Emergence of semifluxons in long 0-$\pi$-0 Josephson junctions as a topological state change

We present a generic, analytical model of the emergence of semifluxons in long 0-$\pi$-0 Josephson junctions and demonstrate its implementation in the context of ultracold matter waves using optical junctions. Semifluxons are well-known topological states at the interface of superconductors (1), related to ordinary quantized magnetic flux or vortices in superfluid systems. They appear in particular when there is a spatially varying tunnel rate in the Josephson junction. This interesting subject has stimulated previous work to implement analogous states in ultracold quantum gases (2). \\[4pt] (1) E. Goldobin, et al., Phys. Rev. Lett., 92, 057005 (2004)\\[0pt] (2) R. Walser, et al., NJP, 10, 045020 (2008)