Quantum light in the turbulent atmosphere

Nonclassical properties of light propagating through the turbulent atmosphere are studied. We demonstrate by numerical simulation that the probability distribution of the transmission coefficient, which characterizes the effects of the atmosphere on the quantum state of light, can be reconstructed by homodyne detection. Nonclassical photonstatistics and, more generally, nonclassical Glauber-Sudarshan functions appear to be more robust against turbulence for weak light fields rather than for bright ones.

Figure 1

Homodyne detection of quantum light generated by the source, $S$, and propagated through the turbulent atmosphere. BS is a 50:50 beam-splitter, ${\text{D}}_1$ and ${\text{D}}_2$ are detectors, LO is the local oscillator.

Figure 2

(Color online) The PDTC is shown for a normal-distribution approximation of Eq. (3) with $\overline{\theta }=0.9,{\sigma }_{\theta }=0.2,{\sigma }_{\phi }=0.2,s=0.01$, and (a) $T_i=0$, (b) 0.1. The solid and the dashed lines are the initially chosen and the reconstructed (from only $5\times {10}^3$ sampling events) PDTC, respectively.

Figure 3

(Color online) $P$ function of the displaced SPATS, for $\text{Im}\left(\alpha \right)=0$, ${\overline{n}}_{\text{th}=1.11}$, (a) $\gamma =1$, (b) 7, (c) 20. The dashed lines show the standard attenuation for $T=e^{-0.3}\approx 0.7408$. The solid lines represent model (3) for $\overline{\theta }=0.3$, ${\sigma }_{\theta }=0.1$, ${\sigma }_{\phi }=0.14$, and $s=0.01$.