Zhujing Xu is currently a Postdoctoral Fellow at Harvard University. She received her B.S. in Physics from University of Science and Technology of China in 2016, and her Ph.D. in Physics from Purdue University in 2022. She has worked on levitated optomechanics and solid-state spins, both in experiments and theory from 2016-2018. In 2018, she started to build a vacuum AFM system in the lab to study quantum vacuum fluctuations and demonstrate phonon energy transfer across the vacuum, which is the content of this thesis.