Crystallization of trapped ions—A quantum approach

Abstract

We present a quantum approach for a system of two or three ions in a Paul's trap. Under the simplifying assumption that the ionic repulsion is inverse square instead of Coulombic, we explicitly solve the time-dependent Schrödinger equation for this system. The quasi-periodic in time nature of the quasi-energy eigenstates provides a good description of both the “crystalline regime” and the “nonchaotic cloud regime” inside the trap. The characteristic size of the “two-ions crystal” in this quantum approach is compared to its value in the usual classical treatment.