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Rotational analogs to magnetic fluxons in conventional Josephson junctionsare predicted to emerge in the ground state of rotating tunnel-coupled annularBose-Einstein condensates (BECs). Such topological condensate-phase structurescan be manipulated by external potentials. We determine conditions forobserving macroscopic quantum tunneling of a fluxon. Rotational fluxons indouble-ring BECs can be created, manipulated, and controlled by externalpotential in different ways than possible in the solid state system, thusrendering them a promising new candidate system for studying and utilizingquantum properties of collective many-particle degrees of freedom.

Rotational Fluxons of Bose-Einstein Condensates in Coplanar Double-Ring Traps