Quantum theory of the stability region of an ion in a Paul trap

A Study of the Characteristics of the Wave Packets of a Paul-Trapped Ion

“…In physics, it means that the motion of a trapped ion is stable in this case. In the present paper, the solutions of the 3D Paul trap are very similar to those in Refs [15] and [16], therefore, we can use the same idea for our treatment.…”

“…where uj(t) = S-Tcos 2 (Sit/2). Equation ( 11) has been studied extensively 115 ' 16 ' 20 ] with the solution…”

“…( 10) and Eq. ( 14) is made under the same procedure as in Refs [15] and [16]. The value of the oscillating frequency fi is generally very large in the Paul trap's experiment, so the convergence always exists even for V >• 10U.…”

“…Theoretical description for the motion of an ion in the Paul trap had been carried out by Brown' 13 ' in principle although no specific calculation was made in his work. For more specific study, the same problem was discussed recently by numerical calculation' 14 ' and the method of function series expansion (FSE),' 15,16 ' in which the relation between the secular motion and micromotion of a Paul-trapped ion and the stability regions of the quantum motion of the ion were studied in detail. Particularly in Ref.…”

“…Particularly in Ref. [16], it was found that the convergence of the function series expansion in the solution of the time-dependent Schrodinger equation corresponds to the stable motion of the trapped ion.…”