On the Validity of the One-Dimensional Description for Ring Polariton Bose–Einstein Condensates

This work is motivated by the active surge in research on ring Bose–Einstein condensates of exciton polaritons, including those with artificially created defects (barriers). Currently, such systems are primarily described within a one-dimensional approach, taking into account that the order parameter depends only on the azimuthal angle. In this work, the profiles of a polariton ring Bose–Einstein condensate in the stationary case have been numerically simulated using the two-dimensional Gross–Pitaevskii equation. The radial profiles of the ground-state wavefunction are obtained for ring confinement potentials of various depths and widths, which have been used to calculate effectively one-dimensional interaction constants for various particle densities in the condensate. The results have been compared with analytical expressions for the linear limit and for a ring of a large radius, and the validity range for these simplified analytical descriptions have been determined.