Abstract
The ultra-cold atomic system is a clean and highly controllable quantum system, which can be used for quantum simulation of important physical problems in many fields such as condensed matter physics, high-energy physics, astrophysics, and chemical reactions. The constructions of optical lattices with different configurations are an important prerequisite for simulating diverse complex quantum systems, especially solid materials. In this work, we use weighted Gerchberg-Saxton algorithm to generate holograms. By using liquid crystal spatial light modulator and high-resolution imaging system, holograms (in momentum space) are transformed into images in real space for constructing various two-dimensional (2D) optical trap arrays, such as simple triangular, hexagonal, square lattice and more complex honeycomb lattice. We load <sup>87</sup>Rb ultra-cold atoms into the 2D optical trap arrays with a minimal spacing of 3 μm in between. This method is versatile and flexible, which is helpful in expanding the application scope of quantum simulation with optical lattices.
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