Quantum Optics with Nanomechanical and Solid State Systems

This thesis presents theoretical studies in an interfacing field of quantum optics, nanomechanics and mesoscopic solid state physics and proposes new methods for the generation of particular quantum states and quantum state transfer for selected hybrid systems. The first part of this thesis focuses on the quantum limit of a macroscopic object, a nanomechanical resonator. This is studied for two different physical systems. The first one is a nanomechanical beam incorporated in a superconducting circuit, in particular a loop-shaped Cooper pair box (CPB) - circuit. We present a scheme for ground state cooling of the flexural mode of the nanomechanical beam. Via the Lorentz force coupling of the beam motion to circulating CPB-circuit currents, energy is transferred to the CPB qubit which acts as a dissipative two-level system. The cooling process is driven by a detuned gate-voltage drive acting on the CPB. We analyze the cooling force spectrum and present analytical expressions for the cooling rate and final occupation number for a wide parameter regime. In particular, we find that cooling is optimized in a strong drive regime, and we present the necessary conditions for ground-state cooling. In a second system, we investigate the creation of squeezed states of a mechanical oscillator (a vibrating membrane or a movable mirror) in an optomechanical setup. An optical cavity is driven by squeezed light and couples via radiation pressure to the mechanical oscillator, effectively providing a squeezed heat-bath for the mechanical oscillator. Under the conditions of laser cooling to the ground state, we find an efficient transfer of squeezing with roughly 60% of light squeezing conveyed to the mechanical oscillator (on a dB scale). We determine the requirements on the carrier frequency and the bandwidth of squeezed light. Beyond the conditions for ground state cooling, we predict mechanical squashing to be observable in current systems. The second part of the thesis is concerned with the state transfer of an arbitrary quantum state. It is shown that by optimizing the time-dependent interaction between a harmonic oscillator and a transmission line, the oscillator quantum state can be transferred to another oscillator via the transmission line, with a fidelity that is independent of the initial state of both oscillators. For a transfer time T the fidelity approaches 1 exponentially in [gamma] T where [gamma] is a characteristic damping rate. Hence, a good fidelity is achieved even for a transfer time of a few damping times. Possible implementations of the theory are discussed. (author)