Quantum Optics

In this chapter we will show how many concepts from quantum optics, such as squeezing, nonclassicality, and quantum entanglement, can be applied to nano-mechanical systems leading to the possibility of realizing the quantized behavior of macroscopic systems [1]. Furthermore, nano-mechanical systems can exhibit a variety of rich nonlinear phenomena as the basic interaction between the nano-mechanical system and the radiation fields is via radiation pressure [2]. This interaction is nonlinear. Thus many nonlinear processes such as electromagnetically induced transparency, optical bistability, and up-conversion of radiation are expected to occur for nano-mechanical systems. Similarly, cavity QED effects such as vacuum Rabi splittings are also expected to occur provided one can design systems such that the interaction of a single photon with the nano-mechanical mirror is large. We note that the work on nano-mechanical systems originated with the discussion of Braginsky and collaborators [3] on how to measure small forces accurately. In this chapter, we will discuss only the fundamental quantum and nonlinear optical effects in nano-mechanical systems interacting with quantized and semiclassical fields.