Entangled states of motion in a two-dimensional ion microtrap array

Two-dimensional arrays of ions trapped in individual, dynamically tunable microtraps are a promising technology for quantum computation and simulation. By controlling the motional excitations of the ions (phonons), one may be able to generate multipartite motional and internal entanglement between ions trapped in such an array and also simulate complex Hamiltonians such as bosons in synthetic gauge fields. We trap three ⁹Be⁺ ions in a microfabricated surface electrode ion trap that has three confining potential wells spaced 30 mm apart on the vertices of an equilateral triangle. By applying static potentials to the trap electrodes, we can individually tune the potential curvatures at each trapping site. When site curvatures are nearly equal, the individual ion motional modes hybridize into collective normal modes that we can excite using resolved motional sideband transitions. Here, we report on our progress toward using these collective excitations to entangle the motion of all three ions. With equal curvatures in all three sites, two normal modes of motion have the same frequency and the third mode is separated by an energy gap. When this mode is occupied by a single phonon, the three ions share this excitation, and their local motion is entangled in a W-type state. We will study the structure of such an entangled state, whether the energy gap protects the entangled state, and, if so, which external perturbations are suppressed by that protection.