  In this letter we present a protocol to engineer interactions confined to
subspaces 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 Fock
subspaces ranging from $\left\vert 0\right\rangle $ to $\left\vert
M\right\rangle $ ($\left\vert N\right\rangle $ to$\ \infty$), and the sliced
one 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 or
AJC 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 steady
superpositions of Fock states confined to the sliced subspace $\left\{
\left\vert N\right\rangle \text{,}\left\vert N+1\right\rangle \right\} $.
