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The Review of Laser Engineering

Nonlinear Resonances of Laser Cooled Ions in a Linear Paul Trap due to the Anharmonicity of the Trap Potential

Toshihiko MORI, Kenji Toyoda, Masayoshi Watanabe, Shinji Urabe

Published Jan 1, 2003• 1 citation
Publisher

Abstract

The anharmonicity of the trap potential influences the motion of trapped and laser-cooled ions. The magnitudes of higher-order components of the trap potential depend on the electrode geometry. In this paper we provide a numerical study of the anharmonicity of linear Paul trap potentials with different electorode geometies. We have also experimentally observed nonlinear resonances of laser-cooled ions, and have studied the effect of anharmonicity in three types of liner Paul trap that have different distances between electrodes.

DOI
10.2184/lsj.31.477

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The anharmonicity of the trap potential influences the motion of trapped and laser-cooled ions. The magnitudes of higher-order components of the trap potential depend on the electrode geometry. In this paper we provide a numerical study of the anharmonicity of linear Paul trap potentials with different electorode geometies. We have also experimentally observed nonlinear resonances of laser-cooled ions, and have studied the effect of anharmonicity in three types of liner Paul trap that have different distances between electrodes.
RF quadrupole linear Paul traps are versatile tools in quantum physics experiments. Linear Paul traps with blade-shaped electrodes have the advantages of larger solid angles for fluorescence collection. But with these kinds of traps, the existence of higher-order anharmonic terms of the trap potentials can cause large heating rate for the trapped ions. In this paper, we theoretically investigate the dependence of higher-order terms of trap potentials on the geometry of blade-shaped traps, and offer an optimized design. A modified blade electrodes trap is proposed to further reduce higher-order anharmonic terms while still retaining large fluorescence collection angle.
Using molecular dynamics simulations we characterize theoretically Coulomb clusters of laser- and sympathetically-cooled ions in a five-wire surface-electrode ion trap. We show that the asymmetry of the trapping potential leads to significantly different cluster structures and ion energy distributions in comparison to conventionally used linear Paul traps and to an asymmetric segregation of the ions in bi-component Coulomb clusters. We explore the impact of our results on the implementation of sympathetic cooling of molecular ions in surface-electrode traps and discuss possible challenges for the realization of such experiments.
In order to demonstrate laser cooling on negatively charged ions, it is necessary to confine the ions in a region free of strong magnetic fields. In the course of this thesis, the pre-existing design of a linear Paul trap was modified and taken into operation. The new design possesses two additional end cap electrodes whose shape provides effective axial confinement without blocking optical access to the trapped particles. The influence of these end cap electrodes on the trapping potential was simulated and compared to experimental results. Measurements with AU- ions show that the trap allows storage of ions for multiple hours. Analysis ofthe storage time suggests that the loading process heats up the trapped ions. The lifetime τHot of the hot ions was determined to be 23(3) min. After thermalization, the lifetime increases to 75(2) min. Measurements of the ion cloud’s radius provide an estimation of the equilibrium temperature T∞ ≈5000 K. The experimentally determined time constant of the cooling process is τcool = 41:6(4) s.
An effective method for determining the geometric parameters of a linear Paul trap is provided and carried out in this paper. The method is based on exciting the secular motion of laser-cooled Ca+ ions in a linear Paul trap with varied trapping potentials. Taking advantage of the segmented structure of the linear Paul trap, both the axial and the radial geometric parameters are obtained by applying external excitation fields to the trapping electrodes directly. The axial geometric parameter of our linear Paul trap is determined to be 0.374(3), and, for the first time, the radial geometric parameter is determined to be 0.928(2).
We theoretically and experimentally examine the effects of anharmonic terms in the trapping potential for linear chains of trapped ions. We concentrate on two different effects that become significant at different levels of anharmonicity. The first is a modification of the oscillation frequencies and amplitudes of the ions' normal modes of vibration for multi-ion crystals, resulting from each ion experiencing a different curvature in the potential. In the second effect, which occurs with increased anharmonicity or higher excitation amplitude, amplitude-dependent shifts of the normal-mode frequencies become important. We evaluate normal-mode frequency and amplitude shifts, and comment on the implications for quantum information processing and quantum state engineering. Since the ratio of the anharmonic to harmonic terms typically increases as the ion–electrode distance decreases, anharmonic effects will become more significant as ion trap sizes are reduced. To avoid unwanted problems, anharmonicities should therefore be taken into account at the design stage of trap development.
A simple method of cooling the transverse motion of an ion cloud in a linear Paul trap with a single axial laser is proposed. Transverse thermal oscillations of ions are indirectly damped by the longitudinal laser friction via an additional radio-frequency potential that resonantly couples two degrees of freedom. The fundamental mechanism of the present cooling scheme is theoretically described with the help of a harmonic oscillator model. It is shown that the indirect cooling rate can be considerably enhanced when the frequencies of the transverse and longitudinal ion oscillations satisfy a certain relation. The validity of theoretical predictions is confirmed through molecular dynamics simulations in which the detailed three-dimensional configuration of a typical Paul trap is incorporated.