arXiv subjects

T. Kuhn

Publications and source records attributed to T. Kuhn.

At least 19 recordsLinked to original sources

arXiv2021

Comparison of the semiclassical and quantum optical field dynamics in a pulse-excited optical cavity with a finite number of quantum emitters

The spectral and temporal response of a set of $N$ quantum emitters embedded in a photonic cavity is studied. Quantum mechanically, such systems can be described by the Tavis-Cummings (TC) model of $N$ two-level systems coupled to a single light mode. Here we compare the full quantum solution of the TC model for different numbers of quantum emitters with its semiclassical limit after a pulsed excitation of the cavity mode. Considering different pulse amplitudes, we find that the spectra obtained from the TC model approach the semiclassical one for an increasing number of emitters $N$. Furthermore they match very well for small pulse amplitudes. While we observe a very good agreement in the temporal dynamics for photon numbers much smaller than $N$, considerable deviations occur in the regime of photon numbers similar to or larger than $N$, which are linked to collapse and revival phenomena. Wigner functions of the light mode are calculated for different scenarios to analyze the quantum state of the light field. We find strong deviations from a coherent state even if the dynamics of the expectation values are still well described by the semiclassical limit. For higher pulse amplitudes Wigner functions similar to those of Schrödinger cat states between two or more quasi-coherent contributions build up.

cond-mat.mes-hall↗

arXiv2020

Phonon-mediated exciton capture in Mo-based transition metal dichalcogenides

Localized excitons play a vital role in the optical response of monolayers of transition metal dichalcogenides and can be exploited as single photon sources for quantum information technology. While the optical properties of such localized excitons are vastly studied, the ultrafast capture process of delocalized excitons into localized potentials is largely unexplored. We perform quantum kinetic calculations of exciton capture via acoustic and optical phonons showing that efficient capture takes place on an ultrafast time scale. The polaron formation in the low-temperature limit leads to higher-energy excitons which can then be efficiently trapped. We demonstrate that the interplay of acoustic and optical phonons leads to an efficient broadening of energy-selection rules. Our studies provide a deep understanding of the carrier trapping from two-dimensional materials into zero-dimensional potentials.

cond-mat.mes-hall↗

arXiv2020

$hp$-Multilevel Monte Carlo Methods for Uncertainty Quantification of Compressible Flows

We propose a novel $hp$-multilevel Monte Carlo method for the quantification of uncertainties in the compressible Navier-Stokes equations, using the Discontinuous Galerkin method as deterministic solver. The multilevel approach exploits hierarchies of uniformly refined meshes while simultaneously increasing the polynomial degree of the ansatz space. It allows for a very large range of resolutions in the physical space and thus an efficient decrease of the statistical error. We prove that the overall complexity of the $hp$-multilevel Monte Carlo method to compute the mean field with prescribed accuracy is, in best-case, of quadratic order with respect to the accuracy. We also propose a novel and simple approach to estimate a lower confidence bound for the optimal number of samples per level, which helps to prevent overestimating these quantities. The method is in particular designed for application on queue-based computing systems, where it is desirable to compute a large number of samples during one iteration, without overestimating the optimal number of samples. Our theoretical results are verified by numerical experiments for the two-dimensional compressible Navier-Stokes equations. In particular we consider a cavity flow problem from computational acoustics, demonstrating that the method is suitable to handle complex engineering problems.

math.NA↗

arXiv2020

Dark Exciton Preparation in a Quantum Dot by a Longitudinal Light Field Tuned to Higher Exciton States

Several important proposals to use semiconductor quantum dots in quantum information technology rely on the control of the dark exciton ground states, such as dark exciton based qubits with a $μ$s life time. In this paper, we present an efficient way to occupy the dark exciton ground state by a single short laser pulse. The scheme is based on an optical excitation with a longitudinal field component featured by, e.g., radially polarized beams or certain Laguerre-Gauss or Bessel beams. Utilizing this component, we show within a configuration interaction approach that high-energy exciton states composed of light-hole excitons and higher dark heavy-hole excitons can be addressed. When the higher exciton relaxes, a dark exciton in its ground state is created.

cond-mat.mes-hall↗

arXiv2020

Semiclassical modeling of coupled quantum dot-cavity systems: From polariton-like dynamics to Rabi oscillations

