Slicing the Fock space for state production and protection

In this paper we present a protocol to engineer interactions confined to subspaces of the Fock space in trapped ions: we show how to engineer upper-bounded, lower-bounded, and sliced Jaynes-Cummings (JC) and anti-Jaynes-Cummings (AJC) Hamiltonians. The upper-bounded (lower-bounded) interaction acting upon Fock subspaces ranges from |0> to |M>(|N> to ∞), and the sliced one confined to Fock subspace ranges from |M> to |N>, whatever M<N. Whereas the upper-bounded JC or AJC interaction is shown to drive any initial state to a steady Fock state |N>, the sliced one is shown to produce steady superpositions of Fock states confined to the sliced subspace {∣N>,∣N+1>}.FAPESPCNPqCAPE