Entanglement evolution of twisted photons in strong atmospheric turbulence

Considering the evolution of the quantum state of a pair of entangled photons in a turbulent atmosphere and using the quadratic approximation to the Kolmogorov model of turbulence, we provide an analytical solution for the dynamical equation (an infinitesimal propagation equation) that describes this evolution in the plane-wave basis. As such, this solution fully incorporates the effect of multiple scattering, caused by the medium. After being converted into a discrete orbital angular momentum (OAM) basis, this solution retains the effect of coupling between different OAM modes on the twin-photon state for arbitrary propagation distances and arbitrary turbulence strengths. We define a minimal set of parameters that determines the entanglement evolution in the regime of strong scintillation. Furthermore, we show that in the limit of weak scintillation, our solutions reduce to those obtained from the single-phase-screen model.

Figure 1

Concurrence as a function of $\mathcal{W}$ resulting from the IPE and from the single-phase-screen (SPS) model, for three values of $\ell$: (a) $\ell =1$, (b) $\ell =3$, and (c) $\ell =5$. The solid lines represent the single-phase-screen model predictions for the respective cases and the discontinuous lines represent the IPE predictions for different values of the normalized turbulence strength $\mathcal{K}$.

Figure 2

Comparison of the curves for (a) the concurrence and (b) the trace, as a function of $\mathcal{W}$ for $\ell =1,3,5$ as predicted by the IPE with $\mathcal{K}=0.1$ (bold lines) and by the SPS model (thin lines).