Tunable double well potential for fractional Josephson two-vortex molecule

We study a fractional Josephson two-vortex molecule in a long Josephson 0-κ-2κ junction. The ground state is degenerate, corresponding to two configurations with topological charges (κ, κ-2π) and (κ-2π, κ) of fractional vortices. We propose to use such a system to study macroscopic quantum phenomena involving fractional vortices. Similar to the previous proposal based on a 0-π-0 junction, the two-vortex-molecule states can be mapped to a double well potential. However, by changing the value of κ during experiment we are able to tune the energy barrier separating the two classical ground states. We calculate characteristic properties (e.g. barrier height, eigenfrequency) and demonstrate that a controlled transition into the quantum regime is possible in such a system.