Separating single- from multi-particle dynamics in nonlinear spectroscopy.

Quantum states depend on the coordinates of all their constituent particles, with essential multi-particle correlations. Time-resolved laser spectroscopy1 is widely used to probe the energies and dynamics of excited particles and quasiparticles such as electrons and holes2,3, excitons4-6, plasmons7, polaritons8 or phonons9. However, nonlinear signals from single- and multiple-particle excitations are all present simultaneously and cannot be disentangled without a priori knowledge of the system4,10. Here, we show that transient absorption-the most commonly used nonlinear spectroscopy-with N prescribed excitation intensities allows separation of the dynamics into N increasingly nonlinear contributions; in systems well-described by discrete excitations, these N contributions systematically report on zero to N excitations. We obtain clean single-particle dynamics even at high excitation intensities and can systematically increase the number of interacting particles, infer their interaction energies and reconstruct their dynamics, which are not measurable via conventional means. We extract single- and multiple-exciton dynamics in squaraine polymers11,12 and, contrary to common assumption6,13, we find that the excitons, on average, meet several times before annihilating. This surprising ability of excitons to survive encounters is important for efficient organic photovoltaics14,15. As we demonstrate on five diverse systems, our procedure is general, independent of the measured system or type of observed (quasi)particle and straightforward to implement. We envision future applicability in the probing of (quasi)particle interactions in such diverse areas as plasmonics7, Auger recombination2 and exciton correlations in quantum dots5,16,17, singlet fission18, exciton interactions in two-dimensional materials19 and in molecules20,21, carrier multiplication22, multiphonon scattering9 or polariton-polariton interaction8.

Measurement of Near-Field Radiative Heat Transfer at Deep Sub-Wavelength Distances using Nanomechanical Resonators.

Near-field radiative heat transfer (NFRHT) measurements often rely on custom microdevices that can be difficult to reproduce after their original demonstration. Here we study NFRHT using plain silicon nitride (SiN) membrane nanomechanical resonators─a widely available substrate used in applications such as electron microscopy and optomechanics─and on which other materials can easily be deposited. We report measurements down to a minimal distance of 180 nm between a large radius of curvature (15.5 mm) glass radiator and a SiN membrane resonator. At such deep sub-wavelength distance, heat transfer is dominated by surface polariton resonances over a (0.25 mm)2 effective area, which is comparable to plane-plane experiments employing custom microfabricated devices. We also discuss how measurements using nanomechanical resonators create opportunities for simultaneously measuring near-field radiative heat transfer and thermal radiation forces (e.g., thermal corrections to Casimir forces).

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.

Light management in ultra-thin photonic power converters for 1310†nm laser illumination.

We designed and optimized ultra-thin single junction InAlGaAs photonic power converters (PPC) with integrated back reflectors (BR) for operation at the telecommunications wavelength of 1310 nm and numerically studied the light trapping capability of three BR types: planar, cubic nano-textured, and pyramidal nano-textured. The PPC and BR geometries were optimized to absorb a fixed percentage of the incident light at the target wavelength by coupling finite difference time-domain (FDTD) calculations with a particle swarm optimization. With 90% absorptance, opto-electrical simulations revealed that ultra-thin PPCs with 5.6- to 8.4-fold thinner absorber layers can have open circuit voltages (Voc) that are 9-12% larger and power conversion efficiencies (PCE) that are 9-10% (relative) larger than conventional thick PPCs. Compared to a thick PPC with 98% absorptance, these ultra-thin designs reduce the absorber layer thickness by 9.5-14.2 times while improving the Voc by 12-14% and resulting in a relative PCE enhancement of 3-4%. Of the studied BR designs, pyramidal BRs exhibit the highest performance for ultra-thin designs, reaching an efficiency of 43.2% with 90% absorptance, demonstrating the superior light trapping capability relative to planar and cubic nano-textured BRs.

Efficient numerical method for predicting nonlinear optical spectroscopies of open systems.

Nonlinear optical spectroscopies are powerful tools for probing quantum dynamics in molecular and nanoscale systems. While intuition about ultrafast spectroscopies is often built by considering impulsive optical pulses, actual experiments have finite-duration pulses, which can be important for interpreting and predicting experimental results. We present a new freely available open source method for spectroscopic modeling, called Ultrafast Ultrafast (UF2) spectroscopy, which enables computationally efficient and convenient prediction of nonlinear spectra, such as treatment of arbitrary finite duration pulse shapes. UF2 is a Fourier-based method that requires diagonalization of the Liouvillian propagator of the system density matrix. We also present a Runge-Kutta-Euler (RKE) direct propagation method. We include open system dynamics in the secular Redfield, full Redfield, and Lindblad formalisms with Markovian baths. For non-Markovian systems, the degrees of freedom corresponding to memory effects are brought into the system and treated nonperturbatively. We analyze the computational complexity of the algorithms and demonstrate numerically that, including the cost of diagonalizing the propagator, UF2 is 20-200 times faster than the direct propagation method for secular Redfield models with arbitrary Hilbert space dimension; it is similarly faster for full Redfield models at least up to system dimensions where the propagator requires more than 20 GB to store; and for Lindblad models, it is faster up to Hilbert space dimension near 100 with speedups for small systems by factors of over 500. UF2 and RKE are part of a larger open source Ultrafast Software Suite, which includes tools for automatic generation and calculation of Feynman diagrams.

