Path integrals and nonlinear optical tweezers

We use path integrals to calculate perturbative corrections the correlation function of a particle under action nonlinear optical tweezers, both in overdamped and underdamped regimes. In cases, it is found that leading order nonlinearities manifest as shifts characteristic frequency system. The results are compared numerical simulations. present calculations enable direct experimental method access trap parameters by analyzing position data, similarly standard harmonic tweezers.