  Motivated by the proposal to simulate para-Bose oscillators in a trapped-ion
setup [C. Huerta Alderete and B. M. Rodr\'iguez-Lara, Phys. Rev. A 95, 013820
(2017)], we introduce an overcomplete, nonorthogonal basis for para-Bose
Hilbert spaces. The states spanning these bases can be experimentally realized
in the trapped-ion simulation via time evolution. The para-Bose states show
both nonclassical and semiclassical statistics on their Fock state
distribution, asymmetric field quadrature variances, and do not minimize the
uncertainty relation for the field quadratures. These properties are
analytically controlled by the para-Bose order and the evolution time; both
parameters might be feasible for fine tuning in the trapped-ion quantum
simulation.
