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Continuous physical interaction between robots and their environment is a requirement in many industrial and household tasks, such as sanding and cleaning. Due to the complex tactile information, these tasks are notoriously difficult to model and to sense. In this article, we introduce a closed-loop control method that is constrained to surfaces. The applications that we target have in common that they can be represented by probability distributions on the surface that correlate to the time the robot should spend in a region. These surfaces can easily be captured jointly with the target distributions using coloured point clouds. We present the extension of an ergodic control approach that can be used with point clouds, based on heat equation-driven area coverage (HEDAC). Our method enables closed-loop exploration by measuring the actual coverage using vision. Unlike existing approaches, we approximate the potential field from non-stationary diffusion using spectral acceleration, which does not require complex preprocessing steps and achieves real-time closed-loop control frequencies. We exploit geometric algebra to stay in contact with the target surface by tracking a line while simultaneously exerting a desired force along that line. Our approach is suitable for fully autonomous and human-robot interaction settings where the robot can either directly measure the coverage of the target with its sensors or by being guided online by markings or annotations of a human expert. We tested the performance of the approach in kinematic simulation using point clouds, ranging from the Stanford bunny to a variety of kitchen utensils. Our real-world experiments demonstrate that the proposed approach can successfully be used to wash kitchenware with curved surfaces, by cleaning the dirt detected by vision in an online manner. Website: https://geometric-algebra.tobiloew.ch/tactile_ergodic_control, Comment: Submitted to the special issue for IEEE Transactions on Robotics (T-RO) on Tactile Robotics

YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO) has favorable macroscopic superconducting properties of $T_\mathrm{c}$ up to 93 K and $H_{c2}$ up to 150 T. However, its nanoscale electronic structure remains mysterious because bulk-like electronic properties are not preserved near the surface of cleaved samples for easy access by local or surface-sensitive probes. It has been hypothesized that Ca-doping at the Y site could induce an alternate cleavage plane that mitigates this issue. We use scanning tunneling microscopy (STM) to study both Ca-free and 10% Ca-doped YBCO, and find that the Ca-doped samples do indeed cleave on an alternate plane, yielding a spatially-disordered partial (Y,Ca) layer. Our density functional theory calculations support the increased likelihood of this new cleavage plane in Ca-doped YBCO. On this surface, we image a superconducting gap with average value 24 $\pm$ 3 meV and characteristic length scale 1-2 nm, similar to Bi-based high-$T_\mathrm{c}$ cuprates, but the first map of gap inhomogeneity in the YBCO family., Comment: corrected typo in metadata author name

A major obstacle to understanding high-Tc cuprates is that superconductivity precludes observing normal-state properties at low temperatures. One prime example is the normal-state spin susceptibility: although its decrease upon cooling far above Tc typifies pseudogap behavior, its behavior at low temperatures is generally unknown. Here, our measurements in high magnetic fields expose the spin susceptibility of YBa2Cu3Oy down to low temperatures. Even though superconductivity is suppressed by the field, we uncover two thermally-activated contributions alongside a residual susceptibility at T=0 due to gapless excitations. We relate these two distinct gaps to short-range charge-density waves and to the formation of spin singlets similar to those found in certain quantum spin systems. These phenomena thus collectively contribute to the pseudogap in the spin susceptibility at low temperature, supplementing short-lived antiferromagnetism known to initiate pseudogap behavior at high temperatures. We therefore propose that the pseudogap should be regarded as a composite property.

This tutorial provides a hands-on entry point about laser locking for atomic vapor research and related research such as laser cooling. We furthermore introduce common materials and methods for the fabrication of vapor cells as a tool for this research. Its aim is not to be exhaustive, but rather to provide an overview about the possible techniques that are actively employed in labs today. Some critical parameters of locked laser system for use with thermal atomic vapors are introduced and discussed. To exemplify this, we describe a versatile locking system that caters for many of the needs we found during our research with thermal atomic vapors. We also emphasize the compromises we took during our decision-making process., Comment: 58 pages, 14 figures

