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.

Cation Engineering in Two-Dimensional Ruddlesden-Popper Lead Iodide Perovskites with Mixed Large A-Site Cations in the Cages.

The Goldschmidt tolerance factor in halide perovskites limits the number of cations that can enter their cages without destabilizing their overall structure. Here, we have explored the limits of this geometric factor and found that the ethylammonium (EA) cations which lie outside the tolerance factor range can still enter the cages of the 2D halide perovskites by stretching them. The new perovskites allow us to study how these large cations occupying the perovskite cages affect the structural, optical, and electronic properties. We report a series of cation engineered 2D Ruddlesden-Popper lead iodide perovskites (BA)2(EAxMA1-x)2Pb3I10 (x = 0-1, BA is n-butylammonium, MA is methylammonium) by the incorporation of a large EA cation in the cage. An analysis of the single-crystal structures reveals that the incorporation of EA in the cage significantly stretches Pb-I bonds, expands the cage, and induces a larger octahedral distortion in the inorganic framework. Spectroscopic and theoretical studies show that such structural deformation leads to a blue-shifted bandgap, sub-bandgap trap states with wider energetic distribution, and stronger photoluminescence quenching. These results enrich the family of 2D perovskites and provide new insights for understanding the structure-property relationship in perovskite materials.

Negative Pressure Engineering with Large Cage Cations in 2D Halide Perovskites Causes Lattice Softening.

Organic-inorganic hybrid halide perovskites are promising semiconductors with tailorable optical and electronic properties. The choice of A-site cation to support a three-dimensional (3D) perovskite structure AMX3 (where M is a metal and X is a halide) is limited by the geometric Goldschmidt tolerance factor. However, this geometric constraint can be relaxed in two-dimensional (2D) perovskites, providing us an opportunity to understand how various A-site cations modulate the structural properties and thereby the optoelectronic properties. Here, we report the synthesis and structures of single-crystal (BA)2(A)Pb2I7 where BA = butylammonium and A = methylammonium (MA), formamidinium (FA), dimethylammonium (DMA), or guanidinium (GA), with a series of A-site cations varying in size. Single-crystal X-ray diffraction reveals that the MA, FA, and GA structures crystallize in the same Cmcm space group, while the DMA imposes the Ccmb space group. We observe that as the A-site cation becomes larger, the Pb-I bond continuously elongates, expanding the volume of the perovskite cage, equivalent to exerting "negative pressure" on the perovskite structures. Optical studies and DFT calculations show that the Pb-I bond length elongation reduces the overlap of the Pb s- and I p-orbitals and increases the optical bandgap, while Pb-I-Pb tilting angles play a secondary role. Raman spectra show lattice softening with increasing size of the A-site cation. These structural changes with enlarged A cations result in significant decreases in photoluminescence intensity and lifetime, consistent with a more pronounced nonradiative decay. Transient absorption microscopy results suggest that the PL drop may derive from a higher concentration of traps or phonon-assisted nonradiative recombination. The results highlight that extending the range of Goldschmidt tolerance factors for 2D perovskites is achievable, enabling further tuning of the structure-property relationships in 2D perovskites.

Global Analysis for Time and Spectrally Resolved Multidimensional Microscopy: Application to CH3NH3PbI3 Perovskite Thin Films.

The advancement of improved photoactive materials, such as those proposed for next-generation solar cells, low-power lighting, and lasing applications, requires a deep understanding of their correlated spatial, spectral, and temporal properties. In principle, correlated time-resolved microscopy techniques are capable of capturing such information. However, the large data sets that encapsulate temporal, spectral, and spatial information create the prodigious challenge of analyzing gigabytes of correlated data, which typically takes enormous computational resources. These challenges motivate the development of robust and efficient data analysis tools to realize fast spatial and spectral decomposition and to gain physical insights that arise from statistical analysis. Herein, we propose a reliable and fast global analysis method based on variable projection and subsampling methods, which exhibits exceptionally high sensitivity to buried spatial and spectral information in large and multidimensional microscopy data sets as compared to traditional methods. The reliability and robustness of this new method is tested on transient absorption and impulsive vibrational microscopy data sets acquired on polycrystalline CH3NH3PbI3 perovskite films.

Low energy excited state vibrations revealed in conjugated copolymer PCDTBT.