Semiconductor quantum dots in photonic cavities are strongly coupled light-matter systems with prospective applications in optoelectronic devices and quantum information processing. Here we present a theoretical study of the coupled exciton--light field dynamics of a planar quantum dot ensemble, treated as two-level systems, embedded in a photonic cavity modeled by Maxwell's equations. When excited by coupling an external short laser pulse into the cavity, we find an exciton-polariton-like behavior for weak excitation and Rabi oscillations for strong excitation with a sharp transition between these regimes. In the transition region we find highly non-linear dynamics involving high harmonics of the fundamental oscillation. We perform a numerical study based on the Finite-Difference-Time-Domain method for the solution of Maxwell's equations coupled to Bloch equations for the quantum dots and also derive an analytical model to describe the coupled cavity-quantum dot system, which allows us to describe the light field dynamics in terms of a Newton-like dynamics in an effective anharmonic potential. From the shape of this potential combined with the initial conditions the transition can be well understood. The model is then extended to a broadened ensemble of quantum dots. For weak excitation the polariton spectrum broadens and the lines slightly shift, however, the sharp transition to the Rabi oscillation regime is still present. Furthermore, we find a second, lower threshold with additional lines in the spectra which can be traced back to Rabi oscillations driven by the polariton modes. Our approach provides new insights in the dynamics of both quantum dot and light field in the photonic structure.

cond-mat.mes-hall↗

arXiv2020

Selection rules for the excitation of quantum dots by spatially structured light beams -- Application to the reconstruction of higher excited exciton wave functions

Spatially structured light fields applied to semiconductor quantum dots yield fundamentally different absorption spectra than homogeneous beams. In this paper, we theoretically discuss the resulting spectra for different light beams using a cylindrical multipole expansion. For the description of the quantum dots we employ a model based on the effective mass approximation including Coulomb and valence band mixing. The combination of a single spatially structured light beam and state mixing allows all exciton states in the quantum dot to become optically addressable. Furthermore, we demonstrate that the beams can be tailored such that single states are selectively excited, without the need of spectral separation. Using this selectivity, we propose a method to measure the exciton wave function of the quantum dot eigenstate. The measurement goes beyond electron density measurements by revealing the spatial phase information of the exciton wave function. Thereby polarization sensitive measurements are generalized by including the infinitely large spatial degree of freedom.

cond-mat.mes-hall↗

arXiv2020

Theory of absorption lineshape in monolayers of transition metal dichalcogenides

The linear absorption spectra in monolayers of transition metal dichalcogenides show pronounced signatures of the exceptionally strong exciton-phonon interaction in these materials. To account for both exciton and phonon physics in such optical signals, we compare different theoretical methods to calculate the absorption spectra using the example of $\mathrm{MoSe_2}$. In this paper, we derive the equations of motion for the polarization either using a correlation expansion up to 4th Born approximation or a time convolutionless master equation. We show that the Born approximation might become problematic when not treated in high enough order, especially at high temperatures. In contrast, the time convolutionless formulation gives surprisingly good results despite its simplicity when compared to higher-order corrrelation expansion and therefore provides a powerful tool to calculate the lineshape of linear absorption spectra in the very popular monolayer materials.

cond-mat.mes-hall↗

arXiv2019

Spatiotemporal dynamics of Coulomb-correlated carriers in semiconductors

When the excitation of carriers in real space is focused down to the nanometer scale, the carrier system can no longer be viewed as homogeneous and ultrafast transport of the excited carrier wave packets occurs. In state-of-the-art semiconductor structures like low-dimensional heterostructures or monolayers of transition metal dichalcogenides, the Coulomb interaction between excited carriers becomes stronger due to confinement or reduced screening. This demands a fundamental understanding of strongly interacting electrons and holes and the influence of Coulomb correlations. To study the corresponding particle dynamics in a controlled way we consider a system of up to two electron-hole pairs exactly within a wave function approach. We show that the excited wave packets contain a non-trivial mixture of free particle and excitonic states. We further scrutinize the influence of Coulomb interaction on the wave packet dynamics revealing its different role for below and above band-gap excitation.

cond-mat.mes-hall↗

arXiv2019

The FAIR Funder pilot programme to make it easy for funders to require and for grantees to produce FAIR Data

There is a growing acknowledgement in the scientific community of the importance of making experimental data machine findable, accessible, interoperable, and reusable (FAIR). Recognizing that high quality metadata are essential to make datasets FAIR, members of the GO FAIR Initiative and the Research Data Alliance (RDA) have initiated a series of workshops to encourage the creation of Metadata for Machines (M4M), enabling any self-identified stakeholder to define and promote the reuse of standardized, comprehensive machine-actionable metadata. The funders of scientific research recognize that they have an important role to play in ensuring that experimental results are FAIR, and that high quality metadata and careful planning for FAIR data stewardship are central to these goals. We describe the outcome of a recent M4M workshop that has led to a pilot programme involving two national science funders, the Health Research Board of Ireland (HRB) and the Netherlands Organisation for Health Research and Development (ZonMW). These funding organizations will explore new technologies to define at the time that a request for proposals is issued the minimal set of machine-actionable metadata that they would like investigators to use to annotate their datasets, to enable investigators to create such metadata to help make their data FAIR, and to develop data-stewardship plans that ensure that experimental data will be managed appropriately abiding by the FAIR principles. The FAIR Funders design envisions a data-management workflow having seven essential stages, where solution providers are openly invited to participate. The initial pilot programme will launch using existing computer-based tools of those who attended the M4M Workshop.

