Axion-like Dark Matter Detection with Mercury-199 Atoms

Abstract

The objective of this dissertation is to search for axion dark matter through the coupling between the axion field and the electric dipole moment(EDM) of mercury-199 atoms. If the axion is the significant fraction of dark matter, the coupling leads to a time-varying nuclear EDM that oscillates at the frequency proportional to the axion mass, $m_{a}$. We use the data that measures the static EDM of $^{199}Hg$ atoms to look for a simple sinusoidal signal on the top of the static EDM value. The Lomb-Scargle periodogram, as a power spectrum estimator, allows us to analyze our unequally spaced EDM data in time. With two different approaches both with and without error weighting, they give a consistent result on no detection of dark matter. The most significant peak among the four EDM periodograms has a false alarm probability of 31$\%$ calculated with the Bootstrap method. The magnitude of the maximum peak can be generated by injecting a sinusoidal signal with the amplitude of 1.81$\times 10^{-29}$ $e \cdot cm$. The smallest periodic signal our measurement can detect as the maximum peak in the periodogram with 95$\%$ confidence in the frequency range of 0 to 6.17$\times 10^{-4}$ Hz is 2.3$\times 10^{-29}$ $e \cdot cm$. The static EDM of $^{199}Hg$ by itself is an important topic. This thesis will only briefly mention it and mainly cover the parts that are relevant to time-varying EDM analysis.