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

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

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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

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 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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Φ=A x 2 + y 2 − 2z2( )

The Basic Penning Trap

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-Q/2

-Q/2

+Q

Magnetized nickel wire wrapped around center measures electron properties

z

x

y

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Electron Motion in the Trap

Three types --> cyclotron, magnetron, and axial motion1. 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

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Fer = mo

ωz2

2

⎛

⎝ ⎜

⎞

⎠ ⎟r;

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ωz

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Fmag = ev

c

⎛

⎝ ⎜

⎞

⎠ ⎟Bo

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⇒ ωc ≡ eBo moc>>ωz

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ωm ≡ δe =ωz

2

2ωc'

=ωc −ωc'

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ωz2 = 4eA

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Electron Motion in the Trap

*Neat Java Applet http://www.particle.kth.se/~fmi/kurs/PhysicsSimulation/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

ATTEN.

A

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φ

INTEGRATOR

~

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ν z

Vo=9.2V

Error Signal

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• 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

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g = 2μ s μb= 2ωsωc

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μsSpin resonance

frequency

Geonium Energy Levels & the g-Factor

n = 0

1

2

3

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ν c

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ν c

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ν a

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ν z

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ν s

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νm

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g = 2ν sν c

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g ≈ 2.000000000110(60)(after removing QED shifts)