cs.DL↗

arXiv2018

Bessel beams revisited: a generalized scheme to derive optical vortices

The electromagnetic field of optical vortices is in most cases derived from vector and scalar potentials using either a procedure based on the Lorenz or the Coulomb gauge. The former procedure has been typically used to derive paraxial solutions with Laguerre-Gauss radial profiles, while the latter procedure has been used to derive full solutions of the wave equation with Bessel radial profiles. We investigate the differences in the derivation procedures applying each one to both Bessel and Laguerre-Gauss profiles. We show that the electromagnetic fields thus derived differ in the relative strength of electric and magnetic contributions. The new solution that arises from the Lorenz procedure in the case of Bessel beams restores a field symmetry that previous work failed to resolve. Our procedure is further generalized and we find a spectrum of fields beyond the Lorenz and Coulomb gauge types. Finally, we describe a possible experiment to test our findings.

physics.optics↗

arXiv2018

Persistent oscillations of the order parameter and interaction quench phase diagram for a confined Bardeen-Cooper-Schrieffer Fermi gas

We present a numerical study of the interaction quench dynamics in a superfluid ultracold Fermi gas confined in a three-dimensional cigar-shaped harmonic trap. In the present paper we investigate the amplitude mode of the superfluid order parameter after interaction quenches which start deep in the BCS phase and end in the BCS-BEC crossover regime. To this end, we exploit the Bogoliubov-de Gennes formalism which takes the confinement potential explicitly into account and provides a microscopic fully coherent description of the system. We find an anharmonic nonlinear oscillation of the modulus of the superfluid order parameter, i.e., of the Higgs mode. This oscillation persists for large times with only a small amplitude modulation being visible. We connect the frequency and the mean value of this oscillation with the breaking of Cooper pairs in the superfluid phase. Additionally, we demonstrate that the occurrence of this persistent oscillation is connected to the onset of chaotic dynamics in our model. Finally, we calculate an interaction quench phase diagram of the Higgs mode for quenches on the BCS side of the BCS-BEC crossover and discuss its properties as a function of the aspect ratio of the cigar-shaped trap.

cond-mat.quant-gas↗

arXiv2018

Dynamical vanishing of the order parameter in a confined Bardeen-Cooper-Schrieffer Fermi gas after an interaction quench

We present a numerical study of the Higgs mode in an ultracold confined Fermi gas after an interaction quench and find a dynamical vanishing of the superfluid order parameter. Our calculations are done within a microscopic density-matrix approach in the Bogoliubov-de Gennes framework which takes the three-dimensional cigar-shaped confinement explicitly into account. In this framework, we study the amplitude mode of the order parameter after interaction quenches starting on the BCS side of the BEC-BCS crossover close to the transition and ending in the BCS regime. We demonstrate the emergence of a dynamically vanishing superfluid order parameter in the spatiotemporal dynamics in a three-dimensional trap. Further, we show that the signal averaged over the whole trap mirrors the spatiotemporal behavior and allows us to systematically study the effects of the system size and aspect ratio on the observed dynamics. Our analysis enables us to connect the confinement-induced modifications of the dynamics to the pairing properties of the system. Finally, we demonstrate that the signature of the Higgs mode is contained in the dynamical signal of the condensate fraction, which, therefore, might provide a new experimental access to the nonadiabatic regime of the Higgs mode.

cond-mat.quant-gas↗

arXiv2017

Phonon impact on optical control schemes of quantum dots: The role of quantum dot geometry and symmetry

Phonons strongly influence the optical control of semiconductor quantum dots. When modeling the electron-phonon interaction in several theoretical approaches the quantum dot geometry is approximated by a spherical structure, though typical self-assembled quantum dots are strongly lens-shaped. By explicitly comparing simulations of a spherical and a lens-shaped dot using a well-established correlation expansion approach we show that indeed lens-shaped dots can be exactly mapped to a spherical geometry when studying the phonon influence on the electronic system. We also give a recipe to reproduce spectral densities from more involved dots by rather simple spherical models. On the other hand, breaking the spherical symmetry has a pronounced impact on the spatio-temporal properties of the phonon dynamics. As an example we show that for a lens-shaped quantum dot the phonon emission is strongly concentrated along the direction of the smallest axis of the dot which is important for the use of phonons for the communication between different dots.

