A Gauge Field Theory of Coherent Matter Waves

Matter-wave is a concept well-entrenched in physics referring to the quantum-mechanical wave-particle duality, where an individual or an ensemble of particles is characterized by de Broglie wavelength. It is nicely exemplified by the flux of atoms extracted from a Bose-Einstein condensate (BEC), where the de Broglie wavelength of individual particles overlaps creating a macroscopic wavefunction. Amongst various applications, the achievement of BEC catalyzed the field of atomtronics –the atom analog of electronics in which atom flux and chemical potential substitute for electric current and potential. As fundamentally non-thermal-equilibrium open quantum systems, even simple atomtronic circuits prove challenging for many-body methods typically used to describe simple BEC dynamics.



In this work, we develop the field-theoretic approach towards atomrtonics systems, aiming to highlight similarities (and differences) between electromagnetic and matter waves. As a starting point, we consider an oscillating current of ultracold neutral atoms whose mutual Van der Waals interactions cause them to repel. We show that the current oscillation imposes temporal coherence across a system: an aspect that is typically absent in many-body physics treatments. Moreover, the velocity associated with the gauge field is tied to that of the atoms, which in turn is influenced by an external potential that acts directly on the atoms. Finally, the quantization of the field introduces the matteron, a massless gauge boson that is an excitation quanta of the field. We expect that the presented formalism will allow leveraging sets of heuristic, analytical, and numerical tools developed for electromagnetics to describe atomtronics circuits more easily.