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Heterostructures made from 2D transition-metal dichalcogenides are known as ideal platforms to explore excitonic phenomena ranging from correlated moir\'e excitons to degenerate interlayer exciton ensembles. So far, it is assumed that the atomic reconstruction appearing in some of the heterostructures gives rise to a dominating localization of the exciton states. We demonstrate that excitonic states in reconstructed MoSe$_2$/WSe$_2$ heterostructures can extend well beyond the moir\'e periodicity of the investigated heterostructures. The results are based on real-space calculations yielding a lateral potential map for interlayer excitons within the strain-relaxed heterostructures and corresponding real-space excitonic wavefunctions. We combine the theoretical results with cryogenic photoluminescence experiments, which support the computed level structure and relaxation characteristics of the interlayer excitons.

The common model to describe exciton-plasmon interaction phenomenologically is the coupled oscillator model. Originally developed for atomic systems rather than solid-state matter, this model treats both excitons and plasmons as single harmonic oscillators coupled via a constant which can be fitted to experiments. In this work, we present a modified coupled oscillator model specifically designed for exciton-plasmon interactions in hybrids composed of two-dimensional excitons, such as in a transition metal dichalcogenide (TMDC) monolayers and metal nanoparticles while maintaining the simplicity of the commonly applied coupled oscillator models. Our approach is based on a microscopic perspective and Maxwell's equations, allowing to analytically derive an effective exciton-plasmon coupling constant. Our findings highlight the importance of the spatial dispersion, i.e., the delocalized nature of TMDC excitons, necessitating the distinction between bright and momentum-dark excitons. Both types of excitons occur at different resonance energies and exhibit a qualitatively different coupling with localized plasmons. We find a strong coupling between the plasmon and momentum-dark excitons, while a weakly coupled bright exciton manifests as an additional, third peak in the spectrum. Consequently, we propose a realistic modeling of the primary spectral features in experiments incorporating three harmonic oscillator equations instead of the conventional two. However, we also shed light on the limitations of the three coupled oscillator model in describing the line shape of extinction and scattering cross section spectra.

We study the dynamical light emission from few-photon Fock states in waveguide-QED with a chiral two-level system. We first investigate the time dynamics of the system by calculating the emitter population and illustrate the breakdown of the weak excitation approximation, for both 1-photon and 2-photon excitation. We show how a 1-photon pulse yields a transmitted long-time spectrum that is identical to the input pulse, despite significant population effects. However, the dynamical spectra and spectral intensity show rich population effects. We also show the differences between 1-photon and 2-photon excitation, where the latter shows clear signatures of nonlinear saturation effects. Analytical and numerically exact matrix product state solutions are shown., Comment: 6 pages, 4 figures

We present a detailed quantum theory and simulations of a few-photon Fock state pulse interacting with a two-level system (TLS) in a waveguide. For a rectangular pulse shape, we present an exact temporal scattering theory for the waveguide-QED system to derive analytical expressions for the TLS population, for 1-photon and 2-photon pulses, for both chiral and symmetric emitters. We also derive the stationary (long time) and time-dependent spectra for 1 photon excitation, and show how these differ at a fundamental level when connecting to TLS population effects. Numerically, we also present matrix product state (MPS) simulations, which allow us to compute more general photon correlation functions for arbitrary quantum pulses, and we use this approach to also show results for Gaussian quantum pulses, and to confirm the accuracy of our analytical results. In addition, we show how significant population TLS effects also occur for pulses relatively long compared to the radiative decay time (showing that a weak excitation approximation cannot be made), and investigate the population signatures, nonlinear features and dynamical behavior as a function of pulse length. These detailed theoretical results extend and complement our related Letter results [Arranz Regidor et al., unpublished, 2024]., Comment: 24 pages, 10 figures

We investigate spin relaxation dynamics of interlayer excitons in a MoSe2/MoS2 heterostructure induced by the Rashba effect. In such a system, Rashba interactions arise from an out-of-plane electric field due to photo-generated interlayer excitons inducing a phonon-assisted intravalley spin relaxation. We develop a theoretical description based on a microscopic approach to quantify the magnitude of Rashba interactions and test these predictions via time-resolved Kerr rotation measurements. In agreement with the calculations, we find that the Rashba-induced intravalley spin mixing becomes the dominating spin relaxation channel above T = 50 K. Our work identifies a previously unexplored spin-depolarization channel in heterostructures which can be used for ultrafast spin manipulation.

