Lattice topology dictates photon statistics

TL;DR

This paper demonstrates that the topology of chiral-symmetric lattices, especially their parity, crucially influences photon statistics during light propagation, enabling control over thermal light characteristics in disordered networks.

Contribution

It reveals how lattice topology and parity determine photon statistics in disordered waveguide arrays, a novel insight into topological effects on light behavior.

Findings

Photon statistics depend on lattice parity in ring topologies.

Adding or removing a site switches photon statistics between super-thermal and sub-thermal.

High disorder suppresses topology-dependent effects due to Anderson localization.

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.