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Feedback control can be used to generate well-determined nonlinear effectivepotentials in an optical trap, a goal whose applications may range fromnon-equilibrium thermodynamics to the generation of non-Gaussian states ofmechanical motion. Here, we investigate the action of an effectivefeedback-generated quartic potential on a levitated nanoparticle within theperturbation regime. The effects of feedback delay are discussed andpredictions from the perturbation theory of a Brownian particle subjected to aquartic anharmonicity are experimentally verified.

Perturbative nonlinear feedback forces for optical levitation experiments