Direct Measurement of the Free Cyclotron Frequency of a Single Particle in a Penning Trap

A measurement scheme for the direct determination of the free cyclotron frequency ${\nu }_c$ of a single particle stored in a Penning trap is described. The method is based on the dressed states of mode coupling. In this novel measurement scheme both radial modes of the single trapped particle are simultaneously coupled to the axial oscillation mode.

Figure 1

Schematic of the Penning trap experiment. The direction of the magnetic field $B$ is indicated by the bold black arrow. The trap consists of five cylindrical electrodes. A shielded transmission line guides the rf drives to a radially segmented trap electrode. A plan view of the segmented electrode is shown below the trap electrodes. The axial detection inductor is connected to another trap electrode.

Figure 2

(a) One single proton in thermal equilibrium with the axial detector. (b) Linewidth $\Delta {\nu }_z$ of the axial dip as a function of the number of protons.

Figure 3

(a) Single proton on resonance with the axial detection system. The “double-dip” spectrum (filled squares) was recorded while a sideband drive was irradiated. The single dip (filled circles) is recorded without sideband drive. (b) “Classical avoided crossing.” For details see text

Figure 4

(a) The principle for the simultaneous determination of all eigenfrequencies of a trapped proton is based on double-dressed states. The axial mode is first dressed with the cyclotron mode. Both cyclotron-dressed states are then coupled to the magnetron mode, which results in four double-dressed states. (b) Experimental result of a double dressing. Applying three rf drives to the trap, both radial modes are simultaneously coupled to the axial mode, which results in a quadruple dip.

Figure 5

This quintuple-dip spectrum was recorded in one measurement and carries all information of the eigenfrequencies of the trapped proton, and thus the free cyclotron frequency ${\nu }_c$.