Controlled flow of excitations and source-to-drain transport in circuits of Rydberg atoms

We study chiral currents of Rydberg excitations in closed circuits of Rydberg atoms. The currents flowing in the circuit can be controlled by a phase pattern imprinted via a Raman scheme and can persist even in the presence of dephasing. Depending on the interplay between the Rabi coupling of Rydberg states and the dipole-dipole atom interaction, the current shows markedly different features. Attaching leads to a ring circuit, we study the source-to-drain transport through the system. Inspired by the rf-and c-SQUIDs we consider rings with one and two local energy offsets or detunings. As a combination of specific phase shifts in going though the localized detunings and as a result of coherent tunneling, we demonstrate how the transport of excitations can be controlled, with a distinctive dependence on the range of interaction.