diversity in amyloid fibers of aggregated human islet amyloid polypeptide (hIAPP), which is involved with type 2 diabetes. The 2D IR spectra reveal that the beta-sheet fibers have a large structural distribution, as evidenced by an inhomogeneously broadened beta-sheet peak and strong coupling to random coil conformations. Structural diversity is an important characteristic of hIAPP because it may be that partly folded peptides cause the disease. This experiment on hIAPP is an example of how computer generation of 2D IR pulse sequences is a key step toward automating 2D IR spectroscopy, so that new pulse sequences can be implemented quickly and a diverse range of systems can be studied more easily.

Wave packet interferometry and quantum state reconstruction by acousto-optic phase modulation

Studies of wave packet dynamics often involve phase-selective measurements of coherent optical signals generated from sequences of ultrashort laser pulses. In wave packet interferometry (WPI), the separation between the temporal envelopes of the pulses must be precisely monitored or maintained. Here we introduce a new (and easy to implement) experimental scheme for phase-selective measurements that combines acousto-optic phase modulation with ultrashort laser excitation to produce an intensity-modulated fluorescence signal. Synchronous detection, with respect to an appropriately constructed reference, allows the signal to be simultaneously measured at two phases differing by 90 degrees. Our method effectively decouples the relative temporal phase from the pulse envelopes of a collinear train of optical pulse pairs. We thus achieve a robust and high signal-to-noise scheme for WPI applications, such as quantum state reconstruction and electronic spectroscopy. The validity of the method is demonstrated, and state reconstruction is performed, on a model quantum system--atomic Rb vapor. Moreover, we show that our measurements recover the correct separation between the absorptive and dispersive contributions to the system susceptibility.

Amide I Vibrational Dynamics ofN-Methylacetamide in Polar Solvents: The Role of Electrostatic Interactions

The vibrational frequency of the amide I transition of peptides is known to be sensitive to the strength of its hydrogen bonding interactions. In an effort to account for interactions with hydrogen bonding solvents in terms of electrostatics, we study the vibrational dynamics of the amide I coordinate of N-methylacetamide in prototypical polar solvents: D2O, CDCl3, and DMSO-d6. These three solvents have varying hydrogen bonding strengths, and provide three distinct solvent environments for the amide group. The frequency-frequency correlation function, the orientational correlation function, and the vibrational relaxation rate of the amide I vibration in each solvent are retrieved by using three-pulse vibrational photon echoes, two-dimensional infrared spectroscopy, and pump-probe spectroscopy. Direct comparisons are made to molecular dynamics simulations. We find good quantitative agreement between the experimentally retrieved and simulated correlation functions over all time scales when the solute-solvent interactions are determined from the electrostatic potential between the solvent and the atomic sites of the amide group.

Exciton Analysis in 2D Electronic Spectroscopy

A theoretical description of femtosecond two-dimensional electronic spectroscopy of multichromophoric systems is presented. Applying the stationary phase approximation to the calculation of photon echo spectra and taking into account exciton relaxation processes, we obtain an analytic expression for numerical simulations of time- and frequency-resolved 2D photon echo signals. The delocalization of one-exciton states, spatial overlaps between the probability densities of different excitonic states, and their influences on both one- and two-dimensional electronic spectra are studied. The nature of the off-diagonal cross-peaks and the time evolution of both diagonal and off-diagonal peak amplitudes are discussed in detail by comparing experimentally measured and theoretically simulated 2D spectra of the natural Fenna-Matthews-Olson (FMO) photosynthetic light-harvesting complex. We find that there are two noncascading exciton energy relaxation pathways.

Spectrally resolved femtosecond 2-colour 3-pulse photon echoes: a new spectroscopic tool to study molecular dynamics

We present a new multidimensional femtosecond spectroscopy technique based on spectrally resolved 2-colour 3-pulse photon echoes for investigating molecular dynamics in a variety of systems including proteins. In this technique the sample is illuminated by two femtosecond 'pump' pulses with wave vectors k1, k2 and wavelength lambda(pump) and a femtosecond 'probe' pulse with wave vector k3 and wavelength lambda(probe). Nonlinear signals are generated in the phase-matching directions k4 = - k1 + k2 + k3 and k6 = - k3 + k1 + k2. These signals are analysed in spectrometers equipped with CCD detectors and the spectra of the signals are recorded for various values of (i) the delay t12 between pulses 1 and 2, (ii) the delay t23 between pulses 2 and 3, and (iii) the wavelengths lambda(pump), lambda(probe). The technique has been used for studying vibrational and electronic dynamics of dye molecules, such as cresyl violet in methanol, and ultra-fast transient processes that occur during the photo-dissociation of carbonmonoxy myoglobin (MbCO) into myoglobin (Mb) and CO.

