arXiv subjects

Oliver Sander

Publications and source records attributed to Oliver Sander.

At least 37 records · Page 2Linked to original sources

arXiv2022

A homogenized bending theory for prestrained plates

The presence of prestrain can have a tremendous effect on the mechanical behavior of slender structures. Prestrained elastic plates show spontaneous bending in equilibrium -- a property that makes such objects relevant for the fabrication of active and functional materials. In this paper we study microheterogeneous, prestrained plates that feature nonflat equilibrium shapes. Our goal is to understand the relation between the properties of the prestrained microstructure and the global shape of the plate in mechanical equilibrium. To this end, we consider a three-dimensional, nonlinear elasticity model that describes a periodic material that occupies a domain with small thickness. We consider a spatially periodic prestrain described in the form of a multiplicative decomposition of the deformation gradient. By simultaneous homogenization and dimension reduction, we rigorously derive an effective plate model as a Γ-limit for vanishing thickness and period. That limit has the form of a nonlinear bending energy with an emergent spontaneous curvature term. The homogenized properties of the bending model (bending stiffness and spontaneous curvature) are characterized by corrector problems. For a model composite -- a prestrained laminate composed of isotropic materials -- we investigate the dependence of the homogenized properties on the parameters of the model composite. Secondly, we investigate the relation between the parameters of the model composite and the set of shapes with minimal bending energy. Our study reveals a rather complex dependence of these shapes on the composite parameters.

math.AP↗

arXiv2022

Slowing down light in a qubit metamaterial

The rapid progress in quantum information processing leads to a rising demand for devices to control the propagation of electromagnetic wave pulses and to ultimately realize a universal and efficient quantum memory. While in recent years significant progress has been made to realize slow light and quantum memories with atoms at optical frequencies, superconducting circuits in the microwave domain still lack such devices. Here, we demonstrate slowing down electromagnetic waves in a superconducting metamaterial composed of eight qubits coupled to a common waveguide, forming a waveguide quantum electrodynamics system. We analyze two complementary approaches, one relying on dressed states of the Autler-Townes splitting, and the other based on a tailored dispersion profile using the qubits tunability. Our time-resolved experiments show reduced group velocities of down to a factor of about 1500 smaller than in vacuum. Depending on the method used, the speed of light can be controlled with an additional microwave tone or an effective qubit detuning. Our findings demonstrate high flexibility of superconducting circuits to realize custom band structures and open the door to microwave dispersion engineering in the quantum regime.

quant-ph↗

arXiv2022

Numerical approaches for investigating quasiconvexity in the context of Morrey's conjecture

Deciding whether a given function is quasiconvex is generally a difficult task. Here, we discuss a number of numerical approaches that can be used in the search for a counterexample to the quasiconvexity of a given function $W$. We will demonstrate these methods using the planar isotropic rank-one convex function \[ W_{\rm magic}^+(F)=\frac{λ_{\rm max}}{λ_{\rm min}}-\log\frac{λ_{\rm max}}{λ_{\rm min}}+\log\det F=\frac{λ_{\rm max}}{λ_{\rm min}}+2\logλ_{\rm min}\,, \] where $λ_{\rm max}\geqλ_{\rm min}$ are the singular values of $F$, as our main example. In a previous contribution, we have shown that quasiconvexity of this function would imply quasiconvexity for all rank-one convex isotropic planar energies $W:\operatorname{GL}^+(2)\rightarrow\mathbb{R}$ with an additive volumetric-isochoric split of the form \[ W(F)=W_{\rm iso}(F)+W_{\rm vol}(\det F)=\widetilde W_{\rm iso}\bigg(\frac{F}{\sqrt{\det F}}\bigg)+W_{\rm vol}(\det F) \] with a concave volumetric part. This example is therefore of particular interest with regard to Morrey's open question whether or not rank-one convexity implies quasiconvexity in the planar case.

math.AP↗

arXiv2021

Conforming Finite Elements for $H(\text{sym}\,\text{Curl})$ and $H(\text{dev}\,\text{sym}\,\text{Curl})$

We construct conforming finite elements for the spaces $H(\text{sym}\,\text{Curl})$ and $H(\text{dev}\,\text{sym}\,\text{Curl})$. Those are spaces of matrix-valued functions with symmetric or deviatoric-symmetric $\text{Curl}$ in a Lebesgue space, and they appear in various models of nonstandard solid mechanics. The finite elements are not $H(\text{Curl})$-conforming. We show the construction, prove conformity and unisolvence, and point out optimal approximation error bounds.

