Lattice topology dictates photon statistics

Abstract

Propagation of coherent light through a disordered network is accompanied by randomization and possible conversion into thermal light. Here, we show that network topology plays a decisive role in determining the statistics of the emerging field if the underlying lattice satisfies chiral symmetry. By examining one-dimensional arrays of randomly coupled waveguides arranged on linear and ring topologies, we are led to a remarkable prediction: the field circularity and the photon statistics in ring lattices are dictated by its parity -- whether the number of sites is even or odd, while the same quantities are insensitive to the parity of a linear lattice. Adding or subtracting a single lattice site can switch the photon statistics from super-thermal to sub-thermal, or vice versa. This behavior is understood by examining the real and imaginary fields on a chiral-symmetric lattice, which form two strands that interleave along the lattice sites. These strands can be fully braided around an even-sited ring lattice thereby producing super-thermal photon statistics, while an odd-sited lattice is incommensurate with such an arrangement and the statistics become sub-thermal. Such effects are suppressed in the limit of high lattice disorder, whereupon Anderson localization arrests the spread of light around the lattice and eliminates topology-dependent phenomena.

7 pages, 6 figures

References in corpus (9)

• Topological Photonics
• Quantum walks of correlated particles
• Quantum Correlations in Two-Particle Anderson Localization
• A photonic thermalization gap in disordered lattices
• Sub-thermal to super-thermal light statistics from a disordered lattice via deterministic control of excitation symmetry
• Thermalization of Strongly Disordered Nonlinear Chains
• Discrete Anderson Speckle
• Interferometric control of the photon-number distribution
• Hanbury Brown and Twiss anticorrelation in disordered photonic lattices

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