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In this paper, we investigate three schemes for implementing Controlled-NOT (CNOT) gates between individual ytterbium (Yb) rare-earth ions doped into yttrium orthovanadate (YVO$_4$ or YVO). Specifically, we investigate the CNOT gates based on magnetic dipolar interactions between Yb ions, photon scattering off a cavity, and a photon interference-based protocol, with and without an optical cavity. We introduce a theoretical framework for precise computations of gate infidelity, accounting for noise effects. We then compute the gate fidelity of each scheme to evaluate the feasibility of their experimental implementation. Based on these results, we compare the performance of the gate schemes and discuss their respective advantages and disadvantages. We conclude that the probabilistic photon interference-based scheme offers the best fidelity scaling with cooperativity and is superior with the current technology of Yb values, while photon scattering is nearly deterministic but slower with less favourable fidelity scaling as a function of cooperativity. The cavityless magnetic dipolar scheme provides a fast, deterministic gate with high fidelity if close ion localization can be realized., Comment: 18 pages, 11 figures

Zeitlin's model is a spatial discretization for the 2-D Euler equations on the flat 2-torus or the 2-sphere. Contrary to other discretizations, it preserves the underlying geometric structure, namely that the Euler equations describe Riemannian geodesics on a Lie group. Here we show how to extend Zeitlin's approach to the axisymmetric Euler equations on the 3-sphere. It is the first discretization of the 3-D Euler equations that fully preserves the geometric structure, albeit restricted to axisymmetric solutions. Thus, this finite-dimensional model admits Riemannian curvature and Jacobi equations, which are discussed., Comment: 24 pages, 4 figures

In a Lie group equipped with a left-invariant metric, we study the minimizing properties of geodesics through the presence of conjugate points. We give criteria for the existence of conjugate points along steady and nonsteady geodesics, using different strategies in each case. We consider both general Lie groups and quadratic Lie groups, where the metric in the Lie algebra $g(u,v)=\langle u,\Lambda v\rangle$ is defined from a bi-invariant bilinear form and a symmetric positive definite operator $\Lambda$. By way of illustration, we apply our criteria to $SO(n)$ equipped with a generalized version of the rigid body metric, and to Lie groups arising from Cheeger's deformation technique, which include Zeitlin's $SU(3)$ model of hydrodynamics on the $2$-sphere. Along the way we obtain formulas for the Ricci curvatures in these examples, showing that conjugate points occur even in the presence of some negative curvature., Comment: 38 pages

This paper presents the design and technical progress of a precision X-Y stage for detector dithering and flexure compensation. The stage is being developed for use in the Magellan InfraRed Multi-Object Spectrograph, MIRMOS. MIRMOS is a very large Nasmyth mounted spectrograph containing a combination of refractive, reflective and diffractive optics mounted on a long cryogenic optical bench. The instrument utilizes five science cameras, each having a custom x-y stage to control the in-plane detector position within each camera, providing both dithering capability for improved sampling, and flexure compensation to correct for image motion that results from the gravity variant operation of the instrument. Designed to operate at 120~K, the stage will accurately control detector position in two orthogonal degrees of freedom, and have manual fine adjustment features to set detector tip, tilt and piston. The piezo-driven flexure stage provides high-resolution backlash-free motion of the detector and is very compact along the optical path, keeping camera length to a minimum. A magnetoresistive bridge provides position feedback in each degree of freedom, greatly reducing hysteresis, which is common in piezoelectric actuators. The system is designed to operate in open loop using a lookup table keyed to the Nasmyth rotator angle for flexure control. Here, the optomechanical design of the stage, electrical control system, and current performance results from early prototype efforts are presented and discussed., Comment: Proceedings of SPIE Astronomical Telescopes + Instrumentation 2024, 11 pages, 10 figures

