arXiv subjects

Peter Degenfeld-Schonburg

Publications and source records attributed to Peter Degenfeld-Schonburg.

18 recordsLinked to original sources

arXiv2026

Steady-state dynamics of quantum frequency combs in microring resonators

Optical frequency combs are utilized in a wide range of optical applications, including atomic clocks, interferometers, and various sensing technologies. They are often generated via four-wave mixing in chip-integrated microring resonators, a method that requires low optical input power due to the high-quality factor of the resonator, making it highly efficient. While the classical properties of optical frequency combs are well established, this work investigates the quantum-mechanical characteristics of the individual comb modes. We derive closed-form analytical expressions describing the squeezing, second-order correlation and joint spectral intensity between the generated signal and idler modes. This comprehensive theoretical framework enables an intuitive understanding and optimization of the quantum features across the comb, revealing conditions for substantial squeezing and entanglement relevant for quantum information processing. Our findings highlight the profound impact of design and dispersion on these quantum properties and offer a foundational tool for chip-integrated quantum applications, including quantum sensing, computing and communication.

quant-ph↗

arXiv2025

Shape Optimization of Eigenfrequencies in MEMS Gyroscopes

Microelectromechanical systems (MEMS) gyroscopes are widely used in consumer and automotive applications. They have to fulfill a vast number of product requirements which lead to complex mechanical designs of the resonating structure. Arriving at a final design is a cumbersome process that relies heavily on human experience in conjunction with design optimization methods. In this work, we apply node-based shape optimization to the design of a MEMS gyroscope. For that purpose, we parametrize the coordinates of the nodes of the finite element method (FEM) mesh that discretize the shapes of the springs. We then implement the gradients of the mechanical eigenfrequencies and typical MEMS manufacturability constraints, with respect to the design parameters, in a FEM code. Using gradient-based optimization we tune the gyroscope's frequency split and shift spurious modes away from the first three multiples of the gyroscope's drive frequency while manufacturability constraints are fulfilled. The resulting optimized design exhibits novel geometrical shapes which defy any human intuition. Overall, we demonstrate that shape optimization can not only solve optimization problems in MEMS design without required human intervention, but also explores geometry solutions which can otherwise not be addressed. In this way, node-based shape optimization opens up a much larger space of possible design solutions, which is crucial for facing the ever increasing product requirements. Our approach is generic and applicable to many other types of MEMS resonators.

cs.CE↗

arXiv2025

Shape Optimization of Geometrically Nonlinear Modal Coupling Coefficients: An Application to MEMS Gyroscopes

Micro- and nanoelectromechanical system (MEMS and NEMS) resonators can exhibit rich nonlinear dynamics as they are often operated at large amplitudes with high quality factors and possess a high mode density with a variety of nonlinear modal couplings. Their impact is strongly influenced by internal resonance conditions and by the strength of the modal coupling coefficients. On one hand, strong nonlinear couplings are of academic interest and promise novel device concepts. On the other hand, however, they have the potential to disturb the linear system behavior on which industrial devices such as gyroscopes and micro mirrors are based on. In either case, being able to optimize the coupling coefficients by design is certainly beneficial. A main source of nonlinear modal couplings are geometric nonlinearities. In this work, we apply node-based shape optimization to tune the geometrically nonlinear 3-wave coupling coefficients of a MEMS gyroscope. We demonstrate that individual coupling coefficients can be tuned over several orders of magnitude by shape optimization, while satisfying typical constraints on manufacturability and operability of the devices. The optimized designs contain unintuitive geometrical features far away from any solution an experienced human MEMS or NEMS designer could have thought of. Thus, this work demonstrates the power of shape optimization for tailoring the complex nonlinear dynamic properties of MEMS and NEMS resonators.

cs.CE↗

arXiv2025

Chip-integrated single-mode coherent-squeezed light source using four-wave mixing in microresonators

