Hybrid qubit-oscillator module with motional states of two trapped interacting atoms

We propose the use of motional states of two interacting atoms trapped in a potential stroboscopically engineered by an optical tweezer as a means to implement a qubit-oscillator system, in analogy to those used in circuit quantum electrodynamics and trapped ions. In our setting, the center of mass degree of freedom of the atoms plays the role of a photon or phonon mode, while the interacting, relative mode acts as a qubit. No internal state is involved in our system, which makes this motional qubit more robust to decoherence. We show that a universal set of bosonic operations, including displacement, rotation, squeezing, and the corresponding set of gates controlled by the qubit, can be implemented through precise temporal modulation of the optical tweezers. We numerically check that gates can be generated with high fidelity, and discuss possible schemes for initial state preparation and final state readout. While we restrict the discussion to a single qubit-oscillator coupler, scalability can be achieved by coupling arrays of atoms via dipolar or Rydberg-dressed interactions.