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Quantum Electronics and Laser Science Conference

Systematic studies of ion motion in a Paul trap by means of self-induced coherences

H. Ebensing, Alex Newburgh, H. Harde

Published May 2, 1993• 0 citations
OpenAlex

Abstract

Using a newly developed technique that takes advantage of self-induced Zeeman coherences,1 we have studied the motion of stored ions in a Paul trap. We demonstrate the potential for measuring the complete spectrum of the ion oscillations consisting of the macro- and micromotion. The influence of the storage parameters and the ion density on the secular frequency is investigated with high spectral resolution.

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Using a newly developed technique that takes advantage of self-induced Zeeman coherences,1 we have studied the motion of stored ions in a Paul trap. We demonstrate the potential for measuring the complete spectrum of the ion oscillations consisting of the macro- and micromotion. The influence of the storage parameters and the ion density on the secular frequency is investigated with high spectral resolution.
We have carried out a molecular-dynamics simulation of hundreds of ions confined in a Paul trap. The simulation includes the trapped particles' micromotion and interparticle Coulomb interactions. We have implemented a random walk in velocity to bring the secular motion to a given temperature which we have numerically measured. When the coupling \ensuremath{\Gamma} is large the ions form concentric shells which undergo a quadrupole oscillation at the rf frequency, while the ions within a shell form a 2D hexagonal lattice. Ion clouds at 5 mK show no rf heating for qz{\mathit{q}}_{\mathit{z}}qz​\ensuremath{\lesssim}0.6, whereas rapid heating is seen for qz{\mathit{q}}_{\mathit{z}}qz​=0.8.
In order to improve the short-term stability of trapped-ion optical clocks, we are developing a frequency standard based on 115 In + / 172 Yb + Coulomb crystals. For this purpose, we have developed scalable segmented Paul traps which allow a high level of control for multiple ion ensembles. In this article, we detail on our recent results regarding the reduction of the leading sources of frequency uncertainty introduced by the ion trap: 2nd-order Doppler shifts due to micromotion and the heating of secular motion, as well as the black-body radiation shift due to warming of the trap. We show that the fractional frequency uncertainty due to each of these effects can be reduced to well below 10 -19 .
The accurate evaluation of the second-order Doppler frequency shift (SODFS) of trapped ions in a linear Paul trap has been studied with experiments and molecular dynamics (MD) simulations. The motion of trapped ions in the trap has three contributions, and we focus on the ion excess micromotion, which is rarely discussed when evaluating the SODFS of ions. Based on the hypothesis that the ion density is uniformly distributed in the radial direction, we propose a model to accurately evaluate the total SODFS for an ion ensemble with temperature less than 100 mK, which consists of three contributions of ion motion. The effectiveness of the model has been verified by MD simulation, and the experimental results of the excess micromotion of trapped ions are consistent with the theory. We believe that our model offers advantages in accurately evaluating the SODFS for the ion trap, especially those of laser-cooled ion microwave clocks based on large ion clouds.
Micromotion of ions in Paul traps has several adverse effects, including alterations of atomic transition line shapes, significant second-order Doppler shifts in high-accuracy studies, and limited confinement time in the absence of cooling. The ac electric field that causes the micromotion may also induce significant Stark shifts in atomic transitions. We describe three methods of detecting micromotion. The first relies on the change of the average ion position as the trap potentials are changed. The second monitors the amplitude of the sidebands of a narrow atomic transition, caused by the first-order Doppler shift due to the micromotion. The last technique detects the Doppler shift induced modulation of the fluorescence rate of a broad atomic transition. We discuss the detection sensitivity of each method to Doppler and Stark shifts, and show experimental results using the last technique.
In this paper, direct observation of micromotion for multiple ions in a laser-cooled trapped ion crystal is discussed along with a measurement technique for micromotion amplitude. Micromotion is directly observed using a time-resolving, single-photon-sensitive camera that provides both fluorescence and position data for each ion on the nanosecond time scale. Micromotion amplitude and phase for each ion in the crystal are measured, allowing this method to be sensitive to tilts and shifts of the ion chain from the null of the radio-frequency quadrupole potential in the linear trap. Spatial resolution makes this micromotion detection technique suitable for complex ion configurations, including two-dimensional geometries. It does not require any additional equipment or laser beams, and the modulation of the cooling lasers or trap voltages is not necessary for detection as it is in other methods.