Mode analysis of higher-order transverse-mode correlation beams in turbulent atmosphere

TL;DR

This paper derives an analytic model for the propagation of Hermite-Gaussian mode entangled photons through turbulent atmosphere, revealing mode crosstalk effects and identifying robust modes for improved quantum communication fidelity.

Contribution

It provides a comprehensive analytic expression for two-photon detection probability considering atmospheric turbulence affecting both photons, advancing understanding of mode crosstalk in quantum channels.

Findings

Mode crosstalk depends on turbulence strength

Certain modes are more robust against atmospheric effects

Mode parity restrictions are relaxed in turbulence

Abstract

Due to the transfer of the angular spectrum of the pump beam to the two-photon state in spontaneous parametric down-conversion the generated twin photons are entangled in Hermite-Gaussian (HG) modes. This enables one using HG modes as an alphabet for quantum communication. For global quantum communication purposes, we derive an analytic expression for two-photon detection probability in terms of HG modes taking into account the effects of the turbulent atmosphere. Our result is more general as it accounts for the propagation of both, signal and idler photons through the atmosphere, as opposed to other works considering one of the photons' propagation in vacuum. We show that while the restrictions on both the parity and order of the down-converted HG fields no longer hold due to the crosstalk between modes when propagating in the atmosphere, the crosstalk is not uniform: there are more robust modes that tend to keep the photons in them. These modes can be employed in order to increase the fidelity of quantum communication.