Time-Resolved Single-Particle X-ray Scattering Reveals Electron-Density Gradients As Coherent Plasmonic-Nanoparticle-Oscillation Source.

Dynamics of optically excited plasmonic nanoparticles are presently understood as a series of scattering events involving the initiation of nanoparticle breathing oscillations. According to established models, these are caused by statistical heat transfer from thermalized electrons to the lattice. An additional contribution by hot-electron pressure accounts for phase mismatches between theory and experimental observations. However, direct experimental studies resolving the breathing-oscillation excitation are still missing. We used optical transient-absorption spectroscopy and time-resolved single-particle X-ray diffractive imaging to access the electron system and lattice. The time-resolved single-particle imaging data provided structural information directly on the onset of the breathing oscillation and confirmed the need for an additional excitation mechanism for thermal expansion. We developed a new model that reproduces all of our experimental observations. We identified optically induced electron density gradients as the initial driving source.

Impact of Optically Pumped Nonequilibrium Steady States on Luminescence Emission of Atomically Thin Semiconductor Excitons.

The interplay of the nonequivalent corners in the Brillouin zone of transition metal dichalcogenides (TMDCs) has been investigated extensively. While experimental and theoretical works contributed to a detailed understanding of the relaxation of selective optical excitations and the related relaxation rates, only limited microscopic descriptions of stationary experiments are available so far. Here we present microscopic calculations for the nonequilibrium steady state properties of excitons during continuous wave pumping exemplary for monolayer MoSe_{2}. We find sharp features in photoluminescence excitation spectra and degree of polarization which result from phonon assisted excitonic transitions dominating over exciton recombination and intervalley exchange coupling.

Extended Spatial Coherence of Interlayer Excitons in MoSe_{2}/WSe_{2} Heterobilayers.

We report on the spatial coherence of interlayer exciton ensembles as formed in MoSe_{2}/WSe_{2} heterostructures and characterized by point-inversion Michelson-Morley interferometry. Below 10 K, the measured spatial coherence length of the interlayer excitons reaches values equivalent to the lateral expansion of the exciton ensembles. In this regime, the light emission of the excitons turns out to be homogeneously broadened in energy with a high temporal coherence. At higher temperatures, both the spatial coherence length and the temporal coherence time decrease, most likely because of thermal processes. The presented findings point towards a spatially extended, coherent many-body state of interlayer excitons at low temperature.

Theory of radial oscillations in metal nanoparticles driven by optically induced electron density gradients.

We provide a microscopic approach to describe the onset of radial oscillation of a silver nanoparticle. Using the Heisenberg equation of motion framework, we find that the coupled ultrafast dynamics of coherently excited electron occupation and the coherent phonon amplitude initiate periodic size oscillations of the nanoparticle. Compared to the established interpretation of experiments, our results show a more direct coupling mechanism between the field intensity and coherent phonons. This interaction triggers a size oscillation via an optically induced electron density gradient occurring directly with the optical excitation. This source is more efficient than the incoherent heating process currently discussed in the literature and well-describes the early onset of the oscillations in recent experiments.

Disentangling Many-Body Effects in the Coherent Optical Response of 2D Semiconductors.

In single-layer (1L) transition metal dichalcogenides, the reduced Coulomb screening results in strongly bound excitons which dominate the linear and the nonlinear optical response. Despite the large number of studies, a clear understanding on how many-body and Coulomb correlation effects affect the excitonic resonances on a femtosecond time scale is still lacking. Here, we use ultrashort laser pulses to measure the transient optical response of 1L-WS2. In order to disentangle many-body effects, we perform exciton line-shape analysis, and we study its temporal dynamics as a function of the excitation photon energy and fluence. We find that resonant photoexcitation produces a blue shift of the A exciton, while for above-resonance photoexcitation the transient response at the optical bandgap is largely determined by a reduction of the exciton oscillator strength. Microscopic calculations based on excitonic Heisenberg equations of motion quantitatively reproduce the nonlinear absorption of the material and its dependence on excitation conditions.

