Analytical and statistical models for laboratory and astrophysical precision measurements

Abstract

The first detection of gravitational waves (GW) by the Laser Interferometer Gravitational wave Detector (LIGO) ushered in a new era of cosmic exploration and with it came a plethora of new ideas and theories. One such idea includes a proposal to use space-based optical lattice atomic clocks as GW detectors. We propose a GW detector comprised of two free falling strontium-87 optical lattice clocks locked together by a single optical baseline. The two clocks will measure Doppler shifts induced in the two satellites by an incident GW in the transverse direction. Using a series of dynamical decoupling (DD) control sequences, we outline a frequency-tunable, narrowband sensor capable of detecting coherent GW sources such as binary inspirals and mergers of black holes and neutron stars. Furthermore, the tunability of the DD sequences allow for the continuous observation of such sources, bridging the gap between space-based detectors such as Laser Interferometer Space Antenna (LISA) and ground-based detectors.

Another important area of research in astrophysics is the search for habitable exoplanets. However, radial velocity (RV) searches for Earth-mass exoplanets in the habitable zone around Sun-like stars are limited by the effects of stellar variability on the host star. In particular, suppression of convective blueshift and brightness inhomogeneities due to photospheric faculae/plage and starspots are the dominant contribution to the variability of such stellar RVs. Gaussian process (GP) regression is a powerful tool for modeling these quasi-periodic variations. We investigate the limits of this technique using 800 days of RVs from the solar telescope on the HARPS-N spectrograph. These data provide a well-sampled time series of stellar RV variations. Into this data set, we inject Keplerian signals with periods between 100 and 500 days and amplitudes between 0.6 and 2.4 m/s. We use GP regression to fit the resulting RVs and determine the statistical significance of recovered periods and amplitudes. We then generate synthetic RVs with the same covariance properties as the solar data to determine a lower bound on the observational baseline necessary to detect low-mass planets in Venus-like orbits around a Sun-like star. Our simulations show that discovering such planets using current-generation spectrographs and GP regression will require more than 12 years of densely sampled RV observations. Furthermore, even with a perfect model of stellar variability, discovering a true exo-Venus with current instruments would take over 15 years. Therefore, next-generation spectrographs and better models of stellar variability are required for detection of such planets.

Because the Sun is not a point source, corrections must be made to the solar telescope RVs that are not necessary for normal exoplanet searches. One such correction is the differential extinction that the top and bottom halves of the Sun experience as they traverse through the Earth's atmosphere. As the top half of the Sun will traverse less of the atmosphere than the bottom half, it will experience less atmospheric scattering and absorption and thus will appear brighter relative to the bottom half. In addition, the rotation axis of the Sun is in general not ideally aligned and consequently the red shifted hemisphere will experience a different amount of extinction than the blue shifted hemisphere, resulting in a systematic RV shift that needs correction. We derive here the correction needed as a function of wavelength and fit this expression to the solar telescope RV data. We show that insufficient SNR exists to make a wavelength dependent correction. Thus we derive the wavelength independent differential atmospheric extinction correction used in the GP regression analysis described above.

Finally, we demonstrate the usefulness of statistical modeling in the world of precision measurements using quantum defects in diamond. The field of integrated circuit (IC) security is interested in non-invasive measurements of IC functionality. We employ the use of substitutional nitrogen-vacancy (NV) defects in the diamond crystal lattice as a high sensitivity, high spatial resolution magnetic field imager. This quantum diamond microscope (QDM) measures the magnetic fields emanating from IC circuit activity and produces a high resolution magnetic field image over a wide field of view (4 by 4 mm). The device under test is chosen as a Xylinx, Artix-7 field programmable gate array (FPGA), which is programmed to activate a user-controlled number of ring oscillators (RO). We take over 1000 magnetic field images of varying numbers of ROs, and use machine learning to automatically predict the number of ROs active given the resulting images. We first use principal component analysis (PCA) as a dimensionality reduction tool, reducing the 100k pixels to just 9 PCA scores. These scores are then fed into a support vector machine (SVM) classifier to predict the number of ROs for each image. We report a prediction accuracy of 89% overall with perfect prediction for large numbers of ROs. We repeat this process for an FPGA that has had the plastic casing etched away in order to place the diamond as close to the silicon die as possible. We show that the improved spatial resolution of the magnetic fields leads to perfect prediction accuracy for even single ROs. These results suggest the use of QDMs and machine learning as a promising way forward in the field IC security.