Quantum dynamics of non-linear optomechanical systems

This thesis explores the dynamics of optomechanical systems, which use radiation pressure to couple together optical and mechanical modes. Such systems display dynamics ranging from the quantum to the classical, with a variety of applications including ground state cooling and precision measurements. In this thesis two different geometries are presented for such a system in the form of the ‘reflective’ and ‘dispersive’ systems. Different aspects of the dynamics are investigated numerically and analytically. Firstly the reflective system is introduced, which consists of a cavity formed from a fixed and a moveable mirror. The optical frequency of the cavity couples linearly to the moveable mirror’s position. This geometry is explored as the cavity is driven by a laser, revealing a range of dynamical states in the mirror as the drive frequency is varied. An alternative geometry is presented in the form of the dispersive optomechanical system. Two fixed mirrors with a partially transmitting membrane at the centre provide a cavity supporting two optical modes, that couple approximately linearly or quadratically to the membrane position, depending on where the membrane is fixed. The system is explored in both linear and quadratic coupling regimes. Quadratic coupling is explored for a single optical mode by selecting a high tunnelling rate through the membrane. The dynamics of the membrane are explored via a similar set of techniques to those applied to the reflective system. Linear coupling for two optical modes is explored in the regimes of blue and red detuning. First resolved sideband cooling is explored, providing an alternative approach ground state cooling (which has been explored for the reflective case). Finally, strongly driving the system over a range of coupling strengths induces classical behaviour, extending from limit cycle oscillations to chaotic motion