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Journal of Physics Conference Series

Numerical Analysis of the Transient Capture Dynamics of Ions by Radio Frequency

Shuo Huang, L J Du, Yaohua Liu

Published Nov 1, 2023• 0 citations
Publisher

Abstract

Abstract The radiofrequency imprisoned ion system can isolate the coupling effect between ion and environment, and is helpful to the precise control of ion quantum state, which is an ideal candidate system for new atomic clocks. In this paper, the coupling effect between imprisoned ion and RF potential field is quantitatively studied by using finite element numerical analysis method. The coupling process of ion and RF phase is established, and the unsteady dynamic process of ion capture is analyzed. The influence of radio frequency amplitude on ion trapping ability and the reasonable range of radio frequency parameters conducive to ion stable confinement are studied. This method can be widely used in the study of ion trap structure and electromagnetic field parameter optimization in the fields of imprisoned ion frequency scale and quantum computing, and is helpful to the development of highly coherent quantum systems.

DOI
10.1088/1742-6596/2650/1/012044

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Abstract The radiofrequency imprisoned ion system can isolate the coupling effect between ion and environment, and is helpful to the precise control of ion quantum state, which is an ideal candidate system for new atomic clocks. In this paper, the coupling effect between imprisoned ion and RF potential field is quantitatively studied by using finite element numerical analysis method. The coupling process of ion and RF phase is established, and the unsteady dynamic process of ion capture is analyzed. The influence of radio frequency amplitude on ion trapping ability and the reasonable range of radio frequency parameters conducive to ion stable confinement are studied. This method can be widely used in the study of ion trap structure and electromagnetic field parameter optimization in the fields of imprisoned ion frequency scale and quantum computing, and is helpful to the development of highly coherent quantum systems.
We have developed an efficient computational scheme for integration of the classical Hamilton equations describing the ion dynamics confined in the radio-frequency field of the Paul trap. It has permitted a quantitative treatment of cold atom-ion resonant collisions in hybrid atom-ion traps with taking into account unremovable ion micromotion caused by the radio-frequency fields (V.S. Melezhik et. al., Phys. Rev. A100, 063406 (2019)). The important element of the hybrid atom-ion systems is the electromagnetic Paul trap confining the charged ion. The oscillating motion of the confined ion is defined by two frequencies of the Paul trap. It is the frequency of the order of 100 kHz due to the constant electric field and the radio-frequency of about 1-2 MHz defined by the alternating electromagnetic field of the ion trap. The necessity to accurately treat the ion motion in the combined field with two time scales defined by these two very different frequencies has demanded to develop the stable computational scheme for integration of the classical Hamilton equations for the ion motion. Moreover, the scheme must be stable on rather long time-interval of the ion collision with the cold atom ∼ 10 × 2/ defined by the atomic trap frequency ∼ 10 kHz and in the moment of the atom-ion collision when the Hamilton equations are strongly coupled. The developed numerical method takes into account all these features of the problem and makes it possible to integrate the system of coupled quantum-semiclassical equations with the necessary accuracy and quantitatively describes the processes of atomic-ion collisions in hybrid traps, including resonance effects.
Abstract Ion confinement technology can be widely used in quantum computation and precision measurement. In ion trapping system, ions are stably trapped in ion trap by the action of external forces.Multi-ion confinement requires the joint action of electric field and magnetic field to make the trapped ions overcome the interaction force between ions and be stably confined in the same specific space. Therefore, the stability of the electric force and the magnetic force determines the stability of ion confinement. Although the electric field and magnetic field provided by traditional commercial instruments is stable, it is not conducive to the miniaturization of the device. According to the previous experiment of ion confinement, we have designed a radio frequency(RF) signal generator that can provide continuous low power and stable high voltage RF electric field for multi-ion confinement system to guarantee the stability of trapped ions in quadrupole linear ion trap, also to improve the tapped ions density.
Ion traps serve as the venue for confining ions and exciting ionic transitions in ion optical clocks, where the geometric dimensions of the electrodes within the ion trap directly impact the performance metrics of the ion optical clocks. In this study, the finite element analysis method was employed to simulate the relationship between the electric field distribution and the dimensions of the electrodes in an endcap ion trap. The simulation data were subjected to curve fitting, with trap depth and potential anharmonicity utilized as the primary evaluation criteria for optimizing ion trap design. The results indicate that the ion trap demonstrates optimal performance when the distance between the radio frequency electrodes is reduced to 0.686 mm, and it is suggested that the chamfer width of the endcap electrode extension be 0.6 mm. Based on this, the study further explored the machining accuracy of certain dimensions, concluding that the required high machining accuracy values for the radio frequency electrodes and the endcap electrodes are ±3 and ±7 μm, respectively, while the aperture machining accuracy requirements are ±3 and ±22 μm, respectively. In addition, the simulation results suggest that a conical surface on the radio frequency electrodes with a height of ∼0.08 mm aids in reducing anharmonicity, although a spherical end surface does not notably improve the electric field distribution. These findings provide a valuable reference for the optimized design and machining of ion traps.
With the increasing number of ion qubits and improving performance of sophisticated quantum algorithms, more and more scalable complex ion trap electrodes have been developed and integrated. Nonlinear ion shuttling operations at the junction are more frequently used, such as in the areas of separation, merging, and exchanging. Several studies have been conducted to optimize the geometries of the radio-frequency (RF) electrodes to generate ideal trapping electric fields with a lower junction barrier and an even ion height of the RF saddle points. However, this iteration is time-consuming and commonly accompanied by complicated and sharp electrode geometry. Therefore, high-accuracy fabrication process and high electric breakdown voltage are essential. In the current work, an effective method was proposed to reduce the junction's pseudo-potential barrier and ion height variation by setting several individual RF electrodes and adjusting each RF voltage amplitude without changing the geometry of the electrode structure. The simulation results show that this method shows the same effect on engineering the trapping potential and reducing the potential barrier, but requires fewer parameters and optimization time. By combining this method with the geometrical shape-optimizing, the pseudo-potential barrier and the ion height variation near the junction can be further reduced. In addition, the geometry of the electrodes can be simplified to relax the fabrication precision and keep the ability to engineer the trapping electric field in real-time even after the fabrication of the electrodes, which provides a potential all-electric degree of freedom for the design and control of the two-dimensional ion crystals and investigation of their phase transition.
This paper reviews the basic principles of ion storage and cooling in the first place, and presents simulation result using a molecular dynamics method on ion distribution and RF heating rate. Based on this result, we evaluate the influence of RF heating effect and micromotions of the ions on frequency standards. Compared to conventional quadrupole trap, a 12-pole trap is able to reduce the RF heating rate of the ion cloud and to enable narrowing the linewidth with the Ramsey method. Moreover, the effective potential in the 12-pole trap has a flat bottom and a steep wall, which is capable of reducing the second order Doppler effect caused by the micromotions and thus helpful to enhance the accuracy and stability of the clock. At last, we review previous work of JPL on high performance, 199Hg+ ion clocks and our present work of laser-cooled, 113Cd+ ion clock based on the multipole trap.