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

Fluorescence-Detected Two-Dimensional Electronic Spectroscopy of a Single Molecule

Single-molecule fluorescence spectroscopy is a powerful method that avoids ensemble averaging, but its temporal resolution is limited by the fluorescence lifetime to nanoseconds at most. At the ensemble level, two-dimensional spectroscopy provides insight into ultrafast femtosecond processes, such as energy transfer and line broadening, even beyond the Fourier limit, by correlating pump and probe spectra. Here, we combine these two techniques and demonstrate coherent 2D spectroscopy of individual dibenzoterrylene (DBT) molecules at room temperature. We excite the molecule in a confocal microscope with a phase-modulated train of femtosecond pulses and detect the emitted fluorescence with single-photon counting detectors. Using a phase-sensitive detection scheme, we were able to measure the nonlinear 2D spectra of most of the DBT molecules that we studied. Our method is applicable to a wide range of single emitters and opens new avenues for understanding energy transfer in single quantum objects on ultrafast time scales.

Interferometric excitation fluorescence lifetime imaging microscopy

Fluorescence lifetime imaging microscopy (FLIM) is a well-established technique with numerous imaging applications. Yet, one of the limitations of FLIM is that it only provides information about the emitting state. Here, we present an extension of FLIM by interferometric measurement of fluorescence excitation spectra. Interferometric Excitation Fluorescence Lifetime Imaging Microscopy (ixFLIM) reports on the correlation of the excitation spectra and emission lifetime, providing the correlation between the ground-state absorption and excited-state emission. As such, it extends the applicability of FLIM and removes some of its limitations. We introduce ixFLIM on progressively more complex systems, directly compare it to standard FLIM, and apply it to quantitative resonance energy transfer imaging from a single measurement.

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.

Coherent Vibrations Promote Charge-Transfer across a Graphene-Based Interface

Discerning the impact of the coherent motion of the nuclei on the timing and efficiency of charge transfer at the donor-acceptor interface is essential for designing performance-enhanced optoelectronic devices. Here, we employ an experimental approach using photocurrent detection in coherent multidimensional spectroscopy to excite a donor aromatic macrocycle and collect the charge transferred to a 2D acceptor layer. For this purpose, we prepared a cobalt phthalocyanine-graphene (CoPc-Gr) interface. Unlike blends, the well-ordered architecture achieved through the physical separation of the two layers allows us to unambiguously collect the electrical signal from graphene alone and associate it with a microscopic understanding of the whole process. The CoPc-Gr interface exhibits an ultrafast electron-transfer signal, stemming from an interlayer mechanism. Remarkably, the signal presents an oscillating time evolution modulated by coherent vibrations originating from the laser-excited CoPc states. By performing Fourier analysis on the beatings and correlating it with the Raman features, along with a comprehensive first-principles characterization of the vibrational coupling in the CoPc excited states, we successfully identify both the orbitals and molecular vibrations that promote the charge transfer at the interface.

Expanding the bandwidth of fluorescence-detected two-dimensional electronic spectroscopy using a broadband continuum probe pulse pair

We demonstrate fluorescence-detected two-dimensional electronic spectroscopy (F-2DES) with a broadband, continuum probe pulse pair in the pump-probe geometry. The approach combines a pump pulse pair generated by an acousto-optic pulse-shaper with precise control of the relative pump pulse phase and time delay with a broadband, continuum probe pulse pair created using the Translating Wedge-based Identical pulses eNcoding System (TWINS). The continuum probe expands the spectral range of the detection axis and lengthens the waiting times that can be accessed in comparison to implementations of F-2DES using a single pulse-shaper. We employ phase-cycling of the pump pulse pair and take advantage of the separation of signals in the frequency domain to isolate rephasing and non-rephasing signals and optimize the signal-to-noise ratio. As proof of principle, we demonstrate broadband F-2DES on a laser dye and bacteriochlorophyll a.

Two-photon excitation two-dimensional fluorescence spectroscopy (2PE-2DFS) of the fluorescent nucleobase 6-MI

Base stacking is fundamentally important to the stability of double-stranded DNA. However, few experiments can directly probe the local conformations and conformational fluctuations of the DNA bases. Here we report a new spectroscopic approach to study the local conformations of DNA bases using the UV-absorbing fluorescent guanine analogue, 6-methyl isoxanthopterin (6-MI), which can be used as a site-specific probe to label DNA. In these experiments, we apply a two-photon excitation (2PE) approach to two-dimensional fluorescence spectroscopy (2DFS), which is a fluorescence-detected nonlinear Fourier transform spectroscopy. In 2DFS, a repeating sequence of four collinear laser pulses (with center wavelength ~ 675 nm and relative phases swept at radio frequencies) is used to excite the lowest energy electronic-vibrational (vibronic) transitions of 6-MI (with center wavelength ~ 340 nm). The ensuing low flux fluorescence is phase-synchronously detected at the level of individual photons and as a function of inter-pulse delay. The 2PE transition pathways that give rise to electronically excited state populations include optical coherences between electronic ground and excited states and non-resonant (one-photon-excited) virtual states. Our results indicate that 2PE-2DFS experiments can provide information about the electronic-vibrational spectrum of the 6-MI monomer, in addition to the conformation-dependent exciton coupling between adjacent 6-MI monomers within a (6-MI)2 dimer. In principle, this approach can be used to determine the local base-stacking conformations of (6-MI)2 dimer-substituted DNA constructs.

Nonlinear Optical Spectroscopy of Molecular Assemblies: What Is Gained and Lost in Action Detection?

