Highlights

## Atomtronic Superfluid Circuits ()

Circuits with condensed bosons can support superflow. Such circuits, if realized, will be used as QUBITs (for quantum computation) or as SQUIDs (for sensing of acceleration or gravitation). We are studying the feasibility and the design considerations for such devices. The key is to develop a theory for the superfluidity in an atomtronic circuit. Such theory goes beyond the traditional framework of Landau and followers, since is involves ''Quantum chaos'' considerations.

Figure: Regime diagram for the stability of flow-states in a superfluid circuit. The axes are: the rotation frequency $\Phi$ of the device; and the interaction $u$. Stable regions are indicated by red color. Blue indicates instability.

Our recent studies are focused in Bose-Hubbard superfluid circuits. The expected results are novel due to the quantum chaos perspective. In particular we predict drastic differences between 3 site rings and rings that have more than 3 sites. In the former instability of flow states is due to swap of separatrices, while in the latter it has to do with a web of non-linear resonances. We also argue that it is not likely to observe coherent operation for rings that have a weak link and more than 5 sites.

Figure: Each point in the left panel represents a stationary state of the ring, and is positioned according to its energy (vertical axis) and its average current (horizontal axis). We see that the ring can support states that features a very large current. The right panel illustrates the "phase-space" of the device. The large-current states are supported by the red chaotic pond. This type of stability goes beyond the traditional analysis, and require familiarity with Kolmogorov-Arnold-Moser theory.