Multi-physics simulations play a crucial role in understanding complex systems. However, their computational demands are often prohibitive due to high dimensionality and complex interactions, such that actual calculations often rely on approximations. To address this, we introduce a data-driven approach to approximate interactions among degrees of freedom of no direct interest and thus significantly reduce computational costs. Focusing on a semiconductor laser as a case study, we demonstrate the superiority of this method over traditional analytical approximations in both accuracy and efficiency. Our approach streamlines simulations, offering promise for complex multi-physics systems, especially for scenarios requiring a large number of individual simulations., Comment: The simulation code and the regression code is available on GitHub under MIT license (https://github.com/stmeinecke/derrom)

We present a data-driven approach to efficiently approximate nonlinear transient dynamics in solid-state systems. Our proposed machine-learning model combines a dimensionality reduction stage with a nonlinear vector autoregression scheme. We report an outstanding time-series forecasting performance combined with an easy to deploy model and an inexpensive training routine. Our results are of great relevance as they have the potential to massively accelerate multi-physics simulation software and thereby guide to future development of solid-state based technologies., Comment: The simulation code and the regression code is available on GitHub under MIT license (https://github.com/stmeinecke/derrom)

Excitons are compound particles formed from an electron and a hole in semiconductors. The impact of this substructure on the phonon-exciton interaction is described by a closed system of microscopic scattering equations. To calculate the actual excitonic thermalization properties beyond the pure bosonic picture, this equation is derived directly from an electron-hole picture within the Heisenberg equation of motion framework. In addition to the well-known bosonic character of the compound particles, we identified processes of a repulsive, fermionic type, as well as attractive carrier exchange contributing to the scattering process. In this analytical study we give general statements about the thermalization of excitons in two and three dimensional semiconductors. We give insights on the strong dependence of the thermalization characteristics of the exciton Bohr radius and the thermalization wavelength. Above all, we analytically provide arguments why a bosonic behavior of excitons - such as an enhanced ground state occupation - requires the dominant phonon scattering to be quasielastic. Acoustic phonons tend to fulfil this, as each scattering event only takes small amounts of energy out of the distribution, while optical phonons tend to prevent macroscopic occupations of the lowest exciton state, since the Pauli repulsion between the individual carriers will then dominate the thermalization dynamics.

Monolayers of transition metal dichalcogenides (TMDC) are direct-gap semiconductors with strong light-matter interactions featuring tightly bound excitons, while plasmonic crystals (PCs), consisting of metal nanoparticles that act as meta-atoms, exhibit collective plasmon modes and allow one to tailor electric fields on the nanoscale. Recent experiments show that TMDC-PC hybrids can reach the strong-coupling limit between excitons and plasmons forming new quasiparticles, so-called plexcitons. To describe this coupling theoretically, we develop a self-consistent Maxwell-Bloch theory for TMDC-PC hybrid structures, which allows us to compute the scattered light in the near- and far-field explicitly and provide guidance for experimental studies. Our calculations reveal a spectral splitting signature of strong coupling of more than $100\,$meV in gold-MoSe$_2$ structures with $30\,$nm nanoparticles, manifesting in a hybridization of exciton and plasmon into two effective plexcitonic bands. In addition to the hybridized states, we find a remaining excitonic mode with significantly smaller coupling to the plasmonic near-field, emitting directly into the far-field. Thus, hybrid spectra in the strong coupling regime can contain three emission peaks., Comment: 16 pages, 6 figures

In recent years, much research has been undertaken to investigate the suitability of two-dimensional materials to act as single-photon sources with high optical and quantum optical quality. Amongst them, transition-metal dichalcogenides, especially WSe$_{2}$, have been one of the subjects of intensive studies. Yet, their single-photon purity and photon indistinguishability, remain the most significant challenges to compete with mature semiconducting systems such as self-assembled InGaAs quantum dots. In this work, we explore the emission properties of quantum emitters in a WSe$_{2}$ monolayer which are induced by metallic nanoparticles. Under quasi-resonant pulsed excitation, we verify clean single-photon emission with a $g^{(2)}(0) = 0.036\pm0.004$. Furthermore, we determine its temperature dependent coherence time via Michelson interferometry, where a value of (13.5$\pm$1.0) ps is extracted for the zero-phonon line (ZPL) at 4 K, which reduces to (9$\pm$2) ps at 8 K. Associated time-resolved photoluminescence experiments reveal a decrease of the decay time from (2.4$\pm$0.1) ns to (0.42$\pm$0.05) ns. This change in decay time is explained by a model which considers a F\"orster-type resonant energy transfer process, which yields a strong temperature induced energy loss from the SPE to the nearby Ag nanoparticle.