This study elucidates the information content that is extracted from action-2D electronic spectroscopy (A-2DES) when the output intensity is not proportional to the number of excitations generated. Such a scenario can be realized in both fluorescence and photocurrent detection because of direct interaction like exciton-exciton annihilation or indirect effects in the signal generation or detection. By means of an intuitive probabilistic model supported by nonlinear response theory, the study concludes that in molecular assemblies the ground-state bleaching contribution can dominate the nonlinear signal and partially or completely hide the stimulated emission. In this case, the spectral effect resembles incoherent mixing, even in the absence of exciton-exciton annihilation, implying reduced information about the excited-state dynamics with an increasing number of chromophores. This finding has important implications for the selection of samples for A-2DES as well as for its interpretation.

Multimode vibrational dynamics and orientational effects in fluorescence-encoded infrared spectroscopy. I. Response function theory

Fluorescence-encoded infrared (FEIR) spectroscopy is an emerging technique for performing vibrational spectroscopy in solution with detection sensitivity down to single molecules. FEIR experiments use ultrashort pulses to excite a fluorescent molecule's vibrational and electronic transitions in a sequential, time-resolved manner, and are therefore sensitive to intervening vibrational dynamics on the ground state, vibronic coupling, and the relative orientation of vibrational and electronic transition dipole moments. This series of papers presents a theoretical treatment of FEIR spectroscopy that describes these phenomena and examines their manifestation in experimental data. This first paper develops a nonlinear response function description of Fourier-transform FEIR experiments for a two-level electronic system coupled to multiple vibrations, which is then applied to interpret experimental measurements in the second paper [L. Whaley-Mayda et al., J. Chem. Phys. 159, 194202 (2023)]. Vibrational coherence between pairs of modes produce oscillatory features that interfere with the vibrations' population response in a manner dependent on the relative signs of their respective Franck-Condon wavefunction overlaps, leading to time-dependent distortions in FEIR spectra. The orientational response of population and coherence contributions are analyzed and the ability of polarization-dependent experiments to extract relative transition dipole angles is discussed. Overall, this work presents a framework for understanding the full spectroscopic information content of FEIR measurements to aid data interpretation and inform optimal experimental design.

Two-Dimensional Infrared Spectroscopy of Isolated Molecular Ions

Two-dimensional infrared (2D IR) spectroscopy of mass-selected, cryogenically cooled molecular ions is presented. Nonlinear response pathways, encoded in the time-domain photodissociation action response of weakly bound N2 messenger tags, were isolated using pulse shaping techniques following excitation with four collinear ultrafast IR pulses. 2D IR spectra of Re(CO)3(CH3CN)3+ ions capture off-diagonal cross-peak bleach signals between the asymmetric and symmetric carbonyl stretching transitions. These cross peaks display intensity variations as a function of pump-probe delay time due to coherent coupling between the vibrational modes. Well-resolved 2D IR features in the congested fingerprint region of protonated caffeine (C8H10N4O2H+) are also reported. Importantly, intense cross-peak signals were observed at 3 ps waiting time, indicating that tag-loss dynamics are not competing with the measured nonlinear signals. These demonstrations pave the way for more precise studies of molecular interactions and dynamics that are not easily obtainable with current condensed-phase methodologies.

Parameter estimation in ultrafast spectroscopy using probability theory

Ultrafast spectroscopy is a powerful technique that utilizes short pulses on the femtosecond time scale to generate and probe coherent responses in molecular systems. While the specific ultrafast methodologies vary, the most common data analysis tools rely on discrete Fourier transformation for recovering coherences that report on electronic or vibrational states and multi-exponential fitting for probing population dynamics, such as excited-state relaxation. These analysis tools are widely used due to their perceived reliability in estimating frequencies and decay rates. Here, we demonstrate that such "black box" methods for parameter estimation often lead to inaccurate results even in the absence of noise. To address this issue, we propose an alternative approach based on Bayes probability theory that simultaneously accounts for both population and coherence contributions to the signal. This Bayesian inference method offers accurate parameter estimations across a broad range of experimental conditions, including scenarios with high noise and data truncation. In contrast to traditional methods, Bayesian inference incorporates prior information about the measured signal and noise, leading to improved accuracy. Moreover, it provides estimator error bounds, enabling a systematic statistical framework for interpreting confidence in the results. By employing Bayesian inference, all parameters of a realistic model system may be accurately recovered, even in extremely challenging scenarios where Fourier and multi-exponential fitting methods fail. This approach offers a more reliable and comprehensive analysis tool for time-resolved coherent spectroscopy, enhancing our understanding of molecular systems and enabling a better interpretation of experimental data.

Higher-Order Multidimensional and Pump-Probe Spectroscopies

Transient absorption and coherent two-dimensional spectroscopy are widely established methods for the investigation of ultrafast dynamics in quantum systems. Conventionally, they are interpreted in the framework of perturbation theory at the third order of interaction. Here, we discuss the potential of higher-(than-third-)order pump-probe and multidimensional spectroscopy to provide insight into excited multiparticle states and their dynamics. We focus on recent developments from our group. In particular, we demonstrate how phase cycling can be used in fluorescence-detected two-dimensional spectroscopy to isolate higher-order spectra that provide information about highly excited states such as the correlation of multiexciton states. We discuss coherently detected fifth-order 2D spectroscopy and its power to track exciton diffusion. Finally, we show how to extract higher-order signals even from ordinary pump-probe experiments, providing annihilation-free signals at high excitation densities and insight into multiexciton interactions.

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.

