Atom chips with two-dimensional electron gases: theory of near surface trapping and ultracold-atom microscopy of quantum electronic systems

We show that current in a two-dimensional electron gas (2DEG) can trap ultracold atoms $<1 \mu$m away with orders of magnitude less spatial noise than a metal trapping wire. This enables the creation of hybrid systems, which integrate ultracold atoms with quantum electronic devices to give extreme sensitivity and control: for example, activating a single quantized conductance channel in the 2DEG can split a Bose-Einstein condensate (BEC) for atom interferometry. In turn, the BEC offers unique structural and functional imaging of quantum devices and transport in heterostructures and graphene.