The Magellan InfraRed Multi-Object Spectrograph (MIRMOS) is a planned next generation multi-object and integral field spectrograph for the 6.5m Magellan telescopes at Las Campanas Observatory in Chile. MIRMOS will perform R$\sim$3700 spectroscopy over a simultaneous wavelength range of 0.886 - 2.404$\mu$m (Y,J,H,K bands) in addition to imaging over the range of 0.7 - 0.886$\mu$m. The integral field mode of operation for MIRMOS will be achieved via an image slicer style integral field unit (IFU) located on a linear stage to facilitate movement into the beam during use or storage while operating in multi-object mode. The IFU will provide a $\rm \sim20"\times26"$ field of view (FoV) made up of $\rm0.84"\times26"$ slices. This will be the largest FoV IFS operating at these wavelengths from either the ground or space, making MIRMOS an ideal instrument for a wide range of science cases including studying the high redshift circumgalactic medium and emission line tracers from ionized and molecular gas in nearby galaxies. In order to achieve the desired image quality and FoV while matching the focal ratio to the multi-object mode, our slicer design makes use of novel freeform surfaces for the pupil mirrors, which require the use of high precision multi-axis diamond milling to manufacture. We present here the optical design and predicted performance of the MIRMOS IFU along with a conceptual design for the opto-mechanical system., Comment: Proceedings of SPIE Astronomical Telescopes + Instrumentation 2024, 9 pages, 6 figures

The sequential resonant excitation of a 2-level quantum system results in the emission of a state of light showing time-entanglement encoded in the photon-number-basis - notions that can be extended to 3-level quantum systems as discussed in a recent proposal. Here, we report the experimental implementation of a sequential two-photon resonant excitation process of a solid-state 3-level system, constituted by the biexciton-, exciton-, and ground-state of a semiconductor quantum dot. The resulting light state exhibits entanglement in time and energy, encoded in the photon-number basis, which could be used in quantum information applications, e.g., dense information encoding or quantum communication protocols. Performing energy- and time-resolved correlation experiments in combination with extensive theoretical modelling, we are able to partially retrieve the entanglement structure of the generated state., Comment: 14 pages (including 5 figures, 56 citations)

A new method is developed for finding exact solitary wave solutions of a generalized Korteweg-de Vries equation with p-power nonlinearity coupled to a linear Schr\"odinger equation arising in many different physical applications. This method yields 22 solution families, with p=1,2,3,4. No solutions for p>1 were known previously in the literature. For p=1, four of the solution families contain bright/dark Davydov solitons of the 1st and 2nd kind, obtained in recent work by basic ansatze applied to the ODE system for travelling waves. All of the new solution families have interesting features, including bright/dark peaks with (up to) p symmetric pairs of side peaks in the amplitude and a kink profile for the nonlinear part in the phase. The present method is fully systematic and involves several novel steps which reduce the travelling wave ODE system to a single nonlinear base ODE for which all polynomial solutions are found by symbolic computation. It is applicable more generally to other coupled nonlinear dispersive wave equations as well as to nonlinear ODE systems of generalized H\'enon-Heiles form., Comment: 45 pages, published version

Every noncompact surface is shown to have a (3,6)-tight triangulation and a characterisation of such triangulations is given in terms of length constraints on the boundary walks of superfaces of a given genus. Applications are given to the generic rigidity of associated countable bar-joint frameworks in R^3. In particular, every noncompact surface has a (3,6)-tight triangulation that is minimally 3-rigid. A proof of Ker\'ekj\'art\'o's classification of noncompact surfaces is also given., Comment: Improved introduction, added references and minor changes. 17 pages and 7 figures

We present spot properties on 32 periodic young stellar objects in IC 5070. Long term, $\sim$5 yr, light curves in the $V$, $R$, and $I$-bands are obtained through the HOYS (Hunting Outbursting Young Stars) citizen science project. These are dissected into six months long slices, with 3 months oversampling, to measure 234 sets of amplitudes in all filters. We fit 180 of these with reliable spot solutions. Two thirds of spot solutions are cold spots, the lowest is 2150 K below the stellar temperature. One third are warm spots that are above the stellar temperature by less than $\sim$2000 K. Cold and warm spots have maximum surface coverage values of 40 percent, although only 16 percent of warm spots are above 20 percent surface coverage as opposed to 60 percent of the cold spots. Warm spots are most likely caused by a combination of plages and low density accretion columns, most common on objects without inner disc excess emission in $K-W2$. Five small hot spot solutions have $<3$ percent coverage and are 3000 - 5000 K above the stellar temperature. These are attributed to accretion, and four of them occur on the same object. The majority of our objects are likely to be accreting. However, we observe very few accretion hot spots as either the accretion is not stable on our timescale or the photometry is dominated by other features. We do not identify cyclical spot behaviour on the targets. We additionally identify and discuss a number of objects that have interesting amplitudes, phase changes, or spot properties., Comment: Accepted for publication by MNRAS. 17 + 7 pages, 7 + 23 figures, 1 table

