  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.
