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Nature Communications

Tracking the extensive three-dimensional motion of single ions by an engineered point-spread function

Yongzhuang Zhou, Man-chao Zhang, Wenbo Su, Chun-Wang Wu, Yi Xie, Ting Chen, Wei Wu, Ping-Xing Chen, Jie Zhang

Published Aug 1, 2024• 7 citations
Publisher

Abstract

Three-dimensional (3D) imaging of individual atoms is a critical tool for discovering new physical phenomena and developing new technologies in microscopic systems. However, the current single-atom-resolved 3D imaging methods are limited to static circumstances or a shallow detection range. Here, we demonstrate a generic dynamic 3D imaging method to track the extensive motion of single ions by exploiting the engineered point-spread function (PSF). We show that the image of a single ion can be engineered into a helical PSF, thus enabling single-snapshot acquisition of the position information of the ion in the trap. A preliminary application of this technique is demonstrated by recording the 3D motion trajectory of a single trapped ion and reconstructing the 3D dynamical configuration transition between the zig and zag structures of a 5-ion crystal. This work opens the path for studies on single-atom-resolved dynamics in both trapped-ion and neutral-atom systems.

DOI
10.1038/s41467-024-49701-3

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Three-dimensional (3D) imaging of individual atoms is a critical tool for discovering new physical phenomena and developing new technologies in microscopic systems. However, the current single-atom-resolved 3D imaging methods are limited to static circumstances or a shallow detection range. Here, we demonstrate a generic dynamic 3D imaging method to track the extensive motion of single ions by exploiting the engineered point-spread function (PSF). We show that the image of a single ion can be engineered into a helical PSF, thus enabling single-snapshot acquisition of the position information of the ion in the trap. A preliminary application of this technique is demonstrated by recording the 3D motion trajectory of a single trapped ion and reconstructing the 3D dynamical configuration transition between the zig and zag structures of a 5-ion crystal. This work opens the path for studies on single-atom-resolved dynamics in both trapped-ion and neutral-atom systems.
As one of the most critical methods for optical super-resolved microscopy, stimulated emission depletion (STED) microscopy has been widely applied in biological and chemical fields, leading to the Nobel prize of 2014 in chemistry. In cold atomic systems, fast and high-resolution microscopy of individual atoms is crucial since it can provide direct information on the dynamics and correlations of the system. Here, we demonstrate nanosecond two-dimensional snapshots of a single trapped ion beyond the optical diffraction limit, by combining the main idea of STED with the quantum state transition control in cold atoms. We achieve a spatial resolution up to 175 nm and a time resolution up to 50 ns simultaneously using a NA=0.1 objective in the experiment, which is improved over ten times compared to direct fluorescence imaging. To show the potential of this method, we applied it to record the motion of the trapped ion and observe one cycle of the secular motion of the ion with a displacement detection sensitivity of 10 nm. Our method provides a powerful tool for probing particles' positions, momenta and correlations, as well as their dynamics in cold atomic systems.
In cold atomic systems, fast and high-resolution microscopy of individual atoms is crucial, since it can provide direct information on the dynamics and correlations of the system. Here, we demonstrate nanosecond-scale two-dimensional stroboscopic pictures of a single trapped ion beyond the optical diffraction limit, by combining the main idea of ground-state depletion microscopy with quantum-state transition control in cold atoms. We achieve a spatial resolution up to 175 nm using a NA=0.1 objective in the experiment, which represents a more than tenfold improvement compared with direct fluorescence imaging. To show the potential of this method, we apply it to observe the secular motion of the trapped ion; we demonstrate a temporal resolution up to 50 ns with a displacement detection sensitivity of 10 nm. Our method provides a powerful tool for probing particle positions, momenta, and correlations, as well as their dynamics in cold atomic systems.
We report on image processing techniques and experimental procedures to determine the lattice-site positions of single atoms in an optical lattice with high reliability, even for limited acquisition time or optical resolution. Determining the positions of atoms beyond the diffraction limit relies on parametric deconvolution in close analogy to methods employed in super-resolution microscopy. We develop a deconvolution method that makes effective use of the prior knowledge of the optical transfer function, noise properties, and discreteness of the optical lattice. We show that accurate knowledge of the image formation process enables a dramatic improvement on the localization reliability. This allows us to demonstrate super-resolution of the atoms' position in closely packed ensembles where the separation between particles cannot be directly optically resolved. Furthermore, we demonstrate experimental methods to precisely reconstruct the point spread function with sub-pixel resolution from fluorescence images of single atoms, and we give a mathematical foundation thereof. We also discuss discretized image sampling in pixel detectors and provide a quantitative model of noise sources in electron multiplying CCD cameras. The techniques developed here are not only beneficial to neutral atom experiments, but could also be employed to improve the localization precision of trapped ions for ultra precise force sensing.
Forces drive all physical interactions. High-sensitivity measurement of the effect of forces enables the quantitative investigation of physical phenomena. Laser-cooled trapped atomic ions are a well-controlled quantum system whose low mass, strong Coulomb interaction, and readily detectable fluorescence signal make them a favorable platform for precision metrology. We demonstrate a three-dimensional sub-attonewton sensitivity force sensor based on a super-resolution imaging of a single trapped ion. The force is detected by measuring the ion's displacement in three dimensions with nanometer precision. Observed sensitivities were 372 ± 9, 347 ± 18, and 808 ± 51 zN/[Formula: see text], corresponding to 24×, 87×, and 21× above the quantum limit. We verified this technique by measuring a 95-zN light pressure force, an important systematic effect in optically based sensors.
Abstract Quantum gas microscopes, which image the atomic occupations in an optical lattice, have opened a new avenue to the exploration of many-body lattice systems. Imaging trapped systems after freezing the density distribution by ramping up a pinning lattice leads, however, to a distortion of the original density distribution, especially when its structures are on the scale of the pinning lattice spacing. We show that this dynamics can be described by a filter, which we call in analogy to classical optics a quantum point spread function. Using a machine learning approach, we demonstrate via several experimentally relevant setups that a suitable deconvolution allows for the reconstruction of the original density distribution. These findings are both of fundamental interest for the theory of imaging and of immediate importance for current quantum gas experiments.