We present a self-consistent Maxwell-Bloch theory to analytically study the interaction between a nanostructure consisting of a metal nanoparticle and a monolayer of transition metal dichalcogenide. For the combined system, we identify an effective eigenvalue equation that governs the center-of-mass motion of the dressed excitons in a plasmon-induced potential. Examination of the dynamical equation of the exciton-plasmon hybrid reveals the existence of bound states with negative eigenenergies, which we interpret as excitons localized in the plasmon-induced potential. The appearance of these bound states in the potential indicates strong coupling between excitons and plasmons. We quantify this coupling regime by computing the scattered light in the near-field explicitly and identify signatures of strong exciton-plasmon coupling with an avoided crossing behavior and an effective Rabi splitting of tens of meV., Comment: 16 pages, 13 figures

Vertical heterostructures (HS) of transition metal dichalcogenides (TMDs) host interlayer excitons (ILX), with electrons and holes residing in different layers. With respect to their intralayer counterparts, ILX feature much longer lifetimes and diffusion lengths, paving the way to excitonic optoelectronic devices operating at room temperature. While the recombination dynamics of ILX has been intensively studied, the formation process and its underlying physical mechanisms are still largely unexplored. Here we use ultrafast transient absorption spectroscopy with a white-light probe, spanning both intralayer and interlayer exciton resonances, to simultaneously capture and time-resolve interlayer charge transfer and ILX formation dynamics in a MoSe$_2$/WSe$_2$ HS. We find that the ILX formation timescale is nearly an order of magnitude (~1 ps) longer than the interlayer charge transfer time (~100 fs). Microscopic calculations attribute the relative delay to an interplay between a phonon-assisted interlayer exciton cascade and subsequent cooling processes, and excitonic wave-function overlap. Our results provide an explanation to the efficient photocurrent generation observed in optoelectronic devices based on TMD HS, as the ILX have an opportunity to dissociate during their thermalization process., Comment: 18 pages, 4 figures

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., Comment: 13 pages, 3 figures

The question of macroscopic occupation and spontaneous emergence of coherence for exciton ensembles has gained renewed attention due to the rise of van der Waals heterostructures made of atomically thin semiconductors. The hosted interlayer excitons exhibit nanosecond lifetimes, long enough to allow for excitonic thermalization in time. Several experimental studies reported signatures of macroscopic occupation effects at elevated exciton densities. With respect to theory, excitons are composite particles formed by fermionic constituents, and a general theoretical argument for a bosonic thermalization of an exciton gas beyond the linear regime is still missing. Here, we derive an equation for the phonon mediated thermalization at densities above the classical limit, and identify which conditions favor the thermalization of fermionic or bosonic character, respectively. In cases where acoustic, quasielastic phonon scattering dominates the dynamics, our theory suggests that transition metal dichalcogenide (TMDC) excitons might be bosonic enough to show bosonic thermalization behaviour and decreasing dephasing for increasing exciton densities. This can be interpreted as a signature of an emerging coherence in the exciton ground state, and agrees well with the experimentally observed features, such as a decreasing linewidth for increasing densities.

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.

Transition metal dichalcogenides (TMDCs) combine both strong light-matter-interaction and strong Coulomb-interaction for the formation of optically excitable excitons. Through radiative feedback control, a mechanism to control the linewidth can be applied, which modifies optical transition spectra. Here, we extend these investigations to the absorption spectra of TMDCs in a variety of geometries with respect to non-Markovian exciton-phonon-scattering contributions. Our approach is based on the self consistent solution of the microscopic Bloch equations and the macroscopic solution of the wave equation. We discuss the formation of a phonon sideband for MoSe$_2$ embedded in SiO$_2$, and two setups for enhancing or suppressing the phonon sideband in the spectrum.

