Title: Determination of principal axes orientation in an ion trap using matter-wave interference

Abstract: We investigate the control mechanism of trap frequencies and determine the orientation of ion trap principal axes. The application of DC voltage to the ground electrodes, commonly employed to finely tune trap frequencies in ion traps, leads to the rotation of the trap principal axes. Analyzing the ion matter-wave interference signal enables us to determine the directions of the trap principal axes. Both the experiments and simulations reveal an avoided-crossing behavior resulting from the coupling between the trap radial axes. Additionally, simulations indicate that symmetric trap structures lack this coupling, suggesting that trap structure asymmetry causes coupling between the axes. The findings of this study offer valuable insights into ion traps for diverse applications in quantum science and technology.