math.NA↗

arXiv2021

OpenIPMC: a free and open source Intelligent Platform Management Controller

OpenIPMC is a free and open source firmware designed to operate as an Intelligent Platform Management Controller (IPMC). An IPMC is a fundamental component of electronic boards conformant to the Advanced Telecommunications Computing Architecture (ATCA) standard, currently being adopted by a number of high energy physics experiments, and is responsible for monitoring the health parameters of the board, managing its power states, and providing board control, debug and recovery functions to remote clients. OpenIPMC is based on the FreeRTOS real-time operating system and is designed to be architecture-independent, allowing it to be built for a variety of different Microcontrollers. Having a fully free and open source code is an innovative aspect for this kind of firmware, allowing full customization by the user. In this work we present the features and structure of OpenIPMC and its example implementations on Xilinx Zynq UltraScale+ (ZynqUS+), Espressif ESP32, and ST Microelectronics STM32 architectures.

physics.ins-det↗

arXiv2021

The Parallel Full Approximation Scheme in Space and Time for a Parabolic Finite Element Problem

The parallel full approximation scheme in space and time (PFASST) is a parallel-in-time integrator that allows to integrate multiple time-steps simultaneously. It has been shown to extend scaling limits of spatial parallelization strategies when coupled with finite differences, spectral discretizations, or particle methods. In this paper we show how to use PFASST together with a finite element discretization in space. While seemingly straightforward, the appearance of the mass matrix and the need to restrict iterates as well as residuals in space makes this task slightly more intricate. We derive the PFASST algorithm with mass matrices and appropriate prolongation and restriction operators and show numerically that PFASST can, after some initial iterations, gain two orders of accuracy per iteration.

math.NA↗

arXiv2021

Flux ramp modulation based MHz frequency-division dc-SQUID multiplexer

We present a MHz frequency-division dc-SQUID multiplexer that is based on flux ramp modulation and a series array of $N$ identical current-sensing dc-SQUIDs with tightly coupled input coil. By running a periodic, sawtooth-shaped current signal through an additional modulation coil being tightly, but non-uniformly coupled to the individual SQUIDs, the voltage drop across the array changes according to the superposition of the flux-to-voltage characteristics of the individual SQUIDs within each cycle of the modulation signal. In this mode of operation, an input signal injected in the input coil of one of the SQUIDs and being quasi-static within a time frame adds a constant flux offset and leads to a phase shift of the associated SQUID characteristics. The latter is inherently proportional to the input signal and can be inferred by channelizing and down-converting the sampled array output voltage. Using a prototype multiplexer as well as a self-developed high-speed readout electronics for real-time phase determination, we demonstrate the simultaneous readout of four signal sources with MHz bandwidth per channel.

physics.ins-det↗

arXiv2020

Quantum non-demolition dispersive readout of a superconducting artificial atom using large photon numbers

Reading out the state of superconducting artificial atoms typically relies on dispersive coupling to a readout resonator. For a given system noise temperature, increasing the circulating photon number $\bar{n}$ in the resonator enables a shorter measurement time and is therefore expected to reduce readout errors caused by spontaneous atom transitions. However, increasing $\bar{n}$ is generally observed to also increase these transition rates. Here we present a fluxonium artificial atom in which we measure an overall flat dependence of the transition rates between its first two states as a function of $\bar{n}$, up to $\bar{n}\approx200$. Despite the fact that we observe the expected decrease of the dispersive shift with increasing readout power, the signal-to-noise ratio continuously improves with increasing $\bar{n}$. Even without the use of a parametric amplifier, at $\bar{n}=74$, we measure fidelities of 99% and 93% for feedback-assisted ground and excited state preparation, respectively.

quant-ph↗

arXiv2020

Versatile Configuration and Control Framework for Real Time Data Acquisition Systems

