arXiv subjects

Marten Richter

Publications and source records attributed to Marten Richter.

At least 19 recordsLinked to original sources

arXiv2026

Correlation functions for quantum dynamics of coupled quasinormal modes and quantum emitters interacting via finite-delay propagating photons

A time-dependent theory for the interactions between spatially separated lossy cavities in a homogeneous background medium using quantized quasinormal modes (QNMs) is presented. The cavities interact via a bath of traveling photons, described by non-bosonic operators that are orthogonal to the open-cavity QNMs. The retarded (i.e., time-delayed) inter-cavity dynamics are fully described by system-bath correlation functions, in which the emission from one cavity appears as the input field for another. Coupling between quantum emitters (described as two-level systems), placed inside a cavity or embedded in an external medium, and the electromagnetic field (cavity modes and bath photons) is included in the theory, which gives rise to both bath-mediated and QNM-mediated interactions between the emitters.

cond-mat.mes-hall↗

arXiv2026

Tensor network methods for bound electron-hole complexes beyond strong and weak confinement in nanoplatelets

In semiconductor nanostructures, optical excitation typically creates bound electron-hole states, such as excitons, trions, and larger complexes. Their relative motion is described by the Wannier equation, which is valid only for spatially extended motion in the Coulomb-dominated, weak-confinement limit. Other small nanostructures, such as quantum dots, are in the confinement-dominated strong confinement regime, where the wavefunction factorizes into independent electron and hole parts. Nanoplatelets are in between the two regimes and require solving an unfactorized higher-dimensional Schrödinger equation, which is computationally expensive. This work demonstrates how tensor networks can partially overcome this problem, using CdSe nanoplatelets as an example. The method is also applicable to related two-dimensional systems. As a demonstration, we calculate the excitonic and trionic ground states, as well as several excited states, for nanoplatelets of varying sizes, including their energies and oscillator strengths. More importantly, overall strategies for using tensor networks in real space for systems under intermediate confinement have been developed.

cond-mat.mes-hall↗

arXiv2026

Quasinormal mode quantization of bound and propagating photons in complex lightguiding nanostructures for integrated devices

Open optical or plasmonic resonators are placed on and connected through surfaces or via waveguides, forming complex lightguiding nanostructures, e.g. for integrated photonic quantum devices. We derive general boundary conditions for quasinormal modes that account for the structure's specific geometry. We then present a general quantization scheme for multiple, interacting quasinormal-mode cavities coupled to quantum emitters and to a non-bosonic bath of propagating photons on waveguides or a surface. We derive a system-bath Hamiltonian with rigorously defined coupling elements that can be computed using Maxwell solvers, including light-matter coupling between the electromagnetic field and quantum emitters. We define system-bath correlation functions for an effective, bath-mediated, and time-delayed interaction between the quasinormal modes and quantum emitters, which is a main ingredient commonly used to simulate open quantum system dynamics.

cond-mat.mes-hall↗

arXiv2026

Green's function expansion for multiple coupled optical resonators with finite retardation using quasinormal modes

The electromagnetic Green's function is a crucial ingredient for the theoretical study of modern photonic quantum devices, but is often difficult or even impossible to calculate directly. We present a numerically efficient framework for calculating the scattered electromagnetic Green's function of a multi-cavity system with spatially separated open cavities (with arbitrary shape, dispersion and loss) and finite retardation times. The framework is based on a Dyson scattering equation that enables the construction of the Green's function from the quasinormal modes of the individual resonators within a few-mode approximation and a finite number of iteration steps without requiring nested integrals. The approach shows excellent agreement with the full numerical Green's function for the example of two coupled dipoles located in the gaps of two metal dimers serving as quasinormal mode cavities, and is easily extended to arbitrarily large separations and multiple cavities.

cond-mat.mes-hall↗

arXiv2025

Ultrafast transition from coherent to incoherent polariton nonlinearities in a hybrid 1L-WS2/plasmon structure

Exciton polaritons based on atomically thin semiconductors are essential building blocks of quantum optoelectronic devices. Their properties are governed by an ultrafast and oscillatory energy transfer between their excitonic and photonic constituents, resulting in the formation of polaritonic quasiparticles with pronounced nonlinearities induced by the excitonic component. In metallic nanoresonators, dissipation phenomena limit the polariton lifetime to a few ten femtoseconds, so short that the role of these polaritons for the nonlinearities of such hybrids is yet unexplored. Here, we use ultrafast two-dimensional electronic spectroscopy (2DES) to uncover coherent polariton dynamics in a hybrid monolayer (1L) WS2/plasmonic nanostructure. With respect to an uncoupled WS2 flake, we observe an over 20-fold, polarization-dependent enhancement of the optical nonlinearity and a rapid evolution of the 2DES spectra within ~70 fs. We relate these dynamics to a transition from coherent polaritons to incoherent excitations, unravel the microscopic optical nonlinearities, and show the potential of coherent polaritons for ultrafast all-optical switching.

