# Multi-mode Time-delay Interferometer for Free-space Quantum Communication

## TL;DR

This paper introduces a stable, compact multi-mode time-delay interferometer designed for free-space quantum communication, demonstrating high visibility measurements for single- and multi-mode states under atmospheric conditions.

## Contribution

The authors present a novel, field-widened Michelson-type interferometer optimized for free-space quantum communication, enabling high-visibility phase measurements across multiple spatial modes.

## Key findings

- Achieved 99.02% visibility for single-mode inputs.
- Achieved 98.38% visibility for multi-mode inputs.
- Successfully measured multi-mode single-photon states with 97.37% visibility.

## Abstract

Quantum communication schemes such as quantum key distribution (QKD) and superdense teleportation provide unique opportunities to communicate information securely. Increasingly, optical communication is being extended to free-space channels, but atmospheric turbulence in free-space channels requires optical receivers and measurement infrastructure to support many spatial modes. Here we present a multi-mode, Michelson-type time-delay interferometer using a field-widened design for the measurement of phase-encoded states in free-space communication schemes. The interferometer is constructed using glass beam paths to provide thermal stability, a field-widened angular tolerance, and a compact footprint. The performance of the interferometer is highlighted by measured visibilities of $99.02\pm0.05\,\%$, and $98.38\pm0.01\,\%$ for single- and multi-mode inputs, respectively. Additionally, high quality multi-mode interference is demonstrated for arbitrary spatial mode structures and for temperature changes of $\pm1.0\,^{\circ}$C. The interferometer has a measured optical path-length drift of $130\,$nm$/\,^{\circ}$C near room temperature. With this setup, we demonstrate the measurement of a two-peaked, multi-mode, single-photon state used in time-phase QKD with a visibility of $97.37\pm 0.01\,\%$.