Efficient Quadrature Squeezing from Biexcitonic Parametric Gain in Atomically Thin Semiconductors.

Modification of electromagnetic quantum fluctuations in the form of quadrature squeezing is a central quantum resource, which can be generated from nonlinear optical processes. Such a process is facilitated by coherent two-photon excitation of the strongly bound biexciton in atomically thin semiconductors. We show theoretically that interfacing an atomically thin semiconductor with an optical cavity makes it possible to harness this two-photon resonance and use the biexcitonic parametric gain to generate squeezed light with input power an order of magnitude below current state-of-the-art devices with conventional third-order nonlinear materials that rely on far off-resonant nonlinearities. Furthermore, the squeezing bandwidth is found to be in the range of several meV. These results identify atomically thin semiconductors as a promising candidate for on-chip squeezed-light sources.

Fermi's Golden Rule for Spontaneous Emission in Absorptive and Amplifying Media.

We demonstrate a fundamental breakdown of the photonic spontaneous emission (SE) formula derived from Fermi's golden rule, in absorptive and amplifying media, where one assumes the SE rate scales with the local photon density of states, an approach often used in more complex, semiclassical nanophotonics simulations. Using a rigorous quantization of the macroscopic Maxwell equations in the presence of arbitrary linear media, we derive a corrected Fermi's golden rule and master equation for a quantum two-level system (TLS) that yields a quantum pumping term and a modified decay rate that is net positive. We show rigorous numerical results of the temporal dynamics of the TLS for an example of two coupled microdisk resonators, forming a gain-loss medium, and demonstrate the clear failure of the commonly adopted formulas based solely on the local density of states.

Excitons in Bilayer MoS_{2} Displaying a Colossal Electric Field Splitting and Tunable Magnetic Response.

van der Waals heterostructures composed of transition metal dichalcogenide monolayers (TMDCs) are characterized by their truly rich excitonic properties which are determined by their structural, geometric, and electronic properties: In contrast to pure monolayers, electrons and holes can be hosted in different materials, resulting in highly tunable dipolar many-particle complexes. However, for genuine spatially indirect excitons, the dipolar nature is usually accompanied by a notable quenching of the exciton oscillator strength. Via electric and magnetic field dependent measurements, we demonstrate that a slightly biased pristine bilayer MoS_{2} hosts strongly dipolar excitons, which preserve a strong oscillator strength. We scrutinize their giant dipole moment, and shed further light on their orbital and valley physics via bias-dependent magnetic field measurements.

Phonon-Assisted Intervalley Scattering Determines Ultrafast Exciton Dynamics in MoSe_{2} Bilayers.

While valleys (energy extrema) are present in all band structures of solids, their preeminent role in determining exciton resonances and dynamics in atomically thin transition metal dichalcogenides (TMDC) is unique. Using two-dimensional coherent electronic spectroscopy, we find that exciton decoherence occurs on a much faster timescale in MoSe_{2} bilayers than that in the monolayers. We further identify two population relaxation channels in the bilayer, a coherent and an incoherent one. Our microscopic model reveals that phonon-emission processes facilitate scattering events from the K valley to other lower-energy Γ and Λ valleys in the bilayer. Our combined experimental and theoretical studies unequivocally establish different microscopic mechanisms that determine exciton quantum dynamics in TMDC monolayers and bilayers. Understanding exciton quantum dynamics provides critical guidance to the manipulation of spin-valley degrees of freedom in TMDC bilayers.

Phonon-Assisted Photoluminescence from Indirect Excitons in Monolayers of Transition-Metal Dichalcogenides.

