Theoretical Studies On Electromagnetically Induced Transparency And Related Effects In Cavity Optomechanical Systems

In the past decades, lots of researches based on cavity optomechanical sys-tems have arisen due to their important applications on precision measurement and high-precision sensors, for example, Casimir force measurement, cooling mechan-ical resonators to their ground state of motion, strong coupling regime between mechanical resonators and cavity fields and so on. Besides, because the sizes and mass of mechanical elements are in transition range from nanometer to micro-scope even macro-scope, cavity optomechanical systems have also been exploit-ed as a tool to test and control quantum properties of macroscopic objects, and promote the understanding of fundamental principle of quantum mechanics, e.g., preparing mechanical squeezed states and macroscopic superposition states, creat-ing optomechanical entanglement between mechanical resonators and cavity fields and so on. In this thesis, we mainly study some quantum nonlinear effects in cavity optomechanical systems, especially electromagnetically induced transparency and related phenomena. These phenomena can be realized by prominently enhanced resonant nonlinearity from quantum interference between different transition path-s. The main content is as follows:1. We introduce and summarize three different effects of electromagnetically induced transparency in A-type atomic media, linearly coupled cavity optomechan-ical systems and quadratically coupled cavity optomechanical systems via some analytical methods such as probability amplitude equations, Heisenberg-Langevin equations and tiny-disturbance method, etc. We also make corresponding physical interpretation for these three effects in dressed state theory, dark state theory and anti-Stokes scattering. In addition, we do compare between them and find out the differences in initial conditions, physical reasons and graphical characteristics, etc. 2. We study the effect of a two-level atomic ensemble on electromagnetically induced transparency in a quadratically coupled optomechanical system under the conditions of large atom-number limit and low-excitation case. We firstly acquire probe-field transmission by solving system’s Heisenberg-Langevin equations in steady-state case and input-output relation. Then we find variation tendency of four parameters relative to electromagnetically induced transparency by analytical expression with an atomic medium being, and find out the dominant parameter via numerical methods, and consequently we discover main effects of atomic media on electromagnetically induced transparency in this system.3. We theoretically investigate the slow-light phenomenon in a quadratically coupled cavity optomechanical system. We work out transmission group delay of probe field which is generated due to rapid phase dispersion induced by electro-magnetically induced transparency effect. By analysis and numerical examination we find the slow light via quadratic coupling has many differences from linear cou-pling cases, and its underlying physical process involves a two-phonon process. We also prove that in quadratically coupled optomechanical systems, almost all phonon energy are from membrane’s oscillation caused by environment tempera-ture, and environment temperature and coupling field power are two indispensable elements in nonlinear coherence. So the slow light can also be tuned by environ-ment temperature besides coupling field power in this system. In addition, the slow light can be realized in an extensive range of parameters even at high temperature, e.g.,200K.In summary, this thesis may be helpful to deepen understanding of quantum properties of macroscopic objects and know some quantum nonlinear effects in hybrid systems. These studies also may be with some reference value for the researches and applications of quantum optics, nonlinear optics and precision measurement, etc.