Singularities in ion trap nonlinear coherent states

We present a theoretical analysis of the k-boson nonlinear coherent states of a two-level trapped ion interacting with two laser fields. Such states are both the zero-energy state of the interaction Hamiltonian and the eigenstates of a deformed annihilation operator. For the single-boson case, we show that the structure of the states and their coherence and minimum-uncertainty properties can be compromised whenever the Lamb-Dicke parameter is one of the roots of certain Laguerre polynomials. We investigate these problems, which are strictly related to the non-analyticity of the deformation function in the annihilation operator.