Atomtronic routing of dipolar bosons in a four-well star potential

The ability to precisely control and predict the evolution of quantum states is a fundamental requirement for advancing quantum technologies. Here, we develop tunable atomic routing protocols based on an integrable model of dipolar bosons confined in a four-well potential with a star-shaped configuration. By adjusting the system parameters, we identify a harmonic dynamical regime of the atomic population that can be treated analytically, providing a complete description of the system's behaviour for precise manipulation. We demonstrate three independent modes of control over the atomic population dynamics under the action of an external field: frequency tuning via variation in the field intensity, directional switching via spatial displacement of the field, and amplitude modulation by varying its duration. These modes operate under two distinct configurations: one source and two drains, and, in reverse order, two sources and one drain. These cases emulate an atomic 1:2 demultiplexer and 2:1 multiplexer, respectively. Our results may contribute to the development of control mechanisms in the design of quantum devices.