Evolution equation for multi-photon states in turbulence

Abstract

The recently developed Wigner functional theory is used to formulate an evolution equation for arbitrary multi-photon states, propagating through a turbulent atmosphere under arbitrary conditions. The resulting evolution equation, which is obtained from an infinitesimal propagation approach, is in the form of a Fokker-Planck equation for the Wigner functional of the state and therefore incorporates functional derivatives. We show consistency with previously obtained solutions from different approaches and consider possible ways to find additional solutions for this equation.