Fig. 1. Schematic of the setup of the two-dimensional defect-free atom arrays. (a) Static and moveable optical tweezers are formed by the SLM and the 2D-AOD, respectively.They combine on the polarization beam splitter (PBS) and then pass through a high NA objective lens, shining on the atoms as an array of optical microtraps. The single atom fluorescence is picked up by a dichroic mirror and imaged by the EMCCD. (b) The mechanism of a single atom moving between static and moveable traps.

Fig. 2. Example of the soldier-like rearrangement, taking ten randomly distributed trapped atoms in one row as an example. The predefined center is marked as a blue triangle in the upper picture. All the atoms line up towards this center in a line, and the path is labeled with blue arrows. The final pattern is shown in the bottom panel.

Fig. 3. Flowchart of the soldier-like algorithm. Sorting process is implemented from up to down.

Fig. 4. Experimental generation of (a) the triangle lattice, (b) the hexagonal lattice, and (c) the Kagome lattice. The patterns include two areas, a target area and a standby area. The standby array is used for refilling the target array. The standby array is designed as a rectangular array that is suitable for soldier-like rearrangement.

Fig. 5. Sorting steps as a function of the target number in the rearrangement of the square lattice.

Fig. 6. Illustration of the sorting process to evaluate the steps in the rearrangement of the square lattice.