Symmetry and Quantum Features in Optical Vortices

Optical vortices are beams of laser light with screw symmetry in their wavefront. With a corresponding azimuthal dependence in optical phase, they convey orbital angular momentum, and their methods of production and applications have become one of the most rapidly accelerating areas in optical physics and technology. It has been established that the quantum nature of electromagnetic radiation extends to properties conveyed by each individual photon in such beams. It is therefore of interest to identify and characterize the symmetry aspects of the quantized fields of vortex radiation that relate to the beam and become manifest in its interactions with matter. Chirality is a prominent example of one such aspect; many other facets also invite attention. Fundamental CPT symmetry is satisfied throughout the field of optics, and it plays significantly into manifestations of chirality where spatial parity is broken; duality symmetry between electric and magnetic fields is also involved in the detailed representation. From more specific considerations of spatial inversion, amongst which it emerges that the topological charge has the character of a pseudoscalar, other elements of spatial symmetry, beyond simple parity inversion, prove to repay additional scrutiny. A photon-based perspective on these features enables regard to be given to the salient quantum operators, paying heed to quantum uncertainty limits of observables. The analysis supports a persistence in features of significance for the material interactions of vortex beams, which may indicate further scope for suitably tailored experimental design.

The scattering matrix and the Green functions

In this chapter, the book begins to develop a perturbative formalism to describe the interactions of quantized fields and, in particular, the interactions of particles in terms of their quantum fields. Quantum scattering requires the description of particle interactions and asymptotic states, which are introduced in detail. The n-point Green functions are defined. An essential part of the chapter is devoted to deriving the reduction of the S-matrix in terms of the Green functions. The compact description of these notions is achieved by introducing the generating functionals of Green functions and the S-matrix. The same constructions are also introduced for the spinor fields.

Entanglement and entropy squeezing in the system of two qubits interacting with a two-mode field in the context of power low potentials

We study the dynamics of two non-stationary qubits, allowing for dipole-dipole and Ising-like interplays between them, coupled to quantized fields in the framework of two-mode pair coherent states of power-low potentials. We focus on three particular cases of the coherent states through the exponent parameter taken infinite square, triangular and harmonic potential wells. We examine the possible effects of such features on the evolution of some quantities of current interest, such as population inversion, entanglement among subsystems and squeezing entropy. We show how these quantities can be affected by the qubit-qubit interaction and exponent parameter during the time evolution for both cases of stationary and non-stationary qubits. The obtained results suggest insights about the capability of quantum systems composed of nonstationary qubits to maintain resources in comparison with stationary qubits.

Superunified Field Theory

This is a briefest possible introduction to the absolute geometry of space, time and matter. Absolute geometry or the post-Euclidean geometry does automatically lead to the superunified theory of quantized fields and fundamental interactions. In general, we have eventually constructed the ultimate system of universal mathematical harmony observed by us as the physical Universe. No work in theoretical physics and pure mathematics directly precedes to this theory we propose. Instead, it accomplishes original Pythagorean (arithmetisation) znd Platonic (geometrization) concepts of natural philosophy integrated afterwards by Jiordano Bruno.

Light propagation in inhomogeneous media, coupled quantum harmonic oscillators and phase transitions

This contribution has two main purposes. First, using classical optics we show how to model two coupled quantum harmonic oscillators and two interacting quantized fields. Second, we present classical analogs of coupled harmonic oscillators that correspond to anisotropic quadratic graded indexed media in a rotated reference frame, and we use operator techniques, common to quantum mechanics, to solve the propagation of light through a particular type of graded indexed medium. Additionally, we show that the system presents phase transitions.