The grating decomposition method: A new approach for understanding polarization‐selective transient grating experiments. I. Theory

Extreme ultraviolet transient gratings: A tool for nanoscale photoacoustics

Collective lattice dynamics determine essential aspects of condensed matter, such as elastic and thermal properties. These exhibit strong dependence on the length-scale, reflecting the marked wavevector dependence of lattice excitations. The extreme ultraviolet transient grating (EUV TG) approach has demonstrated the potential of accessing a wavevector range corresponding to the 10s of nm length-scale, representing a spatial scale of the highest relevance for fundamental physics and forefront technology, previously inaccessible by optical TG and other inelastic scattering methods. In this manuscript we report on the capabilities of this technique in the context of probing thermoelastic properties of matter, both in the bulk and at the surface, as well as discussing future developments and practical considerations.

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.

Observation of Exciton-Exciton Interaction Mediated Valley Depolarization in Monolayer MoSe2

The valley pseudospin in monolayer transition metal dichalcogenides (TMDs) has been proposed as a new way to manipulate information in various optoelectronic devices. This relies on a large valley polarization that remains stable over long time scales (hundreds of nanoseconds). However, time-resolved measurements report valley lifetimes of only a few picoseconds. This has been attributed to mechanisms such as phonon-mediated intervalley scattering and a precession of the valley pseudospin through electron-hole exchange. Here we use transient spin grating to directly measure the valley depolarization lifetime in monolayer MoSe₂. We find a fast valley decay rate that scales linearly with the excitation density at different temperatures. This establishes the presence of strong exciton-exciton Coulomb exchange interactions enhancing the valley depolarization. Our work highlights the microscopic processes inhibiting the efficient use of the exciton valley pseudospin in monolayer TMDs.

Frequency-domain coherent multidimensional spectroscopy when dephasing rivals pulsewidth: Disentangling material and instrument response

Ultrafast spectroscopy is often collected in the mixed frequency/time domain, where pulse durations are similar to system dephasing times. In these experiments, expectations derived from the familiar driven and impulsive limits are not valid. This work simulates the mixed-domain four-wave mixing response of a model system to develop expectations for this more complex field-matter interaction. We explore frequency and delay axes. We show that these line shapes are exquisitely sensitive to excitation pulse widths and delays. Near pulse overlap, the excitation pulses induce correlations that resemble signatures of dynamic inhomogeneity. We describe these line shapes using an intuitive picture that connects to familiar field-matter expressions. We develop strategies for distinguishing pulse-induced correlations from true system inhomogeneity. These simulations provide a foundation for interpretation of ultrafast experiments in the mixed domain.

Two-Dimensional Anisotropy Measurements Showing Local Heterogeneity in a Polymer Melt

In polymers, the rotation of a small solute is nonexponential. Either heterogeneity in the local friction or local anisotropy-a homogeneous process-may be responsible. A new, two-dimensional anisotropy experiment is demonstrated on this problem. In poly(dimethylsiloxane), the rotation of individual solute molecules is found to be exponential, and the observed rate dispersion is primarily due to variation in the local friction. This sample is far from its glass transition. Studies of rate heterogeneity associated with the glass transition must account for the contribution from this polymer-related mechanism.

Anisotropic Picosecond X-ray Solution Scattering from Photo-selectively Aligned Protein Molecules

Anisotropic X-ray scattering patterns of transiently aligned protein molecules in solution are measured by using pump-probe X-ray solution scattering. When a linearly polarized laser pulse interacts with an ensemble of molecules, the population of excited molecules is created with their transition dipoles preferentially aligned along the laser polarization direction. We measured the X-ray scattering from the myoglobin protein molecules excited by a linearly polarized, short laser pulse and obtained anisotropic scattering patterns on 100 ps time scale. An anisotropic scattering pattern contains higher structural information content than a typical isotropic pattern available from randomly oriented molecules. In addition, multiple independent diffraction patterns measured by using various laser polarization orientations will give substantially increased amount of structural information compared with a single isotropic pattern. By monitoring the temporal change of the anisotropic scattering pattern from 100 ps to 1 μs, we observed the orientational dynamics of photo-generated myoglobin with the rotational diffusion time of ∼15 ns.