Phase-stabilized two-dimensional electronic spectroscopy

Two-dimensional (2D) spectroscopy is a powerful technique to study nuclear and electronic correlations between different transitions or initial and final states. Here we describe in detail our development of inherently phase-stabilized 2D Fourier-transform spectroscopy for electronic transitions. A diffractive-optic setup is used to realize heterodyne-detected femtosecond four-wave mixing in a phase-matched box geometry. Wavelength tunability in the visible range is accomplished by means of a 3 kHz repetition-rate laser system and optical parametric amplification. Nonlinear signals are fully characterized by spectral interferometry. Starting from fundamental principles, we discuss the origin of phase stability and the precise calibration of excitation-pulse time delays using movable glass wedges. Automated subtraction of undesired scattering terms removes experimental artifacts. On the theoretical side, the response-function formalism is extended to describe molecules with three electronic levels, and the shape of 2D spectral features is discussed. As an example for this technique, experimental 2D spectra are shown for the dye molecule Nile Blue in acetonitrile at 595 nm, recorded for a series of population times. Simulations explore the influence of different model parameters and qualitatively reproduce the experimental results. We show that correlations between different electronically excited states can be determined from the spectra. The technique described here can be used to measure the third-order response function of complex systems covering several electronic transitions.

Molecular state reconstruction by nonlinear wave packet interferometry

We show that time- and phase-resolved two-color nonlinear wave packet interferometry can be used to reconstruct the probability amplitude of an optically prepared molecular wave packet without prior knowledge of the underlying potential surface. We analyze state reconstruction in pure- and mixed-state model systems excited by shaped laser pulses and propose nonlinear wave packet interferometry as a tool for identifying optimized wave packets in coherent control experiments.

Spectrally resolved femtosecond two-color three-pulse photon echoes: Study of ground and excited state dynamics in molecules

We report the use of spectrally resolved femtosecond two-color three-pulse photon echoes as a potentially powerful multidimensional technique for studying vibrational and electronic dynamics in complex molecules. The wavelengths of the pump and probe laser pulses are found to have a dramatic effect on the spectrum of the photon echo signal and can be chosen to select different sets of energy levels in the vibrational manifold, allowing a study of the dynamics and vibrational splitting in either the ground or the excited state. The technique is applied to studies of the dynamics of vibrational electronic states in the dye molecule Rhodamine 101 in methanol.

Myoglobin-CO substate structures and dynamics: multidimensional vibrational echoes and molecular dynamics simulations

Spectrally resolved infrared stimulated vibrational echo data were obtained for sperm whale carbonmonoxymyoglobin (MbCO) at 300 K. The measured dephasing dynamics of the CO ligand are in agreement with dephasing dynamics calculated with molecular dynamics (MD) simulations for MbCO with the residue histidine-64 (His64) having its imidazole epsilon nitrogen protonated (N(epsilon)-H). The two conformational substate structures B(epsilon) and R(epsilon) observed in the MD simulations are assigned to the spectroscopic A(1) and A(3) conformational substates of MbCO, respectively, based on the agreement between the experimentally measured and calculated dephasing dynamics for these substates. In the A(1) substate, the N(epsilon)-H proton and N(delta) of His64 are approximately equidistant from the CO ligand, while in the A(3) substate, the N(epsilon)-H of His64 is oriented toward the CO, and the N(delta) is on the surface of the protein. The MD simulations show that dynamics of His64 represent the major source of vibrational dephasing of the CO ligand in the A(3) state on both femtosecond and picosecond time scales. Dephasing in the A(1) state is controlled by His64 on femtosecond time scales, and by the rest of the protein and the water solvent on longer time scales.

Femtosecond phase-coherent two-dimensional spectroscopy

Femtosecond phase-coherent two-dimensional (2D) spectroscopy has been experimentally demonstrated as the direct optical analog of 2D nuclear magnetic resonance. An acousto-optic pulse shaper created a collinear three-pulse sequence with well-controlled and variable interpulse delays and phases,which interacted with a model atomic system of rubidium vapor. The desired nonlinear polarization was selected by phase cycling (coadding experimental results obtained with different interpulse phases). This method may enhance our ability to probe the femtosecond structural dynamics of macromolecules.

Two-dimensional femtosecond spectroscopy

The simplest two-dimensional (2D) spectra show how excitation with one (variable) frequency affects the spectrum at all other frequencies, thus revealing the molecular connections between transitions. Femtosecond 2D Fourier transform (2D FT) spectra are more flexible and share some of the remarkable properties of their conceptual parent, 2D FT nuclear magnetic resonance. When 2D FT spectra are experimentally separated into real absorptive and imaginary refractive parts, the time resolution and frequency resolution can both reach the uncertainty limit set for each resonance by the sample itself. Coherent four-level contributions to the signal provide new molecular phase information, such as relative signs of transition dipoles. The nonlinear response can be picked apart by selecting a single coherence pathway (e.g., specifying the relative signs of energy level difference frequencies during different time intervals as in the photon echo). Because molecules are frozen on the femtosecond timescale, femtosecond 2D FT experiments can separate a distribution of instantaneous molecular environments and intramolecular geometries as inhomogeneous broadening. This review provides an introduction to two-dimensional Fourier transform experiments exploiting second- and third-order vibrational and electronic nonlinearities.