Coherent States of Non-Null Torus Knots

TL;DR

This paper constructs and analyzes quantum coherent states corresponding to classical non-null torus knot solutions of Maxwell's equations, establishing a quantum-classical correspondence for topological electromagnetic fields.

Contribution

It introduces a method to create coherent states for knotted electromagnetic fields and computes their key physical observables, linking classical solutions to quantum states.

Findings

Derived explicit coherent states for non-null torus knots

Computed expectation values of physical observables in these states

Established quantum-classical correspondence for topological electromagnetic fields

Abstract

We construct coherent states for the quantized electromagnetic field that correspond to the classical non-null torus knot solutions of Maxwell's equations in vacuum. We derive the displacement operators from the general relation between classical fields and coherent state amplitudes and verify the defining properties of coherent states through direct computation. We determine the observables of the model: field expectation values, energy density, Poynting vector, helicity, photon number, quadrature uncertainties, and correlation functions, and calculate their expectation values in the knotted coherent states in terms of the integer parameters $(n,m,l,s)$ of the classical solutions. As an example, we particularize the construction in the case of the Hopfion coherent state. These results establish the quantum-classical correspondence for this type of vacuum topological electromagnetic systems.