Interfaces of dye molecules and two-dimensional transition metal dichalcogenides (TMDCs) combine strong molecular dipole excitations with high carrier mobilities in semiconductors. F\"orster type energy transfer is one key mechanism for the coupling between both constituents. We report microscopic calculations of a spectrally resolved F\"orster induced transition rate from dye molecules to a TMDC layer. Our approach is based on microscopic Bloch equations which are solved self-consistently together with Maxwells equations. This approach allows to incorporate the dielectric environment of a TMDC semiconductor, sandwiched between donor molecules and a substrate. Our analysis reveals transfer rates in the meV range for typical dye molecules in closely stacked structures, with a non-trivial dependence of the F\"orster rate on the molecular transition energy resulting from unique signatures of dark, momentum forbidden TMDC excitons.

We develop a self-consistent Maxwell-Bloch formalism for the interaction of X-rays with two-dimensional crystalline materials by incorporating the Bloch theorem and Coulomb many-body interaction. This formalism is illustrated for graphene, by calculating the polarization-dependent XANES, formulating expressions for the radiative and Meinter-Auger recombination of core-holes, and the discussion of microscopic insights into the spectral oscillations of EXAFS beyond point scattering theory. In particular, the correct inclusion of lattice periodicity in our evaluation allows us to assign so far uninterpreted spectral features in the Fourier transformed EXAFS spectrum.

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 time scale 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 $\Gamma$ and $\Lambda$ 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 manipulation of spin/valley degrees of freedom in TMDC bilayers., Comment: 6 pages, 4 figures

Nonlinear optical effects such as four-wave mixing and generation of squeezed light are ubiquitous in optical devices and light sources. For new devices operating at low optical power, the resonant nonlinearity arising from the two-photon sensitive bound biexciton in a semiconductor microcavity is an interesting prospective platform. Due to the particularly strong Coulomb interaction in atomically thin semiconductors, these materials have strongly bound biexcitons and operate in the visible frequency range of the electromagnetic spectrum. To remove the strong pump laser from the generated light in optical devices or to simultaneously excite non-degenerate polaritons, a bichromatic-pump configuration with two spectrally separated pump lasers is desirable. In this paper, we theoretically investigate spontanous four-wave mixing and quadrature-squeezing in a bichromatically pumped atomically thin semiconductor microcavity. We explore two different configurations that support degenerate and non-degenerate scattering from polaritons into bound biexcitons, respectively. We find that these configurations lead to the generation strongly single- and two-mode quadrature-squeezed light., Comment: Accepted in Phys. Rev. B

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 allows 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., Comment: Postprint version

A promising route for the development of opto-elelctronic technology is to use terahertz radiation to modulate the optical properties of semiconductors. Here we demonstrate the dynamical control of photoluminescence (PL) emission in few-layer InSe using picosecond terahertz pulses. We observe a strong PL quenching (up to 50%) after the arrival of the terahertz pulse followed by a reversible recovery of the emission on the time scale of 50ps at T =10K. Microscopic calculations reveal that the origin of the photoluminescence quenching is the terahertz absorption by photo-excited carriers: this leads to a heating of the carriers and a broadening of their distribution, which reduces the probability of bimolecular electron-hole recombination and, therefore, the luminescence. By numerically evaluating the Boltzmann equation, we are able to clarify the individual roles of optical and acoustic phonons in the subsequent cooling process. The same PL quenchingmechanismis expected in other van derWaals semiconductors and the effectwill be particularly strong for materials with low carrier masses and long carrier relaxation time, which is the case for InSe. This work gives a solid background for the development of opto-electronic applications based on InSe, such as THz detectors and optical modulators., Comment: The following article has been accepted by Applied Physics Letters. After it is published, it will be found at https://publishing.aip.org/resources/librarians/products/journals/

High-order frequency mixing in graphene using a two-color radiation field consisting of the fundamental and the second harmonic fields of an ultrashort linearly polarized laser pulse is studied. It is shown that the harmonics originated from the interband transitions are efficiently generated in the case of the orthogonally polarized two-color field. In this case, the generated high-harmonics are stronger than those obtained in the parallel polarization case by more than two orders of magnitude. This is in sharp contrast with the atomic and semiconductor systems, where parallel polarization case is more preferable. The physical origin of this enhancement is also deduced from the three-step semi-classical electron-hole collision model, extended to graphene with pseudo-relativistic energy dispersion. In particular, we discuss the influence of the many particle Coulomb interaction on the HHG process within dynamical Hartree-Fock approximation. Our analysis shows that in all cases we have an overall enhancement of the HHG signal compared with the free-charged carrier model due to the electron-hole attractive interaction., Comment: 12 pages, 9 figures

The interplay of the non-equivalent corners in the Brillouin zone of transition metal dichalcogenides have 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. In this manuscript we present microscopic calculations for the non-equilibrium steady state properties of excitons during continuous wave pumping. 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.

