Feedback control for mechanical cooling and squeezing in cavity quantum optomechanics

Cavity optomechanics is a hugely popular research field in which the interaction between photons of light and phonons of mechanical oscillators is studied. It is a promising platform for generating non-classical quantum states at a macroscopic scale and for making devices suitable for photonic quantum computers and quantum communication protocols.
A central challenge in optomechanics is the large amount of noise present in mechanical oscillators at room temperature. In order to be able to observe quantum phenonema, this noise must be eliminated. A well-established method for doing so is feedback cooling, in which a strong probe field interacting with the cavity optomechanical system is used to measure the mechanical position which is then used to apply a feedback force back onto the mechanical oscillator in order to stop its motion, thereby reducing the mechanical noise (quantified by its phonon number) and cooling it down. Such a feedback scheme may also potentially be used to prepare the mechanical oscillator in a squeezed state. In this dissertation, we theoretically investigate two types of feedback cooling schemes.
In one scheme, we use conditional estimation of the quantum state of the optomechanical system to apply feedback using optimal control. We calculate the minimal phonon number and maximum squeezing levels that may be obtained using this feedback scheme. We highlight the inherent difference between the so-called conditional state and unconditional state of the mechanics — a difference which it is often falsely assumed can be brought to zero. We also compare the performance of the scheme under different approximations of the mechanical interaction with its environment and with an adiabatic approximation of the cavity field. Furthermore, we investigate how much the phonon numbers and squeezing levels may be improved using a squeezed probe field.
We also investigate an entirely different feedback scheme, where the output field from the cavity is not measured, but instead sent through a delay line before it is fed back directly into the cavity. This feedback scheme is potentially simpler to set up experimentally. We find that this feedback scheme produces phonon numbers comparable to, but not as low as the previous scheme.
Together, these results pave the way for achieving ground state cooling and squeezing at room temperature in optomechanical systems, which opens the possibility for more interesting quantum information applications.