Equivalent Circuit Models of the Matter Wave Transistor Oscillator

A triple-well atomtronic transistor is an atomic potential consisting of source, gate, and drain potential wells defined by a pair of closely-spaced, gaussian optical barriers. When appropriately configured with a finite temperature Bose-Einstein condensate (BEC) in the source well the system will oscillate and emit a coherent matter wave into the drain in much the same way that an electronic transistor oscillator emits a coherent electromagnetic wave when coupled to the vacuum through an antenna. The underlying physics involving many-body interactions is complex (D.Z. Anderson, Phys. Rev A, 104, 033311 (2021). However, system design and understanding is substantially facilitated by an equivalent circuit model. In such an atomtronic circuit, standard circuit principles and heuristics such as Kirchhoff's voltage (potential difference) and current (atom flux) apply. We describe the principles of the atomtronic transistor oscillator through such equivalent circuits using standard electric circuit concepts. We also discuss the properties of the emitted matter waves, which are distinct from the more familiar de Broglie waves. The waves are well suited to matterwave interferometric sensing.