‘Classical’ coherent state generated by curved surface

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 it differs when propagating on a surface with the uniform curvature, the constant Gaussian curvature surface (CGCS). By generalizing the method of Feynman path integral, an equivalent coherent states solution is demonstrated to describe the beam propagation. The temporal evolution of the Schrödinger equation is analogously translated into a spatial transmission in this derivation, and 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 to that, a physical picture of beam propagation that is identical to the squeezed state is also built. We hope this research can offer a new view on the quantum field in curved space.