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Modern Physics Letters B

Practical single-photon receiving efficiency model based on Gaussian beam propagation

Yang Xue, Lei Shi, Jiahao Li, Tianxiu Li, Jiahua Wei, Longqiang Yu

Published Feb 26, 2021• 1 citation
Publisher

Abstract

Modern optical technology has greatly facilitated the implementation of free-space quantum key distribution. However, the influence of atmosphere on the beam propagation is always unpredictable and could impair the system performance to some extent. It is necessary to develop an efficient model that could describe the beam propagation and receiving. In this paper, a single-photon receiving efficiency model is proposed incorporating the single-photon acquisition probability and channel transmittance based on the Gaussian beam propagation. We also present simulation and experiment of beam-spot size widening through a 0.5 km free-space channel to verify the proposed model. The results show that with the increase of turbulence strengths, the single-photon acquisition probability will degrade more sharply. The single-photon receiving efficiency will decrease with the increment of the ratio between beam centroid deflection and the receiving aperture radius [Formula: see text].

DOI
10.1142/s0217984921501992

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Modern optical technology has greatly facilitated the implementation of free-space quantum key distribution. However, the influence of atmosphere on the beam propagation is always unpredictable and could impair the system performance to some extent. It is necessary to develop an efficient model that could describe the beam propagation and receiving. In this paper, a single-photon receiving efficiency model is proposed incorporating the single-photon acquisition probability and channel transmittance based on the Gaussian beam propagation. We also present simulation and experiment of beam-spot size widening through a 0.5 km free-space channel to verify the proposed model. The results show that with the increase of turbulence strengths, the single-photon acquisition probability will degrade more sharply. The single-photon receiving efficiency will decrease with the increment of the ratio between beam centroid deflection and the receiving aperture radius [Formula: see text].
Two theoretical models of single-photon acquisition probability based on the fundamental-mode Gaussian beam are established for free-space quantum key distribution and are compared in theory and simulation. The parameters that influence the single-photon acquisition probability are the transmitter's tracking-pointing error, the far-field divergence angle, the link distance between the transmitter and receiver and the receiver's antenna aperture. The single-photon acquisition probability is analyzed in the numerical simulation and its orders of magnitude are given for the ground-to-ground, satellite-to-ground and satellite-to-satellite links. The results of the theoretical analysis and the numerical simulation show that it is feasible to acquire single-photon for the satellite-to-ground and satellite-to-satellite quantum key distribution.
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Theoretical model of single photon acquisition probability is established for free-space quantum key distribution.The expression of single photon acquisition probability is deduced from the fundamental-mode Gaussian beam.The parameters that influence the single photon acquisition probability are the transmitter's tracking-pointing error,the far-field divergence angle,the link distance between transmitter and receiver and the receiver's antenna aperture.The single photon acquisition probability is analyzed in numerical simulation for the link between a ground station and a satellite in a low earth orbit and it is normally on the order of 10~(3)~10~(-5).
Abstract Quantum Key Distribution (QKD) has been widely applied due to its theoretical one-time pad encryption. Typically employing laser beam as carrier, quantum states are transmitted through optical fibers or free-space channels, with the latter being more commonly adopted. However, compared to optical fibers, free-space links are more susceptible to external environmental factors, particularly atmospheric conditions. Beam propagation through the atmosphere experiences diffraction, refraction, and intensity attenuation, which can degrade key distribution efficiency and even prevent key generation at the receiver. The atmospheric turbulence poses the most significant challenge in all influencing factors, especially for the commonly encountered moderate-to-strong turbulence regimes. Therefore, in this work, we develop a phase screen model and turbulence-dominated transmittance model to comprehensively investigate the impact of various key parameters on optical beam propagation through turbulent atmospheres. Furthermore, we derive the key rate for the CV-QKD protocol using a TMSV (two-mode squeezed vacuum) state and perform numerical simulations.
The expressions of single-photon acquisition probability are deduced from TEM10 mode Laguerre-Gaussian beams. Single-photon acquisition is analyzed for the links between a ground station and a satellite in a low earth orbit. The results show that single-photon can be acquired by the receiver on the satellite at the maximum probability if highly attenuated laser pulses based on TEM10 mode Laguerre-Gaussian beams are used as single-photon sources and a bright precursor reference pulse can be used to set a short time window. Single-photon acquisition probability is normal on the order of 10-1~10-3. In comparison with the fundamental-mode Gaussian beam, the TEM10 mode Laguerre- Gaussian beams have an advantage because the losses of single-photon acquisition probability can not be caused by the satellite movement. Atmospheric turbulence is considered and the expressions of single- photon acquisition probability are modified.
Multiphoton Quantum Key Distribution (QKD) has recently been proposed to exchange the secret keys using the rotational of polarization over a multi-stage protocol. It has the ability to outperform the weaknesses of a single photon QKD by improving the generation of key rate and distance range. This paper investigates the theoretical aspects of multiphoton QKD protocol’s performance over free space optic (FSO) networks. The most common setup for quantum communication is the single-beam approach. However, the single-beam setup has limitations in terms of high geometrical loss. In this paper, the symmetry multiple-beam for quantum communication which is called as Multiphoton Quantum Communication-Multiple Beam (MQC-MB) is proposed to transmit the multiphoton from the sender to the receiver in order to minimize the impact of geometrical loss that is faced by the single-beam setup. The analysis was carried out through mathematical analysis by establishing the FSO quantum model with the effects of atmospheric and geometrical loss as well as considering atmospheric turbulence modeled by log-normal distribution. The design criteria of FSO, such as the transmitter, receiver, beam divergence, and diameter of apertures, are analytically investigated. The numerical results demonstrate that the MQC-MB outperforms the single-beam in terms of reducing channel loss by about 8 dB and works well under strong turbulence channel. Furthermore, the MQC-MB reduces the quantum bit error rate (QBER) and improves the secret key rate (SKR) as compared to the single-beam system even though the distance between the sender and receiver increases.