The onset of collision dynamics between an ion and a Rydberg atom is studied in a regime characterized by a multitude of collision channels. These channels arise from coupling between a non-polar Rydberg state and numerous highly polar Stark states. The interaction potentials formed by the polar Stark states show a substantial difference in spatial gradient compared to the non-polar state leading to a separation of collisional timescales, which is observed in situ. For collision energies in the range of $k_\textrm{B}\cdot\mu$K to $k_\textrm{B}\cdot$K, the dynamics exhibit a counter-intuitive dependence on temperature, resulting in faster collision dynamics for cold - initially "slow" - systems. Dipole selection rules enable us to prepare the collision pair on the non-polar potential in a highly controlled manner, which determines occupation of the collision channels. The experimental observations are supported by semi-classical simulations, which model the pair state evolution and provide evidence for tunable non-adiabatic dynamics.

We report on the current development of a single photon source based on a long-range interacting room temperature rubidium vapor. We discuss the history of the project, the production of vapor cells, and the observation of Rabi-oscillations in the four-wave-mixing excitation scheme., Comment: 8 pages, 6 figures

The essential building blocks of cuprate superconductors are two-dimensional CuO$_2$ sheets interspersed with charge reservoir layers. In bilayer cuprates, two closely spaced CuO$_2$ sheets are separated by a larger distance from the subsequent pair in the next unit cell. In contrast to single-layer cuprates, prior theoretical work on bilayer systems has predicted two distinct acoustic plasmon bands for a given out-of-plane momentum transfer. Here we report random phase approximation (RPA) calculations for bilayer systems which corroborate the existence of two distinct plasmons bands. We find that the intensity of the lower-energy band is negligibly small, whereas the higher-energy band carries significant spectral weight. We also present resonant inelastic x-ray scattering (RIXS) experiments at the O $K$-edge on the bilayer cuprate Y$_{0.85}$Ca$_{0.15}$Ba$_2$Cu$_3$O$_7$ (Ca-YBCO), which show only one dispersive plasmon branch, in agreement with the RPA calculations. In addition, the RPA results indicate that the dispersion of the higher-energy plasmon band in Ca-YBCO is not strictly acoustic, but exhibits a substantial energy gap of approximately 250 meV at the two-dimensional Brillouin zone center., Comment: 9 pages, 7 figures

In this work, we are presenting an extension of the cooperative dual-task space (CDTS) in conformal geometric algebra. The CDTS was first defined using dual quaternion algebra and is a well established framework for the simplified definition of tasks using two manipulators. By integrating conformal geometric algebra, we aim to further enhance the geometric expressiveness and thus simplify the modeling of various tasks. We show this formulation by first presenting the CDTS and then its extension that is based around a cooperative pointpair. This extension keeps all the benefits of the original formulation that is based on dual quaternions, but adds more tools for geometric modeling of the dual-arm tasks. We also present how this CGA-CDTS can be seamlessly integrated with an optimal control framework in geometric algebra that was derived in previous work. In the experiments, we demonstrate how to model different objectives and constraints using the CGA-CDTS. Using a setup of two Franka Emika robots we then show the effectiveness of our approach using model predictive control in real world experiments.

Geometry is a fundamental part of robotics and there have been various frameworks of representation over the years. Recently, geometric algebra has gained attention for its property of unifying many of those previous ideas into one algebra. While there are already efficient open-source implementations of geometric algebra available, none of them is targeted at robotics applications. We want to address this shortcoming with our library gafro. This article presents an overview of the implementation details as well as a tutorial of gafro, an efficient c++ library targeting robotics applications using geometric algebra. The library focuses on using conformal geometric algebra. Hence, various geometric primitives are available for computation as well as rigid body transformations. The modeling of robotic systems is also an important aspect of the library. It implements various algorithms for calculating the kinematics and dynamics of such systems as well as objectives for optimisation problems. The software stack is completed by python bindings in pygafro and a ROS interface in gafro_ros.

We report on the collisional shift and line broadening of Rydberg states in nitric oxide (NO) with increasing density of a background gas at room temperature. As a background gas we either use NO itself or nitrogen (N$_{2}$). The precision spectroscopy is performed by a sub-Doppler three-photon excitation scheme with a subsequent readout of the Rydberg states realized by the amplification of a current generated by free charges due to collisions. The shift shows a dependence on the rotational quantum state of the ionic core and no dependence on the principle quantum number of the orbiting Rydberg electron. The experiment was performed in the context of developing a trace-gas sensor for breath-gas analysis in a medical application.