The interaction of optically excited excitons in atomically thin semiconductors with residual doping densities leads to many-body effects which are continuously tunable by external gate voltages. Here, we develop a fully microscopic theory to describe the doping-dependent manipulation of the excitonic properties in atomically thin transition metal dichalcogenides. In particular, we establish a diagonalization approach for the Schr\"odinger equation which characterizes the interaction of a virtual exciton with the Fermi sea of dopants. Solving this many-body Schr\"odinger equation provides access to trions as well as a continuum of scattering states. The dynamics of coupled excitons, trions, and scattering continua is subsequently described by Heisenberg equations of motion including mean-field contributions and correlation effects due to the interaction of excitons with trions and scattering continuum states. Our calculations for optical excitation close to the band edge reveal the influence of doping on the exciton resonances in combination with the simultaneous identification of not only ground-, but also excited-, state trion resonances.

Strong Coulomb interactions in atomically thin semiconductors like monolayer WSe$_2$ induce not only tightly bound excitons, but also make their optical properties very sensible to doping. By utilizing a microscopic theory based on the excitonic Heisenberg equations of motion, we systematically determine the influence of doping on the excitonic linewidth, lineshift, and oscillator strength. We calculate trion resonances and demonstrate that the Coulomb coupling of excitons to the trionic continuum generates a non-Markovian interference, which, due to a time retardation, builds up a phase responsible for asymmetric exciton line shapes and increased excitonic linewidths. Our calculated doping dependence of exciton and trion linewidths, lineshifts, and oscillator strengths explains recent experiments. The gained insights provide the microscopic origin of the optical fingerprint of doped atomically thin semiconductors.

The excitonic insulator is an elusive electronic phase exhibiting a correlated excitonic ground state. Materials with such a phase are expected to have intriguing properties such as excitonic high-temperature superconductivity. However, compelling evidence on the experimental realization is still missing. Here, we theoretically propose hybrids of two-dimensional semiconductors functionalized by organic molecules as prototypes of excitonic insulators, with the exemplary candidate WS$_2$-F6TCNNQ. This material system exhibits an excitonic insulating phase at room temperature with a ground state formed by a condensate of interlayer excitons. To address an experimentally relevant situation, we calculate the corresponding phase diagram for the important parameters: temperature, gap energy, and dielectric environment. Further, to guide future experimental detection, we show how to optically characterize the different electronic phases via far-infrared to terahertz (THz) spectroscopy.

In van der Waals heterostructures (HS) consisting of stacked MoSe$_2$ and WSe$_2$ monolayers, optically bright interlayer excitons (ILE) can be observed when the constituent layers are crystallographically aligned. The symmetry of the monolayers allows for two different types of alignment, in which the momentum-direct interlayer transitions are either valley-conserving (R-type alignment) or changing the valley index (H-type anti-alignment). Here, we study the valley polarization dynamics of ILE in magnetic fields up to 30~Tesla by time-resolved photoluminescence (PL). For all ILE types, we find a finite initial PL circular degree of polarization ($DoP$) after unpolarized excitation in applied magnetic fields. For ILE in H-type HS, we observe a systematic increase of the PL $DoP$ with time in applied magnetic fields, which saturates at values close to unity for the largest fields. By contrast, for ILE in R-type HS, the PL $DoP$ shows a decrease and a zero crossing before saturating with opposite polarization. This unintuitive behavior can be explained by a model considering the different ILE states in H- and R-type HS and their selection rules coupling PL helicity and valley polarization.

The dynamics of waveguide-QED systems involving coherent time-delayed feedback give rise to a hierarchy of multi-time correlations within the Heisenberg picture due to the induced non-Markovianity. We propose to perform a projection onto a complete set of states in the Hilbert space to decompose the multi-time correlations into single-time matrix elements. To illustrate the procedure, we consider the paradigmatic example of a two-level system that couples to a semi-infinite waveguide and interacts with quantum light pulses. Our approach complements the range of available methods as it allows calculating the dynamics under the inclusion of additional dissipation channels in a numerically exact and efficient manner for multiphoton pulses of arbitrary shape where memory requirements are known in advance.