Automatic Feynman diagram generation for nonlinear optical spectroscopies and application to fifth-order spectroscopy with pulse overlaps.

Perturbative nonlinear optical spectroscopies are powerful methods to understand the dynamics of excitonic and other condensed phase systems. Feynman diagrams have long provided the essential tool to understand and interpret experimental spectra and to organize the calculation of spectra for model systems. When optical pulses are strictly time ordered, only a small number of diagrams contribute, but in many experiments, pulse-overlap effects are important for interpreting results. When pulses overlap, the number of contributing diagrams can increase rapidly, especially with higher order spectroscopies, and human error is especially likely when attempting to write down all the diagrams. We present an automated Diagram Generator (DG) that generates all the Feynman diagrams needed to calculate any nth-order spectroscopic signal. We characterize all perturbative nonlinear spectroscopies by their associated phase-discrimination condition as well as the time intervals where pulse amplitudes are nonzero. Although the DG can be used to automate impulsive calculations, its greatest strength lies in automating finite pulse calculations where pulse overlaps are important. We consider third-order transient absorption spectroscopy and fifth-order exciton-exciton interaction 2D (EEI2D) spectroscopy, which are described by six or seven diagrams in the impulsive limit, respectively, but 16 or 240 diagrams, respectively, when pulses overlap. The DG allows users to automatically include all relevant diagrams at a relatively low computational cost, since the extra diagrams are only generated for the inter-pulse delays where they are relevant. For EEI2D spectroscopy, we show the important effects of including the overlap diagrams.

Efficient wave optics modeling of nanowire solar cells using rigorous coupled-wave analysis.

We investigate the accuracy of rigorous coupled-wave analysis (RCWA) for near-field computations within cylindrical GaAs nanowire solar cells and discover excellent accuracy with low computational cost at long incident wavelengths but poor accuracy at short incident wavelengths. These near fields give the carrier generation rate, and their accurate determination is essential for device modeling. We implement two techniques for increasing the accuracy of the near fields generated by RCWA and give some guidance on parameters required for convergence along with an estimate of their associated computation times. The first improvement removes Gibbs phenomenon artifacts from the RCWA fields, and the second uses the extremely well-converged far-field absorption to rescale the local fields. These improvements allow a computational speedup between 30 and 1000 times for spectrally integrated calculations, depending on the density of the near fields desired. Some spectrally resolved quantities, especially at short wavelengths, remain expensive, but RCWA is still an excellent method for performing those calculations. These improvements open up the possibility of using RCWA for low-cost optical modeling in a full optoelectronic device model of nanowire solar cells.

Numerical method for nonlinear optical spectroscopies: Ultrafast ultrafast spectroscopy.

We outline a novel numerical method, called Ultrafast Ultrafast (UF2) spectroscopy, for calculating the nth-order wavepackets required for calculating n-wave mixing signals. The method is simple to implement, and we demonstrate that it is computationally more efficient than other methods in a wide range of use cases. The resulting spectra are identical to those calculated using the standard response function formalism but with increased efficiency. The computational speed-ups of UF2 come from (a) nonperturbative and costless propagation of the system time-evolution, (b) numerical propagation only at times when perturbative optical pulses are nonzero, and (c) use of the fast Fourier transform convolution algorithm for efficient numerical propagation. The simplicity of this formalism allows us to write a simple software package that is as easy to use and understand as the Feynman diagrams that organize the understanding of n-wave mixing processes.

Practical witness for electronic coherences.

The origin of the coherences in two-dimensional spectroscopy of photosynthetic complexes remains disputed. Recently, it has been shown that in the ultrashort-pulse limit, oscillations in a frequency-integrated pump-probe signal correspond exclusively to electronic coherences, and thus such experiments can be used to form a test for electronic vs. vibrational oscillations in such systems. Here, we demonstrate a method for practically implementing such a test, whereby pump-probe signals are taken at several different pulse durations and used to extrapolate to the ultrashort-pulse limit. We present analytic and numerical results determining requirements for pulse durations and the optimal choice of pulse central frequency, which can be determined from an absorption spectrum. Our results suggest that for numerous systems, the required experiment could be implemented by many ultrafast spectroscopy laboratories using pulses of tens of femtoseconds in duration. Such experiments could resolve the standing debate over the nature of coherences in photosynthetic complexes.

Quantum state and process tomography of energy transfer systems via ultrafast spectroscopy.

The description of excited state dynamics in energy transfer systems constitutes a theoretical and experimental challenge in modern chemical physics. A spectroscopic protocol that systematically characterizes both coherent and dissipative processes of the probed chromophores is desired. Here, we show that a set of two-color photon-echo experiments performs quantum state tomography (QST) of the one-exciton manifold of a dimer by reconstructing its density matrix in real time. This possibility in turn allows for a complete description of excited state dynamics via quantum process tomography (QPT). Simulations of a noisy QPT experiment for an inhomogeneously broadened ensemble of model excitonic dimers show that the protocol distills rich information about dissipative excitonic dynamics, which appears nontrivially hidden in the signal monitored in single realizations of four-wave mixing experiments.