Resolving Nonlinear Recombination Dynamics in Semiconductors via Ultrafast Excitation Correlation Spectroscopy: Photoluminescence versus Photocurrent Detection

We explore the application of excitation correlation spectroscopy to detect nonlinear photophysical dynamics in two distinct semiconductor classes through time-integrated photoluminescence and photocurrent measurements. In this experiment, two variably delayed femtosecond pulses excite the semiconductor, and the time-integrated photoluminescence or photocurrent component arising from the nonlinear dynamics of the populations induced by each pulse is measured as a function of inter-pulse delay by phase-sensitive detection with a lock-in amplifier. We focus on two limiting materials systems with contrasting optical properties: a prototypical lead-halide perovskite (LHP) solar cell, in which primary photoexcitations are charge photocarriers, and a single-component organic-semiconductor diode, which features Frenkel excitons as primary photoexcitations. The photoexcitation dynamics perceived by the two detection schemes in these contrasting systems are distinct. Nonlinear-dynamic contributions in the photoluminescence detection scheme arise from contributions to radiative recombination in both materials systems, while photocurrent arises directly in the LHP but indirectly following exciton dissociation in the organic system. Consequently, the basic photophysics of the two systems are reflected differently when comparing measurements with the two detection schemes. Our results indicate that photoluminescence detection in the LHP system provides valuable information about trap-assisted and Auger recombination processes, but that these processes are convoluted in a nontrivial way in the photocurrent response and are therefore difficult to differentiate. In contrast, the organic-semiconductor system exhibits more directly correlated responses in the nonlinear photoluminescence and photocurrent measurements, as charge carriers are secondary excitations only generated through exciton dissociation processes. We propose that bimolecular annihilation pathways mainly contribute to the generation of charge carriers in single-component organic semiconductor devices. Overall, our work highlights the utility of excitation correlation spectroscopy in modern semiconductor materials research, particularly in the analysis of nonlinear photophysical processes, which are deterministic for their electronic and optical properties.

Double-quantum spectroscopy of dense atomic vapors: Interplay between Doppler and self-broadenings

In this article, we present a simulation study of the linear and nonlinear spectroscopy of dense atomic vapors. Motivated by recent experiments, we focus on double quantum spectroscopy, which directly probes dipole-dipole interactions. By explicitly including thermal velocity, we show that temperature has an important impact on the self-broadening mechanisms of the linear and nonlinear spectra. We also provide analytical expressions for the response functions in the short time limit using the two-body approximation, which shows that double quantum spectroscopy for atomic vapors directly probes the transition amplitude of the electronic excitation between two atoms. We also propose an expression for the double quantum spectrum that includes the effect of Doppler broadening, and we discuss the effect of density on the spectrum. We show that when Doppler broadening is negligible compared to self-broadening, the double quantum spectrum scales with the atomic density, while when Doppler broadening dominates, it scales as the square of the density.

Progress and Prospects in Optical Ultrafast Microscopy in the Visible Spectral Region: Transient Absorption and Two-Dimensional Microscopy

Ultrafast optical microscopy, generally employed by incorporating ultrafast laser pulses into microscopes, can provide spatially resolved mechanistic insight into scientific problems ranging from hot carrier dynamics to biological imaging. This Review discusses the progress in different ultrafast microscopy techniques, with a focus on transient absorption and two-dimensional microscopy. We review the underlying principles of these techniques and discuss their respective advantages and applicability to different scientific questions. We also examine in detail how instrument parameters such as sensitivity, laser power, and temporal and spatial resolution must be addressed. Finally, we comment on future developments and emerging opportunities in the field of ultrafast microscopy.

Unifying Nonlinear Response and Incoherent Mixing in Action-2D Electronic Spectroscopy

Action-detection has expanded the scope and applicability of 2D electronic spectroscopy, while posing new challenges for the unambiguous interpretation of spectral features. In this context, identifying the origin of cross-peaks at early waiting times is not trivial, and incoherent mixing is often invoked as an unwanted contribution masking the nonlinear signal. In this work, we elaborate on the relation between the nonlinear response and the incoherent mixing contribution by analyzing the action signal in terms of one- and two-particle observables. Considering a weakly interacting molecular dimer, we show how cross-peaks at early waiting times, reflecting exciton-exciton annihilation dynamics, can be equivalently interpreted as arising from incoherent mixing. This equivalence, on the one hand, highlights the information content of spectral features related to incoherent mixing and, on the other hand, provides an efficient numerical scheme to simulate the action response of weakly interacting systems.

Breaking Barriers in Ultrafast Spectroscopy and Imaging Using 100 kHz Amplified Yb-Laser Systems