Squeezed light constitutes a key resource for quantum optical technologies including quantum sensing, computing, communication and metrology. For many applications the generation of squeezed light typically requires at least two nonlinear optical stages involving careful phase and frequency matching to achieve the required mixing of squeezed and coherent light. In our work, we introduce an on-chip system that simplifies the generation of coherent-squeezed light, utilizing only a single squeezing stage. We achieve this by pumping a silicon nitride ($\mathrm{Si_3N_4}$) microring resonator to produce single-mode squeezed light through four-wave mixing at the same frequency as the pump mode, leveraging the inherent $χ^{(3)}$-nonlinearity of the $\mathrm{Si_3N_4}$ resonator. Our on-chip system demonstrates a squeezing of -4.7 dB with a clear perspective towards -10 dB squeezing. We also provide a theoretical model that describes the straightforward yet robust generation of single-mode squeezing at the injection locking point of the ring resonator. In fact, we show that a design with a normal dispersion can be used for robust generation of bright squeezed light without the need for careful suppression of unwanted nonlinear processes. Overall, our findings highlight an approach which drastically simplifies the generation of coherent-squeezed light in photonic integrated circuits.

quant-ph↗

arXiv2025

Nonlinear optical bistability in microring resonators for enhanced phase sensing

Photonic microring resonators are used in a variety of chip-integrated sensing applications where they allow one to measure transmission intensity changes upon external signals with a sensitivity that scales linearly with the Q factor. In this work, we suggest exploiting the nonlinear self-phase-modulation effect to increase the overall sensitivity by an additional gain factor appearing when the operational point of the nonlinear resonator is chosen just at the crossover from the monostable to the bistable regime. We present the theoretical idea together with a first proof of concept experiment displaying a gain factor of 22 on a chip-integrated silicon-nitride resonator.

physics.optics↗

arXiv2024

Optical interferometer using two-mode squeezed light for enhanced chip-integrated quantum metrology

This work discusses the possibility of using two-mode squeezed light to improve the performance of existing sensor technology with the focus on its miniaturization under realistic losses. Therefore, we analyze a system consisting of a part for the two-mode squeezed light generation, a sensor region and a detection stage. Based on a general four-wave mixing (FWM) Hamiltonian caused by the third order susceptibility, we formulate linearized equations that describe the FWM process below the threshold and are used to analyze the squeezing quality between the generated optical signal and idler modes. For a possible realization, the focus is set on the chip-integrated generation using micro-ring resonators. To do so, the impact of the design and the pump light are considered in the derived equations. These equations are used to analyze the usage of two-mode squeezed light in quantum metrology and the application in a Mach-Zehnder interferometer (MZI). Due to the impact of losses in realistic use cases, we show that the main usage is for small and compact devices, which can lead to a quantum improvement up to a factor of ten in comparison of using coherent light only. This enables the use of small squeezing-enhanced sensors with a performance comparable to larger classical sensors.

quant-ph↗

arXiv2024

Thermoelastic Damping in MEMS Gyroscopes at High Frequencies

Microelectromechanical systems (MEMS) gyroscopes are widely used, e.g. in modern automotive and consumer applications, and require signal stability and accuracy in rather harsh environmental conditions. In many use cases, device reliability must be guaranteed under large external loads at high frequencies. The sensitivity of the sensor to such external loads depends strongly on the damping, or rather quality factor, of the high frequency mechanical modes of the structure. In this paper, we investigate the influence of thermoelastic damping on several high frequency modes by comparing finite element simulations with measurements of the quality factor in an application-relevant temperature range. We measure the quality factors over different temperatures in vacuum, to extract the relevant thermoelastic material parameters of the polycrystalline MEMS device. Our simulation results show a good agreement with the measured quantities, therefore proving the applicability of our method for predictive purposes in the MEMS design process. Overall, we are able to uniquely identify the thermoelastic effects and show their significance for the damping of the high frequency modes of an industrial MEMS gyroscope. Our approach is generic and therefore easily applicable to any mechanical structure with many possible applications in nano- and micromechanical systems.

