  Quantum mechanics allows paraparticles with mixed Bose-Fermi statistics that
have not been experimentally confirmed. We propose a trapped-ion scheme whose
effective dynamics are equivalent to a driven para-Bose oscillator of even
order. Our mapping suggest highly entangled vibrational and internal ion states
as the laboratory equivalent of quantum simulated parabosons. Furthermore, we
show the generation and reconstruction of coherent oscillations and para-Bose
analogs of Gilmore-Perelomov coherent states from population inversion
measurements in the laboratory frame. Our proposal, apart from demonstrating an
analog quantum simulator of para-Bose oscillators, provides a quantum state
engineering tool that foreshadows the potential use of paraparticle dynamics in
the design of quantum information systems.