ConspectusUltrafast spectroscopy and imaging have become tools utilized by a broad range of scientists involved in materials, energy, biological, and chemical sciences. Commercialization of ultrafast spectrometers including transient absorption spectrometers, vibrational sum frequency generation spectrometers, and even multidimensional spectrometers have put these advanced spectroscopy measurements into the hands of practitioners originally outside the field of ultrafast spectroscopy. There is now a technology shift occurring in ultrafast spectroscopy, made possible by new Yb-based lasers, that is opening exciting new experiments in the chemical and physical sciences. Amplified Yb-based lasers are not only more compact and efficient than their predecessors but also, most importantly, operate at many times the repetition rate with improved noise characteristics in comparison to the previous generation of Ti:sapphire amplifier technologies. Taken together, these attributes are enabling new experiments, generating improvements to long-standing techniques, and affording the transformation of spectroscopies to microscopies. This Account aims to show that the shift to 100 kHz lasers is a transformative step in nonlinear spectroscopy and imaging, much like the dramatic expansion that occurred with the commercialization of Ti:sapphire laser systems in the 1990s. The impact of this technology will be felt across a great swath of scientific communities. We first describe the technology landscape of amplified Yb-based laser systems used in conjunction with 100 kHz spectrometers operating with shot-to-shot pulse shaping and detection. We also identify the range of different parametric conversion and supercontinuum techniques which now provide a path to making pulses of light optimal for ultrafast spectroscopy. Second, we describe specific instances from our laboratories of how the amplified Yb-based light sources and spectrometers are transformative. For multiple probe time-resolved infrared and transient 2D IR spectroscopy, the gain in temporal span and signal-to-noise enables dynamical spectroscopy measurements from femtoseconds to seconds. These gains widen the applicability of time-resolved infrared techniques across a range of topics in photochemistry, photocatalysis, and photobiology as well as lower the technical barriers to implementation in a laboratory. For 2D visible spectroscopy and microscopy with white light, as well as 2D IR imaging, the high repetition rates of these new Yb-based light sources allow one to spatially map 2D spectra while maintaining high signal-to-noise in the data. To illustrate the gains, we provide examples of imaging applications in the study of photovoltaic materials and spectroelectrochemistry.

Ultrafast transient vibrational action spectroscopy of cryogenically cooled ions

Ultrafast transient vibrational action spectra of cryogenically cooled Re(CO)3(CH3CN)3+ ions are presented. Nonlinear spectra were collected in the time domain by monitoring the photodissociation of a weakly bound N2 messenger tag as a function of delay times and phases between a set of three infrared pulses. Frequency-resolved spectra in the carbonyl stretch region show relatively strong bleaching signals that oscillate at the difference frequency between the two observed vibrational features as a function of the pump-probe waiting time. This observation is consistent with the presence of nonlinear pathways resulting from underlying cross-peak signals between the coupled symmetric-asymmetric C≡O stretch pair. The successful demonstration of frequency-resolved ultrafast transient vibrational action spectroscopy of dilute molecular ion ensembles provides an exciting, new framework for the study of molecular dynamics in isolated, complex molecular ion systems.

High-order pump-probe and high-order two-dimensional electronic spectroscopy on the example of squaraine oligomers

Time-resolved spectroscopy is commonly used to study diverse phenomena in chemistry, biology, and physics. Pump-probe experiments and coherent two-dimensional (2D) spectroscopy have resolved site-to-site energy transfer, visualized electronic couplings, and much more. In both techniques, the lowest-order signal, in a perturbative expansion of the polarization, is of third order in the electric field, which we call a one-quantum (1Q) signal because in 2D spectroscopy it oscillates in the coherence time with the excitation frequency. There is also a two-quantum (2Q) signal that oscillates in the coherence time at twice the fundamental frequency and is fifth order in the electric field. We demonstrate that the appearance of the 2Q signal guarantees that the 1Q signal is contaminated by non-negligible fifth-order interactions. We derive an analytical connection between an nQ signal and (2n + 1)th-order contaminations of an rQ (with r < n) signal by studying Feynman diagrams of all contributions. We demonstrate that by performing partial integrations along the excitation axis in 2D spectra, we can obtain clean rQ signals free of higher-order artifacts. We exemplify the technique using optical 2D spectroscopy on squaraine oligomers, showing clean extraction of the third-order signal. We further demonstrate the analytical connection with higher-order pump-probe spectroscopy and compare both techniques experimentally. Our approach demonstrates the full power of higher-order pump-probe and 2D spectroscopy to investigate multi-particle interactions in coupled systems.

Studies of Local DNA Backbone Conformation and Conformational Disorder Using Site-Specific Exciton-Coupled Dimer Probe Spectroscopy

The processes of genome expression, regulation, and repair require direct interactions between proteins and DNA at specific sites located at and near single-stranded-double-stranded DNA (ssDNA-dsDNA) junctions. Here, we review the application of recently developed spectroscopic methods and analyses that combine linear absorbance and circular dichroism spectroscopy with nonlinear 2D fluorescence spectroscopy to study the local conformations and conformational disorder of the sugar-phosphate backbones of ssDNA-dsDNA fork constructs that have been internally labeled with exciton-coupled cyanine (iCy3)2 dimer probes. With the application of these methods, the (iCy3)2 dimer can serve as a reliable probe of the mean local conformations and conformational distributions of the sugar-phosphate backbones of dsDNA at various critical positions. The results of our studies suggest a possible structural framework for understanding the roles of DNA breathing in driving the processes of protein-DNA complex assembly and function.

Pulse overlap artifacts and double quantum coherence spectroscopy

The double quantum coherence (DQC) signal in nonlinear spectroscopy gives information about the many-body correlation effects not easily available by other methods. The signal is short-lived, consequently, a significant part of it is generated during the pulse overlap. Since the signal is at two times the laser frequency, one may intuitively expect that the pulse overlap-related artifacts are filtered out by the Fourier transform. Here, we show that this is not the case. We perform explicit calculations of phase-modulated two-pulse experiments of a two-level system where the DQC is impossible. Still, we obtain a significant signal at the modulation frequency, which corresponds to the DQC, while the Fourier transform over the pulse delay shows a double frequency. We repeat the calculations with a three-level system where the true DQC signal occurs. We conclude that with realistic dephasing times, the pulse-overlap artifact can be significantly stronger than the DQC signal. Our results call for great care when analyzing such experiments. As a rule of thumb, we recommend that only delays larger than 1.5 times the pulse length should be used.