We report on the far-field photoluminescence intensity distribution of interlayer excitons in MoSe$_{2}$-WSe$_{2}$ heterostacks as measured by back focal plane imaging in the temperature range between 1.7 K and 20 K. By comparing the data with an analytical model describing the dipolar emission pattern in a dielectric environment, we are able to obtain the relative contributions of the in- and out-of-plane transition dipole moments associated to the interlayer exciton photon emission. We determine the transition dipole moments for all observed interlayer exciton transitions to be (99 $\pm$ 1)% in-plane for R- and H-type stacking, independent of the excitation power and therefore the density of the exciton ensemble in the experimentally examined range. Finally, we discuss the limitations of the presented measurement technique to observe correlation effects in exciton ensembles.

Atomically thin layered van der Waals heterostructures feature exotic and emergent optoelectronic properties. With growing interest in these novel quantum materials, the microscopic understanding of fundamental interfacial coupling mechanisms is of capital importance. Here, using multidimensional photoemission spectroscopy, we provide a layer- and momentum-resolved view on ultrafast interlayer electron and energy transfer in a monolayer-WSe$_2$/graphene heterostructure. Depending on the nature of the optically prepared state, we find the different dominating transfer mechanisms: while electron injection from graphene to WSe$_2$ is observed after photoexcitation of quasi-free hot carriers in the graphene layer, we establish an interfacial Meitner-Auger energy transfer process following the excitation of excitons in WSe$_2$. By analysing the time-energy-momentum distributions of excited-state carriers with a rate-equation model, we distinguish these two types of interfacial dynamics and identify the ultrafast conversion of excitons in WSe$_2$ to valence band transitions in graphene. Microscopic calculations find interfacial dipole-monopole coupling underlying the Meitner-Auger energy transfer to dominate over conventional F\"orster- and Dexter-type interactions, in agreement with the experimental observations. The energy transfer mechanism revealed here might enable new hot-carrier-based device concepts with van der Waals heterostructures., Comment: 28 pages, 4 figures

We present a rigorous photonic mode model to describe the strong coupling between a monolayer of $\rm MoSe_2$ and a single gold nanoparticle. The onset of strong coupling is quantified by computing the three-dimensional hybrid quasinormal modes of the combined structure, allowing one to accurately model light-matter interactions without invoking the usual phenomenological theories of strong coupling. We explore the hybrid quasinormal modes as a function of gap size and temperature and find spectral splittings in the range of around 80-110 meV, with no fitting parameters for the material models. We also show how the hybrid modes exhibit Fano-like resonances and quantify the complex poles of the hybrid modes as well as the Purcell factor resonances from embedded dipole emitters. These effects cannot be described with the usual heuristic normal mode theories., Comment: 13 pages, 8 figures

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., Comment: 6 pages, 3 figures

Excitons, Coulomb-bound electron-hole pairs, are the fundamental excitations governing the optoelectronic properties of semiconductors. While optical signatures of excitons have been studied extensively, experimental access to the excitonic wave function itself has been elusive. Using multidimensional photoemission spectroscopy, we present a momentum-, energy- and time-resolved perspective on excitons in the layered semiconductor WSe$_2$. By tuning the excitation wavelength, we determine the energy-momentum signature of bright exciton formation and its difference from conventional single-particle excited states. The multidimensional data allows to retrieve fundamental exciton properties like the binding energy and the exciton-lattice coupling and to reconstruct the real-space excitonic distribution function via Fourier transform. All quantities are in excellent agreement with microscopic calculations. Our approach provides a full characterization of the exciton properties and is applicable to bright and dark excitons in semiconducting materials, heterostructures and devices.

Based on tensor network realizations of path integrals reducing exponential memory scaling to polynomial efficiency and a Liouville space implementation of a time-discrete quantum memory, we investigate a quantum system simultaneously exposed to two structured reservoirs. For this purpose, we employ a numerically exact quasi-2D tensor network combining both diagonal and off-diagonal system-reservoir interactions with a twofold memory for continuous and discrete retardation effects. As a possible example, we study the non-Markovian dynamical interplay between discrete photonic feedback and structured acoustic phonon modes, resulting in emerging inter-reservoir correlations and long-living population trapping within an initially-excited two-level system.

Within the matrix product state framework, we study the non-Markovian feedback dynamics of a two-level system interacting with the electromagnetic field inside a semi-infinite waveguide where the excitation of an atom-photon bound state is possible. Taking the steady-state excitation of the emitter as a figure of merit, we compare the trapped excitation for an initially excited quantum emitter and an emitter prepared via quantized pulses containing up to four photons. In the latter case, we find that for large feedback delay times, multi-photon pulses can yield a significantly higher steady-state excitation than possible with an initially excited emitter since the stimulated emission process can enhance the trapping probability in comparison to the spontaneous decay of an initially excited emitter.

