Stability Diagrams for Paul Ion Traps Driven by Two-Frequencies

Abstract

In this paper, we present and discuss stability diagrams for Paul traps driven by two ac voltages. In contrast to a typical Paul trap, here we suggest a secondary ac voltage whose frequency is twice the frequency of the primary one. The ratio between their amplitudes can be used to expand the region of stability and to access different states of motion of trapped ions. This provides a further mechanism to trap, cool, and manipulate single ions and also to improve the experimental framework where ion clouds and crystals can be prepared and controlled. Such approach opens the possibility of designing more sophisticated trapping architectures, leading to a wide variety of applications on ion trap research and mass analysis techniques.

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“…Neglecting the Universe expansion and the Higgs self-interaction, the Higgs dynamics are described by the Whittaker-Hill equation (cf. [32][33][34][35]) This is a good approximation as long as A k , p and q change adiabatically. The relevant stability charts for the Whittaker-Hill equation have been studied in [20].…”

“…Neglecting the Universe expansion and the Higgs self-interaction, the Higgs dynamics are described by the Whittaker-Hill equation (cf. [32][33][34][35]) d 2 X k dz 2 + [A k + 2p cos 2z + 2q cos 4z] X k 0. This is a good approximation as long as A k , p and q change adiabatically.…”

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“…where a constant A can be thought of as an eigenvalue of the differential operator on the LHS. The analysis of this equation can be found in [29][30][31][32]. According to the Floquet theorem, the solution can be written as a series of the form…”

“…1) where a constant A can be thought of as an eigenvalue of the differential operator on the LHS. The analysis of this equation can be found in [29][30][31][32].…”

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