Nonlinear Microwave Optomechanics

Abstract

The nonlinearity is essential for creation of non-classical states of the cavity or mechanical resonator such as squeezed or cat states. A microwave cavity can be made nonlinear by, for instance, adding Josephson junctions. The mechanical resonator is inherently nonlinear. The radiation pressure interaction between cavity and mechanical resonator is also inherently nonlinear but typically under strong drive of the cavity interaction can be linearized. However, if the optomechanical system is in the strong coupling regime nonlinear quantum effects become observable. These three cases provide the motivation for our studies. We start with backaction analysis of the classical regime of a dc SQUID (superconducting quantum interference device) with an embedded mechanical resonator. Then, we perform quantum analysis to understand how the asymmetry of two Josephson junctions influences the coupling strength of optomechanical interactions such as radiation pressure, cross-Kerr and single-photon beam splitter. Using variational method and self-consistent harmonic approximation we estimate the influence of the radiation pressure coupling and Kerr nonlinearity of the cavity on the effective frequency and dissipation of the cavity. The second part of this thesis focuses on the nonlinearity of the mechanical resonator coupled to the optical/microwave cavity. We study in details the nonlinear optomechanical response and draw the response map to summarize all results of the overcoupled and undercoupled cavity for the red and blue sidebands additionally to the weak and strong drive powers. In the end, w e confirm the developed theory by using it to numerically fit the experimental results.