Abstract
A self-consistent theoretical treatment of a triple-well atomtronic transistor circuit reveals the mechanism of gain, conditions of oscillation, and properties of the subsequent coherent matterwaves emitted by the circuit. A Bose-condensed reservoir of atoms in a large source well provides a chemical potential that drives circuit dynamics. The theory is based on the ansatz that a condensate arises in the transistor gate well as a displaced ground state, that is, one that undergoes dipole oscillation in the well. That gate atoms remain condensed and oscillating is shown to be a consequence of the cooling induced by the emission of a matterwave into the vacuum. Key circuit parameters such as the transistor transconductance and output current are derived by transitioning to a classical equivalent circuit model. Voltage-like and current-like matterwave circuit wave fields are introduced in analogy with microwave circuits, as well as an impedance relationship between the two. This leads to a new notion of a classical coherent matterwave that is the dual of a coherent electromagnetic wave and which is distinct from a deBroglie matterwave associated with cold atoms. Subjecting the emitted atom flux to an atomic potential that will reduce the deBroglie wavelength, for example, will increase the classical matterwave wavelength. Quantization of the classical matterwave fields leads to the dual of the photon that is identified not as an atom but as something else, which is here dubbed a "matteron".
Highlights
This work seeks to elucidate the principles of an atombased transistor oscillator “circuit” [1]
An unintuitive result from the kinetic treatment is that atoms in the gate are colder, Tg < TB, and acquire a higher chemical potential, μg > μs, than those in the source given feedback above a particular threshold value
We note that the spontaneous formation of a Bose condensate in the gate underlies the theory’s prediction of a reverse bias for the atomtronic transistor
Summary
This work seeks to elucidate the principles of an atombased transistor oscillator “circuit” [1]. One involves atom analogs to superconducting devices and circuits, such as Josephson junctions and SQUIDS [8,9,10,11,12,13,14,15] (though it is perhaps notable that atomtronic circuitry does not require cryogenics to operate). These atomtronic circuits operate as closed, i.e., energy-conserving, systems and are interesting from a fundamental viewpoint as well as for their potential in sensing applications. The dual to the feedback provided from the tank circuit to the FET gate corresponds to the difference in barrier heights of the atomtronic transistor
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