Theoretical analysis of anharmonic coupling and cascading Raman signals observed with femtosecond stimulated Raman spectroscopy

Elucidating phonon dephasing mechanisms in layered perovskites with coherent Raman spectroscopies

Organic-inorganic hybrid perovskite quantum wells exhibit electronic structures with properties intermediate between those of inorganic semiconductors and molecular crystals. In these systems, periodic layers of organic spacer molecules occupy the interstitial spaces between perovskite sheets, thereby confining electronic excitations to two dimensions. Here, we investigate spectroscopic line broadening mechanisms for phonons coupled to excitons in lead-iodide layered perovskites with phenyl ethyl ammonium (PEA) and azobenzene ethyl ammonium (AzoEA) spacer cations. Using a modified Elliot line shape analysis for the absorbance and photoluminescence spectra, polaron binding energies of 11.2 and 17.5 meV are calculated for (PEA)2PbI4 and (AzoEA)2PbI4, respectively. To determine whether the polaron stabilization processes influence the dephasing mechanisms of coupled phonons, five-pulse coherent Raman spectroscopies are applied to the two systems under electronically resonant conditions. The prominence of inhomogeneous line broadening mechanisms detected in (AzoEA)2PbI4 suggests that thermal fluctuations involving the deformable organic phase broaden the distributions of phonon frequencies within the quantum wells. In addition, our data indicate that polaron stabilization primarily involves photoinduced reorganization of the organic phases for both systems, whereas the impulsively excited phonons represent less than 10% of the total polaron binding energy. The signal generation mechanisms associated with our fifth-order coherent Raman experiments are explored with a perturbative model in which cumulant expansions are used to account for time-coincident vibrational dephasing and polaron stabilization processes.

Measuring carrier diffusion in MAPbI3 solar cells with photocurrent-detected transient grating spectroscopy

Conventional time-of-flight methods can be used to determine carrier mobilities for photovoltaic cells in which the transit time between electrodes is greater than the RC time constant of the device. To measure carrier drift on sub-ns timescales, we have recently developed a two-pulse time-of-flight technique capable of detecting drift velocities with 100-ps time resolution in perovskite materials. In this method, the rates of carrier transit across the active layer of a device are determined by varying the delay time between laser pulses and measuring the magnitude of the recombination-induced nonlinearity in the photocurrent. Here, we present a related experimental approach in which diffractive optic-based transient grating spectroscopy is combined with our two-pulse time-of-flight technique to simultaneously probe drift and diffusion in orthogonal directions within the active layer of a photovoltaic cell. Carrier density gratings are generated using two time-coincident pulse-pairs with passively stabilized phases. Relaxation of the grating amplitude associated with the first pulse-pair is detected by varying the delay and phase of the density grating corresponding to the second pulse-pair. The ability of the technique to reveal carrier diffusion is demonstrated with model calculations and experiments conducted using MAPbI3 photovoltaic cells.

Stimulated Raman versus Inverse Raman: Investigating Depletion Mechanisms for Super-Resolution Raman Microscopy

Super-resolution fluorescence microscopy has been critical in elucidating the nanoscale structure of biological systems. However, fluorescent labels bring difficulties such as perturbative labeling steps and photobleaching. Thus, label-free super-resolution techniques are of great interest, like our group's 2016 stimulated Raman scattering (SRS) technique, stimulated Raman depletion microscopy (SRDM). Inspired by stimulated emission depletion microscopy, SRDM uses a toroidally shaped beam to deplete the signal formed on the edges of the focal spot, resulting in SRS signal being detected from only a subdiffraction limited region. In initial works, the cause of the depletion was not thoroughly characterized. Here, we conclusively demonstrate suppression mechanisms in SRDM, while also contrasting approaches to super-resolution Raman microscopy on the Stokes and anti-Stokes sides of the spectrum. By monitoring the depletion of both the SRS and inverse Raman scattering (IRS) signal at a range of depletion powers, we observed other four-wave coherent Raman pathways that correspond to the introduction of the femtosecond depletion beam. In addition, we showed the depletion of the IRS signal, paving the way for a super-resolution imaging technique based on IRS, inverse raman depletion microscopy (IRDM). Combined, SRDM and IRDM offer label-free super-resolution imaging over a large spectral range to accommodate a variety of different sample constraints.

