Sub-Picometer Distance Measurement for Testing the Equivalence Principle

Two Semiconductor Laser Tracking Frequency laser distance Gauges (SL-TFGs) now reside at IIT and will be used in the muonium gravity experiment. A TFG measures distances from a few cm to many meters with an accuracy of 0.04 picometers (4 x 10^-14 m) in an averaging time of 30 s. We invented the TFG at the Center for Astrophysics (CfA) for a microarcsecond astrometric interferometer concept that we were developing. We needed to overcome the nm-scale cyclic bias of the standard precision laser gauge. We subsequently realized that the TFG enabled an improved ground-based test of the equivalence principle, which we concluded could be refined to test the differential acceleration of two test substances to an accuracy of 5 x 10^-14 g. We then designed (but did not fly) an equivalence principle test on a sounding rocket that would have achieved an accuracy of 1 x 10^-17 g. The SL-TFG is an updated version of the original TFG that employs telecommunications lasers and modulators.

To measure distance with the TFG, an interferometer having length L_1 is established using reflecting endpoints. A laser is locked to the interferometer. When L_1 changes, the laser’s optical frequency changes. To measure optical frequency, the laser is heterodyned against a second laser. The second laser is locked to a measurement interferometer or a reference cavity of length L_2. Optical frequency is converted to an easily measured radio frequency that is proportional to L_2 – L_1. Each TFG requires a measurement interferometer, a Variable Frequency Source, and a Controller, plus a photodetector and frequency counter for the heterodyne signal.

Phillips will briefly describe the history of the TFG and its application to the CfA and IIT equivalence principle tests, then describe the operation of the TFG in some detail.

(Phillips is now retired from the Harvard-Smithsonian Center for Astrophysics and is doing freelance consulting.)