Transcript Faraday Rotation - The Budker Group

Faraday Rotation
Theory, Application, and Issues
With a neat Tangent
Zachary Marshall
Faraday Rotation





First noticed in 1845 by Michael Faraday
Linearly polarized light near resonance
travels through a material (esp. alkali
metal gas) in a B-Field
The B-Field must have a component in
the direction of propagation.
Polarization rotates
He wrote in his notebook, "I have at last
succeeded in illuminating a magnetic
curve or line of force and in magnetising
a ray of light"
Some Hand Waving
Applied magnetic field creates Zeeman
splitting of energy levels
 LHC and RHC polarized light see different
scattering cross-sections, so different refractive
indices, and so have different phase velocities
 Their different propagation means the linear
polarization of light rotates

Again, with Math
Zeeman shift changes resonance by gFm0Bz
 Dq = V B L
 Dq = p (n- - n+) L / l
 Dq = CRb L [alkali] B / Dl2
 n = S pi c2 ni

Faraday Rotator / Isolator
Optical element rotating the polarization of
light
 Polarizer - Faraday Rotator – Polarizer
 Prevents contamination and “backsplash” of
electromagnetic waves
 Common materials for use in 700-1100 nm
range: terbium doped borosillicate glass and
terbium gallium garnet crystal (TGG).
 They can be magnetized before hand.

For Measuring Number Density


Cell filled with a gas, at least some of which is
an alkali metal (usually below its boiling point)
Tunable laser (e.g. Ti:Saph) through the center
of a cell
What could possibly go wrong?
Optical pumping during measurement
 Laser heats the cell interior


Thermal fluctuations in a cell

Remember: What ever can go wrong, will
go wrong. But there are ways around
each problem.
How else could we find
[Rb]?
Here comes the thermo…
Killian Equations
First developed in the 1920’s, credit is usually
given to Killian (1926).
 d(ln P)/dT = DH/(R T2) (Clausius-Clapeyron)
 In a small range, DH is temp. invar.
 Resulting equation is of the form
log P = A + B/T
 Additional terms like C log T, D / T2 are
common

So What are A and B for Rb?
And what did they get?
Faraday to the Rescue?

Claimed to be the “only safe method.”

But why do we care so much?
Pumping Nobel Gasses
Rubidium is polarized with circularly polarized
laser
 Collisions transfer spin to Xe / He
 Nitrogen prevents immediate spin loss
 Depolarization comes from collisions
 Rb depolarization term
depends on Rb number
density

He-3 Lung Image
And Some Secret Projects…
And in Space
Faraday rotation occurs in the interstellar
medium due to free electrons
 Dq = l2 C * integral of B*ne ds
 If we know ne, we can determine B along
the path to us.


Radio waves going through the
ionosphere rotate as well.