Low energy vibrations in the excited state have been hypothesized to play an important role in quickly and efficiently generating free charges in bulk heterojunctions of some conjugated polymer systems. While time-resolved vibrational spectroscopies seemingly are well poised to address the relationship between kinetics and vibrational motions after initial photoexcitation, uncertainty in the measurement arises due to overlapping signals and difficulties in assigning observed oscillatory signals to the molecular response. Here, we demonstrate a high sensitivity strategy to distinguish between signal oscillations originating from lab noise and those molecular in origin in order to isolate the low energy excited-state vibrations in the model conjugated copolymer PCDTBT. Furthermore, to distinguish modes that may be implicated in different kinetic pathways, coherent signal oscillations extracted from 2-dimensional electronic spectroscopy (2DES) are compared for the polymer in two solvents with different polarities resulting in different kinetics. We observe that the change in solvent affects dynamics on the >2 ps scale but not on the time scale required for free charge generation in heterojunctions (∼200 fs time scale). By the same token, the excited state vibrational modes that appear and disappear based on solvent polarity may also be associated with the slower kinetic process. The observation of low energy vibrational motions coupled to the excited state manifold that persists through the solvent change and thus can be associated with the fast kinetic process supports the hypothesis that direct polaron formation, rather than exciton formation and diffusion followed by interfacial charge separation, is a more likely route toward free charges in organic heterostructures.

Coherent and dissipative quantum process tensor reconstructions in two-dimensional electronic spectroscopy.

A major goal of time-resolved spectroscopy is to resolve the dynamical processes that follow photoexcitation. This amounts to identifying all the quantum states involved and the rates of population transfer between them. Unfortunately, such quantum state and kinetic reconstructions are ambiguous using one-dimensional methods such as transient absorption even when all the states of the system are fully resolved. Higher-dimensionality methods like two-dimensional spectroscopy lift some of the ambiguity, but unless the spectral features are well-separated, current inversion methods generally fail. Here, we show that, using both coherence and population signals of the nonlinear response, it is indeed possible to accurately extract both static and dynamic information from the 2D spectrum even when features are highly congested. Coherences report on the positions of the vibronic states of the system, providing a useful constraint for extracting the full kinetic scheme. We model time-resolved 2D photon echo spectra using a sum-over-states approach and show in which regimes the Hamiltonian and kinetic schemes may be recovered. Furthermore, we discuss how such algorithms may be applied to experimental data and where some of the underlying assumptions may fail. The ability to systematically extract the maximal information content of multidimensional spectroscopic data is an important step toward utilizing the full power of these techniques and elucidating the structure and dynamics of increasingly complex molecular systems.

Ultrafast Imaging of Carrier Cooling in Metal Halide Perovskite Thin Films.

Understanding carrier relaxation in lead halide perovskites at the nanoscale is critical for advancing their device physics. Here, we directly image carrier cooling in polycrystalline CH3NH3PbI3 films with nanometer spatial resolution. We observe that upon photon absorption, highly energetic carriers rapidly thermalize with the lattice at different rates across the film. The initial carrier temperatures vary by many multiples of the lattice temperature across hundreds of nanometers, a factor that cannot be accounted for by excess photon energy above the bandgap alone or in variations of the initial carrier density. Electron microscopy suggests that morphology plays a critical role in determining the initial carrier temperature and that carriers in small crystal domains decay slower than those in large crystal domains. Our results demonstrate that local disorder dominates the observed carrier behavior, highlighting the importance of making local rather than averaged measurements in these materials.

Zooming in on vibronic structure by lowest-value projection reconstructed 4D coherent spectroscopy.

A fundamental goal of chemical physics is an understanding of microscopic interactions in liquids at and away from equilibrium. In principle, this microscopic information is accessible by high-order and high-dimensionality nonlinear optical measurements. Unfortunately, the time required to execute such experiments increases exponentially with the dimensionality, while the signal decreases exponentially with the order of the nonlinearity. Recently, we demonstrated a non-uniform acquisition method based on radial sampling of the time-domain signal [W. O. Hutson et al., J. Phys. Chem. Lett. 9, 1034 (2018)]. The four-dimensional spectrum was then reconstructed by filtered back-projection using an inverse Radon transform. Here, we demonstrate an alternative reconstruction method based on the statistical analysis of different back-projected spectra which results in a dramatic increase in sensitivity and at least a 100-fold increase in dynamic range compared to conventional uniform sampling and Fourier reconstruction. These results demonstrate that alternative sampling and reconstruction methods enable applications of increasingly high-order and high-dimensionality methods toward deeper insights into the vibronic structure of liquids.

Four-dimensional coherent electronic Raman spectroscopy.