Non-Hermitian Hamiltonians for linear and nonlinear optical response: A model for plexcitons

In polaritons, the properties of matter are modified by mixing the molecular transitions with light modes inside a cavity. Resultant hybrid light-matter states exhibit energy level shifts, are delocalized over many molecular units, and have a different excited-state potential energy landscape, which leads to modified exciton dynamics. Previously, non-Hermitian Hamiltonians have been derived to describe the excited states of molecules coupled to surface plasmons (i.e., plexcitons), and these operators have been successfully used in the description of linear and third order optical response. In this article, we rigorously derive non-Hermitian Hamiltonians in the response function formalism of nonlinear spectroscopy by means of Feshbach operators and apply them to explore spectroscopic signatures of plexcitons. In particular, we analyze the optical response below and above the exceptional point that arises for matching transition energies for plasmon and molecular components and study their decomposition using double-sided Feynman diagrams. We find a clear distinction between interference and Rabi splitting in linear spectroscopy and a qualitative change in the symmetry of the line shape of the nonlinear signal when crossing the exceptional point. This change corresponds to one in the symmetry of the eigenvalues of the Hamiltonian. Our work presents an approach for simulating the optical response of sublevels within an electronic system and opens new applications of nonlinear spectroscopy to examine the different regimes of the spectrum of non-Hermitian Hamiltonians.

Two-dimensional electronic spectroscopy of an ultracold gas

Femtosecond coherent multidimensional spectroscopy is demonstrated for an ultracold gas.  A setup for phase modulation spectroscopy is used to probe the 3²S_1/2-2²P_1/2,3/2 transition in an 800μK-cold sample of ⁷Li atoms confined in a magneto-optical trap. The observation of a double quantum coherence response, a signature of interparticle interactions, paves the way for detailed investigations of few- and many-body effects in ultracold gases using this technique. The experiment combines a frequency resolution of 3 GHz with a potential time resolution of 200 fs, which allows for high-resolution studies of ultracold atoms and molecules both in the frequency and in the time domain.

High-sensitivity fluorescence-detected multidimensional electronic spectroscopy through continuous pump-probe delay scan

Fluorescence-detected multidimensional electronic spectroscopy (fMES) promises high sensitivity compared to conventional approaches and is an emerging spectroscopic approach toward combining the advantages of MES with the spatial resolution of a microscope. Here, we present a visible white light continuum-based fMES spectrometer and systematically explore the sensitivity enhancement expected from fluorescence detection. As a demonstration of sensitivity, we report room temperature two-dimensional coherence maps of vibrational quantum coherences in a laser dye at optical densities of ∼2-3 orders of magnitude lower than conventional approaches. This high sensitivity is enabled by a combination of biased sampling along the optical coherence time axes and a rapid scan of the pump-probe waiting time T at each sample. A combination of this approach with acousto-optic phase modulation and phase-sensitive lock-in detection enables measurements of room temperature vibrational wavepackets even at the lowest ODs. Alternative faster data collection schemes, which are enabled by the flexibility of choosing a non-uniform undersampled grid in the continuous T scanning approach, are also demonstrated.

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.

Extreme Ultraviolet Wave Packet Interferometry of the Autoionizing HeNe Dimer

Femtosecond extreme ultraviolet wave packet interferometry (XUV-WPI) was applied to study resonant interatomic Coulombic decay (ICD) in the HeNe dimer. The high demands on phase stability and sensitivity for vibronic XUV-WPI of molecular-beam targets are met using an XUV phase-cycling scheme. The detected quantum interferences exhibit vibronic dephasing and rephasing signatures along with an ultrafast decoherence assigned to the ICD process. A Fourier analysis reveals the molecular absorption spectrum with high resolution. The demonstrated experiment shows a promising route for the real-time analysis of ultrafast ICD processes with both high temporal and high spectral resolution.

High-resolution two-dimensional electronic spectroscopy reveals the homogeneous line profile of chromophores solvated in nanoclusters

Doped clusters in the gas phase provide nanoconfined model systems for the study of system-bath interactions. To gain insight into interaction mechanisms between chromophores and their environment, the ensemble inhomogeneity has to be lifted and the homogeneous line profile must be accessed. However, such measurements are very challenging at the low particle densities and low signal levels in cluster beam experiments. Here, we dope cryogenic rare-gas clusters with phthalocyanine molecules and apply action-detected two-dimensional electronic spectroscopy to gain insight into the local molecule-cluster environment for solid and superfluid cluster species. The high-resolution homogeneous linewidth analysis provides a benchmark for the theoretical modelling of binding configurations and shows a promising route for high-resolution molecular two-dimensional spectroscopy.

Understanding the interaction of single chromophores with nanoparticles remains a challenging task in nanoscience. Here the authors provide insight into the interaction between isolated base-free phthalocyanine molecules and He and Ne nanoclusters in the gas phase using high-resolution two-dimensional spectroscopy.

Imaging dynamic exciton interactions and coupling in transition metal dichalcogenides

Transition metal dichalcogenides (TMDs) are regarded as a possible material platform for quantum information science and related device applications. In TMD monolayers, the dephasing time and inhomogeneity are crucial parameters for any quantum information application. In TMD heterostructures, coupling strength and interlayer exciton lifetimes are also parameters of interest. However, many demonstrations in TMDs can only be realized at specific spots on the sample, presenting a challenge to the scalability of these applications. Here, using multi-dimensional coherent imaging spectroscopy, we shed light on the underlying physics—including dephasing, inhomogeneity, and strain—for a MoSe2 monolayer and identify both promising and unfavorable areas for quantum information applications. We, furthermore, apply the same technique to a MoSe2/WSe2 heterostructure. Despite the notable presence of strain and dielectric environment changes, coherent and incoherent coupling and interlayer exciton lifetimes are mostly robust across the sample. This uniformity is despite a significantly inhomogeneous interlayer exciton photoluminescence distribution that suggests a bad sample for device applications. This robustness strengthens the case for TMDs as a next-generation material platform in quantum information science and beyond.