Exciton fine structure and spin relaxation in semiconductor colloidal quantum dots

Quantum dots (QDs) have discrete quantum states isolated from the environment, making QDs well suited for quantum information processing. In semiconductor QDs, the electron spins can be coherently oriented by photoexcitation using circularly polarized light, creating optical orientation. The optically induced spin orientation could serve as a unit for data storage and processing. Carrier spin orientation is also envisioned to be a key component in a related, though parallel, field of semiconductor spintronics. However, the oriented spin population rapidly loses its coherence by interaction with the environment, thereby erasing the prepared information. Since long-lasting spin orientation is desirable in both areas of investigation, spin relaxation is the central focus of investigation for optimization of device performance. In this Account, we discuss a topic peripherally related to these emerging areas of investigation: exciton fine structure relaxation (EFSR). The radiationless transition occurring in the exciton fine structure not only highlights a novel aspect of QD exciton relaxation but also has implications for carrier spin relaxation in QDs. We focus on examining the EFSR in connection with optical spin orientation and subsequent ultrafast relaxation of electron and hole spin densities in the framework of the exciton fine structure basis. Despite its significance, the study of exciton fine structure in colloidal QDs has been hampered by the experimental challenge arising from inhomogeneous line broadening that obscures the details of closely spaced fine structure states in the frequency domain. In this Account, we show that spin relaxation occurring in the fine structure of CdSe QDs can be probed by a time-domain nonlinear polarization spectroscopy, circumventing the obstacles confronted in the frequency-domain spectroscopy. In particular, by combining polarization sequences of multiple optical pulses with the unique optical selection rules of semiconductors, fast energy relaxation among the QD exciton fine structure states is selectively measured. The measured exciton fine structure relaxation, which is a nanoscale analogue of molecular radiationless transitions, contains direct information on the relaxation of spin densities of electron and hole carriers, that is, spin relaxation in QDs. From the exciton fine structure relaxation rates measured for CdSe nanorods and complex-shaped nanocrystals using nonlinear polarization spectroscopy, we elucidated the implications of QD size and shape on the QD exciton properties as well, for example, size- and shape-scaling laws governing exciton spin flips and how an exciton is delocalized in a QD. We envision that the experimental development and the discoveries of QD exciton properties presented in this Account will inspire further studies toward revealing the characteristics of QD excitons and spin relaxation therein, for example, spin relaxation in QDs made of various materials with different electronic structures, spin relaxation under an external perturbation of QD electronic states using magnetic fields, and spin relaxation of separated electrons and holes in type-II QD heterostructures.

Ultrafast exciton fine structure relaxation dynamics in lead chalcogenide nanocrystals

The rates of fine structure relaxation in PbS, PbSe, and PbTe nanocrystals were measured on a femtosecond time scale as a function of temperature with no applied magnetic field by cross-polarized transient grating spectroscopy (CPTG) and circularly polarized pump-probe spectroscopy. The relaxation rates among exciton fine structure states follow trends with nanocrystal composition and size that are consistent with the expected influence of material dependent spin-orbit coupling, confinement enhanced electron-hole exchange interaction, and splitting between L valleys that are degenerate in the bulk. The size dependence of the fine structure relaxation rate is considerably different from what is observed for small CdSe nanocrystals, which appears to result from the unique material properties of the highly confined lead chalcogenide quantum dots. Modeling and qualitative considerations lead to conclusions about the fine structure of the lowest exciton absorption band, which has a potentially significant bearing on photophysical processes that make these materials attractive for practical purposes.