cond-mat.mes-hall↗

arXiv2021

Spontaneous parametric down-conversion induced by optomechanical gradient forces in nanophotonic waveguides

Optomechanical gradient forces arise from evanescent fields of guided waves in parallel photonic waveguides. When designed to be of attractive nature, they increase exponentially as the gap between the waveguides decreases. Moreover, the amplitude of the gradient force can be well controlled due to its linear dependence on the input laser power. Here, we propose to exploit the intrinsic nonlinear nature of the optomechanical gradient force to induce a tunable 3-wave coupling between the fundamental modes of two doubly clamped nanophotonic beams. For one of the beams having half the width of the other beam, the 1:2 internal resonance between the fundamental modes supports degenerate spontaneous parametric down-conversion (SPDC). We theoretically explore the main feature of the dissipative phase diagram of the underlying degenerate parametric oscillator model to show that the critical point of the SPDC occurs at parameters which are well in reach of state-of-the-art experiments.

physics.optics↗

arXiv2020

Parametric Amplification of Broadband Vibrational Energy Harvesters for Energy-Autonomous Sensors Enabled by Field-Induced Striction

We investigate the influence of parametric excitation on MEMS vibration energy harvesters for energy autonomous sensor systems. In Industry 4.0 (or Industrial IoT) applications, interconnected sensors provide a means of data acquisition for automated control of the manufacturing process. Ensuring a continuous energy supply to the sensors is essential for their reliable operation. Manufacturing machines usually display a wide spectrum of vibration frequencies which needs to be covered by an array of harvester substructures in order to maintain the desired output level. We show that mechanical structures designed to implement a Helmholtz-Duffing oscillator have an increased bandwidth by exploiting several orders of parametric resonances. In contrast to concepts implementing parametric amplification in a multi-mode scenario, our concept is based on a single mechanical mode. Therefore, it is more robust against fabrication tolerances as the relevant multi-mode resonance conditions do not need to be matched on the level of single chips. Using exact transient simulations and semi-analytic models to showcase the relation of the Helmholtz-Duffing oscillator to the damped and driven Mathieu equation, we show that parametric resonances highly increase the bandwidth of the output power whenever high Helmholtz nonlinearities are present. To achieve the required nonlinearities, we suggest nonlinear stress-strain curves and we propose to achieve such nonlinearities through field-induced striction by magneto- or electrostriction. Thus, we are able to propose a novel energy harvester concept incorporating strictive materials that exploits the effects of parametric excitation to achieve broadband vibrational energy harvesting.

physics.app-ph↗

arXiv2020

Nonlinear Dynamical System Model for Drive Mode Amplitude Instabilities in MEMS Gyroscopes

The requirements pertaining to the reliability and accuracy of micro-electromechanical gyroscopic sensors are increasing,as systems for vehicle localization emerge as an enabling factor for autonomous driving. Since micro-electromechanical systems (MEMS) became a mature technology, the modelling techniques used for predicting their behaviour expanded from mostly linear approaches to include nonlinear dynamic effects. This leads to an increased understanding of the various nonlinear phenomena that limit the performance of MEMS sensors. In this work, we develop a model of two nonlinearly coupled mechanical modes and employ it to explain measured drive mode instabilities in MEMS gyroscopes. Due to 3:1 internal resonance between the drive mode and a parasitic mode, energy transfer within the conservative system occurs. From measurements of amplitude response curves showing hysteresis effects, we extract all nonlinear system parameters and conclude that the steady-state model needs to be expanded by a transient simulation in order to fully explain the measured system behaviour.

physics.app-ph↗

arXiv2020

Validating the Critical Point of Spontaneous Parametric Down-Conversion for over 600 Scanning MEMS Micro Mirrors on Wafer-Level

