Cavity Optomechanics With A Bose-Einstein Condensate

Cavity optomechanics is currently the focus of extensive theoretical and ex-perimental investigations and has witnessed spectacular advances in the last few years. An impressive progress was the demonstration of optomechanics effects in situations where the radiation-pressure-driven mechanical oscillator is replaced by a Bose-Einstein condensate. In this thesis I present a hybrid optomechanical system consisting of a BEC trapped inside a single-mode optical cavity with a moving end mirror. This system opens the way to the exploration of a completely new regime of interaction among light, ultracold atoms, and quantum-mechanical nanostructures. I particularly focus on two regime of the interaction between the condensate and the cavity.In collective-dispersive-weak couping regime, the cavity-induced dipole forces provide an optical lattice potential which is collectively sensed by the condensate, but the retro-action of the condensate as a dispersive medium on the cavity field is negligible. Due to the radiation pressure, the lattice depth dynamically depends on the position of the moving mirror, causing a bistable quantum many-body ground state, super-fluid state or Mott-insulator state, of the condensate. We predict a bistable quantum phase transition in this state when the optomechan-ical cavity controlled by a time-dependent input field, and focus on the atomic dynamics following discontinuous jumps of the lattice depth.In collective-dispersive-strong couping regime, the intra-cavity light field has a dual role:it excites a momentum side mode of the condensate which is formally identical with a mechanical oscillator, and acts as a nonlinear spring that couples this oscillator to the moving mirror. We present the dynamics in a regime where the intra-cavity optical field, the mirror, and the side-mode excitation all display bistable behavior. In this regime we find that the classical dynamics of the system exhibits Hamiltonian chaos for appropriate initial condition. We also analyze the quantum correlation between the mirror and the side-mode excitation, predict the possibility of creating a robust entanglement between them in frequency domain.