Pump-Enhanced Continuous-Wave Magnetometry using Nitrogen-Vacancy Ensembles

Ensembles of nitrogen-vacancy centers in diamond are a highly promising platform for high-sensitivity magnetometry, whose efficacy is often based on efficiently generating and monitoring magnetic-field dependent infrared fluorescence. Here we report on an increased sensing efficiency with the use of a 532-nm resonant confocal cavity and a microwave resonator antenna for measuring the local magnetic noise density using the intrinsic nitrogen-vacancy concentration of a chemical-vapor deposited single-crystal diamond. We measure a near-shot-noise-limited magnetic noise floor of 200 pT/$\sqrt{\text{Hz}}$ spanning a bandwidth up to 159 Hz, and an extracted sensitivity of approximately 3 nT/$\sqrt{\text{Hz}}$, with further enhancement limited by the noise floor of the lock-in amplifier and the laser damage threshold of the optical components. Exploration of the microwave and optical pump-rate parameter space demonstrates a linewidth-narrowing regime reached by virtue of using the optical cavity, allowing an enhanced sensitivity to be achieved, despite an unoptimized collection efficiency of <2 %, and a low nitrogen-vacancy concentration of about 0.2 ppb.Comment: 10 pages and 5 figure

Sensing-Throughput Tradeoff for Interweave Cognitive Radio System: A Deployment-Centric Viewpoint

Secondary access to the licensed spectrum is viable only if interference is avoided at the primary system. In this regard, different paradigms have been conceptualized in the existing literature. Of these, Interweave Systems (ISs) that employ spectrum sensing have been widely investigated. Baseline models investigated in the literature characterize the performance of IS in terms of a sensing-throughput tradeoff, however, this characterization assumes the knowledge of the involved channels at the secondary transmitter, which is unavailable in practice. Motivated by this fact, we establish a novel approach that incorporates channel estimation in the system model, and consequently investigate the impact of imperfect channel estimation on the performance of the IS. More particularly, the variation induced in the detection probability affects the detector's performance at the secondary transmitter, which may result in severe interference at the primary users. In this view, we propose to employ average and outage constraints on the detection probability, in order to capture the performance of the IS. Our analysis reveals that with an appropriate choice of the estimation time determined by the proposed model, the degradation in performance of the IS can be effectively controlled, and subsequently the achievable secondary throughput can be significantly enhanced.Comment: 13 pages, 10 figures, Accepted to be published in IEEE Transactions on Wireless Communication

Phase transitions in the condition number distribution of Gaussian random matrices

We study the statistics of the condition number $\kappa=\lambda_{\mathrm{max}}/\lambda_{\mathrm{min}}$ (the ratio between largest and smallest squared singular values) of $N\times M$ Gaussian random matrices. Using a Coulomb fluid technique, we derive analytically and for large $N$ the cumulative $\mathcal{P}[\kappa<x]$ and tail-cumulative $\mathcal{P}[\kappa>x]$ distributions of $\kappa$. We find that these distributions decay as $\mathcal{P}[\kappa<x]\approx\exp\left(-\beta N^2 \Phi_{-}(x)\right)$ and $\mathcal{P}[\kappa>x]\approx\exp\left(-\beta N \Phi_{+}(x)\right)$, where $\beta$ is the Dyson index of the ensemble. The left and right rate functions $\Phi_{\pm}(x)$ are independent of $\beta$ and calculated exactly for any choice of the rectangularity parameter $\alpha=M/N-1>0$. Interestingly, they show a weak non-analytic behavior at their minimum $\langle\kappa\rangle$ (corresponding to the average condition number), a direct consequence of a phase transition in the associated Coulomb fluid problem. Matching the behavior of the rate functions around $\langle\kappa\rangle$, we determine exactly the scale of typical fluctuations $\sim\mathcal{O}(N^{-2/3})$ and the tails of the limiting distribution of $\kappa$. The analytical results are in excellent agreement with numerical simulations.Comment: 5 pag. + 7 pag. Suppl. Material. 3 Figure

Towards More Precise Survey Photometry for PanSTARRS and LSST: Measuring Directly the Optical Transmission Spectrum of the Atmosphere

Motivated by the recognition that variation in the optical transmission of the atmosphere is probably the main limitation to the precision of ground-based CCD measurements of celestial fluxes, we review the physical processes that attenuate the passage of light through the Earth's atmosphere. The next generation of astronomical surveys, such as PanSTARRS and LSST, will greatly benefit from dedicated apparatus to obtain atmospheric transmission data that can be associated with each survey image. We review and compare various approaches to this measurement problem, including photometry, spectroscopy, and LIDAR. In conjunction with careful measurements of instrumental throughput, atmospheric transmission measurements should allow next-generation imaging surveys to produce photometry of unprecedented precision. Our primary concerns are the real-time determination of aerosol scattering and absorption by water along the line of sight, both of which can vary over the course of a night's observations.Comment: 41 pages, 14 figures. Accepted PAS

Random Subsets of Structured Deterministic Frames have MANOVA Spectra

We draw a random subset of $k$ rows from a frame with $n$ rows (vectors) and $m$ columns (dimensions), where $k$ and $m$ are proportional to $n$. For a variety of important deterministic equiangular tight frames (ETFs) and tight non-ETF frames, we consider the distribution of singular values of the $k$-subset matrix. We observe that for large $n$ they can be precisely described by a known probability distribution -- Wachter's MANOVA spectral distribution, a phenomenon that was previously known only for two types of random frames. In terms of convergence to this limit, the $k$-subset matrix from all these frames is shown to be empirically indistinguishable from the classical MANOVA (Jacobi) random matrix ensemble. Thus empirically the MANOVA ensemble offers a universal description of the spectra of randomly selected $k$-subframes, even those taken from deterministic frames. The same universality phenomena is shown to hold for notable random frames as well. This description enables exact calculations of properties of solutions for systems of linear equations based on a random choice of $k$ frame vectors out of $n$ possible vectors, and has a variety of implications for erasure coding, compressed sensing, and sparse recovery. When the aspect ratio $m/n$ is small, the MANOVA spectrum tends to the well known Marcenko-Pastur distribution of the singular values of a Gaussian matrix, in agreement with previous work on highly redundant frames. Our results are empirical, but they are exhaustive, precise and fully reproducible