Version 1
: Received: 24 February 2021 / Approved: 25 February 2021 / Online: 25 February 2021 (13:39:56 CET)
Version 2
: Received: 23 March 2021 / Approved: 23 March 2021 / Online: 23 March 2021 (12:52:31 CET)
Mihalcea, B.M.; Lynch, S. Investigations on Dynamical Stability in 3D Quadrupole Ion Traps. Applied Sciences 2021, 11, 2938, doi:10.3390/app11072938.
Mihalcea, B.M.; Lynch, S. Investigations on Dynamical Stability in 3D Quadrupole Ion Traps. Applied Sciences 2021, 11, 2938, doi:10.3390/app11072938.
Mihalcea, B.M.; Lynch, S. Investigations on Dynamical Stability in 3D Quadrupole Ion Traps. Applied Sciences 2021, 11, 2938, doi:10.3390/app11072938.
Mihalcea, B.M.; Lynch, S. Investigations on Dynamical Stability in 3D Quadrupole Ion Traps. Applied Sciences 2021, 11, 2938, doi:10.3390/app11072938.
Abstract
We firstly discuss classical stability for a dynamical system of two ions levitated in a 3D Radio-Frequency (RF) trap, assimilated with two coupled oscillators. We obtain the solutions of the coupled system of equations that characterizes the associated dynamics. In addition, we supply the modes of oscillation and demonstrate the weak coupling condition is inappropriate in practice, while for collective modes of motion (and strong coupling) only a peak of the mass can be detected. Phase portraits and power spectra are employed to illustrate how the trajectory executes quasiperiodic motion on the surface of torus, namely a Kolmogorov-Arnold-Moser (KAM) torus. In an attempt to better describe dynamical stability of the system, we introduce a model that characterizes dynamical stability and the critical points based on the Hessian matrix approach. The model is then applied to investigate quantum dynamics for many-body systems consisting of identical ions, levitated in 2D and 3D ion traps. Finally, the same model is applied to the case of a combined 3D Quadrupole Ion Trap (QIT) with axial symmetry, for which we obtain the associated Hamilton function. The ion distribution can be described by means of numerical modeling, based on the Hamilton function we assign to the system. The approach we introduce is effective to infer the parameters of distinct types of traps by applying a unitary and coherent method, and especially for identifying equilibrium configurations, of large interest for ion crystals or quantum logic.
Keywords
radiofrequency trap; dynamical stability; eigenfrequency; Paul and Penning trap; Hessian matrix; Hamilton function; bifurcation diagram
Subject
Physical Sciences, Acoustics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received:
23 March 2021
Commenter:
Bogdan Vasile Mihalcea
Commenter's Conflict of Interests:
Author
Comment:
The abstract and introduction have been rephrased to better reflect the focus and results of the paper, as well as the area of applications. The updated version also includes the changes implemented according to the comments and suggestions made by the reviewers, which have resulted in improving the paper and clarifying the issues of interest. In addition, the results are now presented under two sections, entitled Highlights and Conclusions.
Commenter: Bogdan Vasile Mihalcea
Commenter's Conflict of Interests: Author