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Geometric phases are ubiquitous in physics; they act as memories of the transformation of a physical system. In optics, the most prominent examples are the Pancharatnam-Berry phase and the spin-redirection phase. Recent technological…
Chiral quantum optics is a growing field of research where light-matter interactions become asymmetrically dependent on momentum and spin, offering novel control over photonic and electronic degrees of freedom. Recently, the platforms for…
We establish a formal bridge between qubit-based and photonic quantum computing. We do this by defining a functor from the ZX calculus to linear optical circuits. In the process we provide a compositional theory of quantum linear optics…
In 2011, Luc introduced parametric duality for multiple objective linear programs. He showed that geometric duality, introduced in 2008 by Heyde and L\"ohne, is a consequence of parametric duality. We show the converse statement: parametric…
Non-classical correlations in quantum optics as resources for quantum computation are important in the quest for highly-specialized quantum devices. The standard way to investigate such effects relies on either the characterization of the…
We present a consistent theoretical description of few-particle effects in the optical spectra of semiconductor quantum dots, based on a direct-diagonalization approach. We show that, because of the strong Coulomb interaction among…
Beginning with the principle that a closed mechanical composite system is timeless, time can be defined by the regular changes in a suitable position coordinate (clock) in the observing part, when one part of the closed composite observes…
This paper explores the topologies of caustics observed in instruments that employ charged particles, such as electron and ion microscopes. These geometrical figures are studied here using catastrophe theory. The application of this…
The purpose of this short tutorial paper is to review various criteria that have been used to characterize the quantum character of correlations in optical systems, such as "gemellity", QND correlation, intrication, EPR correlation and Bell…
Several noncovariant formulations of the electromagnetic self-force of extended charged bodies, as have been developed in the context of classical models of charged particles, are compared. The mathematical equivalence of the various…
The paraxial approximation to the scalar Helmholtz equation is shown to be equivalent to the Schr\"odinger equation for a quantum harmonic oscillator. This equivalence maps the Gouy-phase of classical wave optics onto the time coordinate of…
Wigner had expressed the opinion that the impossibility of exact measurements of single operators like position operators rendered the notion of geometrical points somewhat dubious in physics. Using Sewell's recent resolution of the…
Lenses, optics and dependent lenses (or equivalently morphisms of containers, or equivalently natural transformations of polynomial functors) are all widely used in applied category theory as models of bidirectional processes. From the…
We consider the propagation of a matter wavepacket of two-level atoms through a square potential created by a super-Gaussian laser beam. We explore the matter wave analog of Goos-H\"{a}nchen shift within the framework of atom optics where…
This chapter reviews the fundamental optical properties and applications of pho-tonic molecules (PMs) - photonic structures formed by electromagnetic coupling of two or more optical microcavities (photonic atoms). Controllable interaction…
Quantum mechanics and classical mechanics are two very different theories, but the correspondence principle states that quantum particles behave classically in the limit of high quantum number. In recent years much research has been done on…
Magneto-optical effect is a fundamental but broad concept in magnetic mediums. Here we propose a scheme for its quantum emulation using ultracold atoms. By representing the light-medium interaction in the quantum-emulation manner, the…
We present exact analogies between the tautochrone problem of mechanics and the squeezed states of quantum optics, to optical lattices. Both phenomena emerge in the same physical system, that of waveguide arrays with non-uniform couplings.…
Since the beginning of quantum mechanics, many puzzling phenomena which distinguish the quantum from the classical world, have appeared such as complementarity, entanglement or contextuality. All of these phenomena are based on the…
Lenses are a mathematical structure for maintaining consistency between a pair of systems. In their ongoing research program, Johnson and Rosebrugh have sought to unify the treatment of symmetric lenses with spans of asymmetric lenses. This…