cond-mat.mes-hall↗

arXiv2017

Quench dynamics of a confined ultracold Fermi gas: Direct visibility of the Goldstone mode in the single-particle excitations

We present a numerical study of a confined ultracold Fermi gas showing that the Goldstone mode of the BCS gap is directly visible in the dynamics of the single-particle excitations. To this end, we investigate the low-energy dynamic response of a confined Fermi gas to a rapid change of the scattering length (i.e., an interaction quench). Based on a fully microscopic time-dependent density-matrix approach within the Bogoliubov-de Gennes formalism that includes a 3D harmonic confinement we simulate and identify the emergence of the Goldstone mode in a cigar-shaped $^6$Li gas. We show that the quench leads to a low-frequency in-phase oscillation of the single-particle occupations. Complete inversion is achieved for occupations corresponding to the lowest-lying single-particle states.

cond-mat.quant-gas↗

arXiv2017

Magnetic-optical transitions induced by twisted light in quantum dots

It has been theoretically predicted that light carrying orbital angular momentum, or twisted light, can be tuned to have a strong magnetic-field component at optical frequencies. We here consider the interaction of these peculiar fields with a semiconductor quantum dot and show that the magnetic interaction results in new types of optical transitions. In particular, a single pulse of such twisted light can drive light-hole-to-conduction band transitions that are cumbersome to produce using conventional Gaussian beams or even twisted light with dominant electric fields.

cond-mat.mes-hall↗

arXiv2017

Systematic study of the influence of coherent phonon wave packets on the lasing properties of a quantum dot ensemble

Coherent phonons can greatly vary light-matter interaction in semiconductor nanostructures placed inside an optical resonator on an ultrafast time scale. For an ensemble of quantum dots as active laser medium phonons are able to induce a large enhancement or attenuation of the emission intensity, as has been recently demonstrated. The physics of this coupled phonon-exciton-photon system consists of various effects, which in the experiment typically cannot be clearly separated, in particular because a rather complex strain pulse impinges on the quantum dot ensemble. Here we present a comprehensive theoretical study how the laser emission is affected by phonon pulses of various shapes as well as by ensembles with different spectral distributions of the quantum dots. This gives insight into the fundamental interaction dynamics of the coupled phonon-exciton-photon system, while it allows us to clearly discriminate between two prominent effects: the adiabatic shifting of the ensemble and the shaking effect. This paves the way to a tailored laser emission controlled by phonons.

cond-mat.mes-hall↗

arXiv2016

Impact of phonons on dephasing of individual excitons in deterministic quantum dot microlenses

Optimized light-matter coupling in semiconductor nanostructures is a key to understand their optical properties and can be enabled by advanced fabrication techniques. Using in-situ electron beam lithography combined with a low-temperature cathodoluminescence imaging, we deterministically fabricate microlenses above selected InAs quantum dots (QDs) achieving their efficient coupling to the external light field. This enables to perform four-wave mixing micro-spectroscopy of single QD excitons, revealing the exciton population and coherence dynamics. We infer the temperature dependence of the dephasing in order to address the impact of phonons on the decoherence of confined excitons. The loss of the coherence over the first picoseconds is associated with the emission of a phonon wave packet, also governing the phonon background in photoluminescence (PL) spectra. Using theory based on the independent boson model, we consistently explain the initial coherence decay, the zero-phonon line fraction, and the lineshape of the phonon-assisted PL using realistic quantum dot geometries.

cond-mat.mes-hall↗

arXiv2016

Formulation of the twisted-light--matter interaction at the phase singularity: beams with strong magnetic fields

The formulation of the interaction of matter with singular light fields needs special care. In a recent article [Phys.~Rev.~A {\bf 91}, 033808 (2015)] we have shown that the Hamiltonian describing the interaction of a twisted light beam having parallel orbital and spin angular momenta with a small object located close to the phase singularity can be expressed only in terms of the electric field of the beam. Here, we complement our studies by providing an interaction Hamiltonian for beams having antiparallel orbital and spin angular momenta. Such beams may exhibit unusually strong magnetic effects. We further extend our formulation to radially and azimuthally polarized beams. The advantages of our formulation are that for all beams the Hamiltonian is written solely in terms of the electric and magnetic fields of the beam and as such it is manifestly gauge-invariant. Furthermore it is intuitive by resembling the well-known expressions in the dipole-electric and dipole-magnetic moment approximations.

physics.optics↗