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arXiv:2504.07484 · Laser Physics Letters

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

V V Tretiakov, Konstantin Kravtsov, Andrey N. Klimov, S. P. Kulik

Published Apr 29, 2024• 3 citations
arXivHTMLPDF

Abstract

Abstract 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.

DOI
10.1088/1612-202x/ad3a56

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Abstract We report on the adaptation of a commercially available fiber-based quantum key distribution (QKD) system with phase-time encoding to free-space operation. The proposed approach minimizes architectural modifications by replacing the single-mode receiving interferometer with a free-space multi-mode delay interferometer, enabling efficient detection of spatially distorted quantum states typical for atmospheric channels. Several interferometer configurations are experimentally investigated, and a multi-mode Michelson interferometer with polarization routing is identified as the optimal solution in terms of interference visibility, loss, and alignment robustness. The impact of chromatic and modal dispersion on phase-time interference is analyzed and shown to be manageable under realistic system parameters. A laboratory QKD experiment demonstrates stable operation with a quantum bit error rate of about 4.5% and a secret key rate of hundreds of bits per second, confirming the feasibility of extending fiber-based QKD platforms to free-space links.
Interference of time-bin encoded signals over free-space optical channels typically requires stringent mode filtering on receivers due to wavefront distortions from atmospheric turbulence, conventionally addressed with adaptive optics. Passive multimode receivers based on field-widened interferometers present a compelling alternative, enabling direct interference without the overhead of wavefront correction. We demonstrate a field-widened interferometer design that is implemented solely with reflective surfaces and achieves a high interference visibility (greater than 0.97) for spatially multimode beams. The interference of the multimode beams is enabled by two imaging systems that consist of a cavity configuration between a spherical concave mirror and a flat mirror. The configuration enables small form-factors, is inherently achromatic, and is based on standard spherical mirrors which reduces the complexity of the system. The interferometer is applicable for spatially multimode and turbulent optical channels, such as satellite communication, and is designed for quantum systems that use time-bin encoded qubits.
Optical communication via free-space channels is attractive for establishing long-range secure quantum networks, but is often hindered by deleterious effects on the transverse spatial mode profile of the beam, caused by propagation through the atmosphere. Additionally, interferometric measurement at the receiver becomes much more difficult with multimode profiles. This study presents a compact time-delay interferometer with high stability and interference visibility for single- and multimode spatial profiles. The results of this study are important for the future of quantum communication networks as well as a wide range of techniques for classical and quantum optical measurement.
Interference of optical signals in free-space channels requires optical receivers to support many spatial modes due to atmospheric turbulence, typically necessitating adaptive optics systems. Field-widened interferometers offer a passive alternative, making them particularly attractive for time-bin encoded signals with delays on the order of one nanosecond. Here, we demonstrate a field-widened, multimode interferometer design that achieves a high interference visibility for spatially multimode beams with large time bin separations. The interference of the multimode beams is enabled using a multi-pass Herriott cell that enables a very long path separation with a small form-factor. The design is tested using both numerical ray-tracing simulations and proof-of-principle demonstrations. We create a prototype interferometer with a path length difference of 12ns and determine that it maintains a high interference visibility with a large field-of-view of 0.4∘0.4^{\circ}0.4∘.
Abstract We report the implementation and field testing of an atmospheric quantum key distribution (QKD) system obtained by adapting the commercially available fiber-based ViPNet-QTS platform. The phase-time state-preparation module, detector electronics, and post-processing procedures were retained, whereas the fiber channel was replaced by external optical devices forming a 400 m urban free-space link. The 1550 nm quantum-channel signal was coupled into a multimode fiber (MMF) at the receiver and analyzed by a free-space multimode delay interferometer, allowing the quantum-cryptographic equipment to remain inside trusted zones. Synchronization and bidirectional pointing were implemented using spectrally separated 850 and 780 nm auxiliary channels. We characterized the channel loss, background-count probability, atmospheric turbulence, and performance of the fast and low-bandwidth tracking loops. Although feedback based on fast steering mirrors strongly reduced the fluctuations of the tracking-beam position at the CMOS sensor, it increased the mean power coupled into the MMF by only 4.07% under the tested conditions. Long-term alignment was instead maintained by low-bandwidth feedback to the motorized mounts, demonstrating that continuous high-bandwidth fine tracking was not required for the investigated 400 m link. During an autonomous four-day QKD experiment, the system operated fully unattended, with no manual intervention in alignment, system control, or post-processing. Secret keys were generated over most of the measurement interval under changing day–night and weather conditions. Temporary interruptions in key generation coincided with strong daylight background, whereas the measured turbulence variations had no similarly direct effect on system operation. These results demonstrate a practical approach to extending existing fiber-based QKD platforms to atmospheric links using an MMF-coupled receiver and a comparatively simple tracking architecture.