Multiple-path interferometer with a single quantum obstacle

– We consider the scattering of particles (kinetic energy ε) by an obstacle which tunnels coherently between two positions (tunnel splitting ∆), for arbitrary values of ε/∆ and scattering strength U . The obstacle mimics two classical scatterers at fixed positions when ε ∆. Interference disappears when ε ∆, but can be recovered if the elastic-scattering channel is detected only. At intermediate values of ε 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. In the familiar double-slit experiment a beam of particles is sent through two slits in a plate and the transmitted intensity is observed on a screen. One finds an interference pattern, thus demonstrating the coherent superposition of the two possible scattering paths. The same result is obtained for the reflection from obstacles, e.g., the bars of a reflection grating. In these experiments the slits or bars only play a passive role. In this paper we consider scattering by a single obstacle, which, however, is by itself a quantum object with states that correspond to different locations (see fig. 1). Allowing for superpositions of these states, we have an obstacle that is delocalized in space. Which reflection or transmission pattern is then observed on the screen? It is straightforward to demonstrate that the quantum obstacle may act as a collection of classical scatterers, in that one observes the corresponding interference pattern on the screen. The condition for interference is that the tunnel splitting ∆ is larger than the kinetic energy ε of the incident particles (fast-tunneling regime). For ∆ ε (slowtunneling regime) the interference pattern from the obstacle disappears, but can be recovered if only the elastic-scattering channel is detected.