The theory of quantum electrodynamics is employed in the description of linear and \nnonlinear optical effects. We study the effects of using a two energy level \napproximation in simplifying expressions obtained from perturbation theory, \nequivalent to truncating the completeness relation. However, applying a two-level \nmodel with a lack of regard for its domain of validity may deliver misleading results. \nA new theorem on the expectation values of analytical operator functions imposes \nadditional constraints on any atom or molecule modelled as a two-level system. We \nintroduce measures designed to indicate occasions when the two-level approximation \nmay be valid. \nAnalysis of the optical angular momentum operator delivers a division into spin \nand orbital parts satisfying electric-magnetic democracy, and determine a new \ncompartmentalisation of the optical angular momentum. An analysis is performed on \nthe recently rediscovered optical chirality, and its corresponding flux, delivering \nresults proportional to the helicity and spin angular momentum in monochromatic \nbeams. A new polarisation basis is introduced to determine the maximum values that \nan infinite family of optical helicity- and spin- type measures may take, and disproves \nrecent claims of ‘superchiral light’. A theoretical description of recent experiments \nrelate helicity- and spin- type measures to the circular differential response of \nmolecules, and show that nodal enhancements to circular dichroism relate only to \nphoton number-phase uncertainty relation and do not signify ‘superchiral’ regions. \nThe six-wave mixing of optical vortex input, in nonlinear media, demonstrates the \nquantum entanglement of pairs of optical vortex modes. The probability for each \npossible output pair displays a combinatorial weighting, associated with Pascal’s \ntriangle. \nA quantum electrodynamic analysis of the effect of a second body on absorption \ncan be extended by integrating over all possible positions of the mediator molecules, \nmodelling a continuous medium. This provides links with both the molecular and \nbulk properties of materials.
The theory of quantum electrodynamics is employed in the description of linear and \nnonlinear optical effects. We study the effects of using a two energy level \napproximation in simplifying expressions obtained from perturbation theory, \nequivalent to truncating the completeness relation. However, applying a two-level \nmodel with a lack of regard for its domain of validity may deliver misleading results. \nA new theorem on the expectation values of analytical operator functions imposes \nadditional constraints on any atom or molecule modelled as a two-level system. We \nintroduce measures designed to indicate occasions when the two-level approximation \nmay be valid. \nAnalysis of the optical angular momentum operator delivers a division into spin \nand orbital parts satisfying electric-magnetic democracy, and determine a new \ncompartmentalisation of the optical angular momentum. An analysis is performed on \nthe recently rediscovered optical chirality, and its corresponding flux, delivering \nresults proportional to the helicity and spin angular momentum in monochromatic \nbeams. A new polarisation basis is introduced to determine the maximum values that \nan infinite family of optical helicity- and spin- type measures may take, and disproves \nrecent claims of ‘superchiral light’. A theoretical description of recent experiments \nrelate helicity- and spin- type measures to the circular differential response of \nmolecules, and show that nodal enhancements to circular dichroism relate only to \nphoton number-phase uncertainty relation and do not signify ‘superchiral’ regions. \nThe six-wave mixing of optical vortex input, in nonlinear media, demonstrates the \nquantum entanglement of pairs of optical vortex modes. The probability for each \npossible output pair displays a combinatorial weighting, associated with Pascal’s \ntriangle. \nA quantum electrodynamic analysis of the effect of a second body on absorption \ncan be extended by integrating over all possible positions of the mediator molecules, \nmodelling a continuous medium. This provides links with both the molecular and \nbulk properties of materials.
This thesis employs molecular quantum electrodynamical theory to analyse the interactions between light and matter for four main processes. The first to be considered is Raman scattering, where the effect of the electrodynamic environment for the centre of spectroscopic interest is considered. This is achieved by engaging a retarded dipole-dipole interaction between the centre and a neighbouring molecule. Physically, this is explained by a virtual photon between the pair of centres. The results predict characteristic new lines on the Raman spectrum, for the species, arising from the engagement of selection rules not limited to those of a two-photon process. \nThe second process, is hyper-Rayleigh scattering, in which a single multipolar coupling is considered in place of the more familiar electric dipole. This modification to the theory subverts the standard selection rules for a three-photon process, which can allow for second-harmonic emission to be generated by a centre of high symmetry, such as a centrosymmetric molecule. \nThe third process offers another means of subverting the standard selection rules for second-harmonic generation, namely by incorporating six-wave mixing. First, the general mechanism is developed and pertinent results are expressed for the widely-deployed depolarisation ratio. Following this, structured light is considered and by utilising orbital angular momentum (OAM) conservation arguments, the pair of harmonic photons are found to display quantum entanglement. Moreover, the relative magnitudes of the possible emissions are found to correspond directly to that of the binomial coefficients. \nThis thesis concludes with a family of novel structures capable of directly generating OAM light. This work exploits symmetry characteristics for a delocalised excitonic structure that can allow for a more complex multipolar emission than that of any isolated centres. The phase of the exciton is shown to display an azimuthal phase progression, a vortex feature most commonly associated with Laguerre-Gaussian light.