Modern physics experiments often utilize FPGA-based systems for real-time data acquisition. Integrated analog electronics demand for complex calibration routines. Furthermore, versatile configuration and control of the whole system is a key requirement. Beside low-level register interface to the FPGA, also access to I$^2$C and SPI buses is often needed to configure the complete system. Calibration through an FPGA is inflexible and yields a complex hardware implementation. On the contrary, calibration through a remote system is possible but considerably slower due to repetitive network accesses. By using SoC-FPGA solutions with a microprocessor, more sophisticated configuration and calibration solutions, as well as standard remote access protocols, can be efficiently integrated in software. Based on Xilinx Zynq US+ SoC-FPGAs, we implemented a versatile control framework. This software framework offers a convenient access to the hardware and a flexible abstraction via remote-procedure calls (RPCs). Based on the open source RPC library gRPC, functionality with low-latent control flow, complex algorithms, data conversions and processing, as well as configuration via external buses can be provided to a client via Ethernet. Furthermore, client interfaces for various programming languages can be generated automatically which eases collaboration among different working groups and integration into existing software. This contribution presents the framework as well as benchmarks regarding latency and data throughput.

eess.SY↗

arXiv2020

The DUNE Framework: Basic Concepts and Recent Developments

This paper presents the basic concepts and the module structure of the Distributed and Unified Numerics Environment and reflects on recent developments and general changes that happened since the release of the first Dune version in 2007 and the main papers describing that state [1, 2]. This discussion is accompanied with a description of various advanced features, such as coupling of domains and cut cells, grid modifications such as adaptation and moving domains, high order discretizations and node level performance, non-smooth multigrid methods, and multiscale methods. A brief discussion on current and future development directions of the framework concludes the paper.

cs.MS↗

arXiv2020

Reducing the impact of radioactivity on quantum circuits in a deep-underground facility

As quantum coherence times of superconducting circuits have increased from nanoseconds to hundreds of microseconds, they are currently one of the leading platforms for quantum information processing. However, coherence needs to further improve by orders of magnitude to reduce the prohibitive hardware overhead of current error correction schemes. Reaching this goal hinges on reducing the density of broken Cooper pairs, so-called quasiparticles. Here, we show that environmental radioactivity is a significant source of nonequilibrium quasiparticles. Moreover, ionizing radiation introduces time-correlated quasiparticle bursts in resonators on the same chip, further complicating quantum error correction. Operating in a deep-underground lead-shielded cryostat decreases the quasiparticle burst rate by a factor fifty and reduces dissipation up to a factor four, showcasing the importance of radiation abatement in future solid-state quantum hardware.

cond-mat.supr-con↗

arXiv2020

Accelerating complex control schemes on a heterogeneous MPSoC platform for quantum computing

Control and readout of superconducting quantum bits (qubits) require microwave pulses with gigahertz frequencies and nanosecond precision. To generate and analyze these microwave pulses, we developed a versatile FPGA-based electronics platform. While basic functionality is directly handled within the FPGA, guaranteeing highest accuracy on the nanosecond timescale, more complex control schemes render impractical to implement in hardware. To provide deterministic timing and low latency with high flexibility, we developed the Taskrunner framework. It enables the execution of complex control schemes, so-called user tasks, on the real-time processing unit (RPU) of a heterogeneous Multiprocessor System-on-Chip (MPSoC). These user tasks are specified conveniently using standard C language and are compiled automatically by the MPSoC platform when loaded onto the RPU. We present the architecture of the Taskrunner framework as well as timing benchmarks and discuss applications in the field of quantum computing.

eess.SY↗

arXiv2019

State preparation of a fluxonium qubit with feedback from a custom FPGA-based platform

We developed a versatile integrated control and readout instrument for experiments with superconducting quantum bits (qubits), based on a field-programmable gate array (FPGA) platform. Using this platform, we perform measurement-based, closed-loop feedback operations with $428 \, \mathrm{ns}$ platform latency. The feedback capability is instrumental in realizing active reset initialization of the qubit into the ground state in a time much shorter than its energy relaxation time $T_1$. We show experimental results demonstrating reset of a fluxonium qubit with $99.4\,\%$ fidelity, using a readout-and-drive pulse sequence approximately $1.5 \, \mathrm{μs}$ long. Compared to passive ground state initialization through thermalization, with the time constant given by $T_1 = ~ 80 \, \mathrm{μs}$, the use of the FPGA-based platform allows us to improve both the fidelity and the time of the qubit initialization by an order of magnitude.

