Constructing a Linear Paul Trap System for Measuring Time-variation of the Electron-Proton Mass Ratio

Attempts at quantum theories of gravity as well as tantalizing astrophysics results suggest a need to examine the stability of fundamental constants with respect to position and time. We have chosen to investigate time-variation of the electron-proton mass ratio (μ), as this dimensionless number is critical to our understanding of fundamental interactions. We plan to observe shifts in certain energy levels sensitive to temporal changes of μ in a molecular ion, possibly O2 , via quantum logic spectroscopy. This technique requires co-trapping the molecular ion with an atomic ion, specifically Be in our proposed experiment. Trapping of the ions gives us very long interrogation time and thus higher precision through the frequency–time uncertainty relation. Quantum logic spectroscopy allows us to sympathetically cool the molecular ion with the atomic ion as well as to prepare and detect its internal states, which are more sensitive to changes of μ. Our proposed experiment, therefore, allows us to not only extract dμ/dt from changes in the frequencies of certain transitions in the molecular ion but also to develop a high-precision spectroscopy method using molecules. This thesis focuses on building the linear Paul trap system that will co-trap the two ions in an approximately harmonic potential well. We have designed and constructed the trap electrodes and are in the process of putting the rest of the system together. We also provide some preliminary designs, which include a procedure and instrumentation to create ultra-high vacuum, circuits for the signals to the trap electrodes, and optics for imaging the trapped ions. Some of these designs are ready for actual construction and assembling of the apparatus; others, for which we have offered our thoughts and questions, need more polishing. Besides designs for the hardware, we also present the motivations behind our experimental goals and the methods to achieve them so that future generations of thesis writers can keep their eyes on the prize and continue to work towards it.