  We show here that the model Hamiltonian used in our paper for ion vibrating
in a q-analog harmonic oscillator trap and interacting with a classical
single-mode light field is indeed obtained by replacing the usual bosonic
creation and annihilation operators of the harmonic trap model by their
q-deformed counterparts. The approximations made in our paper amount to using
for the ion-laser interaction in a q-analog harmonic oscillator trap, the
operator $F_{q}=exp{-(|\epsilon|^2}/2)}exp{i\epsilon A^{\dagger}}exp{i\epsilon
A}$, which is analogous to the corresponding operator for ion in a harmonic
oscillator trap that is $F=exp{-(|\epsilon|^2 /2)}exp{i\epsilon a^{\dagger
}}exp{i\epsilon a}$. In our article we do not claim to have diagonalized the
operator, $F_q = exp{i \epsilon (A^{\dagger}+A)}$, for which the basis states
|g,m> and |e,m> are not analytic vectors.

Quantum Physics;Nuclear Theory