Automatic digital optical heterodyne phase locking loop in the milliradian domain for spaceborne laser interferometry

We developed a digital optical phase locking loop (OPLL) with three advantages, including high precision of phase locking, high control bandwidth up to 2.8 MHz, and automatic laser locking strategy. Spaceborne laser interferometers will be used to measure tiny displacements caused by gravitational waves in millions of kilometers range. A slave laser will be heterodyne phase locked to the incoming weak light at the end of an arm, emitting a higher power light back to the other satellite to measure pathlength variations at the picometer level. Such accuracy requires extremely precise OPLL. We report an experiment to demonstrate a digital OPLL that can automatically lock two independent free-running Nd:YAG lasers with residual phase error below 1mrad/Hz above 0.01 Hz, which is the best performance recorded for digital servos, to our knowledge. Such performance tested under a normal laboratory environment will be highly improved in a vacuum environment with temperature and vibration well controlled. Both the digital OPLL and the automatic strategy were implemented on a field programmable gate array that could be potentially used for future gravitational-wave detection. Our experiment might change the thinking of scientists who study phasemeters of gravitational-wave detection because we are aware that the digital phase locking loop used for "optical phase tracking" is differently designed from "optical phase locking."