Josephson physics in atomtronic devices

Experiments involving interaction of ions with trapped atomic Bose-Einstein condensates are currently discussed at GSI. These experiments may be of relevance for the emerging field of atomtronics which focuses on the development of BEC analogies to electronic devices and circuits. One of the key features of atomtronic experiments is coherent quantum tunneling of the condensate through optical barriers, known as the Josephson effect. Being thoroughly studied in superconductors this effect and various related phenomena still remain little explored in atomic BECs. In particular basic Josephson equations, that are most widely used, neglect completely the finite-size effects and spatial inhomogeneity of the order parameter. My current research aims to investigate the effects of junction geometry and finite size on its dynamics and transport properties. In this talk I will give a brief review of the Josephson effect in general and emphasize the differences in its manifestation between superconductors and trapped atomic BECs. I will also review the present status of experimental and theoretical research related to the Josephson effects in BECs. Finally, I will present my recent results on the phonon-Josephson coupling as one of the finite-size effects under study and give an outline of the further developments in this direction. I will also outline several possibilities to control the dynamics of Josephson junction with trapped ions and ionic beams.