Significant advances in Penning trap measurements of atomic masses and mass ratios of the proton, deuteron, triton, helion, and alpha-particle have occurred in the last five years. These include a measurement of the mass of the deuteron against 12C with 8.5 x 10-12 fractional uncertainty; resolution of vibrational levels of H2+ as mass and the application of a simultaneous measurement technique to the H2+/D+ cyclotron frequency ratio, yielding a deuteron-proton mass ratio at 5 x 10-12; new measurements of HD+/3He+, HD+/T+ and T+/3He+ leading to a tritium beta-decay Q-value with an uncertainty of 22 meV, and atomic masses of the helion and triton at 13 x 10-12; and a new measurement of the mass of the alpha-particle against 12C at 12 x 10-12. Some of these results are in strong disagreement with previous literature values. Their impact in determining a precise proton/electron mass ratio and electron atomic mass from spectroscopy of the HD+ molecular ion is also discussed.

We firstly discuss classical stability for a dynamical system of two ions levitated in a 3D Radio-Frequency (RF) trap, assimilated with two coupled oscillators. We obtain the solutions of the coupled system of equations that characterizes the associated dynamics. In addition, we supply the modes of oscillation and demonstrate the weak coupling condition is inappropriate in practice, while for collective modes of motion (and strong coupling) only a peak of the mass can be detected. Phase portraits and power spectra are employed to illustrate how the trajectory executes quasiperiodic motion on the surface of torus, namely a Kolmogorov-Arnold-Moser (KAM) torus. In an attempt to better describe dynamical stability of the system, we introduce a model that characterizes dynamical stability and the critical points based on the Hessian matrix approach. The model is then applied to investigate quantum dynamics for many-body systems consisting of identical ions, levitated in 2D and 3D ion traps. Finally, the same model is applied to the case of a combined 3D Quadrupole Ion Trap (QIT) with axial symmetry, for which we obtain the associated Hamilton function. The ion distribution can be described by means of numerical modeling, based on the Hamilton function we assign to the system. The approach we introduce is effective to infer the parameters of distinct types of traps by applying a unitary and coherent method, and especially for identifying equilibrium configurations, of large interest for ion crystals or quantum logic.

I extend earlier work that derived a Born rule for nuclear-decay cloud chamber tracks (Mott problem) without invoking quantum measurement axioms. The key ingredient there was the identification of sites at which the cross section for ionization by a passing charged particle is singular at ionization threshold. This singularity arose from a Penning-like process involving molecular polarization in sub-critical vapor clusters. In the present paper, I propose a simple experiment to determine if similar ionization physics takes place in the mica window of a Geiger counter and drives the collimation of spherically-symmetric wavefunctions outside the counter tube into ion tracks inside. The experiment measures the count rate from a radioactive point source as a function of source-window separation. I have performed a proof-of-concept of this experiment; results are consistent with the singular-ionization picture. I consider implications for the Stern-Gerlach experiment and superconducting qubits. I detail further work required to flesh out these results more rigorously.