Topological Frequency Conversion in a Driven Dissipative Quantum Cavity

Recent work (PRX 7, 041008) has shown that a spin coupled to two externally supplied circularly-polarized electromagnetic modes can effectuate a topological, quantized transfer of photons from one mode to the other. Here we study the effect in the case when only one of the modes is externally provided, while the other is a dynamical quantum mechanical cavity mode. Focusing on the signatures and stability under experimentally accessible conditions, we show that the effect persists down to the few-photon quantum limit and that it can be used to generate highly entangled "cat states" of cavity and spin. By tuning the strength of the external drive to a "sweet spot", the quantized pumping can arise starting from an empty (zero photon) cavity state. We also find that inclusion of external noise and dissipation does not suppress but rather stabilizes the conversion effect, even after multiple cavity modes are taken into account.Comment: 12 pages, 6 figure

Data-Driven Generalized Integer Aperture Bootstrapping for Real-Time High Integrity Applications

A new method is developed for integer ambiguity resolution in carrier-phase differential GPS (CDGPS) positioning. The method is novel in that it is (1) data-driven, (2) generalized to include partial ambiguity resolution, and (3) amenable to a full characterization of the prior and posterior distributions of the three-dimensional baseline vector that results from CDGPS. The technique is termed generalized integer aperture bootstrapping (GIAB). GIAB improves the availability of integer ambiguity resolution for high-integrity, safety-critical systems. Current high-integrity CDGPS algorithms, such as EPIC and GERAFS, evaluate the prior risk of position domain biases due to incorrect integer ambiguity resolution without further validation of the chosen solution. This model-driven approach introduces conservatism which tends to reduce solution availability. Common data-driven ambiguity validation methods, such as the ratio test, control the risk of incorrect ambiguity resolution by shrinking an integer aperture (IA), or acceptance region. The incorrect fixing risk of current IA methods is determined by functional approximations that are inappropriate for use in safety-of-life applications. Moreover, generalized IA (GIA) methods incorrectly assume that the baseline resulting from partial ambiguity resolution is zero mean. Each of these limitations is addressed by GIAB, and the claimed improvements are validated by Monte Carlo simulation. The performance of GIAB is then optimized by tuning the integer aperture size to maximize the prior probability of full ambiguity resolution. GIAB is shown to provide higher availability than EPIC for the same integrity requirements.Aerospace Engineering and Engineering Mechanic

The Tristan Chord Resolved

A little-noticed passage from Moritz Hauptmann’s 1853 treatise Die Natur der Harmonik und der Metrik very nearly describes the opening progression of Wagner’s Tristan. The present paper surveys the various analyses of the Tristan chord presented in the theoretical literature and defends an analysis derived from Hauptmann as a viable alternative.Un passage peu remarqué du traité de Moritz Hauptmann, Die Natur der Harmonik und der Metrik, offre une description qui pourrait presque décrire la progression initiale de Tristan de Wagner. Cet article survole différentes analyses de l’accord de Tristan publiées dans la littérature spécialisée, et défend les mérites d’une nouvelle interprétation dérivée de celle d’Hauptmann