Principles of Gravitational-Wave Interferometry

In February 2016, the first detection of gravitational waves was published, and an entirely new field of astronomy was born.  Gravitational waves are distortions of spacetime caused by the motion of massive astronomical bodies, with strains (changes in length per unit length) on the order of 10^-21 or smaller.   In this Immersion participants will learn to perform undergraduate laboratory experiments that show how gravitational wave interferometers such as the Laser Interferometer Gravitational-Wave Observatory (LIGO) improve upon the basic Michelson-Morley interferometer to reach this remarkable sensitivity.

The Immersion consists of four activities.  The first two demonstrate how “folding” an arm of the interferometer (i.e., causing the light to bounce back and forth multiple times) improves sensitivity to changes in distance.  Participants will construct a Herriott delay line, followed by a Fabry-Perot optical cavity, and observe how each responds to the motion of a mirror.  The third activity provides an analogy to gravitational-wave detection by having the participants detect sound waves from a loudspeaker.  Finally, participants will use phase modulation and the technique of heterodyning to “lock” the optical cavity arm to a resonant condition, so that the laser forms a standing wave in the cavity.

While each activity will have a slightly different setup, the general apparatus is shown below.  A HeNe laser (1) is aligned onto a beamsplitter (2).  The two resulting beams travel in perpendicular directions, reflect off mirrors (3b and 4), and interfere at the beamsplitter.  The resulting interference pattern is detected by a photodiode (7).  So far this is the basic Michelson interferometer setup.  The major difference is a partially-transmissive optic inserted at (3a), creating an optical cavity in one arm. 
 

The schedule of activities is as follows:

Day 1 Morning – Alignment of basic Michelson, demonstration of delay line

Day 1 Afternoon – Characterizing the optical cavity arm

Day 2 Morning – Detecting sound waves

Day 2 Afternoon – Locking the optical cavity to resonance

Day 3 Morning – Bonus activity:  turning an interferometer into a wavelength meter (in which participants will learn how a similar setup can measure the wavelength of a laser to a precision of 0.1 nanometers)

Participants will learn the principles of interference, interferometry, and gravitational-wave detection.  They will gain experience in aligning the interferometer, measuring signals with photodiode and oscilloscope, and using basic electronic circuits to create a feedback loop for optical cavity control.  Most importantly, participants will be able to introduce their students to the new, growing field of gravitational-wave astronomy.

Participants should prepare themselves by learning about interference and the Michelson-Morley experiment, and by reading an American Journal of Physics paper on the lab activities that will be provided.  Participants should feel free to bring whatever notebooks or electronic devices they would like for taking notes and photos.  All necessary equipment will be provided.  We will be using a Class IIIA helium-neon laser, and participants will be alerted to necessary safety precautions. 

The cost of the LIGO analogy lab setups is approximately $3,300 plus optical table.  The bonus activity adds another $1,500, but most of that is for a PASCO 850 Interface, common in many high school and college teaching labs, and any substitute analog-to-digital converter would also work.