The standard second-order pseudo-oscillator potential used in many analytical investigations of the properties of ions stored in a Paul trap has serious limitations. In this paper we show that ion-crystal configurations exhibited by 2, 3, and 4 simultaneously stored ions in a Paul trap are not predicted by the standard pseudo-oscillator potential, but are all captured qualitatively and quantitatively by an extended pseudopotential derived in this paper. The power of our extended pseudopotential extends in particular to the prediction of the border lines between different crystal configurations (morphologies) in the Paul trap's $a$, $q$ stability diagram. In the three- and four-ion cases, several of the ion-crystal structures predicted by our improved pseudopotential have never been observed experimentally before. We present them here as a challenge for experiments.
Recently predicted and observed Pauli crystals are structures formed by trapped ultracold non-interacting particles obeying Fermi statistics. The relative positions of the particles are determined by the trapping potential and the Pauli exclusion principle. Measuring all particles at once, their positions tend to be close to vertices of non-trivial polyhedrons. Similar shapes are found for systems of particles bound to the surface of a sphere.
We demonstrate trapping of electrons in a millimeter-sized quadrupole Paul trap driven at 1.6~GHz in a room-temperature ultra-high vacuum setup. Cold electrons are introduced into the trap by ionization of atomic calcium via Rydberg states and stay confined by microwave and static electric fields for several tens of milliseconds. A fraction of these electrons remain trapped longer and show no measurable loss for measurement times up to a second. Electronic excitation of the motion reveals secular frequencies which can be tuned over a range of several tens to hundreds of MHz. Operating a simila…
In this paper, direct observation of micromotion for multiple ions in a laser-cooled trapped ion crystal is discussed along with a novel 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 radiofrequency quadrupole potential in the linear trap. Spatial …
Sympathetic cooling of $^{40}\textbf{Ca}^+$ - $^{27}\textbf{Al}^+$ ion pair crystal in a linear Paul trap
$^{27}$ Al $^+$离子光钟具有室温下黑体辐射漂移小、对磁漂移不敏感等优点，是最有吸引力的光钟之一。然而，在目前没有167 nm激光的情况下，它不能直接激光冷却。这个问题可以通过感应冷却来解决。在这项工作中，一个线性的保罗陷阱被用来捕获$^{40}$钙$^{+}$和$^{27}$铝$^+$离子同时，和一个单一的多普勒冷却$^{40}$钙$^+$离子被用来同情地冷却一个单一的$^{27}$铝$^+$离子。从而成功地合成了一种“亮-暗”双离子晶体。通过测量载波和边带光谱强度的比值，估计晶体的温度约为7 mK。最后，通过对离子晶体的久期运动频率的精确测量，证明了暗离子是$^{27}$ Al $^+$离子，这意味着我们研制的$^{27}$ Al $^+$量子逻辑时钟又向前迈进了一大步.
Precision measurement of the ground-state hyperfine constant for $^9Be^+$ in a linear Paul trap via magnetically insensitive hyperfine transitions
Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences（精密测量科学与技术创新院，中国科学院）；University of the Chinese Academy of Sciences（中国科学院大学）；School of Electronics and IoT, Chongqing Polytechnic University of Electronic Technology（重庆电子工程职业学院电子信息学院）
Sympathetic cooling of $^{113}$Cd$^+$ by laser-cooled $^{40}$Ca$^+$ in a linear Paul trap for Microwave Ion Clocks
本文报道了在线性Paul阱中用激光冷却$^{40}$ Ca $^+$对$^{113}$ Cd $^+$的共振冷却。实现了$^{113}$ Cd $^+$离子的长期低温约束。这些离子的温度测量在$90(10)$ mK，和相应的不确定性所产生的二阶多普勒频移估计为$2\times10^{-17}$的水平。高达$4.2\times10^5$ Cd $^+$离子被限制在阱中，并且测量的限制时间常数为84小时。在约束三小时后，仍然存在$10^5$ Cd $^+$离子，表明这种Ca $^+$ -Cd $^+$双离子体系是令人惊讶的稳定。交流斯塔克位移由钙$^+$激光和荧光诱导，其使用高精度\textit{ab initio}方法小心地估计到$5.4(0.5)\times10^{-17}$的精度。由于死区时间较短，还推导出了Dick-effect限制的Allan偏差。这些结果表明，微波钟的基础上，这种同情冷却计划持有承诺，在提供超高的频率精度和稳定性。
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. Based on the hypothesis that the ion density is uniformly distributed in the radial direction, we propose a new model to accurately evaluate the total SODFS for ion microwave clocks. The effectiveness of the model has been verified both in simulation…