Susceptibility of two-dimensional resonance Raman spectroscopies to cascades involving solute and solvent molecules

Two-dimensional resonance Raman (2DRR) spectroscopies have been used to investigate the structural heterogeneity of ensembles and chemical reaction mechanisms in recent years. Our previous work suggests that the intensities of artifacts may be comparable to the desired 2DRR response for some chemical systems and experimental approaches. In a type of artifact known as a "cascade," the four-wave mixing signal field radiated by one molecule induces a four-wave mixing process in a second molecule. We consider the susceptibility of 2DRR spectroscopy to various types of signal cascades in the present work. Calculations are conducted using empirical parameters obtained for a molecule with an intramolecular charge-transfer transition in acetonitrile. For a fully impulsive pulse sequence, it is shown that "parallel" cascades involving two solute molecules are generally more intense than that of the desired 2DRR response when the solute's mode displacements are 1.0 or less. In addition, we find that the magnitudes of parallel cascades involving both solute and solvent molecules (i.e., a solute-solvent cascade) may exceed that of the 2DRR response when the solute possesses small mode displacements. It is tempting to assume that solute-solvent cascades possess negligible intensities because the off-resonant Raman cross sections of solvents are usually 4-6 orders of magnitude smaller than that of the electronically resonant solute; however, the present calculations show that the difference in solute and solvent concentrations can fully compensate for the difference in Raman cross sections under common experimental conditions. Implications for control experiments and alternate approaches for 2DRR spectroscopy are discussed.

Utilizing Microcavities To Suppress Third-Order Cascades in Fifth-Order Raman Spectra

Nonlinear optical signals in the condensed phase are often accompanied by sequences of lower-order processes, known as cascades, which share the same phase matching and power dependence on the incoming fields and are thus hard to distinguish. The suppression of cascading in order to reveal the desired nonlinear signal has been a major challenge in multidimensional Raman spectroscopy, that is, the χ⁽⁵⁾ signal being masked by cascading signals given by a product of two χ⁽³⁾ processes. Because cascading originates from the exchange of a virtual photon between molecules, it can be manipulated by performing the experiment in an optical microcavity which modifies the density of radiation field modes. Using a quantum electrodynamical (QED) treatment, we demonstrate that the χ⁽³⁾ cascading contributions can be greatly suppressed. By optimizing the cavity size and the incoming pulse directions, we show that up to ∼99.5% suppression of the cascading signal is possible.

Quantum coherence selective 2D Raman-2D electronic spectroscopy

Electronic and vibrational correlations report on the dynamics and structure of molecular species, yet revealing these correlations experimentally has proved extremely challenging. Here, we demonstrate a method that probes correlations between states within the vibrational and electronic manifold with quantum coherence selectivity. Specifically, we measure a fully coherent four-dimensional spectrum which simultaneously encodes vibrational-vibrational, electronic-vibrational and electronic-electronic interactions. By combining near-impulsive resonant and non-resonant excitation, the desired fifth-order signal of a complex organic molecule in solution is measured free of unwanted lower-order contamination. A critical feature of this method is electronic and vibrational frequency resolution, enabling isolation and assignment of individual quantum coherence pathways. The vibronic structure of the system is then revealed within an otherwise broad and featureless 2D electronic spectrum. This method is suited for studying elusive quantum effects in which electronic transitions strongly couple to phonons and vibrations, such as energy transfer in photosynthetic pigment-protein complexes.

Femtosecond Stimulated Raman Exposes the Role of Vibrational Coherence in Condensed-Phase Photoreactivity

