  Nonlinear coherent states are an interesting resource for quantum
technologies. Here we investigate some critical features of the single-boson
nonlinear coherent states, which are theoretically constructed as eigenstates
of the annihilation operator and experimentally realized as stationary states
of a trapped laser-driven ion. We show that the coherence and the
minimum-uncertainty properties of such states are broken for values of the
Lamb-Dicke parameter corresponding to the roots of the Laguerre polynomials,
which enter their explicit expression. The case of the multiboson nonlinear
coherent states is also discussed.