Coherent Interactions between Silicon-Vacancy Centers in Diamond

We report tunable excitation-induced dipole-dipole interactions between silicon-vacancy color centers in diamond at cryogenic temperatures. These interactions couple centers into collective states, and excitation-induced shifts tag the excitation level of these collective states against the background of excited single centers. By characterizing the phase and amplitude of the spectrally resolved interaction-induced signal, we observe oscillations in the interaction strength and population state of the collective states as a function of excitation pulse area. Our results demonstrate that excitation-induced dipole-dipole interactions between color centers provide a route to manipulating collective intercenter states in the context of a congested, inhomogeneous ensemble.

Double-quantum-zero-quantum 2D coherent spectroscopy reveals quantum coherence between collective states in an atomic vapor

We report a novel, to the best of our knowledge, double-quantum-zero-quantum two-dimensional coherent spectroscopy (2DCS) that allows direct detection of the quantum coherence between multiparticle collective states. Through correlating the double-quantum coherence and the zero-quantum coherence, signatures for coherence between collective states can be well isolated as side peaks and readily identified in the 2D spectrum. The experiment is implemented in a vapor of rubidium atoms in a collinear 2DCS setup. Good agreement with a theoretical simulation using density matrix confirms the essential role of the interatomic correlation effect in generating the side peak signals. This 2D spectrum technique paves a new avenue for studying the coherent coupling of highly excited states and many-body properties.

Temperature-dependent local conformations and conformational distributions of cyanine dimer labeled single-stranded-double-stranded DNA junctions by 2D fluorescence spectroscopy

DNA replication and the related processes of genome expression require binding, assembly, and function of protein complexes at and near single-stranded (ss)-double-stranded (ds) DNA junctions. These central protein-DNA interactions are likely influenced by thermally induced conformational fluctuations of the DNA scaffold across an unknown distribution of functionally relevant states to provide regulatory proteins access to properly conformed DNA binding sites. Thus, characterizing the nature of conformational fluctuations and the associated structural disorder at ss-dsDNA junctions is critical for understanding the molecular mechanisms of these central biological processes. Here, we describe spectroscopic studies of model ss-dsDNA fork constructs that contain dimers of "internally labeled" cyanine (iCy3) chromophore probes that have been rigidly inserted within the sugar-phosphate backbones of the DNA strands. Our combined analyses of absorbance, circular dichroism, and two-dimensional fluorescence spectroscopy permit us to characterize the local conformational parameters and conformational distributions. We find that the DNA sugar-phosphate backbones undergo abrupt successive changes in their local conformations-initially from a right-handed and ordered DNA state to a disordered splayed-open structure and then to a disordered left-handed conformation-as the dimer probes are moved across the ss-dsDNA junction. Our results suggest that the sugar-phosphate backbones at and near ss-dsDNA junctions adopt specific position-dependent local conformations and exhibit varying extents of conformational disorder that deviate widely from the Watson-Crick structure. We suggest that some of these conformations can function as secondary-structure motifs for interaction with protein complexes that bind to and assemble at these sites.

Coherent Two-Dimensional and Broadband Electronic Spectroscopies

Over the past few decades, coherent broadband spectroscopy has been widely used to improve our understanding of ultrafast processes (e.g., photoinduced electron transfer, proton transfer, and proton-coupled electron transfer reactions) at femtosecond resolution. The advances in femtosecond laser technology along with the development of nonlinear multidimensional spectroscopy enabled further insights into ultrafast energy transfer and carrier relaxation processes in complex biological and material systems. New discoveries and interpretations have led to improved design principles for optimizing the photophysical properties of various artificial systems. In this review, we first provide a detailed theoretical framework of both coherent broadband and two-dimensional electronic spectroscopy (2DES). We then discuss a selection of experimental approaches and considerations of 2DES along with best practices for data processing and analysis. Finally, we review several examples where coherent broadband and 2DES were employed to reveal mechanisms of photoinitiated ultrafast processes in molecular, biological, and material systems. We end the review with a brief perspective on the future of the experimental techniques themselves and their potential to answer an even greater range of scientific questions.

Frenkel biexcitons in hybrid HJ photophysical aggregates

Frenkel excitons are unequivocally responsible for the optical properties of organic semiconductors and are predicted to form bound exciton pairs (biexcitons). These are key intermediates, ubiquitous in many photophysical processes such as the exciton bimolecular annihilation dynamics in such systems. Because of their spectral ambiguity, there has been, to date, only scant direct evidence of bound biexcitons. By using nonlinear coherent spectroscopy, we identify here bound biexcitons in a model polymeric semiconductor. We find, unexpectedly, that excitons with interchain vibronic dispersion reveal intrachain biexciton correlations and vice versa. Moreover, using a Frenkel exciton model, we relate the biexciton binding energy to molecular parameters quantified by quantum chemistry, including the magnitude and sign of the exciton-exciton interaction the intersite hopping energies. Therefore, our work promises general insights into the many-body electronic structure in polymeric semiconductors and beyond, e.g., other excitonic systems such as organic semiconductor crystals, molecular aggregates, photosynthetic light-harvesting complexes, or DNA.