Femtosecond spectroscopy has revealed coherent wave packet motion time and time again, but the question as to whether these coherences are necessary for reactivity or merely a consequence of the experiment has remained open. For diatomic systems in the gas phase, such as sodium iodide, the dimensionality of the system requires coordinated atomic motion along the reaction coordinate. Coherent dynamics are also readily observed in condensed-phase multidimensional systems such as chromophores in proteins and solvated charge transfer dimers. Is precisely choreographed nuclear motion (i.e., coherence) required for reactivity in these systems? Can this coherence reveal anything about the reaction coordinate? In this Account, we describe our efforts to tackle these questions using femtosecond stimulated Raman spectroscopy (FSRS). Results of four exemplary systems are summarized to illustrate the role coherence can play in condensed-phase reactivity, the exploitation of vibrational coherence to measure vibrational anharmonicities, and the development of two-dimensional FSRS (2D-FSRS). We begin with rhodopsin, the protein responsible for vertebrate vision. The rhodopsin photoreaction is preternaturally fast: ground-state photoproduct is formed in less than 200 fs. However, the reactively important hydrogen out-of-plane motions as well as various torsions and stretches remain vibrationally coherent long after the reaction is complete, indicating that vibrational coherence can and does survive reactive internal conversion. Both the ultrashort time scale of the reaction and the observed vibrational coherence indicate that the reaction in rhodopsin is a vibrationally coherent process. Next we examine the functional excited-state proton transfer (ESPT) reaction of green fluorescent protein. Oscillations in the phenoxy C-O and imidazolinone C═N stretches in the FSRS spectrum indicated strong anharmonic coupling to a low-frequency phenyl wagging mode that gates the ESPT reaction. In this case, the coherence revealed not only itself but also the mode coupling that is necessary for reactivity. Curious as to whether vibrational coherence is a common phenomenon, we examined two simpler photochemical systems. FSRS studies of the charge transfer dimer tetramethylbenzene:tetracyanoquinodimethane revealed many vibrational oscillations with high signal-to-noise ratio that allowed us to develop a 2D-FSRS technique to quantitatively measure anharmonic vibrational coupling for many modes within a reacting excited state. Armed with this technique, we turned our attention to a bond-breaking reaction, the cycloreversion of a cyclohexadiene derivative. By means of 2D-FSRS, the vibrational composition of the excited-state transition state and therefore the reaction coordinate was revealed. In aggregate, these FSRS measurements demonstrate that vibrational coherences persist for many picoseconds in condensed phases at room temperature and can survive reactive internal conversion. Moreover, these coherences can be leveraged to reveal quantitative anharmonic couplings between a molecule's normal modes in the excited state. These anharmonic couplings are the key to determining how normal modes combine to form a reaction coordinate. It is becoming clear that condensed-phase photochemical reactions that occur in 10 ps or less require coordinated, coherent nuclear motion for efficient reactive internal conversion.

Energy flow between spectral components in 2D broadband stimulated Raman spectroscopy

We introduce a general theoretical description of non resonant impulsive femtosecond stimulated Raman spectroscopy in a multimode harmonic model. In this technique an ultrashort actinic pulse creates coherences of low frequency modes and is followed by a paired narrowband Raman pulse and a broadband probe pulse. Using closed-time-path-loop (CTPL) diagrams, the response on both the red and the blue sides of the broadband pulse with respect to the narrowband Raman pulse is calculated, the process couples high and low frequency modes, which share the same ground state. The transmitted intensity oscillates between the red and the blue side, while the total number of photons is conserved. The total energy of the probe signal is periodically modulated in time by the coherence created in the low frequency modes.

Shaped and Feedback-Controlled Excitation of Single Molecules in the Weak-Field Limit

Coherent control uses tailored femtosecond pulse shapes to influence quantum pathways and drive a light-induced process toward a specific outcome. There has been a long-standing debate whether the absorption properties or the probability for population to remain in an excited state of a molecule can be influenced by the pulse shape, even if only a single photon is absorbed. Most such experiments are performed on many molecules simultaneously, so that ensemble averaging reduces the access to quantum effects. Here, we demonstrate systematic coherent control experiments on the fluorescence intensity of a single molecule in the weak-field limit. We demonstrate that a delay scan of interfering pulses reproduces the excitation spectrum of the molecule upon Fourier transformation, but that the spectral phase of a pulse sequence does not affect the transition probability. We generalize this result to arbitrary pulse shapes by performing the first closed-loop coherent control experiments on a single molecule.

Reactive and unreactive pathways in a photochemical ring opening reaction from 2D femtosecond stimulated Raman

Two-dimensional femtosecond stimulated Raman spectroscopy (2D-FSRS) is used to probe the structural evolution of a modified cyclohexadiene as it undergoes a photoinduced ring opening reaction.