Sensors and actuators based on resonant micro-electro-mechanical systems (MEMS), such as scanning micro mirrors, are well-established in automotive and consumer products. As the areas of application broaden, the requirements for the MEMS are increasing. Devices outside of the performance specifications have to be rejected which is costly due to the high processing times of MEMS technologies. In particular, nonlinear system behavior is often found to cause unexpected device failure or performance issues. Thus, accurate simulation or rather system models which account for nonlinear sensor dynamics can not only increase process yield, but more importantly, lead to a comprehensive understanding of the underlying physics and to improved MEMS design. We have studied [1] the possibility of a rather drastic device failure induced by nonlinearities on the example of a resonant scanning MEMS micro mirror. On the level of a few selected chips, we have carefully measured the complex nonlinear system behavior and modeled it by a nonlinear mode-coupling phenomenon known as spontaneous parametric down-conversion (SPDC). The most intriguing feature of SPDC is the sudden change from a rather linear to a nonlinear system behavior at the critical oscillation amplitude. However, the threshold only lies within the range of the mirror's operational amplitude, if certain frequency resonance conditions regarding the mechanical modes are met. Thus, the critical amplitude strongly depends on the frequency spectrum of the MEMS design which in turn is largely influenced by fabrication imperfections. We validate the dependence of the critical amplitude on the resonance condition by measuring it for over 600 micro mirrors on wafer-level. Our work does not only validate the theory of SPDC with measurements on such a large scale, but also demonstrates modeling strategies which are essential for MEMS product design.

physics.app-ph↗

arXiv2019

Spontaneous parametric down-conversion induced by non-degenerate three-wave mixing in a scanning MEMS micro mirror

Scanning micro-mirror actuators are silicon-based oscillatory micro-electro-mechanical systems (MEMS). They enable laser distance measurements for automotive LIDAR applications as well as projection modules for the consumer market. For MEMS applications, the geometric structure is typically designed to serve a number of functional requirements. Most importantly, the mode spectrum contains a single high-Q mode, the drive mode, which per design is expected to yield the only resonantly excited geometric motion during operation. Yet here, we report on the observation of a resonant three-mode excitation via a process known as spontaneous parametric down-conversion. We show that this phenomenon, most extensively studied in the field of nonlinear optics, originates from three-wave coupling induced by geometric nonlinearities. In combination with further Duffing-type nonlinearities, the micro mirror displays a variety of nonlinear dynamical behaviour ranging from stationary state bifurcations to dynamical instabilities observable via amplitude modulations. We are able to explain and emulate all experimental observations using a single fundamental model. In particular, our analysis allows us to understand the conditions for the onset of three-wave down-conversion which if not accounted for in the design of the MEMS structure, can have drastic impact on its functionality even leading to fracture.

cond-mat.mes-hall↗

arXiv2018

Amplitude- and gas pressure-dependent nonlinear damping of high-Q oscillatory MEMS micro mirrors

Silicon-based micro-electromechanical systems (MEMS) can be fabricated using bulk and surface micromachining technology. A micro mirror designed as an oscillatory MEMS constitutes a prominent example. Typically, in order to minimize energy consumption, the micro mirror is designed to have high quality factors. In addition, a phase-locked loop guarantees resonant actuation despite the occurrence of frequency shifts. In these cases, the oscillation amplitude of the micro mirror is expected to scale linearly with the actuation input power. Here, however, we report on an experimental observation which clearly shows an amplitude depletion that is not in accordance with any linear behaviour. As a consequence, the actuation forces needed to reach the desired oscillation amplitude are by multiples higher than expected. We are able to explain the experimental observations accurately by introducing a single degree-of-freedom model including an amplitude-dependent nonlinear damping term. Remarkably, we find that the nonlinear damping shows a clear gas pressure dependency. We investigate the concepts and compare our findings on two different micro mirror design layouts.

cond-mat.mes-hall↗

arXiv2016

Classical and quantum-linearized descriptions of degenerate optomechanical parametric oscillators