Time-Domain Vibrational Action Spectroscopy of Cryogenically Cooled, Messenger-Tagged Ions Using Ultrafast IR Pulses

Herein, we present the initial steps toward developing a framework that will enable the characterization of photoinitiated dynamics within large molecular ions in the gas phase with temporal and energy resolution. We combine the established techniques of tag-loss action spectroscopy on cryogenically trapped molecular ions with ultrafast vibrational spectroscopy by measuring the linear action spectrum of N₂-tagged protonated diglycine (GlyGlyH⁺·N₂) with an ultrafast infrared (IR) pulse pair. The presented time-domain data demonstrate that the excited-state vibrational populations in the tagged parent ions are modulated by the ultrafast IR pulse pair and encoded through the messenger tag-loss action response. The Fourier transform of the time-domain action interferograms yields the linear frequency-domain vibrational spectrum of the ion ensemble, and we show that this spectrum matches the linear spectrum collected in a traditional manner using a frequency-resolved IR laser. Time- and frequency-domain interpretations of the data are considered and discussed. Finally, we demonstrate the acquisition of nonlinear signals through cross-polarization pump-probe experiments. These results validate the prerequisite first steps of combining tag-loss action spectroscopy with two-dimensional IR spectroscopy for probing dynamics in gas-phase molecular ions.

Computational spectroscopy of complex systems

Numerous linear and non-linear spectroscopic techniques have been developed to elucidate structural and functional information of complex systems ranging from natural systems, such as proteins and light-harvesting systems, to synthetic systems, such as solar cell materials and light-emitting diodes. The obtained experimental data can be challenging to interpret due to the complexity and potential overlapping spectral signatures. Therefore, computational spectroscopy plays a crucial role in the interpretation and understanding of spectral observables of complex systems. Computational modeling of various spectroscopic techniques has seen significant developments in the past decade, when it comes to the systems that can be addressed, the size and complexity of the sample types, the accuracy of the methods, and the spectroscopic techniques that can be addressed. In this Perspective, I will review the computational spectroscopy methods that have been developed and applied for infrared and visible spectroscopies in the condensed phase. I will discuss some of the questions that this has allowed answering. Finally, I will discuss current and future challenges and how these may be addressed.

Lock-in detector for accelerated nonlinear imaging

We show that accelerated nonlinear imaging, such as stimulated Raman scattering and pump-probe imaging, is enabled by an order of magnitude reduction of data acquisition time when replacing the exponentially-weighted-moving-average low-pass filter in a lock-in amplifier with a simple-moving-average filter. We show that this simple-moving-average (box) lock-in yields a superior signal-to-noise ratio and suppression of extraneous modulations with short pixel dwell times, if one condition for the relation between the lock-in time constant and modulation frequencies is met. Our results, both theoretical and experimental, indicate that for nonlinear imaging applications, the box lock-in significantly outperforms conventional lock-in detection. These results facilitate the application of ultrafast and nonlinear imaging as a new standard for material characterization.

Phase-modulated rapid-scanning fluorescence-detected two-dimensional electronic spectroscopy

We present a rapid-scanning approach to fluorescence-detected two-dimensional electronic spectroscopy that combines acousto-optic phase-modulation with digital lock-in detection. This approach shifts the signal detection window to suppress 1/f laser noise and enables interferometric tracking of the time delays to allow for correction of spectral phase distortions and accurate phasing of the data. This use of digital lock-in detection enables acquisition of linear and nonlinear signals of interest in a single measurement. We demonstrate the method on a laser dye, measuring the linear fluorescence excitation spectrum as well as rephasing, non-rephasing, and absorptive fluorescence-detected two-dimensional electronic spectra.

Entangled two-photon absorption by atoms and molecules: A quantum optics tutorial

Two-photon absorption (TPA) and other nonlinear interactions of molecules with time-frequency-entangled photon pairs have been predicted to display a variety of fascinating effects. Therefore, their potential use in practical quantum-enhanced molecular spectroscopy requires close examination. This Tutorial presents a detailed theoretical study of one- and two-photon absorption by molecules, focusing on how to treat the quantum nature of light. We review some basic quantum optics theory and then we review the density-matrix (Liouville) derivation of molecular optical response, emphasizing how to incorporate quantum states of light into the treatment. For illustration, we treat in detail the TPA of photon pairs created by spontaneous parametric down conversion, with an emphasis on how quantum light TPA differs from that with classical light. In particular, we treat the question of how much enhancement of the TPA rate can be achieved using entangled states. This Tutorial includes a review of known theoretical methods and results as well as some extensions, especially the comparison of TPA processes that occur via far-off-resonant intermediate states only and those that involve off-resonant intermediate states by virtue of dephasing processes. A brief discussion of the main challenges facing experimental studies of entangled two-photon absorption is also given.

Fluorescence-Detected Pump-Probe Spectroscopy

We introduce a new approach to transient spectroscopy, fluorescence-detected pump-probe (F-PP) spectroscopy, that overcomes several limitations of traditional PP. F-PP suppresses excited-state absorption, provides background-free detection, removes artifacts resulting from pump-pulse scattering, from non-resonant solvent response, or from coherent pulse overlap, and allows unique extraction of excited-state dynamics under certain conditions. Despite incoherent detection, time resolution of F-PP is given by the duration of the laser pulses, independent of the fluorescence lifetime. We describe the working principle of F-PP and provide its theoretical description. Then we illustrate specific features of F-PP by direct comparison with PP, theoretically and experimentally. For this purpose, we investigate, with both techniques, a molecular squaraine heterodimer, core-shell CdSe/ZnS quantum dots, and fluorescent protein mCherry. F-PP is broadly applicable to chemical systems in various environments and in different spectral regimes.

