Reply to "Comment on 'Single two-level ion in an anharmonic oscillator trap: Time evolution of the Q function and population inversion'"

We show here that the model Hamiltonian used in our paper for an ion vibrat ing 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-d eformed counterparts. re approximations made in our paper amount to using, for the ion-laser interaction in a q-analog harmonic oscillator trap, the o perator F-q = e(-(\epsilon\2/2))e(i epsilon A dagger) e(i epsilon A), which is analogous to the corresponding operator for an ion in a harmonic oscill ator trap that is F= e(-(\epsilon\2/2))e(i epsilon A dagger) e(i epsilon A) . Here a and a dagger are the usual creation and annihilation operators, wh ereas A and A dagger are the q-deformed bosonic creation and annihilation o perators. There is no problem with diagonalizing this operator using the ba sis states \g,m] and \e,m], where m stands for the motional number state. I n our paper we do not claim to have diagonalized the operator F-q = e(i eps ilon(A dagger+A)) for which the basis states \g,m] and \e,m] are not analyt ic vectors. [S1050-2947(99)04104-9].