Topological transport and quantum estimation theory in optomechanical systems

Abstract

This thesis focuses on optomechanics, which is the physical description of the force that the electromagnetic radiation exerts on a reflective object. The particles involved are so tiny that a quantum mechanical description is needed. Optomechanics is the median force between a quantum mechanical oscillator and a quanta of light. Hence, it has the potential to assume a major role in future technologies. Quantum transport has been extensively studied in the last few decades, and still offer an important substrate for emerging technologies. In this thesis we studied quantum transport and applied it to a one dimensional system of both bosonic and fermionic particles. We obtained quasi perfect many body transfer. One hurdle from obtaining perfect transfer is due to the opposite possible directions of propagation inside the system. A way to overcome this issue is offered by means of topological insulators, materials which allow unidirectional propagation. We aim to exploit optomechanics in order to transport excitations in a robust way. We engineered an array of microresonators which has the property of a topological insulator and where the mechanical motion spreads into the material in one way only. From an experimental point of view, the realization of this kind of mechanical topological insulator requires a good knowledge of the optomecanical coupling strength. Therefore we used quantum estimation theory to understand which is the best measurement that will lead to an optimal estimation of the optomechanical coupling constant. This will play an important role for cutting-edge technology and applications in communication, phonon-based information storage and signal-processing devices.