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