Cascading and local-field effects in non-linear optics revisited: a quantum-field picture based on exchange of photons

The semi-classical theory of radiation-matter coupling misses local-field effects that may alter the pulse time-ordering and cascading that leads to the generation of new signals. These are then introduced macroscopically by solving Maxwell's equations. This procedure is convenient and intuitive but ad hoc. We show that both effects emerge naturally by including coupling to quantum modes of the radiation field that are initially in the vacuum state to second order. This approach is systematic and suggests a more general class of corrections that only arise in a QED framework. In the semi-classical theory, which only includes classical field modes, the susceptibility of a collection of N non-interacting molecules is additive and scales as N. Second-order coupling to a vacuum mode generates an effective retarded interaction that leads to cascading and local field effects both of which scale as N(2).

Broadband infrared and Raman probes of excited-state vibrational molecular dynamics: simulation protocols based on loop diagrams

Vibrational motions in electronically excited states can be observed either by time and frequency resolved infrared absorption or by off resonant stimulated Raman techniques. Multipoint correlation function expressions are derived for both signals. Three representations which suggest different simulation protocols for the signals are developed. These are based on the forward and the backward propagation of the wavefunction, sum over state expansion using an effective vibrational Hamiltonian or a semiclassical treatment of a bath. We show that the effective temporal (Δt) and spectral (Δω) resolution of the techniques is not controlled solely by experimental knobs but also depends on the system dynamics being probed. The Fourier uncertainty ΔωΔt > 1 is never violated.

How fissors works: observing vibrationally adiabatic conformational change through femtosecond stimulated Raman spectroscopy

With the help of a two-dimensional model system comprising a slow conformational degree of freedom and a higher-frequency vibration, we investigate the molecular-level origin and dynamical information content of femtosecond stimulated Raman spectroscopy (fissors) signals. Our treatment avails itself of the time scale separation between conformational and vibrational modes by incorporating a vibrationally adiabatic approximation to the conformational dynamics. We derive an expression for the fissors signal without resort to the macroscopic concepts of light- and phonon-wave propagation employed in prior coupled-wave analyses. Numerical calculations of fissors spectra illustrate the case of relatively small conformational mass (still large enough that conformational motion does not induce any change in the vibrational quantum number) in which conformational sidebands accompany a central peak in the Raman gain at a conformationally averaged vibrational transition frequency, and the case of a larger conformational mass in which the sidebands merge with the central peak and the frequency of the latter tracks the time-evolving conformational coordinate.

Signatures of discrete breathers in coherent state quantum dynamics

In classical mechanics, discrete breathers (DBs) - a spatial time-periodic localization of energy - are predicted in a large variety of nonlinear systems. Motivated by a conceptual bridging of the DB phenomena in classical and quantum mechanical representations, we study their signatures in the dynamics of a quantum equivalent of a classical mechanical point in phase space - a coherent state. In contrast to the classical point that exhibits either delocalized or localized motion, the coherent state shows signatures of both localized and delocalized behavior. The transition from normal to local modes have different characteristics in quantum and classical perspectives. Here, we get an insight into the connection between classical and quantum perspectives by analyzing the decomposition of the coherent state into system's eigenstates, and analyzing the spacial distribution of the wave-function density within these eigenstates. We find that the delocalized and localized eigenvalue components of the coherent state are separated by a mixed region, where both kinds of behavior can be observed. Further analysis leads to the following observations. Considered as a function of coupling, energy eigenstates go through avoided crossings between tunneling and non-tunneling modes. The dominance of tunneling modes in the high nonlinearity region is compromised by the appearance of new types of modes - high order tunneling modes - that are similar to the tunneling modes but have attributes of non-tunneling modes. Certain types of excitations preferentially excite higher order tunneling modes, allowing one to study their properties. Since auto-correlation functions decrease quickly in highly nonlinear systems, short-time dynamics are sufficient for modeling quantum DBs. This work provides a foundation for implementing modern semi-classical methods to model quantum DBs, bridging classical and quantum mechanical signatures of DBs, and understanding spectroscopic experiments that involve a coherent state.