The photoluminescence (PL) spectrum of transition-metal dichalcogenides (TMDs) shows a multitude of emission peaks below the bright exciton line, and not all of them have been explained yet. Here, we study the emission traces of phonon-assisted recombinations of indirect excitons. To this end, we develop a microscopic theory describing simultaneous exciton, phonon, and photon interaction and including consistent many-particle dephasing. We explain the drastically different PL below the bright exciton in tungsten- and molybdenum-based materials as the result of different configurations of bright and momentum-dark states. In good agreement with experiments, our calculations predict that WSe2 exhibits clearly visible low-temperature PL signals stemming from the phonon-assisted recombination of momentum-dark K-K' excitons.

[An Innovative Regulatory Approach to Stimulate Competition in Long-Distance Passenger Rail Transport]. / Ein innovativer Regulierungsansatz zur Belebung des Wettbewerbs im Schienenpersonenfernverkehr.

Regulatory efforts to introduce effective intramodal competition to the rail sector, in particular to the long-distance intercity market segment, have so far achieved only very limited success in most countries. Germany is a case in point. Even 25 years after the fundamental 1994 'rail structure reform', which eliminated the legal network monopoly of the former Deutsche Bundesbahn (DB), the combined market share of all competitors for long-distance passenger services remains stuck at "significantly below one per cent" (Bundesnetzagentur 2018, 22). This figure stands in stark contrast to the competitors' market shares of some 26% for short-distance (regional) services - where a competition for the market regime has been established - and around 50% of the rail cargo segment - which is governed by an open access regime. In this paper, we make the case for an alternative regulatory regime to substantially increase effective intramodal competition in the intercity rail passenger market. Our proposal addresses, and helps to overcome, the two major entry barriers faced by competitors: the massive investment needs in rolling stock on the one hand and reliable infrastructure access on the other.

Screening of the quantum dot Förster coupling at small distances: erratum.

This erratum corrects the acronym 'ISW' as 'infinite square well'.

Screening of the quantum dot Förster coupling at small distances.

We study the near-field energy transfer rates between two finite size quantum dot disks, generalizing the result of Förster coupling between two point dipoles. In particular, we derive analytical results for the envelope of the electronic wave function for model potentials at the boundaries of quantum dot disks and demonstrate how the Förster interaction is screened as the size of the dots becomes comparable to the dot-dot separation.

Exciton-Scattering-Induced Dephasing in Two-Dimensional Semiconductors.

Enhanced Coulomb interactions in monolayer transition metal dichalcogenides cause tightly bound electron-hole pairs (excitons) that dominate their linear and nonlinear optical response. The latter includes bleaching, energy renormalizations, and higher-order Coulomb correlation effects like biexcitons and excitation-induced dephasing. While the first three are extensively studied, no theoretical footing for excitation-induced dephasing in exciton-dominated semiconductors is available so far. In this Letter, we present microscopic calculations based on excitonic Heisenberg equations of motion and identify the coupling of optically pumped excitons to exciton-exciton scattering continua as the leading mechanism responsible for an optical-power-dependent linewidth broadening (excitation-induced dephasing) and sideband formation. Performing time-, momentum-, and energy-resolved simulations, we quantitatively evaluate the exciton-induced dephasing for the most common monolayer transition metal dichalcogenides and find an excellent agreement with recent experiments.

Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution.

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.

Quantization of Quasinormal Modes for Open Cavities and Plasmonic Cavity Quantum Electrodynamics.

We introduce a second quantization scheme based on quasinormal modes, which are the dissipative modes of leaky optical cavities and plasmonic resonators with complex eigenfrequencies. The theory enables the construction of multiplasmon or multiphoton Fock states for arbitrary three-dimensional dissipative resonators and gives a solid understanding to the limits of phenomenological dissipative Jaynes-Cummings models. In the general case, we show how different quasinormal modes interfere through an off-diagonal mode coupling and demonstrate how these results affect cavity-modified spontaneous emission. To illustrate the practical application of the theory, we show examples using a gold nanorod dimer and a hybrid dielectric-metal cavity structure.

Enhancement of Exciton-Phonon Scattering from Monolayer to Bilayer WS2.

