Mass Spectroscopy Using Single Ion Cyclotron Resonance

An inhomogeneous radio fquency electric field can couple the cyclotron and axid modes of a single icn in a Penning trap. The classical equations of motion are the same as those of a driven quantum mechanical two-level system. We discuss an analog of the A-pulse, which can exchange mode actions, and an analog of avoided crossing. Experimental illustrations are presented. PACS: 07.75.+h, 46.10.+z, 41.70.+t, 32.90.+a Submitted to Phys. Rev. A In experiments to perform precise resonance measurements on single charged particles in a Penning trap[VSD87,VMF88,CWB89], only one of the particle's normal mode motions is typically detected directly. For example, in our recent single ion cyclotron resonance experiment[CWB89,WLB88], only the axial mode couples to our detector. The cyclotron and the magnetron modes are undetected and essentially undamped. Cooling, driving and measuring the frequency of the undetected modes require techniques for coupling them to the detected mode. Wineland and Dehmelt[WID75] suggested that an inhomogeneous rf electric field at the sum or difference frequency of two modes will couple those modes, and that in particular the magnetron mode can be cooled by coupling it to the damped axial mode. The technique was demonstrated experimentally by Van Dyck, Schwinberg, and RQG DehmeltwSD78], Cohen-Tannoudji[COH84] and Brown and Gabrielse[86] discuss rf coupling fields in some generality and kgor. In this paper we develop two particular effects of such coupling fields, using an analogy with a two-state quantum mechanical system to motivate our purely classical results. The data which we present here were taken on an apparatus designed to compare the cycl~aon frequencies of single ions with the eventual goal of measuring ion mass ratios to parts in lo1*. The apparatus, an orthogonally compersated [GAB85], hyperbolic Penning trap in a cryogenic environment is described in references [ C W 8 9 and