Quantum harmonic oscillators model phenomena from electromagnetic fields to molecular vibrations, with excitations represented by bosons such as photons or phonons. Linear interactions that create or annihilate single bosons generate coherent states of light or motion. Introducing higher-order nonlinear interactions produces richer quantum behaviour: second-order interactions enable squeezing, whereas higher-order interactions generate non-Gaussian states useful for continuous-variable quantum computation. However, such interactions are usually weak or require specialized hardware. Hybrid systems, where a linear interaction couples an oscillator to a spin, offer an alternative. Here we combine two spin-dependent linear bosonic interactions to implement up to fourth-order nonlinear bosonic interactions in a single trapped ion, focusing on generalized squeezing. We demonstrate and characterize squeezing, trisqueezing and quadsqueezing; reconstruct the Wigner functions of the resulting states; and achieve quadsqueezing over 100 times faster than conventional methods. The approach has no fundamental limit on the interaction order and applies to any platform supporting spin-dependent linear interactions. Higher-order interactions in quantum harmonic oscillator systems can result in useful effects, but they are hard to engineer. An experiment on a single trapped ion now demonstrates how spin can mediate higher-order nonlinear bosonic interactions.

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Nature

Researchers demonstrate a technique for generating higher-order nonlinear bosonic interactions in a single trapped ion by combining two spin-dependent linear bosonic interactions. By adjusting the detuning frequency between two non-commuting spin-dependent forces, they implement squeezing (2nd order), trisqueezing (3rd order), and quadsqueezing (4th order) interactions. The quadsqueezing interaction is achieved over 100 times faster than conventional methods. Wigner functions of the resulting non-Gaussian quantum states are reconstructed, confirming their non-classical character. This marks the first demonstration of fourth-order generalized squeezing on any platform and the first trisqueezing in an atomic system. The approach has no fundamental limit on interaction order and applies broadly to any platform supporting spin-dependent linear interactions, with implications for continuous-variable quantum computation, quantum simulation, and error correction.

Squeezing, trisqueezing and quadsqueezing in a hybrid oscillator–spin system