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Chinese Physics B

Observation and analysis of the center-of-mass position trajectory for trapped ultracold atoms

Zhi-Xin 志鑫 Duan 段, Rufang Zhao, WU Weitao, Sheng-Jun Yang

Published Oct 22, 2025• 0 citations
Publisher

Abstract

Abstract Optical dipole traps are indispensable tools in ultracold atomic physics, and precise understanding and control of atomic dynamics within the traps are critically important. Here, applying a magnetic gradient to perturb dipole-trapped ultracold atoms, we investigate the trajectory of the center of mass positions (CoMPs) when atoms are either in a single spin state (| F = 1, m F = −1〉) or in the pseudospin-mixed states (| F = 1, m F = −1〉 and | F = 1, m F = 0〉). Unlike just treating the conventional time-of-flight (TOF) imaging as atomic momentum distribution, we present a methodology in-depth for accurate information about the atomic spatial trajectory evolution. This approach circumvents the need for complex and resource-intensive in-situ high-resolution imaging, broadening the accessibility of dynamic studies, and trap characterization across ultracold atoms. It can be directly used for fine-calibrating parameters of the trap potential and studying the atomic dynamical evolution, which will benefit various research areas of ultracold atoms.

DOI
10.1088/1674-1056/ae15f9

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Abstract Optical dipole traps are indispensable tools in ultracold atomic physics, and precise understanding and control of atomic dynamics within the traps are critically important. Here, applying a magnetic gradient to perturb dipole-trapped ultracold atoms, we investigate the trajectory of the center of mass positions (CoMPs) when atoms are either in a single spin state (| F = 1, m F = −1〉) or in the pseudospin-mixed states (| F = 1, m F = −1〉 and | F = 1, m F = 0〉). Unlike just treating the conventional time-of-flight (TOF) imaging as atomic momentum distribution, we present a methodology in-depth for accurate information about the atomic spatial trajectory evolution. This approach circumvents the need for complex and resource-intensive in-situ high-resolution imaging, broadening the accessibility of dynamic studies, and trap characterization across ultracold atoms. It can be directly used for fine-calibrating parameters of the trap potential and studying the atomic dynamical evolution, which will benefit various research areas of ultracold atoms.
The mapping of the potential landscape with high spatial resolution is crucial for quantum technologies based on ultracold atoms. However, the imaging of optical dipole traps is challenging because purely optical methods, commonly used to profile laser beams in free space, are not applicable in a vacuum. In this work, we demonstrate precise in situ imaging of optical dipole traps by probing a hyperfine transition with Ramsey interferometry. Thereby, we obtain an absolute map of the potential landscape with micrometer resolution and shot-noise-limited spectral precision. The idea of the technique is to control the polarization ellipticity of the trap laser beam to induce a differential light shift proportional to the trap potential. By studying the response to polarization ellipticity, we uncover a small but significant nonlinearity in addition to a dominant linear behavior, which is explained by the geometric distribution of the atomic ensemble. Our technique for imaging of optical traps can find wide application in quantum technologies based on ultracold atoms, as it applies to multiple atomic species and is not limited to a particular wavelength or trap geometry.
Abstract Matter-wave diffraction is an important and widely used method for manipulating atomic momentum states and for studying dynamical evolution in ultracold-atom physics. Here, we investigated momentum diffraction of ultracold 87 R b atoms using a short lattice pulse in the presence of a forced harmonic potential. The forced potential is achieved by combining a magnetic field gradient and a crossed-dipole trap. By tuning the gradient field strength and atomic evolution time in the trap, we found that populations of the forward and backward diffractive momentum components exhibit asymmetry relative to the original matter wave, a feature that has often been overlooked or deliberately avoided in previous studies. The factors that induce this asymmetric diffraction are identified and systematically analyzed, including the initial atomic velocity, the trap potential gradient, and the cooperative interactions among atomic spin-momentum modes. A transparent physical picture supported by analytical modeling is presented. This work can provide a better understanding of matter-wave diffraction in the presence of external fields and in complex or imperfect lattice configurations, thereby potentially advancing future research on ultracold atom interferometry and quantum simulation involving multiple spin-momentum modes.
