  We report on the robust experimental accumulation of nonclassicallity of
motion of a single trapped ion. The nonclassicality stems from deterministic
incoherent modulation of thermal phonon number distribution implemented by a
laser excitation of nonlinear coupling between the ion's internal - electronic
levels and external - motional states. We demonstrate that the repetitive
application of this nonlinear process monotonically accumulates the observable
state nonclassicality. The output states converge to a phonon number
distribution with high overlap with a particular Fock state and visible quantum
non-Gaussian aspects including corresponding negative Wigner function. The
resulting oscillator states prove deterministic transition in the hierarchy of
quantum non-Gaussianity up to four phonons. This transition is very robust
against experimental imperfections and produces increasing entanglement
potential.
