  Central spin models, where a single spinful particle interacts with a spin
environment, find wide application in quantum information technology and can be
used to describe, e.g., the decoherence of a qubit over time. We propose a
method of realizing an ultracold quantum simulator of a central spin model with
XX (spin-exchanging) interactions. The proposed system consists of a single
Rydberg atom ("central spin") and surrounding polar molecules ("bath spins"),
coupled to each other via dipole-dipole interactions. By mapping internal
particle states to spin states, spin-exchanging interactions can be simulated.
As an example system geometry, we consider a ring-shaped arrangement of bath
spins, and show how it allows us to exact precise control over the interaction
strengths. We numerically analyze two example dynamical scenarios which can be
simulated in this setup: a decay of central spin polarization, which can
represent qubit decoherence in a disordered environment, and a transfer of an
input spin state to a specific output spin, which can represent the
transmission of a single bit across a quantum network. We demonstrate that this
setup allows us to realize a central spin model with highly tunable parameters
and geometry, for applications in quantum science and technology.