cond-mat.mes-hall↗

arXiv2024

Laterally Extended States of Interlayer Excitons in Reconstructed MoSe$_2$/WSe$_2$ Heterostructures

Heterostructures made from 2D transition-metal dichalcogenides are known as ideal platforms to explore excitonic phenomena ranging from correlated moiré 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 moiré 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.

cond-mat.mes-hall↗

arXiv2024

Quantization of optical quasinormal modes for spatially separated cavity systems with finite retardation

A multi-cavity quantization scheme is developed using quasinormal modes (QNMs) of optical cavities embedded in a homogeneous background medium for cases where retardation is significant in the inter-cavity coupling. Using quantities that can be calculated in computational optics with numerical Maxwell solvers, we extend previous QNM quantization schemes and define a quantitative measure to determine if a separate quantization of QNM cavities is justified or if a joint quantization of the system is necessary. We test this measure for the examples of two coupled one-dimensional dielectric slabs and a dimer of metal nanorods acting as QNM cavities. For sufficiently large separations, the new scheme allows for an efficient treatment of multi-cavity phenomena using parameters defined for the individual cavities. Formulating the Hamiltonian in a familiar system-bath form, the scheme connects the rigorous QNM theory and widespread phenomenological models of open cavities coupled to a shared photonic bath with parameters obtained directly from Maxwell calculations.

cond-mat.mes-hall↗

arXiv2024

Theory of interlayer exciton dynamics in 2D TMDCs Heterolayers under the influence of strain reconstruction and disorder

Monolayers of transition metal dichalcogenides (TMDC) became one of the most studied nanostructures in the last decade. Combining two different TMDC monolayers results in a heterostructure whose properties can be individually tuned by the twist angle between the lattices of the two van-der-Waals layers and the relative placement of the layers, leading to Moiré cells. For small twist angles, lattice reconstruction leads to strong strain fields in the Moiré cells. In this paper, we combine an existing theory for lattice reconstruction with a quantum dynamic theory for interlayer excitons and their dynamics due to exciton phonon scattering using a polaron transformation. The exciton theory is formulated in real space instead of the commonly used quasi-momentum space to account for imperfections in the heterolayer breaking lattice translational symmetry. We can analyze the structure of the localized and delocalized exciton states and their exciton-phonon scattering rates for single phonon processes using Born-Markov approximation and multi-phonon processes using a polaron transformation. Furthermore, linear optical spectra and exciton relaxation Green functions are calculated and discussed. A P-stacked MoSe$_2$/WSe$_2$ heterolayer is used as an illustrative example. It shows excitons localized in the potential generated through the Moiré-pattern and strain and a delocalized continuum. The exciton-phonon relaxation times vary depending on the strain and range from sub-pico seconds up to nanoseconds.

cond-mat.mes-hall↗

arXiv2023

A hierarchical equations of motion (HEOM) analog for systems with delay: illustrated on inter-cavity photon propagation

Over the last two decades, the hierarchical equations of motion (HEOM) of Tanimura and Kubo have become the equation of motion-based tool for numerically exact calculations of system-bath problems. The HEOM is today generalized to many cases of dissipation and transfer processes through an external bath. In spatially extended photonic systems, the propagation of photons through the bath leads to retardation/delays in the coupling of quantum emitters. Here, the idea behind the HEOM derivation is generalized to the case of photon retardation and applied to the simple example of two dielectric slabs. The derived equations provide a simple reliable framework for describing retardation and may provide an alternative to path integral treatments.

quant-ph↗

arXiv2022

Bichromatic four-wave mixing and quadrature-squeezing from biexcitons in atomically thin semiconductor microcavities

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.

cond-mat.mes-hall↗

arXiv2022

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 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.

quant-ph↗

arXiv2022

Enhanced TEMPO algorithm for quantum path integrals with off-diagonal system-bath coupling: applications to photonic quantum networks

