Precision Measurements of the Linearity of Quantum Mechanics and Spin-Gravity Coupling in Mercury Using Optical Pumping Techniques.

This dissertation describes the use of optical pumping techniques in Hg vapor to perform three precision measurements. 1. The nonlinear quantum mechanical parameter, epsilon/h proposed by Stephen Weinberg, was measured and found to be less than 3.8mu Hz. This corresponds to 2.0 times 10^{-20} eV = 2.0 times 10^{ -27} of the binding energy per nucleon. ^{201}Hg (I = 3/2) was optically pumped using a ^{198 }Hg lamp and made to precess at different cone angles, changing the relative populations of the four atomic ground states. A shift in the precision frequencies was measured as a function of the relative populations to set a limit on epsilon.. 2. The spin-dependent component of the gravitational energy in Hg was measured by optically pumping ^{199}Hg and ^ {201}Hg~ultaneously with a ^{204}Hg lamp and causing them to precess. The ratio of Larmor frequencies was measured for two orientations of magnetic field with respect to gravity and the difference was taken to set a limit on the absolute energy difference. This difference was found to be less than 10^{-21} eV. This corresponds to a limit for a scalar-pseudoscalar coupling, such as that for an axion, of 3.4 times rm10^{-10}kg^ {-1} for D(^{199} Hg, ^{201}Hg) and 1.6 times rm10^ {-10}kg^{-1} for D(neutron) ({rm D}equiv(g_{p })_1(g_{s})_2/8pi hbar m_1c).. 3. The g-factor ratio of ^ {199}Hg and ^{201}Hg was determined to be.369139295(36). ^{199}Hg and ^{201 }Hg were optically pumped and made to precess at a relatively high rate to attain a high precision in the frequency ratios. The resulting signal was then fourier transformed and fit in frequency space. The frequency ratios were plotted as a function of light level and extrapolated to obtain a value at zero light level.