It is well established now that light carries both spin and orbital angular momentum which are associated with circular polarisation and helical phase fronts. Orbital angular momentum degrees of freedom recently have been used frequently in quantum information processing as their states are described by vectors in a higher-dimensional Hilbert space which enhances the possibility of realising superior quantum information protocols. On the other hand, quantum coherence, which arises from the superposition principle, is a distinct feature of quantum mechanics that cannot be satisfactorily described by classical physics. Coherence is also identified as essential ingredient for applications of quantum information, computation, and quantum thermodynamics. Three research projects, with their related background information, are presented in this thesis. In the first one, we design a linear optical system to transform the maximally entangled state of a down-converted photon pair into a genuine entangled χ-type state, as this class of genuine entangled states has been showed to have many interesting entanglement properties and can be employed in several quantum information protocols. In the second project, we study the mechanism of angular momentum transfer from light to a dielectric medium when it undergoes total internal reflection. The result shows that the torque associated with angular momentum transfer appears shortly, when the light pulse hits the interface. Finally, we study quantum coherence transfer from a coherence resource initialised in a coherence state to an atomic state by the Jaynes-Cummings model, and we compare it to the coherent operation that uses a resource prepared in a ladder state described by Åberg’s model. We found that a resource in a coherent state is more robust against failures.
In 1992, Les Allen and coworkers within Han Woerdman's group realized that light beams with an azimuthal phase dependence described by an additional exp(iâθ) term, where â can take any integer value and θ is the angular position within the beam, carry an orbital angular momentum. This orbital angular momentum is additional to the spin angular momentum associated with circular polarization. These azimuthally phased beams comprise â intertwined helical phase fronts, skewed with respect to the beam axis, meaning that at all positions within the beam cross section, the wavefront normal and associated momentum density has a well-defined azimuthal component. The insight of Allen and coworkers was that for all beams described in this way, when integrated over the beam cross section, the orbital angular momentum (OAM) is ââ per photon. Laguerre-Gaussian and high-order Bessel beams are both examples of mode families having these properties. A further feature of these beams is that the phase singularity on the beam axis precludes a nonzero on-axis intensity and therefore all such beams with â â 0 have an annular intensity cross section (see Fig. 4.1). The circulation of the optical momentum and energy around the singularity leads them also to be called optical vortices. The further recognition that beams carrying defined amounts of OAM could be created within the laboratory means that over the last 15 years they have formed the basis of many investigations, ranging from the transfer of OAM to microscopic particles (in optical spanners or optical wrenches) to studies of the fundamental properties of light in both the classical and quantum regimes. However, although OAM is an immensely useful concept, one must emphasize that all its properties are simply those predicted by standard electromagnetic theory. The purpose of this chapter is to consider how sets of helical laser modes carrying OAM can be used for information transfer.
By applying a sufficiently intense beam of off-resonant light, simultaneously with a conventional excitation source beam, the efficiencies of one- and two-photon absorption processes may be significantly modified. The nonlinear mechanism that is responsible, known as laser modified absorption, is fully described by a quantum electrodynamical analysis. The origin of the process, which involves stimulated forward Rayleigh-scattering of the auxiliary beam, relates to higher order terms which are secured by a time-dependent perturbation treatment. These terms, usually inconsequential when a single beam of light is present, become prominent under the secondary optical stimulus – even with levels of intensity that are moderate by today’s standards. Distinctive kinds of behaviour may be observed for chromophores fixed in a static arrangement, or for solution- or gas-phase molecules whose response is tempered by a rotational average of orientations. In each case the results exhibit an interplay of factors involving the beam polarisations and the molecular electronic response. Special attention is given to interesting metastable states that are symmetry forbidden by one- or two-photon absorption. Such states may be accessible, and thus become populated, on input of the auxiliary beam. For example, in the one-photon absorption case, terms arise that are more usually associated with three-photon processes, corresponding to very different selection rules. Other kinds of metastable state also arise in the two-photon process, and measuring the effect of applying the stimulus beam to absorbances of such character adds a new dimension to the information content of the associated spectroscopy. Finally, based on these novel forms of optical nonlinearity, there may be new possibilities for quantum non-demolition measurements.