We predict a mechanism for achieving complete population inversion in a continuously driven InAs/GaAs semiconductor quantum dot featuring $V$-type transitions. This highly nonequilibrium steady state is enabled by the interplay between $V$-type interband transitions and a non-Markovian decoherence mechanism, introduced by acoustic phonons. The population trapping mechanism is generalized to a chain of coupled emitters. Exploiting the population inversion, we predict unidirectional excitation transport from one end of the chain to the other without external bias, independent of the unitary interdot coupling mechanism.

The recent accessibility of high quality, charge neutral monolayer transition metal dichalcogenides with narrow exciton linewidths at the homogeneous limit provides an ideal platform to study excitonic many-body interactions. In particular, the possibility to manipulate coherent exciton-exciton interactions, which govern the ultrafast nonlinear optical response, by applying an external magnetic field has not been considered so far. We address this discrepancy by presenting a nonlinear microscopic theory in the coherent limit for optical excitations in the presence of out-of-plane, in-plane, and tilted magnetic fields. Specifically, we explore the magnetic-field-induced exciton and biexciton fine structure and calculate their oscillator strengths based on a Heisenberg equations of motion formalism. Our microscopic evaluations of pump-probe spectra allow to interpret and predict coherent signatures in future wave-mixing experiments.

We have investigated the plasmonic enhancement of the radiation field at various nanostructured multilayer devices, that may be applied in surface enhanced Raman spectroscopy. We apply an image dipole method to describe the effect of surface morphology on the field enhancement in a quasistatic limit. In particular, we compare the performance of a nanostructured silver surface and a layered silver-gold hybrid device. It is found that localized surface plasmon states (LSP) provide a high field enhancement in silver-gold hybrid devices, where symmetry breaking due to surface-defects is a supporting factor. These results are compared to those obtained for multi-shell nanoparticles of spherical symmetry. Calculated enhancement factors are discussed on the background of recent experimental data., Comment: 8 pages, 6 figures

Enhanced Coulomb interactions in monolayer transition metal dichalcogenides cause tightly bound electron-hole pairs (excitons) which 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 (EID). While the first three are extensively studied, no theoretical footing for EID in exciton dominated semiconductors is available so far. In this study, 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 (EID) and sideband formation. Performing time-, momentum-, and energy-resolved simulations, we quantitatively evaluate the EID for the most common monolayer transition metal dichalcogenides and find an excellent agreement with recent experiments.

Low-temperature photoluminescence (PL) of hBN-encapsulated monolayer tungsten diselenide (WSe$_2$) shows a multitude of sharp emission peaks below the bright exciton. Some of them have been recently identified as phonon sidebands of momentum-dark states. However, the exciton dynamics behind the emergence of these sidebands has not been revealed yet. In this joint theory-experiment study, we theoretically predict and experimentally observe time-resolved PL providing microscopic insights into thermalization of hot excitons formed after optical excitation. In good agreement between theory and experiment, we demonstrate a spectral red-shift of phonon sidebands on a timescale of tens of picoseconds reflecting the phonon-driven thermalization of hot excitons in momentum-dark states. Furthermore, we predict the emergence of a transient phonon sideband that vanishes in the stationary PL. The obtained microscopic insights are applicable to a broad class of 2D materials with multiple exciton valleys., Comment: 10 pages, 5 figures

We employ a recently developed quantization scheme for quasinormal modes (QNMs) to study a nonperturbative open cavity-QED system consisting of a hybrid metal-dielectric resonator coupled to a quantum emitter. This hybrid cavity system allows one to explore the complex coupling between a low $Q$ (quality factor) resonance and a high $Q$ resonance, manifesting in a striking Fano resonance, an effect that is not captured by traditional quantization schemes using normal modes or a Jaynes-Cummings (JC) type model. The QNM quantization approach rigorously includes dissipative coupling between the QNMs, and is supplemented with generalized input-output relations for the output electric field operator for multiple modes in the system, and correlation functions outside the system. The role of the dissipation-induced mode coupling is explored in the strong coupling regime between the photons and emitter beyond the first rung of the JC dressed-state ladder. Important differences in the quantum master equation and input-output relations between the QNM quantum model and phenomenological dissipative JC models are found. In a second step, numerical results for the Fock distributions and system as well as output correlation functions obtained from the quantized QNM model for the hybrid structure are compared with results from a phenomenological approach. We demonstrate explicitly how the quantized QNM model manifests in multiphoton quantum correlations beyond what is predicted by the usual JC models., Comment: 26 pages, 12 figures

