Coherent States of Non-Null Torus Knots
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.