Atmospheric Quantum Channels with Weak and Strong Turbulence

The free-space transfer of high-fidelity optical signals between remote locations has many applications, including both classical and quantum communication, precision navigation, clock synchronization, etc. The physical processes that contribute to signal fading and loss need to be carefully analyzed in the theory of light propagation through the atmospheric turbulence. Here we derive the probability distribution for the atmospheric transmittance including beam wandering, beam shape deformation, and beam-broadening effects. Our model, referred to as the elliptic beam approximation, applies to weak, weak-to-moderate, and strong turbulence and hence to the most important regimes in atmospheric communication scenarios.

Figure 1

The PDTs (a) and the corresponding exceedances (b): elliptic-beam approximation, log-normal, and Beam-wandering [24]. The shaded area in (a) shows the experimental PDT from Ref. [28]. The inset in (b) shows the tail of the exceedance. For the log-normal exceedance, it extends to the unphysical region, $\eta >1$ (shaded gray). Further parameters: wavelength 809 nm, initial spot radius $W_0=20\mathrm{mm}$, propagation distance 1.6 km, Rytov parameter ${\sigma }_R^2=1.5$, aperture radius $a=40\mathrm{mm}$, and a deterministic attenuation of 1.25 dB.

Figure 2

The PDTs and the corresponding exceedances, similar to those shown in Fig. 1, but for the case of strong turbulence. Further parameters: wavelength 780 nm, initial spot radius $W_0=50\mathrm{mm}$, propagation distance 2 km, Rytov parameter ${\sigma }_R^2=31.5$, aperture radius $a=150\mathrm{mm}$, and no deterministic attenuation.

Figure 3

Transmitted value of squeezing as a function of the postselection threshold ${\eta }_{\min }$. Initially, squeezed light (to $-2.4\mathrm{dB}$, $\lambda =780\mathrm{nm}$, and spot radius $W_0=25\mathrm{mm}$) is sent through a 1.6 km atmospheric link (${\sigma }_R^2=2.6$) and detected with an aperture radius of $a=75\mathrm{mm}$. The deterministic attenuation is 1.9 dB. The output signal is squeezed by $-0.95\mathrm{dB}$. With the postselection protocol, the squeezing value can be improved depending on the postselection threshold ${\eta }_{\min }$. The theory is shown for the elliptic-beam, log-normal, and Beam-wandering models, compared with the experimental results (shaded area lies within the error bars) from Ref. [7].