Effects of Atmospheric Turbulence on Spatially Entangled Photon Pairs Generated by SPDC

Abstract

Spatially entangled photon pairs are promising resources for free-space quantum communication but, unlike polarization encoding, spatial encoding is directly affected by turbulenceinduced wavefront distortions that reduce coherence between the spatial alternatives defining the quantum state. This thesis studies an effective two-qubit spatial state generated by degenerate Type-I spontaneous parametric down-conversion, in which signal and idler photons occupy two correlated transverse-path alternatives. Entanglement is quantified through concurrence, determined by the off-diagonal coherence of the two-photon density matrix. The atmosphere is modeled as an stochastic phase screen, and the change in concurrence is expressed as an ensemble average of phase differences evaluated at the four positions defining the spatial qubits. Theoretical predictions are derived from the phase structure functions of the Kolmogorov and modified von Kármán models, using the Fried parameter r0 to characterize turbulence strength. Numerical phase screens are generated through a finite Zernike-polynomial expansion with correlated coefficients obtained from model-dependent covariance matrices. Simulations use 500 Zernike modes and 1,000 statistically independent phase screens for each sampled value of r0. The numerical results agree closely with theory for both turbulence models. Concurrence approaches zero for strong turbulence and unity when the turbulent wavefront is coherent across the biphoton state. Entanglement degradation is governed mainly by the relation between r0 and the effective transverse size Δρ′, while the separation d between spatial alternatives has a weaker influence. Both turbulence models give similar predictions at the scalesconsidered, with differences expected near the inner turbulence scale. The framework directly connects atmospheric phase statistics with spatial-entanglement degradation and provides a basis for more robust spatial encodings and future laboratory validation using spatial light modulators.