# Evolution equation for multi-photon states in turbulence

## TL;DR

This paper develops a Wigner functional-based evolution equation for multi-photon quantum states propagating through turbulent atmospheres, unifying different approaches and enabling new solution methods.

## Contribution

It introduces a Fokker-Planck type evolution equation for multi-photon states in turbulence using Wigner functional theory, extending previous methods.

## Key findings

- The evolution equation is consistent with prior solutions.
- The equation is in the form of a Fokker-Planck equation with functional derivatives.
- Potential methods for finding additional solutions are discussed.

## 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.