  We apply reservoir engineering to construct a thermal environment with
controllable temperature in an ultracold atomic Rydberg system. A Boltzmann
distribution of the system's eigenstates is produced by optically driving a
small environment of ultracold atoms, which is coupled to a photonic continuum
through spontaneous emission. This technique provides a useful tool for quantum
simulation of dynamics coupled to a thermal environment. Additionally, we
demonstrate that pure eigenstates, such as Bell states, can be prepared in the
Rydberg atomic system using this method.
