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

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 (\left|F=1, m_F=-1\right>) or in the pseudospin-mixed states (\left|F=1, m_F=-1\right> and \left|F=1, m_F=0\right>). 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.