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A robust drift-safe rendezvous trajectory optimization tool is developed in this work, with applications to orbital rendezvous and proximity operations. The method is based on direct collocation and utilizes a sequential convex programming framework, and is extended from previous work to include passive safety constraints. The tool is then paired with a dispersion analysis framework to allow trajectories to be optimized subject to plant, navigation, and actuator uncertainties. The timing, direction, and magnitude of orbital maneuvers are optimized subject to the expected propellant usage, for a given navigation system performance. Representative trajectories are presented for the LEO flight regime, but the approach can also be applied to GEO and NRHO with minimal modification., Comment: AAS Rocky Mountain Guidance, Navigation and Control Conference, 2023

Nitrogen Vacancy (NV) centers in diamond are a platform for several important quantum technologies, including sensing, communication and elementary quantum processors. In this letter we demonstrate the creation of NV centers by implantation using a deterministic single ion source. For this we sympathetically laser-cool single $^{15}\textrm{N}_2^+$ molecular ions in a Paul trap and extract them at an energy of 5.9\,keV. Subsequently the ions are focused with a lateral resolution of 121(35)\,nm and are implanted into a diamond substrate without any spatial filtering by apertures or masks. After high-temperature annealing, we detect the NV centers in a confocal microscope and determine a conversion efficiency of about 0.6\,$\%$. The $^{15}\textrm{NV}$ centers are characterized by optically detected magnetic resonance (ODMR) on the hyperfine transition and coherence time., Comment: 13 pages, 7 figures

Near Rectilinear Halo Orbits (NRHOs), a subclass of halo orbits around the L1 and L2 Lagrange points, are promising candidates for future lunar gateways in cis-lunar space and as staging orbits for lunar missions. Closed-loop control is beneficial to compensate orbital perturbations and potential instabilities while maintaining spacecraft on NRHOs and performing relative motion maneuvers. This paper investigates the use of nonlinear model predictive control (NMPC) coupled with low-thrust actuators for station-keeping on NRHOs. It is demonstrated through numerical simulations that NMPC is able to stabilize a spacecraft to a reference orbit and handle control constraints. Further, it is shown that the computational burden of NMPC can be managed using specialized optimization routines and suboptimal approaches without jeopardizing closed-loop performance., Comment: 2020 AAS/AIAA Astrodynamics Specialist Conference, Lake Tahoe, California (held virtually)

Ions of the isomer $^{229m}$Th are a topic of high interest for the construction of a "nuclear clock" and in the field of fundamental physics for testing symmetries of nature. They can be efficiently captured in Paul traps which are ideal for performing high precision quantum logic spectroscopy. Trapping and identification of long-lived $^{232}$Th$^{+}$ ions from a laser ablation source was already demonstrated by the TACTICa collaboration on Trapping And Cooling of Thorium Ions with Calcium. The $^{229m}$Th is most easily accessible as $\alpha$-decay daughter of the decay of $^{233}$U. We report on the development of a source for slow Th ions, including $^{229(m)}$Th for the TACTICa experiment. The $^{229(m)}$Th source is currently under construction and comprises a $^{233}$U monolayer, from which $^{229(m)}$Th ions recoil. These are decelerated in an electric field. Conservation of the full initial charge state distribution of the $^{229(m)}$Th recoil ions is one of the unique features of this source. We present ion-flight simulations for our adopted layout and give a final design. This source will provide Th ions in their original charge state at energies suitable for capture in a linear Paul trap for spectroscopy investigations., Comment: 6 pages, 3 figures, PLATAN19 conference proceeding published in Hyperfine Interact 2020

With the number of small Unmanned Aircraft Systems (sUAS) in the national airspace projected to increase in the next few years, there is growing interest in a traffic management system capable of handling the demands of this aviation sector. It is expected that such a system will involve trajectory prediction, uncertainty propagation, and path planning algorithms. In this work, we use linear covariance propagation in combination with a quadratic programming-based collision detection algorithm to rapidly validate declared flight plans. Additionally, these algorithms are combined with a Dynamic, Informed RRT* algorithm, resulting in a computationally efficient algorithm for chance-constrained path planning. Detailed numerical examples for both fixed-wing and quadrotor sUAS models are presented., Comment: Submitted to Advanced Control for Applications