Optical imaging plays a central role in ultracold atom experiments by enabling quantitative measurements of atomic density, temperature, atom number, and condensate dynamics. Achieving high-fidelity absorption imaging requires a well-characterized optical system with accurately calibrated magnification and spatial resolution. In this work, I designed, implemented, and experimentally characterized a dual-view optical imaging platform for future absorption imaging of ultracold sodium atoms. The system consists of two independent three-lens relay imaging systems providing top and side views of the atomic sample. Two low-magnification configurations with nominal magnification 0.6 were developed for imaging the relatively large sodium magneto-optical trap (MOT), while higher-magnification configurations with nominal magnifications of 4 and 10 were designed for Bose–Einstein condensate (BEC) imaging. The work included the integration and optimization of the laser cooling and trapping apparatus, improvements to the magnetic-field control system, and the alignment and calibration of both imaging paths. Characterization using a laser and a USAF 1951 resolution target yielded measured magnifications of 0.653 ± 0.033 and 0.521 ± 0.016 for the side and top MOT imaging systems, with corresponding spatial resolutions of 13.92 µm and 9.84 µm. The BEC imaging systems achieved measured magnifications of 4.094 ± 0.060 (top) and 10.817 ± 0.172 (side), with spatial resolutions of 9.84 µm and 6.20 µm, respectively. These measurements agree well with the theoretical diffraction-limited resolutions of 7.19 µm for the 0.6 and 4 magnification systems and 2.87 µm for the 10 magnification system, with the remaining differences attributed primarily to practical optical aberrations and alignment tolerances. The calibrated dual-view imaging platform provides the spatial resolution and quantitative accuracy required for absorption imaging of ultracold sodium atoms and establishes the experimental foundation for future investigations of sodium magneto-optical traps, Bose–Einstein condensation, and coherent spin dynamics in spinor sodium gases.
We describe a simple time-of-flight technique for measuring the magnetic moment of an optically pumped magneto-optical trap. The technique relies on free-expansion imaging of a cold atom cloud in a small magnetic field gradient without the need to detect spatial separation between magnetic sublevels. We find that the effective acceleration of the cloud can be used to characterize extreme state optical pumping. In the general case, we show that the integrated displacement of the falling cloud can be accurately modeled using rate equation simulations of magnetic sublevel populations, and knowledge of local magnetic fields, field gradients, and light intensities. The agreement between the model and the data allows the reconstruction of magnetic moments and suggests that this technique may be suitable for the measurement of population distributions over a range of optical pumping conditions.
The use of temporal correlations in scattered photons to probe the microscopic dynamics of ultracold quantum gases has emerged as a powerful, minimally destructive approach for in situ analysis. Here, we demonstrate that temporal coherence spectroscopy can quantitatively characterize atomic motion in a magnetic trap, despite the perturbative effects of the probing light. By measuring the first-order correlation function g (1) (τττ ) of light scattered by a 87 Rb cloud confined in a quadrupole trap, we identify radiation-pressure-induced acceleration and heating as the origin of the apparent discrepancy between coherence spectra and temperatures inferred from time-of-flight measurements. A simple dynamical model incorporating these effects restores agreement between theory and experiment, establishing coherence spectroscopy as a reliable in situ probe of velocity distributions in trapped atomic ensembles. Our results pave the way for time-resolved studies of nonequilibrium dynamics and thermalization processes in confined cold gases, complementing conventional destructive imaging techniques.
We propose to utilize density distributions from a series of time-of-flight images of an expanding cloud to reconstruct single-particle correlation functions of trapped ultracold atoms. In particular, we show how this technique can be used to detect off-diagonal correlations of atoms in a quasi-one-dimensional trap, where both real- and momentum-space correlations are extracted at a quantitative level. The feasibility of this method is analyzed with specific examples, taking into account finite temporal and spatial resolutions in experiments.