Vectorial polaritons in the quantum motion of a levitated nanosphere

The strong coupling between photons and bosonic excitations in matter produces hybrid quasiparticle states known as polaritons(1-3). Their signature is the avoided crossing between the eigenfrequencies of the coupled system illustrated by the Jaynes-Cummings Hamiltonian(4). It has been observed in quantum electrodynamics experiments based on atoms(5,6), ions(7), excitons(8-10), spin ensembles(11,12) and superconducting qubits(13). In cavity optomechanics, polariton modes originate from the quantum-coherent coupling of a macroscopic mechanical vibration to the cavity radiation field(14,15). Here we investigate polaritonic modes in the motion of an optically levitated nanosphere(16-22) in the quantum-coherent coupling regime. The particle is trapped in a high vacuum by an optical tweezer and strongly coupled to a single cavity mode by coherent scattering of the tweezer photons(23-27). The two-dimensional motion and optical cavity mode define an optomechanical system with three degrees of freedom. In the strong-coupling regime, we observe hybrid light-mechanical states with a vectorial nature. Our results pave the way towards protocols for quantum information transfer between photonic and phononic components and represent a step towards the demonstration of optomechanical entangled states at room temperature.