Nonreciprocity in various branches of physics has been studied for more than a century, e.g., from classical to quantum mechanics, and from particle to condensed matter. It is particularly interesting to consider nonreciprocal phenomenon in open (non-hermitian) systems. In this dissertation, I use a cryogenic cavity optomechanical system to demonstrate robust nonreciprocal interactions between two phononic resonators. The nonreciprocity, either transient or static, is realized via the cavity mediated optomechanical interaction.
I will start with a pedagogical introduction to nonreciprocity as well as non-hermiticity in physics, followed by a brief review of optomechanics and a theoretical derivation of the nonreciprocity in optomechanical systems. Then I will introduce our experimental realization of the optomechanical system, i.e., the membrane-in-the-middle setup. Next I will present the main result of this dissertation, which includes the experimental demonstration of both transient and static optomechanical nonreciprocity. I will conclude with a discussion of our on-going study of high order exceptional points (the degeneracy in multi-level open systems).