Generating motion for robots that interact with objects of various shapes is a complex challenge, further complicated when the robot's own geometry and multiple desired behaviors are considered. To address this issue, we introduce a new framework based on Geometric Projectors (GeoPro) for constrained optimization. This novel framework allows for the generation of task-agnostic behaviors that are compliant with geometric constraints. GeoPro streamlines the design of behaviors in both task and configuration spaces, offering diverse functionalities such as collision avoidance and goal-reaching, while maintaining high computational efficiency. We validate the efficacy of our work through simulations and Franka Emika robotic experiments, comparing its performance against state-of-the-art methodologies. This comprehensive evaluation highlights GeoPro's versatility in accommodating robots with varying dynamics and precise geometric shapes. For additional materials, please visit: https://www.xueminchi.com/publications/geopro, Comment: 9 pages, 5 figures

Robot programming tools ranging from inverse kinematics (IK) to model predictive control (MPC) are most often described as constrained optimization problems. Even though there are currently many commercially-available second-order solvers, robotics literature recently focused on efficient implementations and improvements over these solvers for real-time robotic applications. However, most often, these implementations stay problem-specific and are not easy to access or implement, or do not exploit the geometric aspect of the robotics problems. In this work, we propose to solve these problems using a fast, easy-to-implement first-order method that fully exploits the geometric constraints via Euclidean projections, called Augmented Lagrangian Spectral Projected Gradient Descent (ALSPG). We show that 1. using projections instead of full constraints and gradients improves the performance of the solver and 2. ALSPG stays competitive to the standard second-order methods such as iLQR in the unconstrained case. We showcase these results with IK and motion planning problems on simulated examples and with an MPC problem on a 7-axis manipulator experiment., Comment: 8 pages, 7 figures, submitted to Robotics and Automation Letters

This paper presents a whole-body robot control method for exploring and probing a given region of interest. The ergodic control formalism behind such an exploration behavior consists of matching the time-averaged statistics of a robot trajectory with the spatial statistics of the target distribution. Most existing ergodic control approaches assume the robots/sensors as individual point agents moving in space. We introduce an approach that decomposes the whole-body of a robotic manipulator into multiple kinematically constrained agents. Then, we generate control actions by calculating a consensus among the agents. To do so, we use an ergodic control formulation called heat equation-driven area coverage (HEDAC) and slow the diffusion using the non-stationary heat equation. Our approach extends HEDAC to applications where robots have multiple sensors on the whole-body (such as tactile skin) and use all sensors to optimally explore the given region. We show that our approach increases the exploration performance in terms of ergodicity and scales well to real-world problems. We compare our method in kinematic simulations with the state-of-the-art and demonstrate the applicability of an online exploration task with a 7-axis Franka Emika robot. Additional material available at https://sites.google.com/view/w-ee-d/, Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

Coded Aperture Imaging (CAI) has been proposed as an alternative collimation technique in nuclear imaging. To maximize spatial resolution small pinholes in the coded aperture mask are required. However, a high-resolution detector is needed to correctly sample the point spread function (PSF) to keep the Nyquist-Shannon sampling theorem satisfied. The disadvantage of smaller pixels, though, is the resulting higher Poisson noise. Thus, the aim of this paper was to investigate if sufficiently accurate CAI reconstruction is achievable with a detector which undersamples the PSF. With the Monte Carlo simulation framework TOPAS a test image with multiple spheres of different diameter was simulated based on the setup of an experimental gamma camera from previous work. Additionally, measured phantom data were acquired. The captured detector images were converted to low-resolution images of different pixel sizes according to the super-resolution factor $k$. Multiple analytical reconstruction methods and a Machine Learning approach were compared based on the contrast-to-noise ratio (CNR). We show, that all reconstruction methods are able to reconstruct both the test image and the measured phantom data for $k \leq 7$. With a synthetic high-resolution PSF and upsampling the simulated low-resolution detector image by bilinear interpolation the CNR can be kept approximately constant. Results of this simulation study and additional validation on measured phantom data indicate that an undersampling detector can be combined with small aperture holes. However, further experiments need to be conducted., Comment: 7 pages, 8 figures