quant-ph↗

arXiv2019

Phonon traps reduce the quasiparticle density in superconducting circuits

Out of equilibrium quasiparticles (QPs) are one of the main sources of decoherence in superconducting quantum circuits, and are particularly detrimental in devices with high kinetic inductance, such as high impedance resonators, qubits, and detectors. Despite significant progress in the understanding of QP dynamics, pinpointing their origin and decreasing their density remain outstanding tasks. The cyclic process of recombination and generation of QPs implies the exchange of phonons between the superconducting thin film and the underlying substrate. Reducing the number of substrate phonons with frequencies exceeding the spectral gap of the superconductor should result in a reduction of QPs. Indeed, we demonstrate that surrounding high impedance resonators made of granular aluminum (grAl) with lower gapped thin film aluminum islands increases the internal quality factors of the resonators in the single photon regime, suppresses the noise, and reduces the rate of observed QP bursts. The aluminum islands are positioned far enough from the resonators to be electromagnetically decoupled, thus not changing the resonator frequency, nor the loading. We therefore attribute the improvements observed in grAl resonators to phonon trapping at frequencies close to the spectral gap of aluminum, well below the grAl gap.

cond-mat.supr-con↗

arXiv2018

The quasiconvex envelope of conformally invariant planar energy functions in isotropic hyperelasticity

We consider conformally invariant energies $W$ on the group $\operatorname{GL}^+(2)$ of $2\times2$-matrices with positive determinant, i.e. $W\colon\operatorname{GL}^+(2)\to\mathbb{R}$ such that \[W(AFB) = W(F) \qquad\text{for all }\; A,B\in\{aR\in\operatorname{GL}^+(2) \,|\, a\in(0,\infty)\,,\; R\in\operatorname{SO}(2)\}\,,\] where $\operatorname{SO}(2)$ denotes the special orthogonal group, and provide an explicit formula for the (notoriously difficult to compute) quasiconvex envelope of these functions. Our results, which are based on the representation $W(F)=h(\frac{λ_1}{λ_2})$ of $W$ in terms of the singular values $λ_1,λ_2$ of $F$, are applied to a number of example energies in order to demonstrate the convenience of the eigenvalue-based expression compared to the more common representation in terms of the distortion $\mathbb{K}:=\frac12\frac{\lVert F\rVert^2}{\det F}$. Special cases of our results can be obtained from earlier works by Astala et al. and Yan.

math.AP↗

arXiv2018

Function space bases in the dune-functions module

The dune-functions Dune module provides interfaces for functions and function space bases. It forms one abstraction level above grids, shape functions, and linear algebra, and provides infrastructure for full discretization frameworks like dune-pdelab and dune-fem. This document describes the function space bases provided by dune-functions. These are based on an abstract description of bases for product spaces as trees of simpler bases. From this description, many different numberings of degrees of freedom by multi-indices can be derived in a natural way. We describe the abstract concepts, document the programmer interface, and give a complete example program that solves the stationary Stokes equation using Taylor-Hood elements.

cs.MS↗

arXiv2018

Software-defined Radio Readout System for the ECHo Experiment

Metallic magnetic calorimeters (MMCs) are cryogenic detectors that offer an excellent energy resolution, a signal rise time of <100 ns, a high dynamic range and almost optimal linearity. MMCs are of high interest for many experiments. One of them, the ECHo experiment, requires the utilization of large MMC detector arrays. The readout of such MMC arrays is a challenging task, which can be tackled using software-defined radios (SDRs). Though SDR is a well-known approach in communications engineering, a dedicated implementation for frequency division multiplexed readout of MMCs is new and one of the technological key elements of the ECHo project. ECHo will be the first experiment to use microwave SQUID multiplexed MMC detectors and therefore pioneering the hardware, firmware and software development in this domain. This paper presents the detailed concepts and current status of the development.

physics.ins-det↗

arXiv2018

Projection-Based Finite Elements for Nonlinear Function Spaces

We introduce a novel type of approximation spaces for functions with values in a nonlinear manifold. The discrete functions are constructed by piecewise polynomial interpolation in a Euclidean embedding space, and then projecting pointwise onto the manifold. We show optimal interpolation error bounds with respect to Lebesgue and Sobolev norms. Additionally, we show similar bounds for the test functions, i.e., variations of discrete functions. Combining these results with a nonlinear Céa lemma, we prove optimal $L^2$ and $H^1$ discretization error bounds for harmonic maps from a planar domain into a smooth manifold. All these error bounds are also verified numerically.

math.NA↗