Quantum theory of the Penning trap: an exploration of the low temperature regime

The objective of this thesis is to develop the quantum theory of the motional degrees of freedom of a charged particle in a Penning trap. The theory is treated within the formalism of quantum optics, and explores the use of dressed-atom methods by exploiting the threefold SU(N) algebraic structure of the problem. The quantum form of the experimental techniques of sideband coupling and driving to the ultra-elliptical regime are examined in this context, and resulting future applications considered. Interpretation of the quantum dynamics of the separate x and y motions of an electron is discussed, motivated by the desire to modify the trapping potential without changing the basic experimental configuration. A detailed discussion of operator methods which exploit the algebraic structure of the problem is given. This results in a clearer understanding of the physical manifestations of a range of unitary transformations upon a general three-dimensional system, and a novel interpretation of the mapping between canonical angular momentum components of isotropic and anisotropic trapping systems. The results highly promote future use of these methods in Penning trap theory, detailing a robust formulation of unitary operations which can be used to prepare the quantum state of a charged particle. The majority of the results can be applied to any Penning trap, but the theory is based throughout upon the “Geonium Chip" trap at Sussex; the scalability and planar design of this trap promotes it as natural candidate in experimental quantum optics and Gaussian quantum information studies. The work in this thesis aims to provide framework for such future applications

Continuous Symmetries and Conservation Laws in Chiral Media

Locally conserved quantities of the electromagnetic field in lossless chiral media are derived from Noether's theorem, including helicity, chirality, momentum, and angular momentum, as well as the separate spin and orbital components of this last quantity. We discuss sources and sinks of each in the presence of current densities within the material, and in some cases, as also generated by inhomogeneity of the medium. A previously obtained result connecting sources of helicity and energy within chiral materials is explored, revealing that association between the two quantities is not restricted to chiral media alone. Rather, it is analogous to the connection between the momentum, and the spin and orbital components of the total angular momentum. The analysis reveals a new quantity, appearing as the "orbital" counterpart of the helicity density in classical electromagnetism

On the conservation of helicity in a chiral medium

We consider the energy and helicity densities of circularly polarised light within a lossless chiral medium, characterised by the chirality parameter β. A form for the helicity density is introduced, valid to first order in β, that produces a helicity of ±\hbar per photon for right and left circular polarisation, respectively. This is in contrast to the result obtained if we use the form of the helicity density employed for linear media. We examine the helicity continuity equation, and show that this modified form of the helicity density is required for consistency with the dual symmetry condition of a chiral medium with a constant value of ε/μ. Extending the results to arbitrary order in β establishes an exact relationship between the energy and helicity densities in a chiral medium

On the conservation of helicity in a chiral medium

We consider the energy and helicity densities of circularly polarised light within a lossless chiral medium, characterised by the chirality parameter β. A form for the helicity density is introduced, valid to first order in β, that produces a helicity of ±\hbar per photon for right and left circular polarisation, respectively. This is in contrast to the result obtained if we use the form of the helicity density employed for linear media. We examine the helicity continuity equation, and show that this modified form of the helicity density is required for consistency with the dual symmetry condition of a chiral medium with a constant value of ε/μ. Extending the results to arbitrary order in β establishes an exact relationship between the energy and helicity densities in a chiral medium

Coherence and catalysis in the Jaynes-Cummings model

There has been substantial interest of late on the issue of coherence as a resource in quantum thermodynamics. To date, however, analyses have focussed on somewhat artificial theoretical models. We seek to bring these ideas closer to experimental investigation by examining the ``catalytic'' nature of quantum optical coherence. Here the interaction of a coherent state cavity field with a sequence of two-level atoms is considered, a state ubiquitous in quantum optics as a model of a stable, classical source of light. The Jaynes-Cummings interaction Hamiltonian is used, so that an exact solution for the dynamics can be formed, and the evolution of the atomic and cavity states with each atom-field interaction analysed. In this way, the degradation of the coherent state is examined as coherence is transferred to the sequence of atoms. The associated degradation of the coherence in the cavity mode is significant in the context of the use of coherence as a thermodynamic resource

Optical helicity and chirality: conservation and sources

We consider the helicity and chirality of the free electromagnetic field, and advocate the former as a means of characterising the interaction of chiral light with matter. This is in view of the intuitive quantum form of the helicity density operator, and of the dual symmetry transformation generated by its conservation. We go on to review the form of the helicity density and its associated continuity equation in free space, in the presence of local currents and charges, and upon interaction with bulk media, leading to characterisation of both microscopic and macroscopic sources of helicity

Controlling the symmetry of inorganic ionic nanofilms with optical chirality

Manipulating symmetry environments of metal ions to control functional properties is a fundamental concept of chemistry. For example, lattice strain enables control of symmetry in solids through a change in the nuclear positions surrounding a metal centre. Light–matter interactions can also induce strain but providing dynamic symmetry control is restricted to specific materials under intense laser illumination. Here, we show how effective chemical symmetry can be tuned by creating a symmetry-breaking rotational bulk polarisation in the electronic charge distribution surrounding a metal centre, which we term a meta-crystal field. The effect arises from an interface-mediated transfer of optical spin from a chiral light beam to produce an electronic torque that replicates the effect of strain created by high pressures. Since the phenomenon does not rely on a physical rearrangement of nuclear positions, material constraints are lifted, thus providing a generic and fully reversible method of manipulating effective symmetry in solids

Spatial control of 2D nanomaterial electronic properties using chiral light beams

Single-layer two-dimensional (2D) nanomaterials exhibit physical and chemical properties which can be dynamically modulated through out-of-plane deformations. Existing methods rely on intricate micromechanical manipulations (e.g., poking, bending, rumpling), hindering their widespread technological implementation. We address this challenge by proposing an all-optical approach that decouples strain engineering from micromechanical complexities. This method leverages the forces generated by chiral light beams carrying orbital angular momentum (OAM). The inherent sense of twist of these beams enables the exertion of controlled torques on 2D monolayer materials, inducing tailored strain. This approach offers a contactless and dynamically tunable alternative to existing methods. As a proof-of-concept, we demonstrate control over the conductivity of graphene transistors using chiral light beams, showcasing the potential of this approach for manipulating properties in future electronic devices. This optical control mechanism holds promise in enabling the reconfiguration of devices through optically patterned strain. It also allows broader utilization of strain engineering in 2D nanomaterials for advanced functionalities in next-generation optoelectronic devices and sensors