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In this letter we present a protocol to engineer interactions confined tosubspaces of the Fock space in trapped ions: we show how to engineer upper-,lower-bounded and sliced Jaynes-Cummings (JC) and anti-Jaynes-Cummings (AJC)Hamiltonians. The upper-bounded (lower-bounded) interaction acting upon Focksubspaces ranging from $\left\vert 0\right\rangle $ to $\left\vertM\right\rangle $ ($\left\vert N\right\rangle $ to$\ \infty$), and the slicedone confined to Fock subspace ranging from $\left\vert M\right\rangle $ to$\left\vert N\right\rangle $, whatever $M<N$. Whereas the upper-bounded JC orAJC interactions is shown to drive any initial state to a steady Fock state$\left\vert N\right\rangle $, the sliced one is shown to produce steadysuperpositions of Fock states confined to the sliced subspace $\left\{\left\vert N\right\rangle \text{,}\left\vert N+1\right\rangle \right\} $.

Slicing the Fock space for state production and protection