Few laboratory studies have investigated the vapor pressures of the volatiles that may be present as ices in the outer solar system; even fewer studies have investigated these species at the temperatures and pressures suitable to the surfaces of icy bodies in the Saturnian and Uranian systems ($\lt$100 K, $\lt10^{-9}$ bar). This study adds to the work of Grundy et al. (2024) in extending the known equilibrium vapor pressures of outer solar system ices through laboratory investigations at very low temperatures. Our experiments with ammonia and oxygen ices provide new thermodynamic models for these species' respective enthalpies of sublimation. We find that ammonia ice, and to a lesser degree oxygen ice, are stable at higher temperatures than extrapolations in previous literature have predicted. Our results show that these ices should be retained over longer periods of time than previous extrapolations would predict, and a greater amount of these solids is required to support observation in exospheres of airless bodies in the outer solar system., Comment: 29 pages, 9 figures, to be published in Planetary and Space Science

Nitrogen vacancy centres in diamond can be used for vector magnetometry. In this work we present a portable vector diamond magnetometer. Its vector capability, combined with feedback control and robust structure enables operation on moving platforms. While placed on a trolley, magnetic mapping of a room is demonstrated and the magnetometer is also shown to be operational in a moving van with the measured magnetic field shifts for the x, y, and z axes being tagged with GPS coordinates. These magnetic field measurements are in agreement with measurements taken simultaneously with a fluxgate magnetometer., Comment: 25 pages, 32 figures

A weak formulation is devised for the K(m,n) equation which is a nonlinearly dispersive generalization of the gKdV equation having compacton solutions. With this formulation, explicit weak compacton solutions are derived, including ones that do not exist as classical (strong) solutions. Similar results are obtained for a nonlinearly dispersive generalization of the gKP equation in two dimensions, which possesses line compacton solutions., Comment: 17 pages, published version

In this review, we describe the current landscape of emergent quantum materials for quantum photonic applications. We focus on three specific solid-state platforms: single emitters in monolayers of transition metal dichalcogenides, defects in hexagonal boron nitride, and colloidal quantum dots in perovskites. These platforms share a unique technological accessibility, enabling the rapid implementation of testbed quantum applications, all while being on the verge of becoming technologically mature enough for a first generation of real-world quantum applications. The review begins with a comprehensive overview of the current state-of-the-art for relevant single-photon sources in the solid-state, introducing the most important performance criteria and experimental characterization techniques along the way. We then benchmark progress for each of the three novel materials against more established (yet complex) platforms, highlighting performance, material-specific advantages, and giving an outlook on quantum applications. This review will thus provide the reader with a snapshot on latest developments in the fast-paced field of emergent single-photon sources in the solid-state, including all the required concepts and experiments relevant to this technology., Comment: 35 pages, 8 figures, review paper

We investigate the geometry of a family of equations in two dimensions which interpolate between the Euler equations of ideal hydrodynamics and the inviscid surface quasi-geostrophic equation. This family can be realised as geodesic equations on groups of diffeomorphisms. We show precisely when the corresponding Riemannian exponential map is non-linear Fredholm of index 0. We further illustrate this by examining the distribution of conjugate points in these settings via a Morse theoretic approach.

We propose a new concept to generate efficient one-third harmonic light from an unseeded third harmonic process in optical fibers. Our concept is based on the dynamic constant (Hamiltonian) of the nonlinear third harmonic generation in optical fibers and includes a periodic array of nonlinear fibers and phase compensation elements. We test our concept with a simulation of the nonlinear interaction between the fundamental and third harmonic modes of a realistic optical fiber, demonstrating high-efficiency one-third harmonic generation. Our work opens a new approach to achieving the so far elusive one-third harmonic generation in optical fibers.

We introduce an adaptable and modular hybrid architecture designed for fault-tolerant quantum computing. It combines quantum emitters and linear-optical entangling gates to leverage the strength of both matter-based and photonic-based approaches. A key feature of the architecture is its practicality, grounded in the utilisation of experimentally proven optical components. Our framework enables the execution of any quantum error correcting code, but in particular maintains scalability for low-density parity check codes by exploiting built-in non-local connectivity through distant optical links. To gauge its efficiency, we evaluated the architecture using a physically motivated error model. It exhibits loss tolerance comparable to existing all-photonic architecture but without the need for intricate linear-optical resource-state-generation modules that conventionally rely on resource-intensive multiplexing. The versatility of the architecture also offers uncharted avenues for further advancing performance standards., Comment: 29 pages, 10 figures. Accepted Quantum journal