Interpretations of High-Order Transient Absorption Spectroscopies.

Transient absorption (TA) spectroscopy is an invaluable tool for determining the energetics and dynamics of excited states. When pump intensities are sufficiently high, TA spectra include both the generally desired third-order response and responses that are higher in order in the field amplitudes. Recent work demonstrated that pump-intensity-dependent TA measurements allow separating the orders of response, but the information content in those higher orders has not been described. We give a general framework for understanding high-order TA spectra. We extend to higher order the fundamental processes of standard TA: ground-state bleach (GSB), stimulated emission (SE), and excited-state absorption (ESA). Each order introduces two new processes: SE and ESA from previously inaccessible highly excited states and negations of lower-order processes. We show the new spectral and dynamical information at each order and show how the relative signs of the signals in different orders can be used to identify which processes dominate.

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.

A witness for coherent electronic vs vibronic-only oscillations in ultrafast spectroscopy.

We report a conceptually straightforward witness that distinguishes coherent electronic oscillations from their vibronic-only counterparts in nonlinear optical spectra of molecular aggregates. Coherent oscillations as a function of waiting time in broadband pump/broadband probe spectra correspond to coherent electronic oscillations in the singly excited manifold. Oscillations in individual peaks of 2D electronic spectra do not necessarily yield this conclusion. Our witness is simpler to implement than quantum process tomography and potentially resolves a long-standing controversy on the character of oscillations in ultrafast spectra of photosynthetic light harvesting systems.

Scaling and localization lengths of a topologically disordered system.

We consider a noninteracting disordered system designed to model particle diffusion, relaxation in glasses, and impurity bands of semiconductors. Disorder originates in the random spatial distribution of sites. We find strong numerical evidence that this model displays the same universal behavior as the standard Anderson model. We use finite-size scaling to find the localization length as a function of energy and density, including localized states away from the delocalization transition. Results at many energies all fit onto the same universal scaling curve.

Correlation length and chirality of the fluctuations in the isotropic phase of nematic and cholesteric liquid crystals.

Light-scattering measurements of the correlation length in the isotropic phase of a nematic liquid crystal reveal a temperature dependence following Landau-de Gennes theory for the isotropic phase with a bare correlation length smaller than has been measured in other liquid crystals. Similar measurements in a cholesteric liquid crystal demonstrate that the correlation length in the isotropic phase is larger than typically found in nematics and that the chirality of the fluctuations in the isotropic phase is slightly higher than the chirality of the cholesteric phase. Landau-de Gennes theory of the cholesteric phase describes the chirality in the cholesteric phase well but predicts that the chirality in the isotropic phase is temperature independent, which is not consistent with the data. There is a discontinuity in the chirality at the cholesteric-isotropic transition of about 15%, which is less than the predictions of Landau-de Gennes theory but more than the typical specific volume discontinuity at transitions to the isotropic phase. Except for a mismatch in the discontinuities at the transition, the chirality data resemble the temperature behavior of variables just below a critical point, in spite of the fact that this system is far from a critical point.

Coherent exciton dynamics in supramolecular light-harvesting nanotubes revealed by ultrafast quantum process tomography.

Long-lived exciton coherences have been recently observed in photosynthetic complexes via ultrafast spectroscopy, opening exciting possibilities for the study and design of coherent exciton transport. Yet, ambiguity in the spectroscopic signals has led to arguments against interpreting them in terms of exciton dynamics, demanding more stringent tests. We propose a novel strategy, quantum process tomography (QPT), for ultrafast spectroscopy and apply it to reconstruct the evolving quantum state of excitons in double-walled supramolecular light-harvesting nanotubes at room temperature from eight narrowband transient grating experiments. Our analysis reveals the absence of nonsecular processes, unidirectional energy transfer from the outer to the inner wall exciton states, and coherence between those states lasting about 150 fs, indicating weak electronic coupling between the walls. Our work constitutes the first experimental QPT in a "warm" and complex system and provides an elegant scheme to maximize information from ultrafast spectroscopy experiments.

Cubic Dresselhaus spin-orbit coupling in 2D electron quantum dots.

We study effects of the oft-neglected cubic Dresselhaus spin-orbit coupling (i.e., directly proportional p3) in GaAs/AlGaAs quantum dots. Using a semiclassical billiard model, we estimate the magnitude of the spin-orbit induced avoided crossings in a closed quantum dot in a Zeeman field. Using previous analyses based on random matrix theory, we calculate corresponding effects on the conductance through an open quantum dot. Combining our results with an experiment on an 8 microm2 quantum dot [D. M. Zumbühl, Phys. Rev. B 72, 081305 (2005)10.1103/PhysRevB.72.081305] suggests that (1) the GaAs Dresselhaus coupling constant gamma is approximately 9 eV A3, significantly less than the commonly cited value of 27.5 eV A3, and (2) the majority of the spin-flip effects can come from the cubic Dresselhaus term.