Free-space quantum links under diverse weather conditions

Free-space optical communication links are promising channels for establishing secure quantum communication. Here we study the transmission of nonclassical light through a turbulent atmospheric link under diverse weather conditions, including rain or haze. To include these effects, the theory of light transmission through atmospheric links in the elliptic-beam approximation presented by Vasylyev et al. [D. Vasylyev et al., Phys. Rev. Lett. 117, 090501 (2016)] is further generalized. It is demonstrated, with good agreement between theory and experiment, that low-intensity rain merely contributes additional deterministic losses, whereas haze also introduces additional beam deformations of the transmitted light. Based on these results, we study theoretically the transmission of quadrature squeezing and Gaussian entanglement under these weather conditions.

Figure 1

Scheme of optical beam transmission through the turbulent and scattering atmosphere. The beam with initial beam-spot radius $W_0$ undergoes random deformations and deflections while propagating in the atmospheric link of length $L$. A part of the radiation field is scattered and absorbed, which is the source of additional extinction losses. The transmitted beam is cut by the circular receiver aperture of radius $a$.

Figure 2

Elliptic-beam approximation PDT (solid line) compared with the experimental PDT (dashed line). The measurement was performed at night on 24 August 2016 at 00:20 (local time); the data acquisition time is 12 s. The other parameters are a wavelength of 780 nm, the initial spot radius $W_0=20$ mm, the aperture radius $a=75$ mm, the Rytov parameter ${\sigma }_R^2=1.78$, the beam divergence parameter due to random scattering $\mathrm{\Xi }=5$, and the extinction factor ${\chi }_{\mathrm{ext}}=0.51$. The last three parameters are derived from the fitting procedure of the theoretical PDT to the experimental data.

Figure 3

Elliptic-beam approximation PDT (solid line) compared with the experimental PDT (dashed line). The measurement was performed at night on 24 August 2016 at 02:00 (local time); the data acquisition time is 9 s. The estimated from the fit Rytov parameter is ${\sigma }_R^2=1.05$, the beam divergence parameter $\mathrm{\Xi }=12$, and ${\chi }_{\mathrm{ext}}=0.40$.

Figure 4

Influence of haze on transmission characteristics of the atmospheric channel. The PDT with the inclusion of random scattering due to haze (solid line) is calculated for the same parameters as in Fig. 2, i.e., it corresponds to the experimental data. The PDT without inclusion of haze (dashed line) is theoretically deduced; extinction losses are ${\chi }_{\mathrm{ext}}=0.94$ due to molecular absorption.

Figure 5

Experimental (dashed line) and theoretically fitted (solid line) PDTs for atmospheric quantum channel in the presence of rainfall. The measurement was performed at daytime on 08 June 2016 at 11:15 (local time); the data acquisition time is 14 s. The estimated Rytov parameter ${\sigma }_R^2=2.88$, the beam divergence parameter due to scattering on haze $\mathrm{\Xi }=0.2$, the path-averaged rain intensity $\overline{\mathcal{I}}=3.2\text{mm}/\text{h}$, and ${\chi }_{\mathrm{ext}}=0.43$.

Figure 6

Atmospheric channel transmittance distribution with (solid line) and without (dashed line) light rain. The latter PDT includes additional extinction losses ${\chi }_{\mathrm{ext}}=0.94$ due to molecular absorption. The solid line corresponds to the elliptic-beam model fit in Fig. 5, whereas the dashed line is theoretically deduced.

Figure 7

Transmitted value of squeezing as a function of postselection threshold ${\eta }_{\min }$. The input light is squeezed to $-2.4$ dB and sent through three atmospheric channels presented in Figs. 2, 3, 5. The predicted behaviors are theoretically evaluated on the basis of the experimental PDTs. The solid line corresponds to the nighttime channel with the Rytov parameter ${\sigma }_R^2=1.78$, divergence parameter $\mathrm{\Xi }=5$, extinction losses ${\chi }_{\mathrm{ext}}=0.51$, and mean transmittance $\langle \eta \rangle =0.36$. The dashed line corresponds to the rainy daytime channel with ${\sigma }_R^2=2.88,\mathrm{\Xi }=0.2,{\chi }_{\mathrm{ext}}=0.43$, and $\langle \eta \rangle =0.29$. The dash-dotted line corresponds to the nighttime channel with haze, ${\sigma }_R^2=1.05,\mathrm{\Xi }=12,{\chi }_{\mathrm{ext}}=0.40$, and $\langle \eta \rangle =0.26$. For all curves the additional losses on optical components ${\eta }_{\mathrm{opt}}=0.88$ and detection efficiency ${\eta }_{\det }=0.9$ are included. All other parameters are the same as in Fig. 2.

Figure 8

Shaded areas represent the regions where the entanglement can be verified by applying the Simon entanglement test, which is a function of the squeezing parameter $\xi$ and of the coherent displacement $|\langle \widehat{a}\rangle |$. The solid, dashed, and dash-dotted lines correspond to the bounds of the region where entanglement survives, for the respective channels listed in the caption of Fig. 7.