"Classical" coherent state generated by curved surface

TL;DR

This paper introduces a new way to model Gaussian laser beam propagation on curved surfaces using generalized coherent states, revealing unique quantum field behaviors influenced by surface curvature.

Contribution

It generalizes the Feynman path integral method to derive coherent states for beam propagation on curved surfaces, linking curvature to quantum state properties.

Findings

Gaussian curvature affects transmitted momentum proportional to sqrt(K)

Beam propagation on curved surfaces resembles squeezed states

New perspective on quantum fields in curved space

Abstract

Analogous coherent states are deduced from classical optical fields on curved surface in this paper. The Gaussian laser beam, as a fundamental mode, cannot be adequately simulated by coherent states due to their inherent diffraction in flat space. But things will be different when it propagates on a surface with uniform curvature called the constant Gaussian curvature surface (CGCS). By generalizing the method of Feynman path integral, an equivalent coherent states solution is demonstrated here to describe the beam propagation. The temporal evolution of the Schrodinger equation is analogously translated into a spatial transmission in this derivation, we obtain the expression of quantized momentum transmitted on curved surface, which is proportional to the square root of the Gaussian curvature $K$. In addition, we build a beam propagation picture identical to the squeezed state. We hope this research can give a new view on the quantum field in curved space.