Recent advances in the development of modern quantum technologies have opened the possibility of studying the interplay between spontaneous parametric down-conversion and optomechanics, two of the most fundamental nonlinear optical processes. Apart from practical reasons, such scenario is very interesting from a fundamental point of view, because it allows exploring the optomechanical interaction in the presence of a strongly quantum-correlated field, the spontaneously down-converted mode. In this work we analyze such problem from two approximate but valuable perspectives: the classical limit and the limit of small quantum fluctuations. We show that, in the presence of optomechanical coupling, the well-known classical phase diagram of the optical problem gets modified by the appearance of new dynamical instabilities. As for the quantum-mechanical description, we prove the ability of the squeezed down-converted field to cool down the mechanical motion not only to thermal but also to squeezed thermal mechanical states, and in a way that can be much less sensitive to parameters (e.g., detuning of the driving laser) than standard sideband cooling.

quant-ph↗

arXiv2016

Degenerate optomechanical parametric oscillators: cooling in the vicinity of a critical point

Degenerate optomechanical parametric oscillators are optical resonators in which a mechanical degree of freedom is coupled to a cavity mode that is nonlinearly amplified via parametric down-conversion of an external pumping laser. Below a critical pumping power the down-converted field is purely quantum-mechanical, making the theoretical description of such systems very challenging. Here we introduce a theoretical approach that is capable of describing this regime, even at the critical point itself. We find that the down-converted field can induce significant mechanical cooling and identify the process responsible of this as a cooling-by-heating mechanism. Moreover, we show that, contrary to naive expectations and semi-classical predictions, cooling is not optimal at the critical point, where the photon number is largest. Our approach opens the possibility for analyzing further hybrid dissipative quantum systems in the vicinity of critical points.

quant-ph↗

arXiv2015

Self-Consistent Projection Operator Theory in Nonlinear Quantum Optical Systems: A case study on Degenerate Optical Parametric Oscillators

Nonlinear quantum optical systems are of paramount relevance for modern quantum technologies, as well as for the study of dissipative phase transitions. Their nonlinear nature makes their theoretical study very challenging and hence they have always served as great motivation to develop new techniques for the analysis of open quantum systems. In this article we apply the recently developed self-consistent projection operator theory to the degenerate optical parametric oscillator to exemplify its general applicability to quantum optical systems. We show that this theory provides an efficient method to calculate the full quantum state of each mode with high degree of accuracy, even at the critical point. It is equally successful in describing both the stationary limit and the dynamics, including regions of the parameter space where the numerical integration of the full problem is significantly less efficient. We further develop a Gaussian approach consistent with our theory, which yields sensibly better results than the previous Gaussian methods developed for this system, most notably standard linearization techniques.

quant-ph↗

arXiv2014

Self-Consistent Projection Operator Theory for Quantum Many-Body Systems

We derive an exact equation of motion for the reduced density matrices of individual subsystems of quantum many-body systems of any lattice dimension and arbitrary system size. Our projection operator based theory yields a highly efficient analytical and numerical approach. Besides its practical use it provides a novel interpretation and systematic extension of mean-field approaches and an adaption of open quantum systems theory to settings where a dynamically evolving environment has to be taken into account. We show its high accuracy for two significant classes of complex quantum many-body dynamics, unitary evolutions of non-equilibrium states in closed and stationary states in driven-dissipative systems.

quant-ph↗

arXiv2011

Signatures of single site addressability in resonance fluorescence spectra

Pioneering methods in recent optical lattice experiments allow to focus laser beams down to a spot size that is comparable to the lattice constant. Inspired by this achievement, we examine the resonance fluorescence spectra of two-level atoms positioned in adjacent lattice sites and compare the case where the laser hits only one atom (single site addressing) with cases where several atoms are illuminated. In contrast to the case where the laser hits several atoms, the spectrum for single site addressing is no longer symmetric around the laser frequency. The shape of the spectrum of fluorescent light can therefore serve as a test for single site addressing. The effects we find can be attributed to a dipole-dipole interaction between the atoms due to mutual exchange of photons.

quant-ph↗