New Value for the Deuteron to Proton Mass Ratio from Precision Measurements of the Cyclotron Frequencies of H+ and D+ 2

This thesis describes the relevant background, process, and results of two measurements of the cyclotron frequency ratio (CFR) of H2+/D+ as measured using a hyperbolic Penning trap, to determine the deuteron-to-proton mass ratio m(d)/m(p). The first of these measurements was done using the "alternating-technique" in which the H2+ and D+ ions are simultaneously trapped, but measured separately, with the ion being measured centered in the trap as the other ion is held in a 2 mm cyclotron orbit before exchanging the positions of the ions to measure the newly centered ion. This measurement resulted in a value of m(d)/m(p) = 1.999 007 501 274(38), which has an uncertainty three times smaller than the current CODATA value. The second measurement detailed in this thesis attempted to improve upon the precision of the first by performing simultaneous measurements of cyclotron frequency on the H2+ and D+ ions. This method, which was developed at MIT and only used for four ion pairs of m/q ~ 30, had not been used in over a decade, and never for light ions such as H2+ and D+. Using this method we obtained a value of m(d)/m(p) = 1.000 007 501 272(9), reducing our uncertainty by a factor of 4 from our previous measurement. Cyclotron frequency ratio measurement using H2+ is complicated by the 20 bound vibrational energy states and over 200 metastable rotational energy states which it can be found in. These energy states shift the mass of the H2+ due to the mass energy relation E=mc^2, and must be accounted for in the precision measurement of the CFR. The vibrational energy states could be observed using the alternating measurement technique and clearly identified using the simultaneous measurement technique. This, to our knowledge, is the first demonstration of observation of quantum excitation through direct mass-measurement. Correction was made for rotational quantum energy to the alternating-technique results by the approximation of mass shift through maximum likelihood estimation using a model of rotational excitation. Increased resolution using the simultaneous measurement technique allowed the fitting of specific rotational states to measurements taken, using the minimization of chi-squared when comparing our data to known rovibrational energy levels, drastically reducing the contribution to uncertainty from rotational quantum excitation.