Deterministic Mechanical Wigner Negativity via Nonlinear Cavity Quantum Optomechanics in the Unresolved-Sideband Regime

Non-Gaussian quantum states of mechanical motion exhibiting Wigner negativity offer promising capabilities for quantum technologies and tests of fundamental physics. Within the field of cavity quantum optomechanics, deterministic preparation of nonclassical mechanical states with such Wigner negativity is a highly sought goal but is challenging as the intracavity interaction Hamiltonian is linear in mechanical position. Here, we show that, despite this form of interaction, by utilizing the nonlinearity of the cavity response with mechanical position, mechanical Wigner negativity can be prepared deterministically in the unresolved-sideband regime, without additional nonlinearities, nonclassical drives, or conditional measurements. In particular, we find that Wigner negativity can be prepared with an optical pulse, even without single-photon strong coupling, and the negativity persists in the steady state of a continuously driven system. Our results deepen our understanding of cavity-enhanced radiation pressure and establish a pathway for deterministic preparation of nonclassical mechanical states in the unresolved sideband regime.