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Why do we need quantization to describe vision? What are the quadrature operators of the electromagnetic field? Is it possible to measure them? What are the characteristic functions useful for? In this brief tutorial we provide the…
We continue the study, from a semiclassical viewpoint, of Calvo and Picon's operators, as manipulating photon states in quantum communication. In a previous paper, we defined a one-dimensional model operator and studied it analytically…
There has been substantial calculational progress in the last few years for gauge theory amplitudes which involve massless four dimensional particles. One of the central ingredients in this has been the ability to keep precise track of the…
In order to characterize quantum states within the context of information geometry, we propose a generalization of the Gaussian model, which we called the Hermite-Gaussian model. We obtain the Fisher-Rao metric and the scalar curvature for…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
We propose a new configuration for realizing torsional optomechanics: an optically trapped windmill-shaped dielectric interacting with Laguerre-Gaussian cavity modes containing both angular and radial nodes. In contrast to existing schemes,…
Optomechanical systems combine extreme sensitivity and bandwidth in the control of mechanical motion, of interest for various applications. Integrated on a chip, actuated and detected all-optically by a single laser, they could disrupt…
Multimode Gaussian states are a versatile resource for quantum information technologies and have been realized across a wide range of physical platforms. Recent progress in the large-scale generation of such states provides a key ingredient…
Semiclassical approximations for various representations of a quantum state are constructed on a single (Lagrangian) surface in phase space, but it is not available for chaotic systems. An analogous evolution surface underlies semiclassical…
We develop a new method of representation of quantum states in terms of the displaced number states. We call it representation, where is an amplitude of the base displaced states. In particular, representation was obtained for set of the…
We consider a new approach to describe a quantum optical Bose-system with internal Gell-Mann symmetry by the SU(3)-symmetry polarization map in Hilbert space. The operational measurement in density (or coherency) matrix elements for the…
Vector modes are well-defined field distributions with spatially varying polarisation states, rendering them irreducible to the product of a single spatial mode and a single polarisation state. Traditionally, the spatial degree of freedom…
Different families of states, which are solutions of the time-dependent free Schr\"odinger equation, are imported from the harmonic oscillator using the Quantum Arnold Transformation introduced in a previous paper. Among them, infinite…
The Ince-Gaussian modes form a complete set of solutions to the paraxial wave equation parametrized by an ellipticity parameter {\epsilon}, enabling a continuous transition between Laguerre-Gaussian and Hermite-Gaussian modes While each…
Traditional superoscillation focusing typically requires complex optimization of the incident light field. These complexities may limit the practical application of superoscillation. High-order radially polarized Laguerre-Gaussian beams…
We extend the off-diagonal geometric phase [Phys. Rev. Lett. {\bf 85}, 3067 (2000)] to mixed quantal states. The nodal structure of this phase in the qubit (two-level) case is compared with that of the diagonal mixed state geometric phase…
A Hermitian quantum phase operator is formulated that mirrors the classical phase variable with proper time dependence and satisfies trigonometric identities. The eigenstates of the phase operator are solved in terms of Gegenbauer…
For any orthogonal polynomials system on real line we construct an appropriate oscillator algebra such that the polynomials make up the eigenfunctions system of the oscillator hamiltonian. The general scheme is divided into two types: a…
An operator formalism for bosonic $\beta-\gamma$ systems on arbitrary algebraic curves is introduced. The classical degrees of freedom are identified and their commutation relations are postulated. The explicit realization of the algebra…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…