Abstract
The efficient coupling of photons from a free-space quantum channel into a single-mode optical fiber (SMF) has important implications for quantum network concepts involving SMF interfaces to quantum detectors, atomic systems, integrated photonics, and direct coupling to a fiber network. Propagation through atmospheric turbulence, however, leads to wavefront errors that degrade mode matching with SMFs. In a free-space quantum channel, this leads to photon losses in proportion to the severity of the aberration. This is particularly problematic for satellite-Earth quantum channels, where atmospheric turbulence can lead to significant wavefront errors. This report considers propagation from low-Earth orbit to a terrestrial ground station and evaluates the efficiency with which photons couple either through a circular field stop or into an SMF situated in the focal plane of the optical receiver. The effects of atmospheric turbulence on the quantum channel are calculated numerically and quantified through the quantum bit error rate and secure key generation rates in a decoy-state BB84 protocol. Numerical simulations include the statistical nature of Kolmogorov turbulence, sky radiance, and an adaptive-optics system under closed-loop control.
Highlights
Propagation of coherent light through atmospheric turbulence leads to wavefront errors that enlarge the classical irradiance and quantum probability distributions at a focus
Results from detailed numerical simulations of a satelliteEarth quantum channel downlink demonstrate that a 200-Hz closed-loop bandwidth AO system can substantially enhance the performance of the channel, including the case where single-mode optical fiber (SMF) are part of the quantum receiver system
These results are timely given the emergence of quantum technologies that integrate optical waveguides and SMFs with quantum systems and the recent advancements in space-to-Earth quantum communication.[36,37,38,39]
Summary
Propagation of coherent light through atmospheric turbulence leads to wavefront errors that enlarge the classical irradiance and quantum probability distributions at a focus. The effects of atmospheric turbulence on SMF-coupling efficiency have been considered previously for classical optical channels. Ma et al.[11] measured SMF-coupling efficiencies and bit error rates over an 11.8-km free-space optical-communication system using an erbium-doped fiber amplifier and showed favorable agreement with a model based on the statistical nature of turbulence. Appendix A reviews the analytic solution for power coupling efficiency of a diffraction-limited optical field into an SMF where the SMF mode is approximated by a Gaussian function This result defines the optimum relationship between the size of the fiber mode and a diffraction-limited focus.
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