A single trapped ion in a finite range trap

Research highlights: → We present a method to describe dynamics of an ion confined in a finite size trap. → The trap is modeled with a potential in the context of an f-deformed oscillator. → The ion exhibits nonclassical properties such as squeezing and quantum interference. → Also this system can be used to generate highly excited motional Fock state. → The Hilbert space size effects and nano traps can be investigated by this model. - Abstract: This paper presents a method to describe dynamics of an ion confined in a realistic finite range trap. We model this realistic potential with a solvable one and we obtain dynamical variables (raising and lowering operators) of this potential. We consider coherent interaction of this confined ion in a finite range trap and we show that its center-of-mass motion steady state is a special kind of nonlinear coherent states. Physical properties of this state and their dependence on the finite range of potential are studied.