A multi-mode free-space delay interferometer with no refractive compensation elements for phase-encoded QKD protocols

We demonstrate a compensation-free approach to the realization of multi-mode delay interferometers, mainly for use in phase-encoded quantum key distribution (QKD). High interference visibility of spatially multi-mode beams in unbalanced Michelson or Mach–Zehnder interferometers with a relatively wide range of delays is achieved by the appropriate choice of the transverse size of the beam. We provide a simple theoretical model that gives a direct connection between the visibility of interference, the delay and the beam parameters. The performed experimental study confirms our theoretical findings and demonstrates measured visibility of up to 0.95 for a delay of 2 ns. Our approach’s simplicity and robust performance make it a practical choice for the implementation of QKD systems, where a quantum signal is received over a multi-mode fiber. The important application of such a configuration is an intermodal QKD system, where the free-space atmospheric communication channel is coupled into a span of the multi-mode fiber, delivering the spatially distorted beam to the remote receiver with minimal coupling loss.