With the increasing interest in proximity and docking operations, there is a growing interest in spacecraft relative motion control. This paper extends a previously proposed constrained relative motion approach based on chained positively invariant sets to the case where the spacecraft dynamics are controlled using output feedback on noisy measurements and are subject to stochastic disturbances. It is shown that non-convex polyhedral exclusion zone constraints can be handled. The methodology consists of a virtual net of static equilibria nodes in the Clohessy-Wiltshire-Hill frame. Connectivity between nodes is determined through the use of chance-constrained admissible sets, guaranteeing that constraints are met with a specified probability., Comment: Submitted to the 2020 American Control Conference

Thorium ions exhibit unique nuclear properties with high relevance for testing symmetries of nature, and Paul traps feature an ideal experimental platform for performing high precision quantum logic spectroscopy. Loading of stable or long-lived isotopes is well-established and relies on ionization from an atomic beam. A different approach allows trapping short-lived isotopes available as alpha-decay daughters, which recoil from a thin sample of the precursor nuclide. A prominent example is the short-lived $^{229\text{m}}$Th, populated in a decay of long-lived $^{233}$U. Here, ions are provided by an external source and are decelerated to be available for trapping. Such setups offer the option to trap various isotopes and charge states of thorium. Investigating this complex procedure, we demonstrate the observation of single $^{232}$Th$^+$ ions trapped, embedded into and sympathetically cooled via Coulomb interactions by co-trapped $^{40}$Ca$^+$ ions. Furthermore, we discuss different options for a non-destructive identification of the sympathetically cooled thorium ions in the trap, and describe in detail our chosen experimental method, identifying mass and charge of thorium ions from the positions of calcium ions, as their fluorescence is imaged on a CCD camera. These findings are verified by means of a time-of-flight signal when extracting ions of different mass-to-charge ratio from the Paul trap and steering them into a detector.

Single dopant atoms or dopant-related defect centers in a solid state matrix provide an attractive platform for quantum simulation of topological states, for quantum computing and communication, due to their potential to realize a scalable architecture compatible with electronic and photonic integrated circuits. The production of such quantum devices calls for deterministic single atom doping techniques because conventional stochastic doping techniques are cannot deliver appropriate architectures. Here, we present the fabrication of arrays of praseodymium color centers in YAG substrates, using a deterministic source of single laser-cooled Pr$^+$ ions. The beam of single Pr$^+$ ions is extracted from a Paul trap and focused down to 30(9) nm. Using a confocal microscope we determine a conversion yield into active color centers up to 50% and realizing a placement accuracy of better than 50 nm., Comment: 9 pages, 7 figures

Precision optical spectroscopy of exotic ions reveals accurate information about nuclear properties such as charge radii and magnetic and quadrupole moments. Thorium ions exhibit unique nuclear properties with high relevance for testing symmetries of nature. We report loading and trapping of single $^{232}$Th$^+$ ions in a linear Paul trap, embedded into and sympathetically cooled by small crystals of trapped $^{40}$Ca$^+$ ions. Trapped Th ions are identified in a non-destructive manner from the voids in the laser-induced Ca fluorescence pattern emitted by the crystal, and alternatively, by means of a time-of-flight signal when extracting ions from the Paul trap and steering them into an external detector. We have loaded and handled a total of 231 individual Th ions. We reach a time-of-flight detection efficiency of $\gtrsim 95\, \%$, consistent with the quantum efficiency of the detector. The sympathetic cooling technique is expected to be applicable for other isotopes and various charge states of Th e.g., for future studies of $^{229m}$Th., Comment: 5 pages, 4 figures

We show nanoscopic transmission microscopy, using a deterministic single particle source and compare the resulting images in terms of signal-to-noise ratio, with those of conventional Poissonian sources. Our source is realized by deterministic extraction of laser-cooled calcium ions from a Paul trap. Gating by the extraction event allows for the suppression of detector dark counts by six orders of magnitude. Using the Bayes experimental design method, the deterministic characteristics of this source are harnessed to maximize information gain, when imaging structures with a parametrizable transmission function. We demonstrate such optimized imaging by determining parameter values of one and two dimensional transmissive structures., Comment: 8 pages, 7 figures, From SPIE Conference Volume 9900, Quantum Optics, J\"urgen Stuhler; Andrew J. Shields; Brussels, Belgium, April 03, 2016

