Squeezing Enhancement and Adiabatic Elimination in Quantum Feedback Networks

Abstract

Classical feedback control and system theory are playing an important role in modelling, controlling and analysing complex devices in many branches of engineering. Recent developments like quantum computers and miniaturisation of existing applications and devices are increasing the importance of the ability to control systems with quantum effects. Efforts have been made recently to extent the simplicity and power of the language of classical control theory to quantum mechanical systems. Within this framework of “Quantum Feedback Networks” we are investigating two problems. The first problem concerns the enhancement of squeezed states. It has been observed that the squeezing effect of squeezing devices can be enhancement by measurement based feedback techniques or use of optical cavities. We are investigating the possibility of feedback enhanced squeezing using coherent feedback control. Considered is a static ideal squeezing devices interacting with a single mode cavity undergoing coherent feedback using a beam splitter. We show that the overall squeezing of the output depends on the beam-splitter’s reflectivity and that we are thus able to enhance the squeezing by choosing an appropriate configuration of the beam-splitter. In the second part we investigate the question of compatibility of a rigorous approach to the adiabatic elimination of some degrees of freedom of a quantum mechanical systems and instantaneous feed-forward and feedback limits for quantum mechanical networks. The commutativity of both limits is not obvious but frequently assumed in quantum optics. We show that both limit procedures are instances of Schur complements and prove the commutativity of both limits by generalising a statement about successive Schur complements.

Date of Award	07 Jun 2013
Original language	English
Awarding Institution	Aberystwyth University
Supervisor	John Gough (Supervisor) & Rolf Gohm (Supervisor)