Two-dimensional tunneling in a SQUID

Traditionally quantum tunneling in a static SQUID is studied on the basis of a classical trajectory in imaginary time under a two-dimensional potential barrier. The trajectory connects a potential well and an outer region crossing their borders in perpendicular directions. In contrast to that main-path mechanism, a wide set of trajectories with components tangent to the border of the well can constitute an alternative mechanism of multi-path tunneling. The phenomenon is essentially non-one-dimensional. Continuously distributed paths under the barrier result in enhancement of tunneling probability. A type of tunneling mechanism (main-path or multi-path) depends on character of a state in the potential well prior to tunneling.