Evolution and decay of an Alice ring in a spinor Bose-Einstein condensate

We use first-principles-derived numerical simulations to investigate the long-time evolution of a half-quantum vortex ring, an Alice ring, arising from the decay dynamics of an isolated monopole in the polar phase of a dilute spin-1 Bose-Einstein condensate. In particular, we study the lifetime and decay characteristics of the Alice ring under different experimentally relevant conditions. We observe that, in a 87Rb condensate with a homogeneous external magnetic field, a well-centered Alice ring may survive for over 160 ms, and that during its lifetime it can contract back into a monopole, which again converts into an Alice ring. Interestingly, we notice an additional Alice ring, with an opposite topological charge, to emerge during the decay dynamics within the condensate, leading to the coexistence of two Alice rings in the same cloud. Shortly after this coexistence, the original Alice ring breaks into a line-like defect referred to as an Alice string. We find that the location of the initial isolated monopole correlates with the winding direction of the scalar phase in the produced vortex ring, a phenomenon which we utilize to create two Alice rings with opposite charges and opposite winding directions. Such created Alice ring and anti-Alice ring naturally annihilate each other in the subsequent evolution.