The field of atomtronics seeks to implement analogues of electronic circuits with ultracold quantum gases confined to configurable potentials (traps), both for future quantum devices, such as inertial sensors, and also for fundamental research into particle transport. At the heart of the atomtronic perspective, and most engineering disciplines, are lumped abstraction models that, in the electronics context, allow complex circuits to be represented as a series of simple electronic elements. Although these models are useful, in that they hide complex parts of the underlying microscopic physics, they must not leave out so much information as to be unable to make reliable predictions about the system dynamics.
The experimental study presented investigates the utility of the lumped circuit model in describing an atomtronic LRC-resonator circuit, composed of two superfluid reservoirs connected by a channel (weak link). We find that the circuit model can be used to model superfluid transport, but one must take into consideration the contact inductance. We examine the resistivity of the weak link and find an Ohmic relationship, consistent with a contact resistance which manifests as phase slips at the weak link exit coupling to either turbulent or sound modes.