The correlations between different quantum-mechanical degrees of freedom of molecular species dictate their chemical and physical properties. Generally, these correlations are reflected in the optical response of the system but in low-order or low-dimensionality measurement the signals are highly averaged. Here, we describe a novel four-dimensional coherent spectroscopic method that directly correlates within and between the manifold of electronic and vibrational states. The optical response theory is developed in terms of both resonant and non-resonant field-matter interactions. Using resonance to select coherences on specific electronic states creates opportunities to directly distinguish coherent dynamics on the ground and electronically excited potentials. Critically, this method is free from lower-order signals that have plagued other electronically non-resonant vibrational spectroscopies. The theory presented here compliments recent work on the experimental demonstration of the 4D spectroscopic method described. We highlight specific means by which non-trivial effects such as anharmonicity (diagonal and off-diagonal), mode-specific vibronic coupling, and curvature of the excited states manifest in different projections of the 4D spectrum.

Stable and high-power few cycle supercontinuum for 2D ultrabroadband electronic spectroscopy.

Broadband supercontinuum (SC) pulses in the few cycle regime are a promising source for spectroscopic and imaging applications. However, SC sources are plagued by poor stability, greatly limiting their utility in phase-resolved nonlinear experiments such as 2D photon echo spectroscopy (2D PES). Here, we generated SC by two-stage filamentation in argon and air starting from 100 fs input pulses, which are sufficiently high-power and stable to record time-resolved 2D PE spectra in a single laser shot. We obtain a total power of 400 µJ/pulse in the visible spectral range of 500-850 nm and, after compression, yield pulses with duration of 6 fs according to transient-grating frequency-resolved optical gating (TG-FROG) measurements. We demonstrate the method on the laser dye, Cresyl Violet, and observe coherent oscillations indicative of nuclear wavepacket dynamics.

Quantum coherence spectroscopy reveals complex dynamics in bacterial light-harvesting complex 2 (LH2).

Light-harvesting antenna complexes transfer energy from sunlight to photosynthetic reaction centers where charge separation drives cellular metabolism. The process through which pigments transfer excitation energy involves a complex choreography of coherent and incoherent processes mediated by the surrounding protein and solvent environment. The recent discovery of coherent dynamics in photosynthetic light-harvesting antennae has motivated many theoretical models exploring effects of interference in energy transfer phenomena. In this work, we provide experimental evidence of long-lived quantum coherence between the spectrally separated B800 and B850 rings of the light-harvesting complex 2 (LH2) of purple bacteria. Spectrally resolved maps of the detuning, dephasing, and the amplitude of electronic coupling between excitons reveal that different relaxation pathways act in concert for optimal transfer efficiency. Furthermore, maps of the phase of the signal suggest that quantum mechanical interference between different energy transfer pathways may be important even at ambient temperature. Such interference at a product state has already been shown to enhance the quantum efficiency of transfer in theoretical models of closed loop systems such as LH2.

Real-time mapping of electronic structure with single-shot two-dimensional electronic spectroscopy.

Electronic structure and dynamics determine material properties and behavior. Important time scales for electronic dynamics range from attoseconds to milliseconds. Two-dimensional optical spectroscopy has proven an incisive tool to probe fast spatiotemporal electronic dynamics in complex multichromophoric systems. However, acquiring these spectra requires long point-by-point acquisitions that preclude observations on the millisecond and microsecond time scales. Here we demonstrate that imaging temporally encoded information within a homogeneous sample allows mapping of the evolution of the electronic Hamiltonian with femtosecond temporal resolution in a single-laser-shot, providing real-time maps of electronic coupling. This method, which we call GRadient-Assisted Photon Echo spectroscopy (GRAPE), eliminates phase errors deleterious to Fourier spectroscopies while reducing the acquisition time by orders of magnitude using only conventional optical components. In analogy to MRI in which magnetic field gradients are used to create spatial correlation maps, GRAPE spectroscopy takes advantage of a similar type of spatial encoding to construct electronic correlation maps. Unlike magnetic resonance, however, this spatial encoding of the nonlinear polarization along the excitation frequency axis of the two-dimensional spectrum results in no loss in signal while simultaneously reducing overall noise. Correlating the energy transfer events and electronic coupling occurring in tens of femtoseconds with slow dynamics on the subsecond time scale is fundamentally important in photobiology, solar energy research, nonlinear spectroscopy, and optoelectronic device characterization.

Long-lived quantum coherence in photosynthetic complexes at physiological temperature.

