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.
Categories: quant-ph nucl-th