Faraday Rotation Theory, Application, and Issues With a neat Tangent Zachary Marshall

Faraday Rotation First noticed in 1845 by Michael Faraday First noticed in 1845 by Michael Faraday Linearly polarized light near resonance travels through a material (esp. alkali metal gas) in a B-Field 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. The B-Field must have a component in the direction of propagation. Polarization rotates 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" 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 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 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 Their different propagation means the linear polarization of light rotates

Again, with Math Zeeman shift changes resonance by g F  0 B z Zeeman shift changes resonance by g F  0 B z  V B L  V B L  n - - n + ) L /  n - - n + ) L /  = C Rb L [alkali] B /  2  = C Rb L [alkali] B /  2 n =  p i c 2 n i n =  p i c 2 n i

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 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) 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 Tunable laser (e.g. Ti:Saph) through the center of a cell

What could possibly go wrong? Optical pumping during measurement Optical pumping during measurement Laser heats the cell interior Laser heats the cell interior Thermal fluctuations in a cell Thermal fluctuations in a cell Remember: What ever can go wrong, will go wrong. But there are ways around each problem. 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). First developed in the 1920’s, credit is usually given to Killian (1926). d(ln P)/dT =  H/(R T 2 ) (Clausius-Clapeyron) d(ln P)/dT =  H/(R T 2 ) (Clausius-Clapeyron) In a small range,  H is temp. invar. In a small range,  H is temp. invar. Resulting equation is of the form Resulting equation is of the form log P = A + B/T Additional terms like C log T, D / T 2 are common Additional terms like C log T, D / T 2 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.” Claimed to be the “only safe method.” But why do we care so much? But why do we care so much?

Pumping Nobel Gasses Rubidium is polarized with circularly polarized laser Rubidium is polarized with circularly polarized laser Collisions transfer spin to Xe / He Collisions transfer spin to Xe / He Nitrogen prevents immediate spin loss Nitrogen prevents immediate spin loss Depolarization comes from collisions Depolarization comes from collisions Rb depolarization term depends on Rb number density 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 Faraday rotation occurs in the interstellar medium due to free electrons  = 2 C * integral of B*n e ds  = 2 C * integral of B*n e ds If we know n e, we can determine B along the path to us. If we know n e, we can determine B along the path to us. Radio waves going through the ionosphere rotate as well. Radio waves going through the ionosphere rotate as well.