Multiple-path interferometer with a single quantum obstacle
We consider the scattering of particles (kinetic energy e) by an obstacle which tunnels coherently between two positions (tunnel splitting Δ), for arbitrary values of e/Δ and scattering strength U. The obstacle mimics two classical scatterers at fixed positions when eΔ. Interference disappears when e >> Δ, but can be recovered if the elastic-scattering channel is detected only. At intermediate values of e there is a systematic interplay of the coherent tunnel motion and the ballistic particle motion. We show that the transmission probability can remain finite even in the limit U → ∞ because the particle can evade the obstacle systematically. We discuss the realization of a quantum obstacle in mesoscopic systems.