Multiprobe Time Reversal for High-Fidelity Vortex-Mode-Division Multiplexing Over a Turbulent Free-Space Link

The orbital angular momentum (OAM) of photons presents a degree of freedom for enhancing the secure key rate of free-space quantum key distribution (QKD) through mode-division multiplexing (MDM). However, atmospheric turbulence can lead to substantial modal crosstalk, which is a long-standing challenge to MDM for free-space QKD. Here, we show that the digital generation of time-reversed wavefronts for multiple probe beams is an effective method for mitigating atmospheric turbulence. We experimentally characterize seven OAM modes after propagation through a 340-m outdoor free-space link and observe an average modal crosstalk as low as 13.2% by implementing real-time time reversal. The crosstalk can be further reduced to 3.4% when adopting a mode spacing $\mathrm{\ensuremath{\Delta}}\ensuremath{\ell}$ of 2. We implement a classical MDM system as a proof-of-principle demonstration, and the bit error rate is reduced from $3.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ to be less than $1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ through the use of time reversal. We also propose a practical and scalable scheme for high-speed, mode-multiplexed QKD through a turbulent link. The modal crosstalk can be further reduced by using faster equipment. Our method can be useful to various free-space applications that require crosstalk suppression.