The collision-induced polarizability of a pair of hydrogen molecules

Collision-induced light scattering, impulsive stimulated scattering, and subpicosecond-induced birefringence all depend on the transient changes Deltaalpha in molecular polarizabilities that occur when molecules collide. Ab initio results for Deltaalpha are needed to permit comparisons with accurate experimental results for these spectra and for refractive index virial coefficients and dielectric virial coefficients. In this work, we provide results for Deltaalpha for a pair of hydrogen molecules, treated at CCSD(T) level, with an aug-cc-pV5Z (spdf) basis set. Our values replace the best previous ab initio results for the variation of Deltaalpha with intermolecular separation, the self-consistent-field results obtained by Bounds [Mol. Phys. 38, 2099 (1979)] with a relatively small (3s2p) basis set for H2. For the six geometrical configurations studied by Bounds, the inclusion of correlation and improvements in the basis tend to increase both the trace Deltaalpha(0)0 and the anisotropy Deltaalpha2m of the pair polarizability. The change in the anisotropy is relatively small, but our values for the trace differ by factors of 2 or more from Bounds' results. For use in computing experimental line shapes, intensities, and virial coefficients, we have calculated Deltaalpha for 18 different relative orientations of a pair of H2 molecules, with the intermolecular separation R ranging from 2 a.u. (3 a.u. for a linear pair) to 10 a.u. The H2 bond length is fixed at the vibrationally averaged internuclear separation in the ground state r=1.449 a.u. Our results agree well with the CCSD(T) results for Deltaalpha obtained by Maroulis [J. Phys. Chem. A 104, 4772 (2000)] for two pair configurations of H2...H2 (linear and T-shaped) at a fixed internuclear distance of R=6.5 a.u. in a [6s4p1d] basis. As the intermolecular distance increases (for R>or=8 a.u.), the spherical-tensor components of Deltaalpha converge to the results from a long-range model that includes dipole-induced-dipole (DID) interactions, higher-multipole induction, nonuniformity of the local field, hyperpolarization, and van der Waals dispersion. Deviations from the first-order DID model are still evident for R between 8 and 10 a.u. in most orientations of the pair. At shorter range, overlap damping, exchange, and orbital distortion reduce both Deltaalpha0(0) and Deltaalpha(2)0 below their long-range limiting forms.

Mechanism and Origin of Exciton Spin Relaxation in CdSe Nanorods

The dynamics of exciton spin relaxation in CdSe nanorods of various sizes and shapes are measured by an ultrafast transient polarization grating technique. The measurement of the third-order transient grating (3-TG) signal utilizing linear cross-polarized pump pulses enables us to monitor the history of spin relaxation among the bright exciton states with a total angular momentum of F = +/-1. From the measured exciton spin relaxation dynamics, it is found that the effective mechanism of exciton spin relaxation is sensitive to the size of the nanorod. Most of the measured cross-polarized 3-TG signals show single-exponential spin relaxation dynamics, while biexponential spin relaxation dynamics are observed in the nanorod of the largest diameter. This analysis suggests that a direct exciton spin flip process between the bright exciton states with F = +/-1 is the dominant spin relaxation mechanism in small nanocrystals, and an indirect spin flip via the dark states with F = +/-2 contributes as the size of the nanocrystal increases. This idea is examined by simulations of 3-TG signals with a kinetic model for exciton spin relaxation considering the states in the exciton fine structure. Also, it is revealed that the rate of exciton spin relaxation has a strong correlation with the diameter, d, of the nanorod, scaled by the power law of 1/d4, rather than other shape parameters such as length, volume, or aspect ratio.

Nanocrystal shape and the mechanism of exciton spin relaxation

The rate of exciton spin relaxation (flips) between the bright exciton states (F = +/-1) of CdSe nanocrystals is reported as a function of shape, for dots and nanorods. The spin relaxation is measured using an ultrafast transient grating method with a crossed linearly polarization sequence. It is found that the spin relaxation rate depends on the radius, not length, of the nanocrystals. That observation is explained by deriving an expression for the electronic coupling matrix element that mixes the bright exciton states.

Dynamics within the Exciton Fine Structure of Colloidal CdSe Quantum Dots

Evidence for an interaction between the quantum dot exciton fine structure states F = +/-1 is obtained by measuring the dynamics of transitions among those states, exciton spin relaxation or flipping. An ultrafast transient grating experiment based on a crossed-linear polarization grating is reported. By using the quantum dot selection rules for absorption of circularly polarized light, it is demonstrated that it is possible to detect transitions between nominally degenerate fine structure states, even in a rotationally isotropic system. The results for colloidal CdSe quantum dots reveal a strong size dependence for the exciton spin relaxation rate from one bright exciton state (F = +/-1) to the other in CdSe colloidal quantum dots at 293 K, on a time scale ranging from femtoseconds to picoseconds, depending on the quantum dot size. The results are consistent with an interaction between those states attributed to a long-range contribution to the electron-hole exchange interaction.