Macroscopic quantum states in quantum optics

This DPhil will involve proposing new methods for generating macroscopic quantum states and exploring the resilience of these states to interactions with the environment. The work will be theoretical but with a close eye on real world applicability as Jack will be working alongside Michael Vanner at Imperial to apply these results to optomechanical systems.
Defining macroscopicity is a difficult and often controversial task, with many competing measures existing. This work will aim to propose new protocols which maximise the macroscopicity of quantum states with respect to a range of macroscopic measures and non-classicality criteria.
Jack's masters project at Oxford focused on theoretically developing a protocol for generating measurement-induced macroscopic Schrodinger cat states via a multistep procedure in cavity optomechanics. Jack will begin his DPhil by building on this work. Further analysis of the phase-space structure and macroscopicity of these states will allow for the successfulness of the protocol to be properly assessed. This will allow Jack to improve his knowledge and skill set in areas such as quasi-probability distributions, generalised measurements, Krauss operators, decoherence mechanisms, quantum metrology, optomechanics, measures of macroscopicity and programming in Matlab and qutip (Python). All these skills will be necessary to tackle further problems in this area. Initial results indicate that this protocol can produce values of macroscopicity greater than similar existing proposals, even when decoherence and thermal occupation are considered, and so the ideas it introduces will contribute to the long-standing goal of generating quantum phenomena at a macroscopic scale.
A more general problem, not specific to any particular physical set-up, will then be addressed. An input state and a probe system interact through some unitary. What is the best measurement strategy on the probe system in order to maximise the macroscopicity of the output state? A range of coupling hamiltonians, probe states and other constraints will be considered. Knowing which measurement to make on a probe system to enhance a particular macroscopicity measure will be a useful experimental tool and results of this work will be used to devise further protocols for macroscopic state preparation in cavity optomechanics. Jack will be working with Benjamin Yadin on this project who has made significant contributions in the area of macroscopicity.
Many authors have proposed measures of macroscopicity based on non-classical features of quantum states, this work aims to more deeply explore the connection between macroscopicity and non-classical features, and also further investigate how the phase-space features of the states relate to these measures.

This thesis will address key questions in quantum foundations, provide a greater insight into the quantum-to-classical transition and allow for the proposal of more in-depth tabletop experiments that explore the interface between quantum mechanics and gravity; collapse models and different proposals for a theory of quantum gravity will be explored. The further study of macroscopic quantum states in cavity optomechanics will impact the development of weak force sensing technologies and will enable further studies in other areas of quantum optics.