Photosynthetic antenna complexes capture and concentrate solar radiation by transferring the excitation to the reaction center that stores energy from the photon in chemical bonds. This process occurs with near-perfect quantum efficiency. Recent experiments at cryogenic temperatures have revealed that coherent energy transfer--a wave-like transfer mechanism--occurs in many photosynthetic pigment-protein complexes. Using the Fenna-Matthews-Olson antenna complex (FMO) as a model system, theoretical studies incorporating both incoherent and coherent transfer as well as thermal dephasing predict that environmentally assisted quantum transfer efficiency peaks near physiological temperature; these studies also show that this mechanism simultaneously improves the robustness of the energy transfer process. This theory requires long-lived quantum coherence at room temperature, which never has been observed in FMO. Here we present evidence that quantum coherence survives in FMO at physiological temperature for at least 300 fs, long enough to impact biological energy transport. These data prove that the wave-like energy transfer process discovered at 77 K is directly relevant to biological function. Microscopically, we attribute this long coherence lifetime to correlated motions within the protein matrix encapsulating the chromophores, and we find that the degree of protection afforded by the protein appears constant between 77 K and 277 K. The protein shapes the energy landscape and mediates an efficient energy transfer despite thermal fluctuations.

Two-dimensional spectroscopy can distinguish between decoherence and dephasing of zero-quantum coherences.

Recent experiments on a variety of photosynthetic antenna systems have revealed that coherences among electronic states persist longer than previously anticipated. In an ensemble measurement, the observed dephasing of a coherent state can occur because of either disorder across the ensemble or decoherence from interactions with the bath. Distinguishing how much such disorder affects the experimentally observed dephasing rate is paramount for understanding the role that quantum coherence may play in energy transfer through these complexes. Here, we show that two-dimensional electronic spectra can distinguish between the limiting cases of homogeneous dephasing (decoherence) and inhomogeneous dephasing by examining how the quantum beat frequency changes within a cross peak. For the antenna complex LH2 isolated from Rhodobacter sphaeroides , we find that dephasing of the coherence between the B850 and B800 rings arises predominantly from inhomogeneity. In contrast, within the Fenna-Matthews-Olson (FMO) complex from Chlorobium tepidum , dephasing of the coherence between the first two excitons appears quite homogeneous. Thus, the observed dephasing rate sets an upper bound on decoherence for the LH2 complex while establishing both an upper and lower bound for the FMO complex.

Long range excitonic transport in a biomimetic system inspired by the bacterial light-harvesting apparatus.

Photosynthesis, the process by which energy from sunlight drives cellular metabolism, relies on a unique organization of light-harvesting and reaction center complexes. Recently, the organization of light-harvesting LH2 complexes and dimeric reaction center-light-harvesting I-PufX core complexes in membranes of purple non-sulfur bacteria was revealed by atomic force microscopy [S. Bahatyrova et al., Nature (London) 430, 1058 (2004)]. Here, we discuss optimal exciton transfer in a biomimetic system closely modeled on the structure of LH2 and its organization within the membrane using a Markovian quantum model with dissipation and trapping added phenomenologically. In a deliberate manner, we neglect the high level detail of the bacterial light-harvesting complex and its interaction with the phonon bath in order to elucidate a set of design principles that may be incorporated in artificial pigment-scaffold constructs in a supramolecular assembly. We show that our scheme reproduces many of the most salient features found in their natural counterpart and may be largely explained by simple electrostatic considerations. Most importantly, we show that quantum effects act primarily to enforce robustness with respect to spatial and spectral disorder between and within complexes. The implications of such an arrangement are discussed in the context of biomimetic photosynthetic analogs capable of transferring energy efficiently across tens to hundreds of nanometers.

Fully refocused multi-shot spatiotemporally encoded MRI: robust imaging in the presence of metallic implants.

OBJECT: An approach has been recently introduced for acquiring arbitrary 2D NMR spectra or images in a single scan, based on the use of frequency-swept RF pulses for the sequential excitation and acquisition of the spins response. This spatiotemporal-encoding (SPEN) approach enables a unique, voxel-by-voxel refocusing of all frequency shifts in the sample, for all instants throughout the data acquisition. The present study investigates the use of this full-refocusing aspect of SPEN-based imaging in the multi-shot MRI of objects, subject to sizable field inhomogeneities that complicate conventional imaging approaches. MATERIALS AND METHODS: 2D MRI experiments were performed at 7 T on phantoms and on mice in vivo, focusing on imaging in proximity to metallic objects. Fully refocused SPEN-based spin echo imaging sequences were implemented, using both Cartesian and back-projection trajectories, and compared with k-space encoded spin echo imaging schemes collected on identical samples under equal bandwidths and acquisition timing conditions. RESULTS: In all cases assayed, the fully refocused spatiotemporally encoded experiments evidenced a ca. 50 % reduction in signal dephasing in the proximity of the metal, as compared to analogous results stemming from the k-space encoded spin echo counterparts. CONCLUSION: The results in this study suggest that SPEN-based acquisition schemes carry the potential to overcome strong field inhomogeneities, of the kind that currently preclude high-field, high-resolution tissue characterizations in the neighborhood of metallic implants.

