The coupling of the motion of two ion species in separate Penning traps via a common tank circuit is discussed. The enhancement of the coupling assisted by the tank circuit is demonstrated by an avoided crossing behavior measurement of the motional modes of two coupled ions. An intermittent laser cooling method for sympathetic cooling is proposed and a theoretical description is provided. The technique enables tuning of the coupling strength between two ion species in separate traps and thus allows for efficient sympathetic cooling of an arbitrary type of single ion for high‐precision Penning‐trap experiments.

We report on the successful demonstration of a novel scheme for detecting optical transitions in highly charged ions. We applied it to determine the frequency of the dipole-forbidden 2p ^{2}P_{1/2}-^{2}P_{3/2} transition in the fine structure of ^{40}Ar^{13+} using a single ion stored in the harmonic potential of a Penning trap. Our measurement scheme does not require detection of fluorescence, instead it makes use of the continuous Stern-Gerlach effect. Our value of 679.216464(4)_{stat}(5)_{syst}  THz is in reasonable agreement with the current best literature values and improves its uncertainty by a factor of 24.

The ideal Penning trap consists of a uniform magnetic field and an electrostatic quadrupole potential. Cylindrically-symmetric deviations thereof are parametrized by the coefficients Bη and Cη, respectively. Relativistic mass-increase aside, the three characteristic eigenfrequencies of a charged particle stored in an ideal Penning trap are independent of the three motional amplitudes. This threefold harmonicity is a highly-coveted virtue for precision experiments that rely on the measurement of at least one eigenfrequency in order to determine fundamental properties of the stored particle, such as its mass. However, higher-order contributions to the ideal fields result in amplitude-dependent frequency-shifts. In turn, these frequency-shifts need to be understood for estimating systematic experimental errors, and eventually for correcting them by means of calibrating the imperfections. The problem of calculating the frequency-shifts caused by small imperfections of a near-ideal trap yields nicely to perturbation theory, producing analytic formulas that are easy to evaluate for the relevant parameters of an experiment. In particular, the frequency-shifts can be understood on physical rather than purely mathematical grounds by considering which terms actually drive them. Based on identifying these terms, we derive general formulas for the first-order frequency-shifts caused by any perturbation parameter Bη or Cη.

The ideal Penning trap consists of a uniform magnetic field and an electrostatic quadrupole potential. In the classical low-energy limit, the three characteristic eigenfrequencies of a charged particle trapped in this configuration do not depend on the amplitudes of the three eigenmotions. No matter how accurate the experimental realization of the ideal Penning trap, its harmonicity is ultimately compromised by special relativity. Using a classical formalism of first-order perturbation theory, we calculate the relativistic frequency-shifts associated with the motional degrees of freedom for a spinless particle stored in an ideal Penning trap, and we compare the results with the simple but surprisingly accurate model of relativistic mass-increase.

The atomic masses of Kr-82,Kr-83 and Xe-131,Xe-134 have been measured using the Florida State Penning trap mass spectrometer with Kr-84,Kr-86 and Xe-129,Xe-132 used as reference masses. The results are M(Kr-82) = 81.913 481 159(9) u, M(Kr-83) = 82.914 126 519(12) u, M(Xe-131) = 130.905 084 137(14) u, and M(Xe-134) = 133.905 393 032(13) u.

The atomic masses of the three most abundant isotopes of strontium, Sr-86,Sr-87,Sr-88, and of the six most abundant isotopes of ytterbium, Yb-170,Yb-171,Yb-172,Yb-173,Yb-174,Yb-176, have been obtained from measurements of cyclotron frequency ratios of pairs of ions simultaneously trapped in a Penning trap. Our results, with one standard deviation uncertainty, are M(Sr-86) = 85.909 260 730 9 (91) u, M(Sr-87) = 86.908 877 497 0 (91) u, M(Sr-88) = 87.905 612 257 1 (97) u, and M(Yb-170) = 169.934 767 241 (18) u, M(Yb-171) = 170.936 331 514 (19) u, M(Yb-172) = 171.936 386 655 (18) u, M(Yb-173) = 172.938 216 213 (18) u, M(Yb-174) = 173.938 867 539 (18) u, M(Yb-176) = 175.942 574 702 (22) u. These results have application to photon-recoil determinations of the fine-structure constant.