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 photon-statistics and, more generally, nonclassical Glauber-Sudarshan functions appear to be more robust against turbulence for weak light fields rather than for bright ones.
The propagation of polarization-entangled states of light through fluctuating loss channels in the turbulent atmosphere is studied, including the situation of strong losses. We consider violations of Bell inequalities by light, emitted by a parametric down-conversion source, after transmission through the turbulent atmosphere. It is shown by analytical calculations, that in the presence of background radiation and dark counts, fluctuating loss channels may preserve entanglement properties of light even better than standard loss channels, when postselected measurements are applied.
We demonstrate experimentally how orbital-angular-momentum entanglement of two photons evolves under influence of atmospheric turbulence. We find that the quantum channel capacity is surprisingly robust: Its typical horizontal decay distance is of the order of 2 kilometers, demonstrating the potential of photonic orbital angular momentum for free-space quantum communication in a metropolitan environment.
One of the most important properties of orbital angular momentum (OAM) of photons is that the Hilbert space required to describe a general quantum state is infinite dimensional. In principle, this could allow for encoding arbitrarily large amounts of quantum information per photon, but in practice, this potential is limited by decoherence and errors. To determine whether photons with OAM are suitable for quantum communication, we numerically simulated their passage through a turbulent atmosphere and the resulting errors. We also proposed an encoding scheme to protect the photons from these err…
Due to the transfer of the angular spectrum of the pump beam to the two-photon state in spontaneous parametric down-conversion the generated twin photons are entangled in Hermite-Gaussian (HG) modes. This enables one using HG modes as an alphabet for quantum communication. For global quantum communication purposes, we derive an analytic expression for two-photon detection probability in terms of HG modes taking into account the effects of the turbulent atmosphere. Our result is more general as it accounts for the propagation of both, signal and idler photons through the atmosphere, as opposed …
We provide a rigorous treatment of the entanglement properties of two-mode Gaussian states in atmospheric channels by deriving and analyzing the input-output relations for the corresponding entanglement test. A key feature of such turbulent channels is a non-trivial dependence of the transmitted continuous-variable entanglement on coherent displacements of the quantum state of the input field. Remarkably, this allows one to optimize the entanglement certification by modifying local coherent amplitudes using a finite, but optimal amount of squeezing. In addition, we propose a protocol which, in…
The photon density operator function is used to calculate light beam propagation through turbulent atmosphere. A kinetic equation for the photon distribution function is derived and solved using the method of characteristics. Optical wave correlations are described in terms of photon trajectories that depend on fluctuations of the refractive index. It is shown that both linear and quadratic disturbances produce sizable effects for long-distance propagation. The quadratic terms are shown to suppress the correlation of waves with different wave vectors. We examine the intensity fluctuations of p…
Violations of Bell inequalities are better preserved by turbulent atmospheric channels than by comparable optical fibers in the scenario of copropagating entangled photons [A.A. Semenov and W. Vogel, Phys. Rev. A 81, 023835 (2010); arXiv:0909.2492]. Here we reexamine this result for the case of counterpropagation also considering the fact that each receiver registers so-called double-click events, which are caused by dark counts, stray light, and multi-photon entangled pairs. We show that advantages of the atmospheric links are feasible only for the copropagation scenario in the case of strong…
The statistical fluctuations in free-space links in the turbulent atmosphere are important for the distribution of quantum signals. To that end, we first study statistics generated by the turbulent atmosphere in an entanglement based free-space quantum key distribution (QKD) system. Using the insights gained from this analysis, we study the effect of link fluctuations on the security and key generation rate of decoy state QKD concluding that it has minimal effect in the typical operating regimes. We then investigate the novel idea of using these turbulent fluctuations to our advantage in QKD e…