A flexible and scalable, fully software-based lock-in amplifier for nonlinear spectroscopy

We demonstrate a cost-effective, fully software-based lock-in amplifier (LIA) implemented on a commercial computer. The device is designed for application in nonlinear spectroscopy, such as transient absorption and coherent multidimensional spectroscopy, but may also be used in any other application. The performance of our device is compared to a state-of-the-art commercial LIA with nearly identical results for both devices. Advantages of our device over commercial hardwired electronic LIAs are the improved flexibility in the data analysis and the possibility of arbitrary up-scaling of the number of LIA channels.

Pulse area dependence of multiple quantum coherence signals in dilute thermal gases

In the general framework of open quantum systems, we assess the impact of the pulse area on single and double quantum coherence (1QC and 2QC) signals extracted from fluorescence emitted by dilute thermal gases. We show that 1QC and 2QC signals are periodic functions of the pulse area, with distinctive features that reflect the particles' interactions via photon exchange, the polarizations of the laser pulses, and the observation direction.

Multidimensional electronic spectroscopy in high-definition-Combining spectral, temporal, and spatial resolutions

Over the past two decades, coherent multidimensional spectroscopies have been implemented across the terahertz, infrared, visible, and ultraviolet regions of the electromagnetic spectrum. A combination of coherent excitation of several resonances with few-cycle pulses, and spectral decongestion along multiple spectral dimensions, has enabled new insights into wide ranging molecular scale phenomena, such as energy and charge delocalization in natural and artificial light-harvesting systems, hydrogen bonding dynamics in monolayers, and strong light-matter couplings in Fabry-Pérot cavities. However, measurements on ensembles have implied signal averaging over relevant details, such as morphological and energetic inhomogeneity, which are not rephased by the Fourier transform. Recent extension of these spectroscopies to provide diffraction-limited spatial resolution, while maintaining temporal and spectral information, has been exciting and has paved a way to address several challenging questions by going beyond ensemble averaging. The aim of this Perspective is to discuss the technological developments that have eventually enabled spatially resolved multidimensional electronic spectroscopies and highlight some of the very recent findings already made possible by introducing spatial resolution in a powerful spectroscopic tool.

Optical two-dimensional coherent spectroscopy of many-body dipole-dipole interactions and correlations in atomic vapors

Many-body interactions and correlations in atomic ensembles are fundamental in understanding many-body effects such as collective and emergent phenomena and also play an important role in various atom-based applications. Optical two-dimensional coherent spectroscopy (2DCS) provides a powerful tool to measure many-body interactions and correlations. Here, we present the study of many-body dipole-dipole interactions and correlations in potassium and rubidium atomic vapors by using double-quantum and multi-quantum 2DCS. The results show that double-quantum 2DCS provides sensitive and background-free detection of weak dipole-dipole interaction between atoms with a mean separation up to about 16 μm, and multi-quantum 2DCS can excite and detect multi-atom states (Dicke states) with up to eight correlated atoms. The technique of optical 2DCS can provide a new approach to study many-body physics in atomic ensembles and can be potentially implemented to measure many-body effects in cold atoms and other atomic/molecular systems.

Hidden Silicon-Vacancy Centers in Diamond

We characterize a high-density sample of negatively charged silicon-vacancy (SiV^{-}) centers in diamond using collinear optical multidimensional coherent spectroscopy. By comparing the results of complementary signal detection schemes, we identify a hidden population of SiV^{-} centers that is not typically observed in photoluminescence and which exhibits significant spectral inhomogeneity and extended electronic T_{2} times. The phenomenon is likely caused by strain, indicating a potential mechanism for controlling electric coherence in color-center-based quantum devices.

Photocurrent-Detected 2D Electronic Spectroscopy Reveals Ultrafast Hole Transfer in Operating PM6/Y6 Organic Solar Cells

The performance of nonfullerene-acceptor-(NFA)-based organic solar cells is rapidly approaching the efficiency of inorganic cells. The chemical versatility of NFAs extends the light-harvesting range to the infrared, while preserving a considerably high open-circuit-voltage, crucial to achieve power-conversion efficiencies >17%. Such low voltage losses in the charge separation process have been attributed to a low-driving-force and efficient exciton dissociation. Here, we address the nature of the subpicosecond dynamics of electron/hole transfer in PM6/Y6 solar cells. While previous reports focused on active layers only, we developed a photocurrent-detected two-dimensional spectroscopy to follow the charge transfer in fully operating devices. Our measurements reveal an efficient hole-transfer from the Y6-acceptor to the PM6-donor on the subpicosecond time scale. On the contrary, at the same time scale, no electron-transfer is seen from the donor to the acceptor. These findings, putting ultrafast spectroscopy in action on operating optoelectronic devices, provide insight for further enhancing NFA solar cell performance.

Frequency comb-based multidimensional coherent spectroscopy bridges the gap between fundamental science and cutting-edge technology

Optical multidimensional coherent spectroscopy (MDCS) has become a powerful and routine technique for studying optical properties of a wide range of materials. However, current implementations of MDCS have spectral resolution and acquisition speed limitations. In this Perspective, I describe how frequency comb technology can be used to overcome the limitations and also show the recent progress that has been made in this field.