Final-State Constrained Optimal Control via a Projection Operator Approach

In this paper we develop a numerical method to solve nonlinear optimal control problems with final-state constraints. Specifically, we extend the PRojection Operator based Netwon's method for Trajectory Optimization (PRONTO), which was proposed by Hauser for unconstrained optimal control problems. While in the standard method final-state constraints can be only approximately handled by means of a terminal penalty, in this work we propose a methodology to meet the constraints exactly. Moreover, our method guarantees recursive feasibility of the final-state constraint. This is an appealing property especially in realtime applications in which one would like to be able to stop the computation even if the desired tolerance has not been reached, but still satisfy the constraints. Following the same conceptual idea of PRONTO, the proposed strategy is based on two main steps which (differently from the standard scheme) preserve the feasibility of the final-state constraints: (i) solve a quadratic approximation of the nonlinear problem to find a descent direction, and (ii) get a (feasible) trajectory by means of a feedback law (which turns out to be a nonlinear projection operator). To find the (feasible) descent direction we take advantage of final-state constrained Linear Quadratic optimal control methods, while the second step is performed by suitably designing a constrained version of the trajectory tracking projection operator. The effectiveness of the proposed strategy is tested on the optimal state transfer of an inverted pendulum

The topological Faraday effect cannot be observed in a realistic sample

A striking feature of 3 dimensional (3D) topological insulators (TIs) is the theoretically expected topological magneto-electric (TME) effect, which gives rise to additional terms in Maxwell's laws of electromagnetism with an universal quantized coefficient proportional to half-integer multiples of the fine structure constant $\alpha$. In an ideal scenario one therefore expects also quantized contributions in the magneto-optical response of TIs. We review this premise by taking into account the trivial dielectric background of the TI bulk and potential host substrates, and the often present contribution of itinerant bulk carriers. We show that (i) one obtains a non-universal magneto-optical response whenever there is impedance mismatch between different layers and (ii) that the detectable signals due to the TME rapidly approach vanishingly small values as the impedance mismatch is detuned from zero. We demonstrate that it is methodologically impossible to deduce the existence of a TME exclusively from an optical experiment in the thin film limit of 3D TIs at high magnetic fields

Topolectrical circuits

Invented by Alessandro Volta and F\'elix Savary in the early 19th century, circuits consisting of resistor, inductor and capacitor (RLC) components are omnipresent in modern technology. The behavior of an RLC circuit is governed by its circuit Laplacian, which is analogous to the Hamiltonian describing the energetics of a physical system. We show that topological semimetal band structures can be realized as admittance bands in a periodic RLC circuit, where we employ the grounding to adjust the spectral position of the bands similar to the chemical potential in a material. Topological boundary resonances (TBRs) appear in the impedance read-out of a topolectrical circuit, providing a robust signal for the presence of topological admittance bands. For experimental illustration, we build the Su-Schrieffer-Heeger circuit, where our impedance measurement detects a TBR related to the midgap state. Due to the versatility of electronic circuits, our topological semimetal construction can be generalized to band structures with arbitrary lattice symmetry. Topolectrical circuits establish a bridge between electrical engineering and topological states of matter, where the accessibility, scalability, and operability of electronics synergizes with the intricate boundary properties of topological phases.Comment: 11 pages, 4 figure

Enhanced spin-orbit coupling in core/shell nanowires

The spin-orbit coupling (SOC) in semiconductors is strongly influenced by structural asymmetries, as prominently observed in bulk crystal structures that lack inversion symmetry. Here, we study an additional effect on the SOC: the asymmetry induced by the large interface area between a nanowire core and its surrounding shell. Our experiments on purely wurtzite GaAs/AlGaAs core/shell nanowires demonstrate optical spin injection into a single free-standing nanowire and determine the effective electron g-factor of the hexagonal GaAs wurtzite phase. The spin relaxation is highly anisotropic in time-resolved micro-photoluminescence measurements on single nanowires, showing a significant increase of spin relaxation in external magnetic fields. This behavior is counterintuitive compared to bulk wurtzite crystals. We present a model for the observed electron spin dynamics highlighting the dominant role of the interface-induced SOC in these core/shell nanowires. This enhanced SOC may represent an interesting tuning parameter for the implementation of spin-orbitronic concepts in semiconductor-based structures

Enhanced Spectral Density of a Single Germanium Vacancy Center in a Nanodiamond by Cavity-Integration

Color centers in diamond, among them the negatively-charged germanium vacancy (GeV$^-$), are promising candidates for many applications of quantum optics such as a quantum network. For efficient implementation, the optical transitions need to be coupled to a single optical mode. Here, we demonstrate the transfer of a nanodiamond containing a single ingrown GeV- center with excellent optical properties to an open Fabry-P\'erot microcavity by nanomanipulation utilizing an atomic force microscope. Coupling of the GeV- defect to the cavity mode is achieved, while the optical resonator maintains a high finesse of F = 7,700 and a 48-fold spectral density enhancement is observed. This article demonstrates the integration of a GeV- defect with a Fabry-P\'erot microcavity under ambient conditions with the potential to extend the experiments to cryogenic temperatures towards an efficient spin-photon platform.Comment: 6 pages, 3 figures. The article has been accepted by Applied Physics Letters. It is found at https://doi.org/10.1063/5.0156787. Added acknowledgment: S.S. acknowledges support of the Marie Curie ITN project LasIonDef (GA n.956387

A Polymorphism in the Processing Body Component Ge-1 Controls Resistance to a Naturally Occurring Rhabdovirus in Drosophila.

Hosts encounter an ever-changing array of pathogens, so there is continual selection for novel ways to resist infection. A powerful way to understand how hosts evolve resistance is to identify the genes that cause variation in susceptibility to infection. Using high-resolution genetic mapping we have identified a naturally occurring polymorphism in a gene called Ge-1 that makes Drosophila melanogaster highly resistant to its natural pathogen Drosophila melanogaster sigma virus (DMelSV). By modifying the sequence of the gene in transgenic flies, we identified a 26 amino acid deletion in the serine-rich linker region of Ge-1 that is causing the resistance. Knocking down the expression of the susceptible allele leads to a decrease in viral titre in infected flies, indicating that Ge-1 is an existing restriction factor whose antiviral effects have been increased by the deletion. Ge-1 plays a central role in RNA degradation and the formation of processing bodies (P bodies). A key effector in antiviral immunity, the RNAi induced silencing complex (RISC), localises to P bodies, but we found that Ge-1-based resistance is not dependent on the small interfering RNA (siRNA) pathway. However, we found that Decapping protein 1 (DCP1) protects flies against sigma virus. This protein interacts with Ge-1 and commits mRNA for degradation by removing the 5' cap, suggesting that resistance may rely on this RNA degradation pathway. The serine-rich linker domain of Ge-1 has experienced strong selection during the evolution of Drosophila, suggesting that this gene may be under long-term selection by viruses. These findings demonstrate that studying naturally occurring polymorphisms that increase resistance to infections enables us to identify novel forms of antiviral defence, and support a pattern of major effect polymorphisms controlling resistance to viruses in Drosophila.This is the final version of the article. It first appeared from PLOS via http://dx.doi.org/10.1371/journal.ppat.100538