Measurement of second-order response without perturbation

We study the second order response functions of a colloidal particle being subjected to an anharmonic potential. Contrary to typical response measurements which require an external perturbation, here we experimentally confirm a recently developed approach where the system's susceptibilities up to second order are obtained from the particle's equilibrium trajectory [PCCP $\mathrm{{\bf 17}}$, 6653 (2015)]. The measured susceptibilities are in quantitative agreement with those obtained from the response to an external perturbation.