Versatile Control of a Hybrid Spin-Oscillator System in Trapped Ions

Hybrid spin-oscillator systems present unique opportunities for quantum computing, metrology, and the creation of exotic quantum states. We establish versatile control over a hybrid system formed by trapped ions, which enables us to embrace the hybrid aspect of these systems. We discuss two applications resulting from this expanded hybrid control.

First, we demonstrate the generation of arbitrary superpositions of nonclassical quantum harmonic oscillator states. We interleave spin-dependent nonlinear oscillator interactions with mid-circuit measurements of the spin, which preserve the coherence of the oscillator. This enables the creation of superpositions of squeezed, trisqueezed, and quadsqueezed states. These states, with independent control over the complex-valued squeezing parameter, the probability amplitude of each constituent, and their spatial separation, have never been demonstrated before.

Second, we utilize the hybrid system to encode a Z₂ gauge field coupled to bosonic matter and conduct a quantum simulation of the real-time dynamics of an elementary Z₂ gauge link and Z₂ plaquette.