Methods to generate, manipulate, and measure optical and atomic fields with global or local angular momentum have a wide range of applications in both fundamental physics research and technology development. In optics, the engineering of angular momentum states of light can aid studies of orbital angular momentum (OAM) exchange between light and matter. The engineering of optical angular momentum states can also be used to increase the bandwidth of optical communications or serve as a means to distribute quantum keys, for example. Similar capabilities in Bose-Einstein condensates are being investigated to improve our understanding of superfluid dynamics, superconductivity, and turbulence, the last of which is widely considered to be one of most ubiquitous yet poorly understood subjects in physics. The first part of this two-part dissertation presents an analysis of techniques for measuring and manipulating quantized vortices in BECs. The second part of this dissertation presents theoretical and numerical analyses of new methods to engineer the OAM spectra of optical beams. The superfluid dynamics of a BEC are often well described by a nonlinear Schrodinger equation. The nonlinearity arises from interatomic scattering and enables BECs to support quantized vortices, which have quantized circulation and are fundamental structural elements of quantum turbulence. With the experimental tools to dynamically manipulate and measure quantized vortices, BECs are proving to be a useful medium for testing the theoretical predictions of quantum turbulence. In this dissertation we analyze a method for making minimally destructive in situ observations of quantized vortices in a BEC. Secondly, we numerically study a mechanism to imprint vortex dipoles in a BEC. With these advancements, more robust experiments of vortex dynamics and quantum turbulence will be within reach. A more complete understanding of quantum turbulence will enable principles of microscopic fluid flow to be related to the statistical properties of turbulence in a superfluid. In the second part of this dissertation we explore frequency mixing, a subset of nonlinear optical processes in which one or more input optical beam(s) are converted into one or more output beams with different optical frequencies. The ability of parametric nonlinear processes such as second harmonic generation or parametric amplification to manipulate the OAM spectra of optical beams is an active area of research. In a theoretical and numerical investigation, two complimentary methods for sculpting the OAM spectra are developed. The first method employs second harmonic generation with two non-collinear input beams to develop a broad spectrum of OAM states in an optical field. The second method utilizes parametric amplification with collinear input beams to develop an OAM-dependent gain or attenuation, termed dichroism for OAM, to effectively narrow the OAM spectrum of an optical beam. The theoretical principles developed in this dissertation enhance our understanding of how nonlinear processes can be used to engineer the OAM spectra of optical beams and could serve as methods to increase the bandwidth of an optical signal by multiplexing over a range of OAM states.
We demonstrate that light propagation in reciprocal chiral photonic media admits a unified description in terms of an emergent Dirac structure in helicity space. Starting from Maxwell's equations, we reformulate the electromagnetic field as a four-component spinor governed by an effective non-Hermitian optical Dirac equation. In this representation, the magnetoelectric response of the chiral medium appears as a helicity-dependent background that modifies the spectrum and eigenmodes, while the breaking of the spin-degenerate condition generates the intrinsic spin-orbit coupling between helicity and orbital degrees of freedom. After projection onto the positive-frequency sector, the theory reduces to an exact two-level helicity-orbital model. This model is found to have an analytical solution and describes coherent Rabi-like oscillations between spin-orbit-coupled vector modes. Chirality controls the helicity splitting and detuning, whereas the electromagnetic mismatch of the medium determines the coupling strength responsible for oscillatory spin-orbit conversion. The resulting dynamics is constrained by exact conservation of the total angular momentum, leading to reversible conversion between spin and orbital angular momentum with well-defined selection rules. Our work establishes an optical Dirac framework for structured light in chiral media, and provides experimentally accessible predictions for chirality-controlled oscillations, polarization dynamics, and orbital angular momentum conversion in structured optical fields.