Development of an Undergraduate Lab to Measure the Zeeman Effect
Matt Guthrie
Advisor: Jacek Borysow
Justification
Absorption
The Zeeman Effect
Measuring the emission spectra of atoms undergoing
stimulated emission encompasses many important
techniques in spectroscopy (and therefore laboratory
techniques and data analysis). I am developing an advanced
undergraduate experiment for measuring the Zeeman Effect
in Cesium vapor with the intent of reinforcing both optical and
quantum mechanical theory normally learned in
undergraduate physics curricula. This experimental
procedure is being developed to compliment a current
experiment designed to measure the hyperfine structure of
Rubidium vapor. The main features of present apparatus are
a (near infrared 780nm) laser diode, a PID laser controller, a
lock-in amplifier, and a Fabry-Pérot interferometer (to
calibrate the laser timing). The new procedure for measuring
the Zeeman Effect will incorporate a strong electromagnet
and a new laser diode (852nm).
Absorption is the term chosen for when an atom absorbs a
photon and enters an excited energy state.
The stimulated emission of the unperturbed Cesium atom (shown
in the Cesium section), in the presence of a uniform magnetic
field, acquires a different Hamiltonian (describing the total energy
of the system.
Cesium
Cesium can absorb a photon from the ground state.
Cesium is excited by light with a wavelength of 852 nm.
(μ is the magnetic moment of the valence electron). The
perturbed Hamiltonian gives rise to the splitting of emission
lines, shown in the following figure.
A typical senior undergraduate physics teaching laboratory will
already have most of the equipment necessary to perform this
experiment.
The central (and most expensive) parts of the experiment are the
lock-in amplifier, the laser mount (and temperature and current
controllers), the Fabry-Pérot interferometer, a large magnet, and the
spectrum analyzer controller.
In addition to these relatively common pieces of laboratory equipment,
an experiment examining the Zeeman effect in Cesium will require
only three additional pieces of equipment. These are:
1. The vial of Cesium
2. A new laser diode
The Cesium is the most expensive of these items, running about
$500 for a vial (from Thorlabs). Any magnet can be used (which are
quite common in a physics laboratory), as long as it provides a
uniform magnetic field for the length of the vial of Cesium. A laser
diode emitting with a wavelength of 852 nm can be found for as low
as $14 (again from Thorlabs).
Spontaneous Emission
An atom in an excited state is in an unstable equilibrium. The
atom relaxes from the excited state by emitting a photon with an
energy equal to the difference in energies of the two states.
Keeping these things in mind, the combined cost of new materials is
less than $600, which is relatively modest for a physics laboratory
experiment.
Diode Lasers
The main difference between examining the hyperfine structure of
Rubidium and examining the Zeeman effect in Cesium is the
requirement of the frequency of laser used for stimulated
emission.
This experiment examines the change in the emission spectrum
of Cesium.
Cost Analysis
Stimulated Emission
For the purposes of this experiment, it is necessary to control the
absorption and emission of the Cesium atoms.
Stimulated emission is the induced absorption and spontaneous
emission of an atom. A controlled light source incident on the
atom causes it to jump to an excited state. While in the excited
state, another photon comes and perturbs the atom which causes
it to relax into a lower energy state and emit a photon.
The laser diode used for examining the Zeeman effect is a diode
laser with a wavelength of 852 nm. The current diode used has
an extremely large divergence angle (~10° from the normal) and
must be collimated before being used for stimulated emission.
Experimental Setup
References and Contact Information
I would first like to acknowledge Michigan Technological
University’s Physics department for consistently funding my
research interests.
I would also like to acknowledge Michigan Technological
University for consistently taking my money.
The figure illustrating the Zeeman effect is from
http://faculty.gvsu.edu/majumdak/public_html/OnlineMaterials/ModPhys/QM/Quantum3d_part2.htm
The pictures I used for the explanation of absorption and
emission were taken from the website of two students at the
University of Twente (in the Netherlands). Their website is located
at http://physics.schooltool.nl/quantumoptics/.
Figures in the Cesium section were taken from Wikipedia.
The emission spectrum of unperturbed Cesium was given to me
from my advisor..
Matt Guthrie
200 2nd St.
Houghton, MI 49931
Magnet
Reference
Department of Physics
Attn: Matt Guthrie
Michigan Technological University
1400 Townsend Dr.
Houghton, MI 49931