Evolution of moments in atmospheric scintillation

Abstract

Evolution equations for the moments of a photonic quantum state propagating through atmospheric turbulence are derived. These evolution equations are obtain from an evolution equation for the characteristic functional of the state, incorporating all spatiotemporal degrees of freedom. The measured quantities, such as the intensity or photon distribution, of the evolving state can be expressed in terms of such moments without having to know the exact final state. The case of an initial coherent state is considered as an example.