Coherent fifth-order visible-infrared spectroscopies: ultrafast nonequilibrium vibrational dynamics in solution

Obtaining a detailed description of photochemical reactions in solution requires measuring time-evolving structural dynamics of transient chemical species on ultrafast time scales. Time-resolved vibrational spectroscopies are sensitive probes of molecular structure and dynamics in solution. In this work, we develop doubly resonant fifth-order nonlinear visible-infrared spectroscopies to probe nonequilibrium vibrational dynamics among coupled high-frequency vibrations during an ultrafast charge transfer process using a heterodyne detection scheme. The method enables the simultaneous collection of third- and fifth-order signals, which respectively measure vibrational dynamics occurring on electronic ground and excited states on a femtosecond time scale. Our data collection and analysis strategy allows transient dispersed vibrational echo (t-DVE) and dispersed pump-probe (t-DPP) spectra to be extracted as a function of electronic and vibrational population periods with high signal-to-noise ratio (S/N > 25). We discuss how fifth-order experiments can measure (i) time-dependent anharmonic vibrational couplings, (ii) nonequilibrium frequency-frequency correlation functions, (iii) incoherent and coherent vibrational relaxation and transfer dynamics, and (iv) coherent vibrational and electronic (vibronic) coupling as a function of a photochemical reaction.

Femtosecond stimulated Raman spectroscopy using a scanning multichannel technique

A scanning multichannel technique (SMT) has been implemented in femtosecond stimulated Raman spectroscopy (FSRS). By combining several FSRS spectra detected at slightly different positions of the spectrograph via SMT, we have eliminated the systematic noise patterns ("fixed pattern noise") due to the variation in sensitivity and noise characteristics of the individual charge-coupled device (CCD) pixels. In nonresonant FSRS, solvent subtraction can effectively remove the systematic noise pattern even without SMT. However, in the case of resonant FSRS, we show that a similar solvent subtraction procedure is ineffective at removing the noise patterns without SMT. Application of SMT results in averaged FSRS spectra with improved signal-to-noise ratios that approach the shot-noise limit.

Re-evaluation of rhodopsin's relaxation kinetics determined from femtosecond stimulated Raman lineshapes

This work presents a theoretical treatment of the vibrational line shape generated in a femtosecond stimulated Raman spectroscopy (FSRS) experiment under conditions in which the probed vibration undergoes a significant frequency shift during its free induction decay. This theory is applied to simulate the FSRS lineshapes previously observed in rhodopsin (Kukura et al. Science 2005, 310, 1006). The previously determined relaxation times for formation of the trans-photoproduct of rhodopsin were calculated using an incorrect equation for the time dependence of the observed frequency shifts. Here the data are reanalyzed by calculation of the corrected frequency sweep occurring during the vibrational free induction decay. It is shown that the calculated frequency shifts and general conclusions of the original work are sound but that the coherent vibrational frequency shifts of the C(10), C(11), and C(12) hydrogen-out-of-plane vibrations occur with a 140 fs time constant rather than the previously reported 325 fs time constant. This time constant provides an important constraint for models of the dynamics of the cis to trans isomerization process.

Quantum theory of time-resolved femtosecond stimulated Raman spectroscopy: direct versus cascade processes and application to CDCl3

We present a quantum mechanical wave packet treatment of time-resolved femtosecond stimulated Raman spectroscopy (FSRS), or two-dimensional (2D) FSRS, where a vibrational coherence is initiated with an impulsive Raman pump which is subsequently probed by FSRS. It complements the recent classical treatment by Mehlenbacher et al. [J. Chem. Phys. 131, 244512 (2009)]. In this 2D-FSRS, two processes can occur concurrently but with different intensities: a direct fifth-order process taking place on one molecule, and a cascade process comprising two third-order processes on two different molecules. The cascade process comprises a parallel and a sequential cascade. The theory is applied to the 2D-FSRS of CDCl(3) where calculations showed that: (a) the cascade process is stronger than the direct fifth-order process by one order of magnitude, (b) the sidebands assigned to C-Cl E and A(1) bends, observed on both sides of the Stokes C-D stretch frequency, are not due to anharmonic coupling between the C-D stretch and the C-Cl bends, but are instead due to the coherent anti-Stokes Raman spectroscopy (CARS) and coherent Stokes Raman spectroscopy (CSRS) fields produced in the first step of the cascade process, (c) for each delay time between the femtosecond impulsive pump and FSRS probe pulses, the line shape of the sidebands shows an inversion symmetry about the C-D stretch frequency, and this is due to the 180(∘) phase difference between the CARS and CSRS fields that produced the left and right sidebands, and (d) for each sideband, the line shape changes from positive Lorentzian to dispersive to negative Lorentzian, then to negative dispersive and back to positive Lorentzian with the period of the bending vibration, and it is correlated with the momentum of the wave packet prepared on the ground-state surface by the impulsive pump along the sideband normal coordinate.