Single-Particle Self-Excited Oscillator

Abstract

Electronic feedback is used to self-excite the axial oscillation of a single electron in a Penning trap. Large, stable, easily detected oscillations arise even in an anharmonic potential. Amplitudes are controlled by adjusting the feedback gain, and frequencies can be made nearly independent of amplitude fluctuations. Quantum jump spectroscopy of a perpendicular cyclotron motion reveals the absolute temperature and amplitude of the self-excited oscillation. The possibility to quickly measure parts per billion frequency shifts could open the way to improved measurements of e ÿ , e , p, and p magnetic moments. DOI: 10.1103/PhysRevLett.94.113002 PACS numbers: 32.80.Pj, 12.20.Fv, 42.50.Lc The harmonic motion of an oscillator can be excited and sustained with a driving force derived from its own oscillation. A wide range of macroscopic oscillators are operated as self-excited oscillators (SEOs), from the electromechanical clock [1] and its ubiquitous quartz successors, to the nanomechanical cantilevers used in atomic force microscopes [2] and sensitive electrometers [3]. A microscopic SEO is more difficult to realize because such small signals and driving forces are involved. The possibility of realizing a one-ion SEO in a Paul trap was once discussed [4], and self-driven feedback cooling of a oneelectron oscillator has been realized [5].In this Letter we demonstrate a microscopic, oneparticle SEO for the first time. The axial motion of a single electron suspended in a Penning trap is driven by an electric field derived from the current that its motion induces in an electrical circuit. The principal challenge is in stabilizing the electron's oscillation amplitude, an amplitude measured here using quantum jump spectroscopy of a perpendicular cyclotron motion. The frequency stability and the signal-to-noise ratio allow detection of a five parts in 10 10 frequency shift in a few seconds-a sensitivity that allows the detection of a one-quantum change in the electron cyclotron energy and an electron spin flip. Likely applications are improved measurements of the electron, positron, proton, and antiproton magnetic moments.The oscillation which is self-excited is that of a single electron (charge ÿe and mass m) along the central axis (ẑ) of a cylindrical Penning trap [6] (Fig.

Probing a Single Isolated Electron: New Measurements of the Electron Magnetic Moment and the Fine Structure Constant

“…A change in cyclotron or spin state is revealed byν z shifts (Fig. 18a-b) of a one-electron self-exited oscillator (SEO) [6]. The electron's axial oscillation induces a signal in a resonant circuit that is amplified and fed back to drive the oscillation.…”

“…D'Urso, R. Van Handel, B. Odom and D. Hanneke [6]. The harmonic motion of an oscillator can be excited and sustained with a driving force derived from its own oscillation.…”

“…16a). A one-electron quantum cyclotron [4], cavity-inhibited spontaneous emission [24], a self-excited oscillator (SEO) [6], and a cylindrical Penning trap [1] contribute to the extremely small uncertainty. For the first time, spectroscopy is done with the lowest cyclotron and spin levels of a single electron fully resolved via quantum nondemolition (QND) measurements [4], and a cavity shift of g is directly observed.…”

“…Electronic feedback that self-excites the axial oscillation of a single electron in a Penning trap is used to detect spin flips and one-quantum cyclotron excitations [6]. Large, stable, easily detected oscillations arise even in an anharmonic potential.…”

Towards electron-electron entanglement in Penning traps

“…The magnetic bottle also enables single-shot quantum-non-demolition measurements of one-quantum changes in cyclotron and spin energies, by coupling these to small but detectable shifts in ω z [9].…”