Layered transition metal dichalcogenides exhibit the emergence of a direct bandgap at the monolayer limit along with pronounced excitonic effects. In these materials, interaction with phonons is the dominant mechanism that limits the exciton coherence lifetime. Exciton-phonon interaction also facilitates energy and momentum relaxation, and influences exciton diffusion under most experimental conditions. However, the fundamental changes in the exciton-phonon interaction are not well understood as the material undergoes the transition from a direct to an indirect bandgap semiconductor. Here, we address this question through optical spectroscopy and microscopic theory. In the experiment, we study room-temperature statistics of the exciton line width for a large number of mono- and bilayer WS2 samples. We observe a systematic increase in the room-temperature line width of the bilayer compared to the monolayer of 50 meV, corresponding to an additional scattering rate of ∼0.1 fs-1. We further address both phonon emission and absorption processes by examining the temperature dependence of the width of the exciton resonances. Using a theoretical approach based on many-body formalism, we are able to explain the experimental results and establish a microscopic framework for exciton-phonon interactions that can be applied to naturally occurring and artificially prepared multilayer structures.

Strain Control of Exciton-Phonon Coupling in Atomically Thin Semiconductors.

Semiconducting transition metal dichalcogenide (TMDC) monolayers have exceptional physical properties. They show bright photoluminescence due to their unique band structure and absorb more than 10% of the light at their excitonic resonances despite their atomic thickness. At room temperature, the width of the exciton transitions is governed by the exciton-phonon interaction leading to strongly asymmetric line shapes. TMDC monolayers are also extremely flexible, sustaining mechanical strain of about 10% without breaking. The excitonic properties strongly depend on strain. For example, exciton energies of TMDC monolayers significantly redshift under uniaxial tensile strain. Here, we demonstrate that the width and the asymmetric line shape of excitonic resonances in TMDC monolayers can be controlled with applied strain. We measure photoluminescence and absorption spectra of the A exciton in monolayer MoSe2, WSe2, WS2, and MoS2 under uniaxial tensile strain. We find that the A exciton substantially narrows and becomes more symmetric for the selenium-based monolayer materials, while no change is observed for atomically thin WS2. For MoS2 monolayers, the line width increases. These effects are due to a modified exciton-phonon coupling at increasing strain levels because of changes in the electronic band structure of the respective monolayer materials. This interpretation based on steady-state experiments is corroborated by time-resolved photoluminescence measurements. Our results demonstrate that moderate strain values on the order of only 1% are already sufficient to globally tune the exciton-phonon interaction in TMDC monolayers and hold the promise for controlling the coupling on the nanoscale.

Quantized pseudomodes for plasmonic cavity QED.

We present a quantized pseudomode theory for solving system-level cavity quantum electrodynamics with quantum emitters coupled to plasmonic resonators. Exploiting the Green function response of a silver nanoparticle and an exact solution for the input-output coupling, we study the non-Markovian coupling regimes of multi-mode vacuum Rabi oscillations and coherently pumped multi-photon resonances from the higher lying ladder states of collective plasmon modes. The nonlinear pumping regime also facilitates pronounced population inversion of a single two-level atom through multiphoton resonances dominated by dark plasmons.

Phonon Sidebands in Monolayer Transition Metal Dichalcogenides.

Excitons dominate the optical properties of monolayer transition metal dichalcogenides (TMDs). Besides optically accessible bright exciton states, TMDs exhibit also a multitude of optically forbidden dark excitons. Here, we show that efficient exciton-phonon scattering couples bright and dark states and gives rise to an asymmetric excitonic line shape. The observed asymmetry can be traced back to phonon-induced sidebands that are accompanied by a polaron redshift. We present a joint theory-experiment study investigating the microscopic origin of these sidebands in different TMD materials taking into account intra- and intervalley scattering channels opened by optical and acoustic phonons. The gained insights contribute to a better understanding of the optical fingerprint of these technologically promising nanomaterials.