Van der Waals heterostructures composed of transition metal dichalcogenide monolayers (TMDs) 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 manyparticle 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., Comment: 7 Pages, 4 Figures

We study the near-field energy transfer rates between two finite size quantum dot disks, generalizing the result of F\"orster coupling between two point dipoles. In particular, we derive analytical results for the envelope of the electronic wavefunction for model potentials at the boundaries of quantum dot disks and demonstrate how the F\"orster interaction is screened as the size of the dots becomes comparable to the dot-dot separation., Comment: 5 pages, 2 figures

The equilibrium and non-equilibrium optical properties of single-layer transition metal dichalcogenides (TMDs) are determined by strongly bound excitons. Exciton relaxation dynamics in TMDs have been extensively studied by time-domain optical spectroscopies. However, the formation dynamics of excitons following non-resonant photoexcitation of free electron-hole pairs have been challenging to directly probe because of their inherently fast timescales. Here we use extremely short optical pulses to non-resonantly excite an electron-hole plasma and show the formation of two-dimensional excitons in single-layer MoS2 on the timescale of 30 fs via the induced changes to photo-absorption. These formation dynamics are significantly faster than in conventional 2D quantum wells and are attributed to the intense Coulombic interactions present in 2D TMDs. A theoretical model of a coherent polarization that dephases and relaxes to an incoherent exciton population reproduces the experimental dynamics on the sub-100-fs timescale and sheds light into the underlying mechanism of how the lowest-energy excitons, which are the most important for optoelectronic applications, form from higher-energy excitations. Importantly, a phonon-mediated exciton cascade from higher energy states to the ground excitonic state is found to be the rate-limiting process. These results set an ultimate timescale of the exciton formation in TMDs and elucidate the exceptionally fast physical mechanism behind this process.

A semiconductor quantum dot (QD) is an attractive resource to generate polarization-entangled photon pairs. We study the excitonic spin precession (flip-flop) in a family of QDs with different excitonic fine-structure splitting (FSS) and its impact on the entanglement of photons generated from the excitonic-biexcitonic radiative cascade. Our results reveal that coherent processes leave the time post-selected entanglement of QDs with finite FSS unaffected while changing the eigenstates of the system. The flip-flop's precession is observed via quantum tomography through anomalous oscillations of the coincidences in the rectilinear basis. A theoretical model is constructed with the inclusion of an excitonic flip-flop rate and is compared with a two-photon quantum tomography measurement on a QD exhibiting the spin flip-flop mechanism. A generalization of the theoretical model allows estimating the degree of entanglement as a function of the FSS and the spin-flip rate. For a finite temporal resolution, the negativity is found to be oscillating with respect to both the FSS and the spin-flip rate. This oscillatory behavior disappears for perfect temporal resolution and maximal entanglement is retrieved despite the flip-flop process.

We establish an important connection between coherent quantum feedback and the Ornstein-Uhlenbeck process in quantum optics. We show that an emitter with fluctuating energy levels in front of a mirror results in an Ornstein-Uhlenbeck process for electronic populations, although the fluctuation of the energy levels is assumed to be uncorrelated in time and space. Based on a Heisenberg equation of motion description of the quantum feedback dynamics, we discuss additionally the impact of phase noise on the population dynamics and provide examples in which noise itself is not detrimental but supports and enhances typical features of quantum feedback such as self-stabilization.

Spin systems in solid state materials are promising qubit candidates for quantum information or quantum sensing. A major prerequisite here is the coherence of spin phase oscillations. In this work, we show a control sequence which, by applying RF pulses of variable detuning, allows to increase the spin phase oscillation visibility and to perform DC magnetometry as well. We experimentally demonstrate the scheme on single NV centers in diamond and analytically describe how the NV electron spin phase oscillations behave in the presence of classical noise models. We hereby introduce detuning as the enabling factor that modulates the filter function of the sequence, in order to achieve a visibility of the Ramsey fringes comparable to or longer than the Hahn-echo $T_2$ time and an improved sensitivity to DC magnetic fields in various experimental settings.