Ferrodark Solitons in a Spin-1 Bose-Einstein Condensate

Explore the fascinating world of ferrodark solitons in spin-1 Bose-Einstein condensates through this comprehensive lecture. Delve into the exact propagating topological excitations associated with Z2 symmetry in the easy-plane phase of ferromagnetic spin-1 Bose-Einstein condensates. Discover how these excitations manifest as kinks in the transverse magnetization and learn about the conditions necessary for their propagation. Examine the two types of ferrodark solitons: the low energy branch with positive inertial mass and the higher energy branch with negative inertial mass. Investigate the unique maximum speed limit for these solitons and how it differs from limits set by Bogoliubov excitations. Understand the concept of physical mass in relation to the number density dip and its negative nature for both soliton types. Finally, explore the behavior of solitons in finite one-dimensional systems subject to linear potentials, including oscillations caused by transitions between the two types at maximum speed.