Geonium A Fake but Useful Atom BoBo

Overview What is Geonium and why is it useful? A little bit of history What is a Penning trap? Penning trap components and diagram Measurement Techniques Overview of the g-Factor Useful Results

What is Geonium and Why is it Useful? Not an actual atom! A single electron (or positron) confined inside of a Penning trap Called “Geonium” because it is essentially an electron bound to the earth Can measure g-factor and electron radius to great precision e-e-

Some History Hans Dehmelt of the University of Washington first quasi-permanently trapped an electron in 1973 after 17 years of work On October 12, 1989 he and Wolfgang Paul of Bonn University receive the Nobel Prize for Physics for their work on isolating individual electrons and ions and making exact measurements of them

What is a Penning Trap? Predecessor in measuring electron magnetic moment and g-factor: electrons stored in the field of a positive-ion cloud diffusing in a dense inert gas, polarized by spin- exchange collisions with optically polarized sodium vapor and depolarized by magnetic resonance Problem: too many electrons Solution: the Penning trap replaces the space-charge field with a high-vacuum quadrupole trap and the alkali vapor with an atomic beam. (Liquid Helium Temperatures ~4K) Benefit: using the Penning trap, a single electron can be confined near the axis for many months!

Penning Trap Components Top and bottom conducting caps have charge -Q/2 and center tube has charge +Q --> quadrupolar electrostatic field described by scalar potential: Uniform magnetic field B o along the z-axis Magnetized nickel wire around the center of the electrode creates “bottle field” used to measure properties of trapped electron

The Basic Penning Trap -Q/2 +Q Magnetized nickel wire wrapped around center measures electron properties z x y

Electron Motion in the Trap Three types --> cyclotron, magnetron, and axial motion 1.Axial: electron moves along the symmetry axis of the trap (z) changing directions with sinusoidal frequency as it gets too close to the charged caps (A>0, same constant as potential) 2.Cyclotron: small circular orbits resulting from the opposition between the radial electric and centripetal magnetic forces 3.Magnetron: Slow drift around the symmetry axis

Electron Motion in the Trap *Neat Java Applet

Measurement The axial frequency is at radio/television range, acting like an LC oscillator, so a reference signal can be used and adjusted to see both the absorption and dispersion modes of the axial resonator ATTEN. A INTEGRATOR ~ V o =9.2V Error Signal

The electron spin g-factor or gyromagnetic ratio is the ratio of the magnetic dipole moment to the mechanical angular momentum of a system Contributes to Zeeman effect and thus can be calculated from spectral lines Can be used to find magnetic moment The g-Factor Spin resonance frequency

Geonium Energy Levels & the g-Factor n = (after removing QED shifts)