Single-shot ultrabroadband two-dimensional electronic spectroscopy of the light-harvesting complex LH2.

Here we present two-dimensional (2D) electronic spectra of the light-harvesting complex LH2 from purple bacteria using coherent pulses with bandwidth of over 100 nm FWHM. This broadband excitation and detection has allowed the simultaneous capture of both the B800 and B850 bands using a single light source. We demonstrate that one laser pulse is sufficient to capture the entire 2D electronic spectrum with a high signal-to-noise ratio. At a waiting time of 800 fs, we observe population transfer from the B800 to B850 band as manifested by a prominent cross peak. These results will enable observation of the dynamics of biological systems across both ultrafast (<1 ps) and slower (>1 ms) timescales simultaneously.

Single-shot gradient-assisted photon echo electronic spectroscopy.

Two-dimensional electronic spectroscopy (2D ES) maps the electronic structure of complex systems on a femtosecond time scale. While analogous to multidimensional NMR spectroscopy, 2D optical spectroscopy differs significantly in its implementation. Yet, 2D Fourier spectroscopies still require point-by-point sampling of the time delay between two pulses responsible for creating quantum coherence among states. Unlike NMR, achieving the requisite phase stability at optical frequencies between these pulse pairs remains experimentally challenging. Nonetheless, 2D optical spectroscopy has been successfully demonstrated by combining passive and active phase stabilization along with precise control of optical delays and long-term temperature stability, although the widespread adoption of 2D ES has been significantly hampered by these technical challenges. Here, we exploit an analogy to magnetic resonance imaging (MRI) to demonstrate a single-shot method capable of acquiring the entire 2D spectrum in a single laser shot using only conventional optics. Unlike point-by-point sampling protocols typically used to record 2D spectra, this method, which we call GRadient-Assisted Photon Echo (GRAPE) spectroscopy, largely eliminates phase errors while reducing the acquisition time by orders of magnitude. By incorporating a spatiotemporal encoding of the nonlinear polarization along the excitation frequency axis of the 2D spectrum, GRAPE spectroscopy achieves no loss in signal while simultaneously reducing overall noise. Here, we describe the principles of GRAPE spectroscopy and discuss associated experimental considerations.

Non-Uniform Excited State Electronic-Vibrational Coupling of Pigment-Protein Complexes.

Photosynthetic organisms exploit interacting quantum degrees of freedom, namely intrapigment electron-vibrational (vibronic) and interpigment dipolar couplings (J-coupling), to rapidly and efficiently convert light into chemical energy. These interactions result in wave function configurations that delocalize excitation between pigments and pigment vibrations. Our study uses multidimensional spectroscopy to compare two model photosynthetic proteins, the Fenna-Matthews Olson (FMO) complex and light harvesting 2 (LH2), and confirm that long-lived excited state coherences originate from the vibrational modes of the pigment. Within this framework, the J-coupling of vibronic pigments should have a cascading effect in modifying the structured spectral density of excitonic states. We show that FMO effectively couples all of its excitations to a uniform set of vibrations while in LH2, its two chromophore rings each couple to a unique vibrational environment. We simulate energy transfer in a simple model system with non-uniform vibrational coupling to demonstrate how modification of the vibronic coupling strength can modulate energy transfer. Because increasing vibronic coupling increases internal relaxation, strongly coupled vibronic states can act as an energy funnel, which can potentially benefit energy transport.

Magnetic resonance detection: spectroscopy and imaging of lab-on-a-chip.

This mini-review is focused on the use of nuclear magnetic resonance (NMR) spectroscopy and imaging to study processes on lab-on-a-chip devices. NMR as an analytical tool is unmatched in its impact across nearly every area of science, from biochemistry and medicine to fundamental chemistry and physics. The controls available to the NMR spectroscopist or imager are vast, allowing for everything from high level structural determination of proteins in solution to detailed contrast imaging of organs in-vivo. Unfortunately, the weak nuclear magnetic moment of the nucleus requires that a very large number of spins be present for an inductively detectable signal, making the use of magnetic resonance as a detection modality for microfluidic devices especially challenging. Here we present recent efforts to combat the inherent sensitivity limitation of magnetic resonance for lab-on-a-chip applications. Principles and examples of different approaches are presented that highlight the flexibility and advantages of this type of detection modality.