Electrical Noise Produced by Micron-Sized Particles above a Surface Paul Trap
University of California, Berkeley（加州大学伯克利分校）；Challenge Institute for Quantum Computation, University of California, Berkeley（加州大学伯克利分校量子计算挑战研究所）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
We experimentally study two-dimensional (2D) Coulomb crystals in the "radial-2D" phase of a linear Paul trap. This phase is identified by a 2D ion lattice aligned entirely with the radial plane and is created by imposing a large ratio of axial to radial trapping potentials. Using arrays of up to 19 $^{171}$Yb$^+$ ions, we demonstrate that the structural phase boundaries and vibrational mode frequencies of such crystals are well-described by the pseudopotential approximation, despite the time-dependent ion positions driven by intrinsic micromotion. We further observe that micromotion-induced he…
Trapping of electrons and $^{40}\textrm{Ca}^+$ ions in a dual-frequency Paul trap
Helmholtz-Institut Mainz（海姆霍兹美因茨研究所）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（GSI重离子研究中心有限公司）；QUANTUM, Institut für Physik, Johannes Gutenberg-Universität（约翰内斯·古腾堡大学量子物理研究所）；Institute of Nuclear Science and Technology, Sichuan University（四川大学核科学与技术学院）；Key Laboratory of Radiation Physics and Technology of the Ministry of Education, Institute of Nuclear Science and Technology, Sichuan University（四川大学核科学与技术学院辐射物理与技术教育部重点实验室）；Charles University, Faculty of Mathematics and Physics（查理斯大学数学与物理学院）；Delta Q, IMJ Institute of Research & Department of Physics, Moodlakatte Institute of Technology（莫德拉卡特理工学院IMJ研究所量子部门）；Heinrich Heine University Düsseldorf（杜塞尔多夫海涅大学）
Transient dynamics of parametric driving for single-electron image current detection in a Paul trap
University of California, Berkeley（加州大学伯克利分校）；Challenge Institute for Quantum Computation, University of California, Berkeley（加州大学伯克利分校量子计算挑战研究所）；School of Physics, Huazhong University of Science and Technology（华中科技大学物理学院）
Probing high-frequency gravitational waves with entangled vibrational qubits in linear Paul traps
KEK Theory Center（高能加速器研究机构理论中心）；The Graduate University for Advanced Studies, SOKENDAI（高级研究大学院大学（SOKENDAI））；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）
We present the design and construction of a new experimental apparatus for the trapping of single Ba$^+$ ions in the center of curvature of an optical-quality hemispherical mirror. We describe the layout, fabrication and integration of the full setup, consisting of a high-optical access monolithic `3D-printed' Paul trap, the hemispherical mirror, a diffraction-limited in-vacuum lens (NA = 0.7) for collection of atomic fluorescence and a state-of-the art ultra-high vacuum vessel. This new apparatus enables the study of quantum electrodynamics effects such as strong inhibition and enhancement of…
Intrinsic anharmonic effects on the phonon frequencies and effective spin-spin interactions in a quantum simulator made from trapped ions in a linear Paul trap
The motion of an ion in a radiofrequency (rf) Paul trap is described by the Mathieu equation and the associated stability parameters that are proportional to the rf and dc electric field gradients. Here, a higher-order, iterative method to accurately solve the stability parameters from measured secular frequencies is presented. It is then used to characterize an endcap trap by showing that the trap's radial asymmetry is dominated by the dc field gradients and by measuring the relation between the applied voltages and the gradients. The results are shown to be in good agreement with an electros…