The method of photon distribution function (PDF) is used to study fluctuations of light beams propagating through a turbulent atmosphere. Our analysis concerns the regime of saturated fluctuations. The focus is on the phenomena of beam wandering and the effect of partial coherence on photon density fluctuations. It is shown that the size of the quasiclassical part of wandering decreases with the propagation distance, while the quantum part increases. We explain this qualitative difference by beam fragmentation, which is accompanied by a loss of correlation between individual parts. The effect …
Orbital angular momentum of photons is an intriguing system for the storage and transmission of quantum information, but it is rapidly degraded by atmospheric turbulence. Understanding the noise processes that affect photons is essential if we desire to protect them. In this paper we use the infinitesimal propagation equation of Roux to derive a discrete Lindblad equation, and numerically study the form of the most relevant Lindblad operators. We find that the dominant Lindblad operators are those that shift the angular momentum by one unit. We explore possible schemes to protect quantum infor…
The evolution of an entangled photon state propagating through a turbulent atmosphere is formulated in terms of a set of coupled first order differential equations, by using an infinitesimal propagation approach. The orbital angular momentum (OAM) basis is used to described the density matrix of the state. Although the analysis is done in the paraxial limit for a monochromatic optical field, the formalism is comprehensive in the sense that it does not require any assumptions about the strength of the turbulence and it can incorporate any spectral model for the turbulence. As a comparative exam…
In this work, we present an extensive analysis on the nature and performance of Ince-Gauss beams, elliptical solutions of the paraxial wave equation that have orbital angular momentum, as information carriers in turbulent atmosphere. We perform numerical simulations of the propagation of these beams, and focus on the effects that the order, degree and ellipticity parameters have on the robustness of the beams. We find that the choice of basis in which a mode is constructed does not greatly influence the mode performance and it is instead strongly affected by the combination of order and degree…
The effect of a random phase screen on laser beam wander in a turbulent atmosphere is studied theoretically. The method of photon distribution function is used to describe the photon kinetics of both weak and strong turbulence. By bringing together analytical and numerical calculations, we have obtained the variance of beam centroid deflections caused by scattering on turbulent eddies. It is shown that an artificial distortion of the initial coherence of the radiation can be used to decrease the wandering effect. The physical mechanism responsible for this reduction and applicability of our ap…
Circular-beam approximation for quantum channels in a turbulent atmosphere
Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine（乌克兰国家科学院博戈留博夫理论物理研究所）；Kyiv Academic University（基辅学术大学）；Kyiv School of Economics（基辅经济学校）
The photon density operator function is used to describe the propagation of single-photon pulses through a turbulent atmosphere. The effects of statistical properties of photon source and the effects of a random phase screen on the variance of photon counting are studied. A procedure for reducing the total noise is discussed. The physical mechanisms responsible for this reduction are explained.
Scattering by atmospheric turbulence is one of the main challenges in creating long free-space optical links, and specifically links of entangled photons. Classical compensation methods are hard to apply to entangled photons, due to inherently low signal to noise ratios and the fragility of entanglement. We have recently shown that we can use the bright laser beam that pumps spontaneous parametric down conversion to control the spatial correlations between entangled photons for compensating their scattering. In this work, we apply the pump-shaping technique to compensate for scrambling of corr…
The quasiclassical distribution function for photon density in the phase space is obtained from solution of the kinetic equation. This equation describes propagation of paraxial laser beams in the Earth atmosphere where "collision integral" embodies the influence of turbulence. The anisotropy of photon distribution is shown and explained. For long propagation path, the explicit expression for fourth-order moment of light is obtained as a sum of linear and quadratic forms of the average distribution function. This moment describes a spatial correlation of four light waves, giving the informatio…
Collisionless Boltzmann equation is used to describe the intensity correlations in partially saturated and fully saturated regimes in terms of photon distribution function in the phase space. Explicit expression for fourth moment of the light fields is obtained for the case of moderate and strong turbulence. Such expression consists of two terms accounting for two regions in the phase space that independently contribute to the correlation function. It is shown that present solution agrees with previous results for fully saturated regime. Additionally it embodies the effect of partially saturat…
