Geonium A Fake but Useful Atom

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GeoniumA Fake but Useful Atom
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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

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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-
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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

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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!

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Penning Trap Components

• Top and bottom conducting caps have charge -Q/2
  and center tube has charge Q --gt quadrupolar
  electrostatic field described by scalar
  potential
• Uniform magnetic field Bo along the z-axis
• Magnetized nickel wire around the center of the
  electrode creates bottle field used to measure
  properties of trapped electron

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

• Three types --gt cyclotron, magnetron, and axial
  motion
• 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 (Agt0, same constant as potential)
• Cyclotron small circular orbits resulting from
  the opposition between the radial electric and
  centripetal magnetic forces
• Magnetron Slow drift around the symmetry axis

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Electron Motion in the Trap

• Neat Java Applet
• http//www.particle.kth.se/fmi/kurs/PhysicsSi
  mulation/Lectures/01B/

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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

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The g-Factor

• 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

Spin resonance frequency
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Geonium Energy Levels the g-Factor
(after removing QED shifts)