14 May 2018 Effect of lattice topology on photon statistics
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Coherent light traversing disordered media usually attains a random field both in amplitude and phase with independent Gaussian statistics and results in thermal light (associated with Bose-Einstein photon-number statistics) upon ensemble averaging. This is expected according to the central limit theorem, which dictates the addition of a large number of independent random variables leads to a normal (Gaussian) distribution. Here, we show that certain network topologies that light travels within preclude the central limit theorem and result in non-Gaussian statistics. We realize such networks in the form of evanescently-coupled waveguide arrays (photonic lattices) and obtain the photon statistics at the output by time gating and averaging over multiple realizations of disordered photonic lattices. The effect of lattice topology, however, only exists when the photonic lattice is endowed with chiral-symmetric eigenmode pairs a disorder-immune symmetry where the eigenmodes appear in pairs with oppositely signed eigenvalues and the coherent input field satisfies certain conditions. We specifically examine one-dimensional arrays of randomly coupled identical waveguides (off-diagonal disorder) arranged on linear and ring topologies. The emerging field exhibits super-thermal statistics (associated with modified Bose-Einstein photon-number statistics) only for ring lattices with even parity and linear lattices (independent of its parity), whereas input coherent fields traversing ring lattices with odd parity attain sub-thermal statistics. By controlling the relative phase of a coherent input field exciting two neighboring lattice sites, we also demonstrate a deterministic tuning of photon-number statistics, namely photon bunching, while maintaining the mean photon number fixed.
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H. Esat Kondakci, H. Esat Kondakci, Ayman F. Abouraddy, Ayman F. Abouraddy, Bahaa E. A. Saleh, Bahaa E. A. Saleh, "Effect of lattice topology on photon statistics", Proc. SPIE 10659, Advanced Photon Counting Techniques XII, 106590L (14 May 2018); doi: 10.1117/12.2305749; https://doi.org/10.1117/12.2305749

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