Evolutionary Optimization of Radiative Losses in Low-dimensional Systems of Dipole Emitters

In this work we utilize the differential evolution algorithm to determine the best geometries of atoms characterized by dipole transitions in a vacuum that can sustain states with the longest radiative lifetime. Our findings indicate that such dipole emitters generally form quasi-regular structures with specific geometries, which are heavily influenced by the minimum interatomic distance r
min
and the underlying physics that governs the reduction of radiative losses. Interestingly, for various amount of atoms we obtained three regions of r
min
with different geometries: linear chains for small distances less than 0.4λ
0
, fragments of triangular lattice for intermediate distances and fragments of square lattice for large distances close to λ
0
. However, we discover that predicting the specific arrangements in small ensembles is challenging, especially based on knowledge established for larger arrays. Interestingly, we find that states derived from bound states in continuum in infinite lattices exhibit the most subradiance across a wide range of r
min
values.