Dynamical Belyi maps

We study the dynamical properties of a large class of rational maps with exactly three ramification points. By constructing families of such maps, we obtain infinitely many conservative maps of degree $d$; this answers a question of Silverman. Rather precise results on the reduction of these maps yield strong information on the rational dynamics.Comment: 21 page

Long-lived driven solid-state quantum memory

We investigate the performance of inhomogeneously broadened spin ensembles as quantum memories under continuous dynamical decoupling. The role of the continuous driving field is two-fold: first, it decouples individual spins from magnetic noise; second and more important, it suppresses and reshapes the spectral inhomogeneity of spin ensembles. We show that a continuous driving field, which itself may also be inhomogeneous over the ensemble, can enhance the decay of the tails of the inhomogeneous broadening distribution considerably. This fact enables a spin ensemble based quantum memory to exploit the effect of cavity protection and achieve a much longer storage time. In particular, for a spin ensemble with a Lorentzian spectral distribution, our calculations demonstrate that continuous dynamical decoupling has the potential to improve its storage time by orders of magnitude for the state-of-art experimental parameters

Nanodiamonds carrying quantum emitters with almost lifetime-limited linewidths

Nanodiamonds (NDs) hosting optically active defects are an important technical material for applications in quantum sensing, biological imaging, and quantum optics. The negatively charged silicon vacancy (SiV) defect is known to fluoresce in molecular sized NDs (1 to 6 nm) and its spectral properties depend on the quality of the surrounding host lattice. This defect is therefore a good probe to investigate the material properties of small NDs. Here we report unprecedented narrow optical transitions for SiV colour centers hosted in nanodiamonds produced using a novel high-pressure high-temperature (HPHT) technique. The SiV zero-phonon lines were measured to have an inhomogeneous distribution of 1.05 nm at 5 K across a sample of numerous NDs. Individual spectral lines as narrow as 354 MHz were measured for SiV centres in nanodiamonds smaller than 200 nm, which is four times narrower than the best SiV line previously reported for nanodiamonds. Correcting for apparent spectral diffusion yielded a homogeneous linewith of about 200 MHz, which is close to the width limit imposed by the radiative lifetime. These results demonstrate that the direct HPHT synthesis technique is capable of producing nanodiamonds with high crystal lattice quality, which are therefore a valuable technical material

Sensing remote nuclear spins

Sensing single nuclear spins is a central challenge in magnetic resonance based imaging techniques. Although different methods and especially diamond defect based sensing and imaging techniques in principle have shown sufficient sensitivity, signals from single nuclear spins are usually too weak to be distinguished from background noise. Here, we present the detection and identification of remote single C-13 nuclear spins embedded in nuclear spin baths surrounding a single electron spins of a nitrogen-vacancy centre in diamond. With dynamical decoupling control of the centre electron spin, the weak magnetic field ~10 nT from a single nuclear spin located ~3 nm from the centre with hyperfine coupling as weak as ~500 Hz is amplified and detected. The quantum nature of the coupling is confirmed and precise position and the vector components of the nuclear field are determined. Given the distance over which nuclear magnetic fields can be detected the technique marks a firm step towards imaging, detecting and controlling nuclear spin species external to the diamond sensor

Towards a large-scale quantum simulator on diamond surface at room temperature

Strongly-correlated quantum many-body systems exhibits a variety of exotic phases with long-range quantum correlations, such as spin liquids and supersolids. Despite the rapid increase in computational power of modern computers, the numerical simulation of these complex systems becomes intractable even for a few dozens of particles. Feynman's idea of quantum simulators offers an innovative way to bypass this computational barrier. However, the proposed realizations of such devices either require very low temperatures (ultracold gases in optical lattices, trapped ions, superconducting devices) and considerable technological effort, or are extremely hard to scale in practice (NMR, linear optics). In this work, we propose a new architecture for a scalable quantum simulator that can operate at room temperature. It consists of strongly-interacting nuclear spins attached to the diamond surface by its direct chemical treatment, or by means of a functionalized graphene sheet. The initialization, control and read-out of this quantum simulator can be accomplished with nitrogen-vacancy centers implanted in diamond. The system can be engineered to simulate a wide variety of interesting strongly-correlated models with long-range dipole-dipole interactions. Due to the superior coherence time of nuclear spins and nitrogen-vacancy centers in diamond, our proposal offers new opportunities towards large-scale quantum simulation at room temperatures

Meaning and definition:Skepticism and semantics in twelfth-century Arabic Philosophy

The theory of essential definitions is a fundamental anti-sceptic element of the Aristotelian-Avicennian epistemology. In this theory, when we distinguish the genus and the specific differentia of a given essence we thereby acquire a scientific understanding of it. The aim of this article is to analyse systematically the sceptical reasons, arguments and conclusions against real definitions of three major authorities of twelfth-century Arabic philosophy: Fahr al-Din al-Razi, Sihab al-Din al-Suhrawardi and Abu l-Barakat al-Badadi. I focus on showing how their refutation of our capacity to provide essential definitions of things is rooted in their semantic theory: we only know things under certain descriptions which are identical to the meanings of the words that we use to refer to them, yet these descriptions do not capture the essences of things in themselves. The best result one can achieve with Aristotelian-Avicennian scientific definitions is a "nominal definition". With this, Razi, Suhrawardi and Abu l-Barakat will put some serious epistemic limitations on our capacity to attain scientific knowledge of things, at least as Aristotle and Avicenna would have it

Grand unified theory constrained supersymmetry and neutrinoless double beta decay

We analyze the contributions to the neutrinoless double $\beta$ decay ($0\nu\beta\beta$-decay) coming from the Grand Unified Theory (GUT) constrained Minimal Supersymmetric Standard Model (MSSM) with trilinear R-parity breaking. We discuss the importance of two-nucleon and pion-exchange realizations of the quark-level $0\nu\beta\beta$-decay transitions. In this context, the questions of reliability of the calculated relevant nuclear matrix elements within the Renormalized Quasiparticle Random Phase Approximation (pn-RQRPA) for several medium and heavy open-shell nuclei are addressed. The importance of gluino and neutralino contributions to $0\nu\beta\beta$-decay is also analyzed. We review the present experiments and deduce limits on the trilinear R-parity breaking parameter $\lambda_{111}'$ from the non-observability of $0\nu\beta\beta$-decay for different GUT constrained SUSY scenarios. In addition, a detailed study of limits on the MSSM parameter space coming from the $B \to X_s \gamma$ processes by using the recent CLEO and OPAL results is performed. Some studies in respect to the future $0\nu\beta\beta$-decay project GENIUS are also presented.Comment: 29 pages, 8 figure