Multitime system correlations functions are relevant in various areas of physics and science, dealing with system-bath interaction including spectroscopy and quantum optics, where many of these schemes include an off-diagonal system bath interaction. Here we extend the enhanced TEMPO algorithm for quantum path integrals using tensor networks [Phys. Rev. Lett. 123, 240602 (2019)] to open quantum systems with off-diagonal coupling beyond a single two level system. We exemplify the approach on a coupled cavity waveguide system with spatially separated quantum two-state emitters, though many other applications in material science are possible, including entangled photon propagation, photosynthesis spectroscopy and on-chip quantum optics with realistic dissipation.

quant-ph↗

arXiv2021

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.

physics.optics↗

arXiv2020

Quantized quasinormal mode description of non-linear cavity QED effects from coupled resonators with a Fano-like resonance

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.

cond-mat.mes-hall↗

arXiv2020

Fluctuation-dissipation theorem and fundamental photon commutation relations in lossy nanostructures using quasinormal modes

We provide theory and formal insight on the Green function quantization method for absorptive and dispersive spatial-inhomogeneous media in the context of dielectric media. We show that a fundamental Green function identity, which appears, e.g., in the fundamental commutation relation of the electromagnetic fields, is also valid in the limit of non-absorbing media. We also demonstrate how the zero-point field fluctuations yields a non-vanishing surface term in configurations without absorption, when using a more formal procedure of the Green function quantization method. We then apply the presented method to a recently developed theory of photon quantization using quasinormal modes [Franke et al., Phys. Rev. Lett. 122, 213901 (2019)] for finite nanostructures embedded in a lossless background medium. We discuss the strict dielectric limit of the commutation relations of the quasinormal mode operators and present different methods to obtain them, connected to the radiative loss for non-absorptive but open resonators. We show exemplary calculations of a fully three-dimensional photonic crystal beam cavity, including the lossless limit, which supports a single quasinormal mode and discuss the limits of the commutation relation for vanishing damping (no material loss and no radiative loss).

cond-mat.mes-hall↗

arXiv2020

Image dipoles approach to the local field enhancement in nanostructured Ag-Au hybrid devices

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.

physics.optics↗

arXiv2020

Tensor network strategies for calculating biexcitons and trions in monolayer 2D materials beyond the ground state

Recently in [Phys. Rev. B 99, 241301(R) (2019)] tensor networks build upon logical circuits were briefly introduced to retrieve exciton and biexciton states. Compared to a conventional approach the tensor network methods scales logarithmic instead of linear in the grid points of the Brioullin zone and linear instead of exponential in the number of electrons and holes. This enables calculations with higher precision on the full Brioullin zone than previously possible. In this paper extensive details for an efficient implementation and the corresponding mathematical background are presented. In particular this includes applications and results for excitons, trions and biexcitons (for monolayer MoS$_2$ as example), going beyond the initial brief introduction. Furthermore strategies for calculating selective excited bound states and tests of common approximations are discussed making use of the high accuracy full Brioullin zone treatment of the tensor network method.

cond-mat.mes-hall↗

arXiv2019

Efficient near-field to far-field transformations for quasinormal modes of optical cavities and plasmonic resonators

We describe an efficient near-field to far-field transformation for optical quasinormal modes, which are the dissipative modes of open cavities and plasmonic resonators with complex eigenfrequencies. As an application of the theory, we show how one can compute the reservoir modes (or regularized quasinormal modes) outside the resonator, which are essential to use in both classical and quantum optics. We subsequently demonstrate how to efficiently compute the quantum optical parameters necessary in the theory of quantized quasinormal modes [Franke et al., Phys. Rev. Lett. 122, 213901 (2019)]. To confirm the accuracy of our technique, we directly compare with a Dyson equation approach currently used in the literature (in regimes where this is possible), and demonstrate several order of magnitude improvement for the calculation run times. We also introduce an efficient pole approximation for computing the quantized quasinormal mode parameters, since they require an integration over a range of frequencies. Using this approach, we show how to compute regularized quasinormal modes and quantum optical parameters for a full 3D metal dimer in under one minute on a standard desktop computer. Our technique is exemplified by studying the quasinormal modes of metal dimers and a hybrid structure consisting of a gold dimer on top of a photonic crystal beam. In the latter example, we show how to compute the quantum optical parameters that describe a pronounced Fano resonance, using structural geometries that cannot practically be solved using a Dyson equation approach. All calculations for the spontaneous emission rates are confirmed with full-dipole calculations in Maxwell's equations and are shown to be in excellent agreement.

physics.optics↗