We realize a single particle microscope by using deterministically extracted laser cooled $^{40}$Ca$^+$ ions from a Paul trap as probe particles for transmission imaging. We demonstrate focusing of the ions with a resolution of 5.8$\;\pm\;$1.0$\,$nm and a minimum two-sample deviation of the beam position of 1.5$\,$nm in the focal plane. The deterministic source, even when used in combination with an imperfect detector, gives rise to much higher signal to noise ratios as compared with conventional Poissonian sources. Gating of the detector signal by the extraction event suppresses dark counts by 6 orders of magnitude. We implement a Bayes experimental design approach to microscopy in order to maximize the gain in spatial information. We demonstrate this method by determining the position of a 1$\,\mu$m circular hole structure to an accuracy of 2.7$\,$nm using only 579 probe particles., Comment: 7 pages, 6 figures

We experimentally demonstrate nanoscopic transmission microscopy relying on a deterministic single particle source. This increases the signal-to-noise ratio with respect to conventional microscopy methods, which employ Poissonian particle sources. We use laser-cooled ions extracted from a Paul trap, and demonstrate remote imaging of transmissive objects with a resolution of 8.6 $\pm$ 2.0nm and a minimum two-sample deviation of the beam position of 1.5nm. Detector dark counts can be suppressed by 6 orders of magnitudes through gating by the extraction event. The deterministic nature of our source enables an information-gain driven approach to imaging. We demonstrate this by performing efficient beam characterization based on a Bayes experiment design method., Comment: 5 pages, 4 figures

We investigate spin and optical properties of individual nitrogen-vacancy centers located within 1-10 nm from the diamond surface. We observe stable defects with a characteristic optically detected magnetic resonance spectrum down to lowest depth. We also find a small, but systematic spectral broadening for defects shallower than about 2 nm. This broadening is consistent with the presence of a surface paramagnetic impurity layer [Tisler et al., ACS Nano 3, 1959 (2009)] largely decoupled by motional averaging. The observation of stable and well-behaved defects very close to the surface is critical for single-spin sensors and devices requiring nanometer proximity to the target., Comment: 5 pages, 4 figures, and Supplementary Material

This report, one of a series of country studies on higher education and employment particularly in continuing professional education, looks at recent developments in Germany. The first of six chapters offers a series of definitions of central concepts and focuses the paper's discussion on continuing education offered by higher education institutions and on their own responsibility. Chapter II looks at the development and importance of continuing education describing the traditional role of continuing education, the current state of these services as demand and employment has changed, and comparison with other industrialized nations. Chapter III describes in detail the continuing education offered by higher education institutions from types of programs, teaching techniques, and integration into the structure of universities to career-orientation and further education provided by connected institutions. Chapter IV briefly describes non-university programs. Chapter V discusses the challenges and problems facing continuing professional education including admission and qualification of participants, certification and record keeping, finance, teaching staff and teaching methods, and competition and collaboration with other providers. Chapter VI concludes by evaluating the current status of university services and suggesting future directions. Includes 58 references and a 25-item bibliography. (JB)

The development of social problem-solving skills in preschool children (namely, cooperative play, sharing, taking turns, understanding another person's feelings, helping, and the verbal resolution of conflict) was assessed following instruction under three conditions. A total of 35 children, of whom 18 attended a formally structured preschool program (Ausubelian) and 17 attended an informal program (Piagetian), were randomly assigned to three experimental groups. The first group received advance organizer instruction in general strategies for using the six target social problem-solving skills, followed by related activity sessions. The second group received instruction in particular instances of each skill in a sequence of related activities, while members of the third group were introduced to these skills during sociodramatic play activities. Following instruction, members of the first and second treatment groups were significantly better at using these skills than were those participating in the third group; in addition, the first group was significantly better than the second group at skill use. There was strong internal consistency of performance among posttest tasks for the first group, as compared with performances on tasks by the latter two groups. (MP)