Towards quantum information processing with two interacting neutral atoms in an optical tweezer*

We propose implementing a qubit-oscillator system derived from the motional states of two neutral atoms confined in an optical tweezer, which continuously interact via zero-range interaction. We find that (i) anharmonicity generated from the interaction allows us to isolate two-level qubit states in the relative motion, and (ii) a bosonic mode in the center-of-mass motion can be manipulated by adjusting the nonlinearities of optical potential. To obtain full control of the potential, three superimposed optical tweezer traps with time-varying trap depths are considered. We then discuss how to create various bosonic gate operations, e.g. controlled displacement, controlled squeezing, etc. Our protocol utilizes native interactions and quantum statistics as a natural resource for engineering nonlinearities in motional states to generate a qubit without involving internal levels. It reduces the decoherence from magnetic fields and differential Stark shifts, and further paves the way toward applications including spatially-resolved inertial sensing and quantum simulation of a spin-boson model with full quantum control.