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The strong coupling between elementary excitations of the electromagneticfield (photons) and quantized mechanical vibrations (phonons) produces hybridquasi-particle states, known as phonon-polaritons. Their typical signature isthe avoided crossing between the eigenfrequencies of the coupled system, asparadigmatically illustrated by the Jaynes-Cummings Hamiltonian, and observedin quantum electrodynamics experiments where cavity photons are coupled toatoms, ions, excitons, spin ensambles and superconducting qubits. In this work,we demonstrate the generation of phonon-polaritons in the quantum motion of anoptically-levitated nanosphere. The particle is trapped in high vacuum by anoptical tweezer and strongly coupled to a single cavity mode by coherentscattering of the tweezer photons. The two-dimensional motion splits into twonearly-degenerate components that, together with the optical cavity mode,define an optomechanical system with three degrees-of-freedom. As such, whenentering the strong coupling regime, we observe hybrid light-mechanical stateswith a dispersion law typical of tripartite quantum systems. Remarkably, theindependent components of motion here identify a physical vibration directionon a plane that, similarly to the polarization of light, confers a vectorialnature to the polariton field. Our results pave the way to novel protocols forquantum information transfer between photonic and phononic components andrepresent a key-step towards the demonstration of optomechanical entangledstates at room temperature.

Vectorial polaritons in the quantum motion of a levitated nanosphere