Non-linear Bosonic Interactions in a Spin-oscillator System

Higher-order nonlinear interactions on a quantum harmonic oscillator lead to increasingly nonclassical and resourceful quantum states. Some of these interactions go beyond the Gaussian formalism and, hence, serve as a resource for real-time quantum simulation of many-body models, with the potential to surpass the capabilities of classical hardware. However, studying these interactions has been challenging as they typically become exponentially weaker with increasing order. Hybrid systems, where an oscillator is coupled to an additional spin, provide an effective solution.

Using the motion of a trapped ion coupled to its spin, we present the experimental implementation of a new protocol relying solely on spin-dependent bosonic linear interactions to generate up to fourth-order interactions [1]. Focusing on generalised squeezing, we demonstrate and characterise squeezing, trisqueezing, and quadsqueezing interactions; the fourth-order quadsqueezing interaction is over 100 times stronger than possible with conventional methods. Our approach imposes no fundamental limit on interaction order and applies universally to platforms supporting spin-dependent linear bosonic interactions. Strong higher-order nonlinear interactions unlock the study of fundamental quantum optics, quantum simulation, and computation in a hitherto unexplored regime.